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Science Education CollectionIntroduction to Light MicroscopyURL: /science-education/5041The light microscope is an instrument used by researchers in many different fields to magnify specimens to as much as a thousand times their original size. In its simplest form, it is composed of a clear lens that magnifies the sample and a light source to illuminate it. However, mostlight microscopes are much more complex and house numerous fine-tuned lenses with tightly controlled dimensions all within the body of the microscope itself and in components such as the objectives and eyepieces. In this video, the major components of the light microscope are described and their uses and functions are explained in detail. The basic principles of magnification, focus, and resolution are also introduced. Basic light microscope operation begins with bringing light to the sample and ensuring that the light source is of the correct intensity, directionality, and shape in order to produce the best quality image. Next, the sample must be magnified properly and brought into focus to view the region of interest. There are many practical applications for light microscopy including the viewing of stained or unstained cells and tissues, resolving small details of specimens, and even magnifying a region of interest during surgery to assist with complex procedures on the micron scale.The light microscope is an instrument used for magnifying research specimens. Light microscopes are an invaluable analytical tool that have the potential to allow scientific investigators to view objects at 1000 times their original size. As you will see, the light microscope operates via some very basic principles but has nearly limitless applications for visualizing specimens in the lab.As its name implies the light microscope requires a light source, which produces light that can be focused, by a condenser lens, onto the sample. The light that illuminates the specimen reaches a lens known as the objective lens, which creates a magnified image that is inverted, or turned upside down. The eyepiece, or ocular lens, further magnifies the image, which the eye then receives. Additional optical elements can be introduced into the light path to right the image, so that the eye sees it in the correct orientation. Microscopes that utilize multiple lenses like the one you see here are referred to as compound microscopes.In a compound microscope, the total magnification is calculated by multiplying the magnification of the objective lens by the magnification of the ocular lens, or eye piece. With a 40X objective lens and a 10X ocular lens, the total magnification is 400X.To help estimate the size of objects under the microscope, an eyepiece reticle, a scale that’s projected over the image can be used. At higher magnification, the tick marks in the eyepiece reticle will represent smaller distances, than when viewed at lower magnifications.In addition to magnification, another aspect of microscope optics is resolution. Resolution refers to the shortest resolvable distance between two objects under the scope. As the heads of these characters becomes more and more clear, and the resolution increases, the shortest observable distance between them decreases.The main components of the light microscope include the objectives, the eyepieces, the specimen stage and specimen holder, the light source, the field diaphragm, the condenser and aperture, and the coarse and fine focus knobs.The objectives are responsible for most of the magnification and resolution of the microscope. They are mounted on a rotating nosepiece in such a way that as the objectives are changed, the focal plane stays the same – a property referred to as parafocality. An objective can be marked with the magnification, the numerical aperature, or N.A., the type of immersion medium required, the coverslip thickness that should be used when mounting samples, and the working distance - the distance from the tip of the lens element to the focal plane in the sample.The numerical aperture, again, defined as N.A., is a measure of how well a microscope objective can gather light. High N.A. objectives allow lightat oblique angles to pass through while low N.A.objectives require more direct light. The resolution of an objective can be calculated from the numerical aperture, given the wavelength of light.The light source, field diaphragm, aperture, and condenser are all responsible for producing the light and delivering it to the sample.The light source is typically a low voltage halogen bulb that can be adjusted to control light intensity.The light then passes through a variety of filters and into the field diaphragm, which controls the area of the specimen to be illuminated.Next is the condenser, which focuses bright, light on the specimen, the cone of illumination around the specimen is controlled by the condenser and must be adjusted depending on the objective that’s used.To begin using the light microscope, place a sample containing the region of interest on the microscope stage, center it directly over the objective, and secure it into place using the stage clips.Next, turn on the light source and switch to the lowest powered objective.Next, focus the low powered objective by moving it in the z-direction using an initial adjustment of the coarse adjustment knob, and then rotating the fine adjustment knobs to bring the object in sharp focus. Take care not to hit the slide or stage with the objective as this could damage the lens.Then, locate the area of interest by looking through the eye pieces while adjusting the knobs to move the slide in the x and y directions. The size of the field of view will decrease drastically as you move from a low magnification, to higher magnification.Centering the lowest powered objective on the area of interest before moving to higher power greatly increases the chances of finding the desired specimen.Once the sample has been located at low power and is in focus, move to the higher power objective that will be used for acquiring images. Optimize the quality of the lighting by first adjusting the field diaphragm so that the diaphragm itself is just outside of the field of view.Next, adjust the condenser diaphragm so that the settings match the numerical aperture of the objective in use.Finally, adjust the focus again. This time only using the fine adjustment knob.You are now ready to take images of your specimen.Light microscopy has the potential to visualize a wide range of specimens, and various configurations of the compound microscope exists to suit many different applications.Here, you see a researcher preparing to work under a surgical microscope. These microscopes are generally suspended on a movable arm and are stereoscopic, meaning that they allow light to pass to the viewer and also a camera mounted on the microscope. This surgical microscope is being used in a kidney transplantation procedure, in mice.In this clip, you see a researcher looking through a dissecting microscope, while picking out the perfect drosophila larvae for further dissection , in order to expose the body wall muscles so the neuromuscular junction can be studied.Here you can see an inverted compound microscope, which has an objective below the stage, being prepared for a microinjection technique. This procedure, known as somatic cell nuclear transfer, is an important method for generating transgenic animals and creating clones.You’ve just watched JoVE’ introduction to Light Microscopy.In this video we reviewed: what a microscope is and how it works, its many components, how to make adjustments to them, and how to acquire quality images. Thanks for watching!。
下面剖析英语六级阅读真题长难句(5)，希望考生在练习同时思考长难句的句子结构。
1. Connected to a wave-front sensor that tracks and measures the course of a laser beam into the eye and back, the aluminum mirror detects the deficiencies of the cornea, the transparent protective layer covering the lens of the human eye. (2003. 阅读.6. Text 4)【译文】通过与跟踪并测量激光射入眼中并反射回来的路径的波前感受器相连，铝制镜片能够检测到眼角膜的缺陷，眼角膜是覆盖在眼球上一层透明的起保护作用的薄膜。
【析句】主句the alumium mirror detects the deficiencies of the cornea,主句后，the transpartent protective layer...作the cornea的同位语短语，其中covering the lens of the human eye是现在分词作定语修饰the yer, 而主句前，connected to a wave-front sensor...是过去分词作主句主语the aluminum的定语，而a wave-front sensor后有that引导的定语从句修饰。
2. The highly precise data from the two instruments - which, Bille hopes, will one day be found at the opticians all over the world - serve as a basis for the production of completely individualized contact lenses that correct and enhance the wearer's vision. (2003. 阅读. 6. Text 4)【译文】比利希望，未来这两种仪器收集到的高度精确的数据能为全世界的眼镜商所用，为生产完全个性化且能矫正和提高佩戴者视力的隐形眼镜打下基础。
Lead Salt Quantum Dots:the Limit of Strong Quantum ConfinementFRANK W.WISEDepartment of Applied Physics,Cornell University,Ithaca,New York 14853Received March 23,2000ABSTRACTNanocrystals or quantum dots of the IV -VI semiconductors PbS,PbSe,and PbTe provide unique properties for investigating the effects of strong confinement on electrons and phonons.The degree of confinement of charge carriers can be many times stronger than in most II -VI and III -V semiconductors,and lead salt nanostructures may be the only materials in which the electronic energies are determined primarily by quantum confine-ment.This Account briefly reviews recent research on lead salt quantum dots.IntroductionThe properties of semiconductor nanocrystals or quantum dots (QDs)have received significant attention in the past decade.Following pioneering work by Efros and Ekimov,1Brus,2and Henglein,3many II -VI and III -V materials have been prepared as QDs.Much progress has been achieved in the areas of synthesis,structural characteriza-tion,electronic and optical properties,and thermodynam-ics of semiconductor QDs.Overviews of the subject and recent research are listed in ref 4.Many of the interesting and potentially useful proper-ties of nanocrystals can be understood at the level of undergraduate quantum mechanics.When a particle (an electron in this case)is confined to a volume in space,two things happen:it acquires kinetic energy (referred to as confinement energy),and its energy spectrum becomes discrete.In a bulk semiconductor,the conduc-tion electrons are free to move around in the solid,so their energy spectrum is almost continuous,and the density of allowed electron states per unit energy increases as the square-root of energy (Figure 1a).If one can synthesize a piece of the semiconductor so small that the electron “feels”confined,the continuous spectrum will become discrete and the energy gap will increase,as indicated in Figure 1b.What sets the size scale at which the electron feels confined?The crystallite must be comparable to the Bohr radius of the bound state of an electron and a hole.Such an electron -hole pair (called an exciton)is analo-gous to a hydrogen atom and can be thought of as the lowest excited electronic state of the bulk solid.Anelectron -hole pair in a QD is usually referred to as an exciton,even when the charge carriers are bound by the confining potential rather than the Coulomb interaction.As Figure 1illustrates,control of size allows us to engineer the optical properties of a semiconductor:strong absorption occurs at certain photon energies,at the expense of reduced absorption at other energies.Light always interacts with one electron -hole pair regardless of the size of the semiconductor,so the total or integrated absorption does not change.Ideally,the density of states becomes a series of delta functions (narrow spikes)in the QD,so those transitions must be very strong to conserve the integrated absorption.The strong transitions are the result of concentration of the optical transition strength into a few narrow energy intervals.Ordinarily,the optical properties of a material do not depend on the intensity of the light,and as a result,light beams do not interact with each other.However,at high-enough intensities,materials become nonlinear s the light changes the material properties,which can then be sensed by a separate “probe”light beam or by the beam that changes the material itself.Optical nonlinearities can be used to implement switches based on light energy,which are potentially much faster than electrical switches,for example.Optical nonlinearities are generally strongest when the photon energy matches an optical transition in the solid;this property is referred to as resonant enhance-ment of the nonlinearity.With their strong absorptions,quantum dots offer the potential for strong resonantly enhanced optical nonlinearities and are thus candidate materials for applications such as optical switching and information processing.This qualitative picture of the effects of quantum confinement in semiconductors is supported by rigorous theoretical calculations by Efros and Efros,1Brus,2and Schmitt-Rink et al.5According to Schmitt-Rink et al.,theFrank Wise received a B.S.degree in engineering physics from Princeton University (1980),an M.S.degree in electrical engineering from the University of California,Berkeley (1982),and a Ph.D.degree in applied physics from Cornell University (1989).From 1982to 1984he worked on advanced integrated circuit development at Bell Laboratories,Murray Hill,NJ.Since 1989he has been in the Department of Applied Physics at Cornell.FIGURE 1.Density of electron states in bulk and size-quantized semiconductor.The optical absorption spectrum is roughly propor-tional to the density of states.Acc.Chem.Res.2000,33,773-78010.1021/ar970220q CCC:$19.00©2000American Chemical SocietyVOL.33,NO.11,2000/ACCOUNTS OF CHEMICAL RESEARCH773Published on Web08/03/2000linear and resonant nonlinear optical properties will exhibit the greatest enhancement when the nanocrystal radius R is much smaller than the Bohr radius of the exciton(a B)in the parent bulk material.This motivates the study of semiconductor QDs in the strong-confine-ment limit,where R/a B,1.Large optical nonlinearities are expected as long as the QD transitions are not broadened excessively(Figure1c). The magnitude and origin of the line-broadening are critical;any broadening opposes the spectral concentra-tion of transition strength that comes from quantum confinement.The dominant intrinsic source of line broad-ening is expected to be coupling of the exciton to phonons s the optical transitions in QDs are inherently vibronic in nature,similar to those of a large molecule. This motivates studies of the strength of carrier-phonon interactions in nanocrystals.Despite the effort that has gone into investigations of QDs in recent years,little experimental work has been done with samples that strongly confine both charge carriers.The difficulty of attaining the strong-confinement regime becomes clear when one considers the Bohr radii of excitons in semiconductors,which are typically∼10nm or less.Some examples are given in Table1.For some phenomena the degree of localization of the individual charge carriers is relevant.If a e and a h are the Bohr radii of the electron and hole(imagine the charge carrier bound to a localized impurity,e.g.),then strong confinement occurs when R,a e,a h.1In semiconductors with large hole masses(i.e.,most II-VI and III-V materi-als),it is impossible to achieve strong quantum confine-ment in this sense.To investigate the strong-confinement limit,QDs of narrow-gap materials such as PbSe or InSb are desirable. Even in InSb,a h)2nm,so strong confinement of the hole will be impossible.In contrast,a e)a h)23nm in PbSe.The similarly small electron and hole masses of the lead salts(PbS,PbSe,and PbTe)imply large confinement energies,split about equally between carriers.The elec-tronic spectra of QDs of the lead salts are thus simple, with energy spacings that can be much larger than the energy gaps of the bulk materials(which are0.2-0.4eV). The generic form of the energy levels of PbS or PbSe QDs is shown in Figure2.In contrast,the spectra of II-VI and III-V QDs are relatively congested due to closely spaced hole levels and are complicated significantly by valence-band mixing.6,7Another potential advantage for studies of nanocrystal physics is the possibility of achieving strong quantum confinement of charge carriers without the properties being dominated by the surface of the QD.This is illustrated in Table2.The influence of the surface onQD properties is complicated and remains controversial,so reducing this influence can be valuable in determiningintrinsic QD properties.A final interesting feature of thelead salts is that they crystallize in the cubic sodiumchloride structure,with every atom at a site of inversionsymmetry.Structures with such high symmetry should beuseful for assessing the intrinsic polarity of strongly size-quantized electron states.The electronic structure has implications for the criticalissue of exciton-phonon coupling in QDs,via the proper-ties of the excited-state charge distribution.Although thecoupling of electrons and holes to polar phonons is strongin the lead salts due to their ionicity,the exciton-phononcoupling should be small.In the strong-confinement limitthe electron and hole have identical wave functions andcan be thought of as lying on top of each other,cancelingeach other’s coupling to the lattice.Thus,the coupling topolar phonons(which depends on the net charge inho-mogeneity of the excited state)should vanish.5The optical phonons of the bulk lead salts are highlydispersive,and the frequencies of the long-wavelengthlongitudinal and transverse optical phonons differ by afactor ing qualitative Fourier transform thinking,decreasing the size of a crystal corresponds to moving tolarger wave vectors(shorter wavelengths)on a bulkphonon dispersion relation.This will produce an observ-able change in phonon frequency if the phonons aredispersive.The difference betweenωLO andωTO facilitatesobservation of the effects of coupling the bulk plane wavemodes in the nanostructure.These properties contrastwith the nearly flat and nearly degenerate optical phonondispersion in II-VI and III-V semiconductors and makethe lead salts valuable for studies of phonon confinement.To summarize,lead salt QDs provide clear and uniqueopportunities for studying the properties of a strongly size-quantized electronic system.R/a B)0.04is achieved withexisting samples(examples are given below),and R/a B≈0.02is possible.For comparison,in commonly studiedCdSe QDs the minimum value of R/a B≈0.16.MostTable1.Bohr Radii of Excitons in RepresentativeSemiconductorsmaterial exciton Bohr radius(nm)CuCl1CdSe6PbS20InAs34PbSe46InSb54FIGURE2.General form of the first few electron and hole energylevels of PbS or PbSe QDs.The states are labeled by the quantumnumbers j(total angular momentum)andπ(parity):|jπ〉.Table2.Percentage of Atoms on the Surface of QDsof CdSe and PbSe with the Indicated RadiiR/a B CdSe PbSe130%5%0.390%15%0.145%774ACCOUNTS OF CHEMICAL RESEARCH/VOL.33,NO.11,2000exciton physics depends on the volume of the exciton,i.e., (R/a B)3,so the degree of confinement possible with the lead salts can be many times stronger than in II-VI and III-V materials.As one measure of this,the confinement energy can easily be several times the bulk energy gap in the lead salts,compared to about one-half the bulk energy gap in CdSe.The lead salts have potential advantages over other materials with regard to the nonlinear optical response due to the possibilites of achieving stronger confinement of the excitons and smaller intrinsic line widths due to reduced exciton-phonon coupling.Finally, QDs of narrow-gap materials should be relevant for applications:strong confinement can be achieved in a structure whose lowest-energy optical transition occurs at technologically important wavelengths in the near-infrared region of the electromagnetic spectrum. Synthesis and CharacterizationEarly work on lead salt materials produced some evidence of size-quantized electronic states.Thin films of the lead salts were grown as early as1960,and produced evidence of confinement in one dimension(i.e.,a quantum well in today’s language)8as well as suggestions of three-dimensional confinement in crystallites of the polycrys-talline films.9,10The first intentionally synthesized IV-VI QDs exhibited increases in the energy gap that were attributed to quantum size effects.11However,structuredabsorption spectra were typically not observed,probably owing to a broad distribution of particle sizes.The synthesis of high-quality,monodisperse PbS QDs in poly-(vinyl alcohol)(PVA)was reported in1990.12Machol et al.duplicated that synthesis and succeeded in increasing the concentration of QDs as well as producing dense thin films of QDs.13More recently,the controllable fabrication of PbS and PbSe QDs with diameters between3and20 nm in glass hosts has been demonstrated.14-17PbTe crystallites exhibiting exciton peaks blue-shifted from the bulk energy gap have been fabricated,but no structural characterization was reported.18The PbS QDs in silicate glass14offer excellent proper-ties.The narrow size distribution(∆R/R≈4%)is il-lustrated by the isolated exciton transitions visible in the room-temperature absorption spectrum shown in Figure 3.Even with excitation1eV above the lowest exciton,the luminescence spectrum emitted by these QDs is a single peak with a Stokes shift(reflecting primarily inhomoge-neous broadening from the distribution of particle sizes) of75meV.Well-characterized dyes are not available as reference samples in the infrared,so an AlInAs/GaInAs quantum well laser structure was used to roughly estimate the luminescence quantum yield of∼0.1at room tem-perature.19For QD sizes between5and10nm,resonantly excited excitons decay with time constants of∼1ns.20The initial relaxation of electrons in many QD samples occurs in∼10ps and is thought to be due to fast trapping of one charge carrier or relaxation to a long-lived“dark”state21 from which recombination is spin-forbidden.The small luminescence Stokes shift,bright luminescence,and absence of rapid carrier trapping(in addition to the structural characterization)all indicate the high quality of these structures.The synthesis and characterization of monodisperse PbSe QDs was reported by Lipovskii and co-workers.17To our knowledge PbSe has the largest Bohr radius(46nm) of any material synthesized as QDs in glass or colloid.QDs with diameters between2and15nm were produced,so the confinement is extreme in these QDs.A typical optical absorption spectrum is shown in Figure4.The variation of the lowest exciton energy with size is also plotted along with the results of calculations to be described below. Electronic StatesA conceptually simple way to calculate the electron states of a QD is to impose spatial confinement on the electron states of the bulk material.In this effective-mass or envelope function approach,22the wave functions are forced to zero at the boundary of the QD.Kang performed an envelope function calculation of the electronic struc-ture of PbS and PbSe QDs.23The envelope function calculation provides the energy spectrum and wave func-tions(Figure2),as well as dipole transition strengths and selection rules.The results of the calculation agree well with measured properties of PbS QDs down to3nm in diameter.Measured and calculated spectra are compared in Figure3a as an example,and energy levels for several samples of PbS QDs are shown in Figure3b.In the smallest(3-nm diameter)structures the exciton energy is 2eV,which is5times the bulk energy gap.Theelectronic FIGURE 3.(a)Absorption spectrum and calculated transition strengths of8.5-nm-diameter PbS QDs in oxide glass.(b)Measured and calculated exciton energies(plotted on a logarithmic scale)as a function of the size of PbS QDs.The dark lines indicate nearly degenerate transitions between the states indicated in Figure2.VOL.33,NO.11,2000/ACCOUNTS OF CHEMICAL RESEARCH775states of these structures are truly dominated by quantum confinement.Kang’s calculation was the first application of the envelope function approach to a narrow-gap material.This work demonstrates the utility of the multiband envelope function approach with the explicit inclusion of band nonparabolicity.Some features of the analysis differ from that of II -VI and III -VI materials.Two specific issues that are important for QD physics are the following:(1)The transition dipole moment in lead salt QDs has a contribution from the envelope in addition to the usual dipole moment of the Bloch functions.This has conse-quences for the inter-and intraband transitions,and thus the one-and two-photon spectra.(2)Fine structure arising from electron -hole Coulomb and exchange interactions has been a subject of much interest recently,21and these many-body perturbations are included in Kang’s analysis.The Coulomb interaction does not split the lowest exciton in lead salt QDs.The exchange interaction has an inter-unit-cell component that vanishes in other materials in addition to the intra-unit-cell com-ponent that is enhanced by quantum confinement.How-ever,the magnitude of the exchange splitting is only ∼10meV in even the smallest lead salt QDs.This is smaller than in II -VI compounds.The deviation between Kang’s calculations and mea-surements of PbSe QDs with diameters between 3.5and 7nm (Figure 4b)is significant and may signal the breakdown of the effective mass approximation.The envelope function theory is not expected to be valid for the smallest (∼2nm)QDs,which are only a few lattice constants in diameter.The envelope function calculation also fails to account for some transitions observed in PbS and PbSe QDs.Examples are the features near 0.8and 1.0eV in Figure 3a.The constant-energy surfaces in k-space are slightly anisotropic in PbS and PbSe,and Kang treats the aniso-tropy as a perturbation to an otherwise isotropic model.A calculation following Kang’s but treating the anisotropy exactly does indeed predict transitions that do not appear in the isotropic model.24Work is in progress to apply this approach to PbTe QDs,25which are interesting because the constant-energy surfaces of PbTe are extremely aniso-tropic.Vibrational ModesThe vibrational modes of QDs have not received the extensive attention paid the electronic states.An accurate description of the vibrational modes of QDs is fundamen-tally important and is of course a prerequisite to under-standing the electron -phonon coupling in QDs.A rigorous theoretical treatment of the optical vibra-tional modes of semiconductor QDs was published in 1994,26and was followed by calculations of the Raman and infrared cross sections of these modes.27The theory accounts for both electromagnetic and mechanical bound-ary conditions at the surface of the QD,and the key overall prediction is that the modes in general have mixed transverse and longitudinal character as well as electro-magnetic and mechanical nature.The acoustic modes of QDs can often be modeled by assuming that the dot is an elastic continuum.28Applica-tion of spherical boundary conditions at the surface of the QD produces discrete torsional and spheroidal eigen-modes.The spheroidal modes with angular momenta l )0(a spherical breathing mode)and l )2(an ellipsoidal mode)should be Raman-active.29Krauss et al.extended the theoretical framework de-veloped by Roca and co-workers to account for the unusual phonon dispersion of the lead salts,and calcu-lated the vibrational frequencies for modes with angular momenta up to l )2.The most interesting feature of this calculation is a band of infrared-active modes with frequencies around 100cm -1for l )1.This band is far from the zone center frequencies ωTO )65cm -1and ωLO )210cm -1.Krauss and co-workers then measured the Raman scattering (Figure 5)and far-infrared absorption spectraFIGURE 4.(a)Measured absorption spectrum (line)and calculated dipole transitions (bars)of 8.5-nm PbSe QDs.(b)Measured (symbols)and calculated (line)energies of the lowest exciton in PbSe QDs of varying size.Reproduced with permission from ref 17.FIGURE 5.Raman spectrum of 3-nm PbS QDs.Vertical bars indicate calculated mode frequencies.776ACCOUNTS OF CHEMICAL RESEARCH /VOL.33,NO.11,2000of PbS QDs.The results are consistent with the theoretical predictions and cannot be accounted for by prior models. These measurements thus confirm the influence of elec-trostatic and mechanical boundary conditions on the vibrational modes of QDs and can be considered an observation of the true optical modes of a semiconductor QD.30Electron-Phonon CouplingIn the strong-confinement limit,the size-quantized elec-tron and hole ideally have identical wave functions,and the coupling to polar phonons should vanish.Coupling to acoustic phonons occurs through deformation potential and piezoelectric interactions.The sodium chloride crystal structure of the lead salts is centrosymmetric and thus not piezoelectric,so the deformation potential coupling is isolated.QDs of the lead salts are thus well-suited to test theoretical predictions of the vibronic nature of the excited states and the homogeneous line shape.Once the electronic wave functions and vibrational modes were known,they could be used to calculate the coupling of excitons to optical modes.For all sizes,the coupling strength(in units of the energy of the vibrational mode with l)0)S<10-4.In terms of a shifted harmonic oscillators model(as commonly used to describe dyemolecules,e.g.),S can be thought of as the mean number of vibrational quanta involved in an optical transition.Experimentally,the exciton-phonon coupling in QDs has traditionally been inferred from overtones in the Raman spectrum.31Krauss measured the overtone spec-trum of3-nm PbS QDs in polymer host and obtained the coupling strength S≈0.7for the dominant optical mode with l)0.32This value is4orders of magnitude larger than that calculated from the intrinsic electronic states of the QD and would imply that one charge carrier is highly localized in the QD.What is the origin of this huge discrepancy?Rapid(∼10ps)trapping of photoexcited charge carriers is observed with PbS QDs in polymer hosts.33Trapped charge builds up on the QDs during the steady-state Raman measurements,producing local elec-tric fields.Such fields could easily polarize the exciton and produce the apparently large coupling to optical modes.A correct measurement of the coupling to polar phonons in these samples would therefore have to be made before appreciable decay of the photocreated exciton occurs,i.e., on the subpicosecond time scale.Exciton-phonon couplings can be obtained from a three-pulse photon echo(3PPE)experiment,34which allows determination of the coupling on the femtosecond time scale.Krauss measured the3PPE signal from excitons in PbS QDs using40-fs pulses.A typical signal,which is proportional to the electronic polarization,is shown in Figure6a along with a theoretical fit.The polarization is modulated at the acoustic phonon frequency(70cm-1), with only a small component at the optical phonon frequency(215cm-1).The best-fit exciton-phonon cou-plings are S acoustic)0.1and S optical)0.01.The modulation is even clearer in the saturated-absorption signal(Figure 6b),which monitors exciton population rather than polarization.The relative strengths of the optical and acoustic modes obtained by Fourier transforming the data of Figure6b agree with those obtained from the3PPE experiment.Calculation of the acoustic phonon coupling also predicts S acoustic∼0.1.These experiments lead to several conclusions:33(1)Steady-state Raman measurement can overestimate the coupling to optical phonons by a factor of∼100in QDs of narrow-gap materials.(2)The actual coupling to optical phonons is very small (S optical)0.01)due to net charge neutrality and is at least 10times smaller than values obtained for QDs in other material systems.(3)The coupling to acoustic modes is larger than the coupling to optical modes.The last two conclusions are consistent with the original theoretical predictions of Schmitt-Rink et al.for a QD in the limit of strong quantum confinement.5Lead salts appear to be the only material system for which this is true.Temperature Dependence of the Energy GapAn interesting and illustrative consequence of the elec-tronic and vibrational properties discussed above is the variation of the QD energy levels with temperature.For virtually all semiconductors,the temperature dependence of the energy gap is well-known experimentally.In bulk materials the temperature coefficient of the energy gap d E g/d T has contributions from lattice thermal expansion and electron-phonon interactions.In the limit of a narrow energy band,theoretical analysis of d E g/d T pro-FIGURE6.(a)Three-pulse photon echo signal(solid line)from3-nm PbS QDs,along with theoretical fit(dashed).(b)Saturated-absorption signal.Reproduced with permission from ref33.VOL.33,NO.11,2000/ACCOUNTS OF CHEMICAL RESEARCH777duces an energy level independent of temperature,as expected for an isolated atom.35In QDs,we define the energy gap E g as the energy of the lowest exciton transi-tion.Studies generally report that the gap depends on temperature similarly to the energy gap of the bulk material.36Olkhovets and co-workers studied PbS QDs with di-ameter between 3and 16nm in glass and polymer hosts.37a B )20nm in PbS,so the samples span the range from nearly bulk material to the strong-confinement limit.The exciton energies are determined from peaks in the optical absorption spectra measured at temperatures from 12to 300K.Typical experimental data are shown in Figure 7,and it is immediately evident that the spectra of smaller QDs are almost independent of temperature.The mea-sured values of d E g /d T are plotted versus QD size in Figure 8.d E g /d T approaches the bulk value (∼500µeV/K)in the largest QDs and is nearly zero for the smallest QDs.The same trend is found with PbSe QDs.These are the first observations that the temperature coefficient of the energygap depends strongly on the size of a semiconductor and is nearly zero in the smallest structures.The dominant contributions to the temperature varia-tion of the energy gap of a QD come from the lattice dilation and electron -phonon coupling.A qualitative explanation of the observed size-dependence of d E g /d T will be given here;quantitative details that produce the calculated line in Figure 8can be found in ref 37.The effects of lattice thermal expansion diminish as the size of the structure decreases because the QD energy levels are determined more by the size of the structure rather than by the lattice constant.The effects of electron -phonon coupling on the energy levels can be calculated with perturbation theory.The energy denominators that appear in such a treatment lead to the well-known conclusion that coupling to nearby energy levels gives the greatest influence on a given level.The contribution to d E g /d T from electron -phonon coupling decreases with decreasing size simply because the spacing between the quantum-confined energy levels (i.e.,the denominator)increases.The fact that the energy gap becomes indepen-dent of temperature in the smallest QDs can therefore ultimately be understood as a consequence of strong quantum confinement.In QDs of II -VI and III -V materi-als,the intraband energy differences do not approach the bulk energy gap.As a result,d E g /d T is similar to the bulk value.Future DirectionsAll of the studies described here indicate that lead salt QDs should have extremely narrow spectral lines.This homogeneous or single-particle line width is not observed because of the inhomogeneous broadening that arises from the distribution in particle sizes.Optical spectro-scopic techniques are available for determining the ho-mogeneous line width under inhomogeneous broadening,but it would probably be more decisive to measure the spectra directly in single-particle experiments.Very narrow (µeV)excitation and luminescence lines have been ob-served from single QDs,38and it would be interesting to do similar experiments with the lead salts.With regard to optical applications,the inhomogeneous broadening in ensemble samples and the difficulty of producing material with high concentration of QDs sig-nificantly reduce the effectiveness of QDs.It should also be pointed out that even the narrow spectral lines observed in single-QD experiments tend to move with time;38this “spectral diffusion”is another source of effective line broadening.Applications such as optical switching motivate the development of materials with large optical nonlinearities.Kang and Krauss have mea-sured ultrafast absorption saturation (one manifestation of optical nonlinearity)in PbS and PbSe QDs,but only at very high fluence (∼0.1mJ/cm 2).39One of the “holy grails”of QD science is the development of a laser with a QD active medium.A currently debated issue that arises in the context of laser development is whether charge carriers injected into higher excited states of a QD will beFIGURE 7.Absorption spectra of 8.5-nm (a)and 4.5-nm (b)PbS QDs recorded at 12,100,200,and 300K.Adapted from ref 37.FIGURE 8.dEg/dT for PbS QDs.Symbols are experimental values,and the line is the result of calculations.Adapted from ref 37.778ACCOUNTS OF CHEMICAL RESEARCH /VOL.33,NO.11,2000。
a r X i v :q u a n t -p h /0511174v 1 17 N o v 2005Teleportation and spin squeezing utilizing multimode entanglement of light withatomsK.Hammerer 1,E.S.Polzik 2,3,J.I.Cirac 11Max-Planck–Institut f¨u r Quantenoptik,Hans-Kopfermann-Strasse,D-85748Garching,Germany2QUANTOP,Danish Research Foundation Center for Quantum Optics,DK 2100Copenhagen,Denmark3Niels Bohr Institute,DK 2100Copenhagen,Denmark We present a protocol for the teleportation of the quantum state of a pulse of light onto the collective spin state of an atomic ensemble.The entangled state of light and atoms employed as a resource in this protocol is created by probing the collective atomic spin,Larmor precessing in an external magnetic field,offresonantly with a coherent pulse of light.We take here for the first time full account of the effects of Larmor precession and show that it gives rise to a qualitatively new type of multimode entangled state of light and atoms.The protocol is shown to be robust against the dominating sources of noise and can be implemented with an atomic ensemble at room temperature interacting with free space light.We also provide a scheme to perform the readout of the Larmor precessing spin state enabling the verification of successful teleportation as well as the creation of spin squeezing.PACS numbers:03.67.Mn,32.80.QkI.INTRODUCTIONQuantum teleportation -the disembodied transport of quantum states -has been demonstrated so far in sev-eral seminal experiments dealing with purely photonic [1]or atomic [2]systems.Here we propose a protocol for the teleportation of a coherent state carried initially by a pulse of light onto the collective spin state of ∼1011atoms.This protocol -just as the recently demonstrated direct transfer of a quantum state of light onto atoms [3]-is particularly relevant for long distance entanglement distribution,a key resource in quantum communication networks [4].Our scheme can be implemented with just coherent light and room-temperature atoms in a single vapor cell placed in a homogeneous magnetic field.Existing proto-cols in Quantum Information (QI)with continuous vari-ables of atomic ensembles and light [4]are commonly de-signed for setups where no external magnetic field is ap-plied such that the interaction of light with atoms meets the Quantum non-demolition (QND)criteria [5,6].In contrast,in all experiments dealing with vapor cells at room-temperature [3,7]it is,for technical reasons,ab-solutely essential to employ magnetic fields.In experi-ments [3,7]two cells with counter-rotating atomic spins were used to comply with both,the need for an exter-nal magnetic field and the one for an interaction of QND character.So far it was believed to be impossible to use a single cell in a magnetic field to implement QI protocols,since in this case -due to the Larmor precession -scat-tered light simultaneously reads out two non-commuting spin components such that the interaction is not of QND type.In this paper we do not only show that it is well possible to make use of the quantum state of light and atoms created in this setup but we demonstrate that -for the purpose of teleportation [8,9]-it is in factbetter to do so.As compared to the state resulting from the common QND interaction the application of an external magnetic field enhances the creation of correlations between atoms and light,generating more and qualitatively new,multimode type of entanglement.The results of the paper can be summarized as follows:(i )Larmor precession in an external magnetic field enhances the creation of entanglement when a collective atomic spin is probed with off-resonant light.The resulting entanglement involves multiple modes and is stronger as compared to what can be achieved in a comparable QND interaction.(ii )This type of entangled state can be used as a resource in a teleportation protocol,which is a simple generalization of the standard protocol [8,9]based on Einstein-Podolsky-Rosen (EPR)type of entanglement.For the experimentally accessible parameter regime the teleportation fidelity is close to optimal.The protocol is robust against imperfections and can be implemented with state of the art technique.(iii )Homodyne detection of appropriate scattering modes of light leaves the atomic state in a spin squeezed state.The squeezing can be the same as attained from a comparable QND measurement of the atomic spin [10,11].The same scheme can be used for atomic state read-out of the Larmor precessing spin,necessary to verify successful teleportation.We would like to note that it was shown recently in [12]that the effect of a magnetic field can enhance the capacity of a quantum memory in the setup of two cells.Teleportation in the setup of a single cell without mag-netic field was addressed in [13].The paper is organized as follows:The three points above are presented in sections II,III and IV,in this order.Some of the details in the calculations of sections III and IV are moved to appendices B and C.2II.INTERACTIONWe consider an ensemble of N at Alkali atoms with total ground state angular momentum F ,placed in a constant magnetic field causing a Zeeman splitting of Ωand ini-tially prepared in a fully polarized state along x .The collective spin of the ensemble is then probed by an offresonant pulse which propagates along z and is linearly polarized along x .Thorough descriptions of this inter-action and the final state of light and atoms after the scattering can befoundin [14,15,16,17,18]and espe-cially in [19,20,21,22]for the specific system we have in mind.We derive the final state here with a special focus on the effects of Larmor precession and light prop-agation in order to identify the light modes which are actually populated in the scattering process.In appendix A we show that the interaction is ade-quately described by a HamiltonianH =H at +H li +V,H at =Ω√N ph N at F a 1σΓ/2A ∆where N ph is the over-all number of photons in the pulse,a 1is a constant characterizing the ground state’s vector polarizability,σis the scattering cross section,Γthe decay rate,∆the detuning and A the effective beam cross section.Changing to a rotating frame with respect to H at by defining X I (t )=exp(−iH at t )X exp(iH at t )and evaluat-ing the Heisenberg equations for these operators yields the following Maxwell-Bloch equations∂t X I (t )=κT cos(Ωt )p (0,t ),(2a)∂t P I (t )=κT sin(Ωt )p (0,t ),(2b)(∂t +c∂z )x (z,t )=κcT[cos(Ωt )P I (t )−sin(Ωt )X I (t )]δ(z ),(∂t +c∂z )p (z,t )=0,where ∂t (z )denotes the partial derivative with respect to t (z ).These equations have a clear interpretation.Light noise coming from the field in quadrature with the classi-cal probe piles up in both,the X and P spin quadrature,but it alternately affects only one or the other,changing with a period of 1/Ω.Conversely atomic noise adds to the in phase field quadrature only and the signal comes alternately from the X and P spin quadrature.The out of phase field quadrature is conserved in the interaction.To solve this set of coupled equations it is convenient to introduce a new position variable,ξ=ct −z ,to elim-inate the z dependence.New light quadratures defined by ¯x (ξ,t )=x (ct −ξ,t ),¯p (ξ,t )=p (ct −ξ,t )also have a simple interpretation:ξlabels the slices of the pulse moving in and out of the ensemble one after the other,starting with ξ=0and terminating at ξ=cT .The Maxwell equations now read∂t ¯p (ξ,t )=0,(2c)∂t ¯x (ξ,t )=κcT[cos(Ωt )P I (t )−sin(Ωt )X I (t )]δ(ct −ξ).(2d)The solutions to equations (2a,2b,2c)areX I (t )=X I (0)+κT t 0d τcos(Ωτ)¯p (cτ,0),(3a)P I (t )=P I (0)+κT t 0d τsin(Ωτ)¯p (cτ,0),(3b)¯p (ξ,t )=¯p (ξ,0)(3c)and the formal solution to (2d)is¯x (ξ,t )=¯x (ξ,0)+(3d)+κT [cos(Ωξ/c )P I (ξ/c )−sin(Ωξ/c )X I (ξ/c )].As mentioned before,both atomic spin quadratures are affected by light but,as is evident from the solutions for X (t ),P (t ),they receive contributions from different and,in fact,orthogonal projections of the out-of-phase field.As we will show in the following,the corresponding projections of the in-phase field carry in turn the signal of atomic quadratures after the interaction.It is there-fore convenient to explicitly introduce operators for these modes [21].We define a cosine component before the in-teractionp in c = T Td τcos(Ωτ)¯p (cτ,0),(4a)x in c =TTd τcos(Ωτ)¯x (cτ,0)(4b)and a sine component p in s ,x ins with cos(Ωτ)replaced by sin(Ωτ).In frequency space these modes consist of spec-tral components at sidebands ωc ±Ωand are closely re-lated to the sideband modulation modes introduced in3[26]for the description of two photon processes.It is eas-ily checked that these modes are asymptotically canon-ical,[x in c ,p in c ]=[x in s ,p ins ]=i [1+O (n −10)]≃i ,and inde-pendent,[x in c ,p in s ]=O (n −10)≃0,if we assume n 0≫1for n 0=ΩT ,the pulse length measured in periods of Larmor precession.In terms of these modes the atomic state after the in-teraction X out =X I (T ),P out =P I (T )is given by X out =X in +κ2p inc ,P out =P in +κ2p ins .(5a)The final state of cosine (sine)modes is de-scribed by x out c(s),p outc(s),defined by equations (4)with ¯x (cτ,0),¯p (cτ,0)replaced by ¯x (cτ,T ),¯p (cτ,T )respec-tively.Since the out-of-phase field is conserved we have triviallyp out c =p in c ,p out s =p in s .(5b)Deriving the corresponding expressions for the cosine andsine components of the field in phase,x out c ,x outs ,raises some difficulties connected to the back action of light onto itself.This effect can be understood by noting that a slice ξof the pulse receives a signal of atoms at a time ξ/c [see equation (3d)]which,regarding equations (3a,3b),in turn carry already the integrated signal of all slices up to ξ.Thus,mediated by the atoms,light acts back on itself.The technicalities in the treatment of this effect are given in appendix B where we identify relevant ”back action modes”,x c ,1,p c ,1,x s ,1,p s ,1,in terms of which one can express x out c =x in c +κ2P in +κ√2 2p in s ,1,(5c)x out s=x in s −κ2X in−κ√2 2p in c ,1.(5d)The last two terms in both lines represent the effect of back action,part of which involves the already defined cosine and sine components of the field in quadrature.The remaining part is subsumed in the back action modes which are again canonical and independent from all other modes.Equations (5)describe the final state of atoms and the relevant part of scattered light after the pulse has passed the atomic ensemble and are the central result of this section.Treating the last terms in equations (5c,5d)as noise terms,it is readily checked by means of the separa-bility criteria in [27]that this state is fully inseparable,i.e.it is inseparable with respect to all splittings be-tween the three modes.For the following teleportation protocol the relevant entanglement is the one between atoms and the two light modes.Figure 1shows the von Neumann entropy E vN of the reduced state of atoms in its dependence on the coupling strength κand in com-parison with the entanglement created without magnetic field in a pure QND interaction of atoms and light.The amount of entanglement is significantly enhanced.FIG.1:Von Neumann Entropy of the reduced state of atoms versus coupling strength kappa for the state of equation 5(full line)and for the state generated without magnetic field in a pure QND interaction (dashed line)with the same cou-pling strength.Application of a magnetic field significantly enhances the amount of light-atom entanglement.III.TELEPORTATION OF LIGHT ONTOATOMSIn this section we will show how the multimode entan-glement between light and atoms generated in the scat-tering process can be employed in a teleportation proto-col which is a simple generalization of the standard proto-col for continuous variable teleportation using EPR-type entangled states [8,9].We first present the protocol and evaluate its fidelity and then analyze its performance un-der realistic experimental conditions.A.Basic protocolFigure 2depicts the basic scheme which,as usually,consists of a Bell measurement and a feedback operation.Input The coherent state to be teleported is encoded in a pulse which is linearly polarized orthogonal to the classical driving pulse and whose carrier frequency lies at the upper sideband,i.e.at ωc +Ω.The pulse envelope has to match the one of the classical pulse.As is shown in appendix B,canonical operators y,q with [y,q ]=i de-scribing this mode can conveniently be expressed in terms of cosine and sine modulation modes,analogous to equa-tions (4),defined with respect to the carrier frequency.One findsy =12(y s +q c ),q =−12(y c −q s ).(6)A coherent input amounts to having initially ∆y 2=∆q 2=1/2and an amplitude y , q with mean photon number n ph =( y 2+ q 2)/2.Bell measurement This input is combined at a beam splitter with the classical pulse and the scattered light.At the ports of the beam splitter Stokes vector compo-nents S y and S z are measured by means of standard po-larization measurements.Given the classical pulse in xFIG.2:Scheme for teleportation of light onto atoms:As de-scribed in section II,a classical pulse(linearly polarized along x)propagating along the positive z direction is scattered offan atomic ensemble contained in a glass cell and placed in a constant magneticfield B along x.Classical pulse and scat-tered light(linearly polarized along y)are overlapped with a with a coherent pulse(linearly polarized along z)at beam splitter B S.By means of standard polarization measurements Stokes vector components S y and S z are measured at one and the other port respectively,realizing the Bell measurement. The Fourier components at Larmor frequencyΩof the corre-sponding photocurrents determine the amount of conditional displacement of the atomic spin which can be achieved by ap-plying a properly timed transverse magneticfield b(t).See section III A for details.polarization this amounts to a homodyne detection of in-and out-of-phasefields of the orthogonal polarization component.The resulting photocurrents are numerically demodulated to extract the relevant sine and cosine com-ponents at the Larmor frequency[20].Thus one effec-tively measures the commuting observables˜x c=12 x out c+y c,˜x s=12 x out s+y s ,(7)˜q c=12 p out c−q c ,˜q s=12 p out s−q s .Let the respective measurement results be given by ˜Xc,˜X s,˜Q c and˜Q s.Feedback Conditioned on these results the atomic state is then displaced by an amount˜X s−˜Q c in X and −˜X c−˜Q s in P.This can be achieved by means of two fast radio-frequency magnetic pulses separated by a quar-ter of a Larmor period.In the ensemble average thefinal state of atoms is simply given byXfin=X out+˜x s−˜q c,Pfin=P out−˜x c−˜q s.(8)This description of feedback is justified rigorously in ap-pendix C.Relating these expressions to input operators,wefind by means of equations(5),(6)and(7)Xfin= 1−κ√2 2p in c+12x in s−16 κ2 P in−121−κ√√2 2p in s,1+q.(9b)This is the main result of this section.Teleportationfidelity Taking the mean of equations (9)with respect to the initial state all contributions due to input operators and back action modes vanish such that Xfin = y and Pfin = q .Thus,the am-plitude of the coherent input light pulse is mapped on atomic spin quadratures as desired.In order to prove faithful teleportation also the variances have to be con-served.It is evident from(9)that thefinal atomic spin variances will be increased as compared to the coherent input.These additional terms describe unwanted excess noise and have to be minimized by a proper choice of the couplingκ.As afigure of merit for the telepor-tation protocol we use thefidelity,i.e.squared over-lap,of input andfinal state.Given that the means are transmitted correctly thefidelity is found to be F= 2 (1+2(∆Xfin)2)(1+2(∆Pfin)2) −1/2.The variances of thefinal spin quadratures are readily calculated tak-ing into account that all modes involved are independent and have initially a normalized variance of1/2.In this way a theoretical limit on the achievablefidelity can be derived depending solely on the coupling strengthκ.In figure3we take advantage of the fact that the amount of entanglement between light and atoms is a monotonously increasing function ofκsuch that we can plot thefi-delity versus the entanglement.This has the advantage that we can compare the performance of our teleporta-tion protocol with the canonical one[8,9]which uses a two-mode squeezed state of the same entanglement as a resource and therefore maximizes the teleportationfi-delity for the given amount of entanglement.No physical state can achieve a higherfidelity with the same entan-glement.This follows from the results of[30]where it was shown that two-mode squeezed states minimize the EPR variance(and therefore maximize the teleportation fidelity)for given entanglement.The theoreticalfidelity achievable in our protocol is maximized forκ≃1.64cor-responding to F≃.77.But also for experimentally more feasible values ofκ≃1can thefidelity well exceed the classical limit[28,29]of1/2and,moreover,compari-son with the values achievable with a two-mode squeezed state shows that our protocol is close to optimal.FIG.3:(a)Theoretical limit on the achievablefidelity F ver-sus entanglement between atoms and light measured by the von Neumann entropy E vN of the reduced state of atoms.The grey area is unphysical.For moderate amounts of entangle-ment our protocol is close to optimal.(b)Coupling strengthκversus entanglement.The dashed lines indicate the maximal fidelity of F=.77which is achieved forκ=1.64.B.Noise effects and Gaussian distributed input Under realistic conditions the teleportationfidelity will be degraded by noise effects like decoherence of the atomic spin state,light absorption and reflection losses and also because the coupling constantκis experimen-tally limited to valuesκ≃1.On the other hand the classicalfidelity bound to be beaten will be somewhat higher than1/2since the coherent input states will nec-essarily be drawn according to a distribution with afinite width in the mean photon number¯n.In this section we analyze the efficiency of the teleportation protocol un-der these conditions and show that it is still possible to surpass any classical strategy for the transmission and storage of coherent states of light[28,29].During the interaction atomic polarization decays due to spontaneous emission and collisional relaxation.In-cluding a transverse decay thefinal state of atoms is given byX out= √βf X,(10a) P out= √βf P.(10b)as follows from the discussion in appendix A.βis the atomic decay parameter and f X,f P are Langevin noise operators with zero mean.Their variance is experimen-tally found to be close to the value corresponding to a coherent state such that f2X = f2P =1/2.Light absorption and reflection losses can be taken into account in the same way asfinite detection efficiency.For example the statistics of measurement outcome˜X s will not stem from the signal mode˜x s alone but rather from the noisy mode√ǫfx,swhereǫis the photon loss parameter and f x,s is a Langevin noise operator of zero mean and variance f2x,s =1/2.Analogous expres-sions have to be used for the measurements of˜x c,˜q s and ˜q c which will be adulterated by Langevin terms f x,c,f q,s and f q,c respectively.In principle each of the measure-ment outcomes can be fed back with an independently chosen gain but for symmetry reasons it is enough to distinguish gain coefficients g x,g q for the measurement outcomes of sine and cosine components of x and q re-spectively.Including photon loss,finite gain and atomic decay,as given in(10),equations(8),describing thefinal state of atoms after the feed back operation,generalize toXfin= βf X+g x √ǫf x,s (11a)−g q √ǫf q,c ,Pfin= βf P−g x √ǫf x,c (11b)−g q √ǫf q,s .For non unit gains a given coherent amplitude( y , q ) will not be perfectly teleported onto atoms and the cor-respondingfidelity will be degraded by this mismatch according toF( y , q )=2[1+2(∆Xfin)2][1+2(∆Pfin)2]·exp−( y − Xfin )21+2(∆Pfin)2 .If the input amplitudes are drawn ac-cording to a Gaussian distribution p( y , q )=exp[−( y 2+ q 2)/2¯n]/2π¯n with mean photon number¯n the averagefidelity[with respect to ( y , q )]is readily calculated.The exact expression in terms of initial operators can then be derived by means of equations(5),(6),(7)and(11)but is not particularly enlightening.Infigure4we plot the averagefidelity, optimized with respect to gains g x,g q,in its dependence on the atomic decayβfor various values of photon loss ǫ.We assume a realistic valueκ=0.96for the coupling constant and a mean number of photons¯n=4for the distribution of the coherent input.For feasible values ofβ,ǫ 0.2the averagefidelity is still well above the classical bound on thefidelity[28,29].This proves that the proposed protocol is robust against the dominating noise effects in this system.The experimental feasibility of the proposal is illus-trated with the following example.Consider a sam-ple of N at=1012Cesium atoms in a glass cell placed in a constant magneticfield along the x-direction caus-ing a Zeeman splitting ofΩ=350kHz in the F=4 ground state multiplet.The atoms are pumped into m F=4and probed on the D2(F=4→F′=3,4,5)FIG.4:(a)Averagefidelity achievable in the presenceof atomic decayβ,reflection and light absorption lossesǫ=8%,12%,16%,couplingκ=0.96and Gaussian dis-tributed input states with mean photon number¯n=4.Thefi-delity benchmark is in this case5/9(dashed line).(b)Respec-tive optimal values for gains g x(solid lines)and g q(dashedlines).transition.The classical pulse contains an overall num-ber of N ph=2.51013photons,is detuned to the blueby∆=1GHz,has a duration T=1ms and can have an effective cross section of A≃6cm2due to thermalmotion of atoms.Under these conditions the tensor polarizability can be neglected(∆/ωhfs≃10−1).Also n0=ΩT=350justifies the use of independent scatter-ing modes.The couplingκ≃1and the depumping ofground state populationη≃10−1as desired.IV.SPIN SQUEEZING AND STATE READ-OUTIn this section we present a scheme for reading out either of the atomic spin components X,P by means of a probe pulse interacting with the atoms in the one way as described in section II.The proposed scheme allows one,on the one hand,to verify successful receipt of the coherent input subsequent to the teleportation protocol of section III and,on the other hand,enables to generate spin squeezing if it is performed on a coherent spin state. It is well known[15,31]and was demonstrated exper-imentally[10,11]that the pure interaction V,as given in equation(1),can be used to perform a QND measure-ment of either of the transverse spin components.At first sight this seems not to be an option in the scenario under consideration since the local term H at,account-ing for Larmor precession,commutes with neither of the spin quadratures such that the total Hamiltonian does not satisfy the QND criteria[5,6].As we have shown in section II Larmor precession has two effects:Scattered light is correlated with both transverse components andsuffers from back action mediated by the atoms.Thus, in order to read out a single spin component one has to overcome both disturbing effects.Our claim is that this can be achieved by a simultane-ous measurement of x outc,p outs,p outs,1or x outs,p outc,p outc,1 if,respectively,X or P is to be measured.In the follow-ing we consider in particular the former case but every-thing will hold with appropriate replacements also for a measurement of P.As shown infigure5the set of observablesx outc,p outs,p outs,1can be measured simultaneously by a measurement of Stokes component S y after aπ/2rota-tion is performed selectively on the sine component of the scattered light.The cosine component of the corre-sponding photocurrent will give an estimate of x outcandthe sine component of p outs.Multiplying the photocur-rent’s sine component by the linear function defining the back action mode,equation(B1),will give in additionan estimate of p outs,1.Note that thefield out of phase is conserved in the interaction such thatp outs,1=p in s,1,p outc,1=p in c,1,(12) i.e.the results will have shot noise limited variance.It is then evident from equation(5c)that the respective photocurrents together with an a priori knowledge ofκare sufficient to estimate the mean X .The conditional variances after the indicated measure-ments are∆X2|{x out c,p out s,p out s,1}=(∆X in)222,(13b)corresponding to a pure state.Obviously the variance in X is squeezed by a factor(1+κ2/2)−1.Note that the squeezing achieved in a QND measurement without magneticfield but otherwise identical parameters is given by(1+κ2)−1.From this we conclude that the quality of the estimate for X ,as measured f.e.by input-output coefficients known from the theory of QND measurements [5,6],can be the same as in the case without Larmor precession albeit only for a higher couplingκ. Equations(13)are conveniently derived by means of the formalism of correlation matrices [32].For the operator valued vector R=(X,P, x c,p c,x s,p s,x c,1,p c,1,x s,1,p s,1)equations(5),(12) and(B2)define via R out=S(κ) R in a symplectic linear transformation S(κ).The contributions of p in c,2andp in s,2to x outs,1and x outc,1as given in(B2)are treated as noise and do not contribute to the symplectic trans-formation S but enter the input-output relation for the correlation matrix as an additional noise term as follows.The correlation matrix is as usually defined byγi,j=tr{ρ(R i R j+R j R i)}.The initial state is then an10×10identity matrix and thefinal state is γout=S(κ)S(κ)T+γnoise where the diagonal matrixFIG.5:Scheme for spin measurement:After the scattering a π/2rotation is performed on the scattered light modulated at the Larmor frequency such as to affect only the sine(cosine) component.Standard polarization measurement of S y and appropriate postprocessing allows to read out the mean of X(P),leaving the atoms eventually in a spin squeezed state.γnoise=diag[0,0,0,0,0,0,1,0,1,0](κ/2)4/15accountsfor noise contributions due correlations to second order back action modes c.f.equations(B2).In order to evaluate the atomic variances after a measurement ofx out c ,p outs,p outs,1the correlation matrixγout is split upinto blocks,γout= A C C T Bwhere A is the2×2subblock describing atomic variances. Now,the state A′after the measurement can be found by evaluating[32]A′=A−limx,n→∞C1(∆−iΓ/2) a01+ia1 F×(A3)8 with real dimensionless coefficients a j of order unity andΓthe excited states’decay rate.The non-hermitian partof the resulting Hamilton operator describes the effectof light absorption and loss of ground state populationdue to depumping in the course of interaction.In thefollowing we will focus on the coherent interaction and,for the time being,take into account only the hermitiancomponent.The effects of light absorption and atomicdepumping are treated below.Coherent interaction Since scattering of light occurspredominantly in the forward direction[22]it is legiti-mate to adopt a one dimensional model such that the(negative frequency component of the)electricfield prop-agating along z is given byE(−)(z,t)=E(−)(z) ey+E(−)(z,t) e xE(−)(z)=ρ(ωc) b dωa†(ω)e−ikzE(−)(z,t)=ρ(ωc)ωc/4πǫ0Ac and A denotes the pulse’scross sectional area,N ph the overall number of photonsin the pulse and T its duration.We restrict thefieldin x polarization to the classical probe pulse,since onlythe coupling of atoms to the y polarization is enhancedby the coherent probe.Furthermore we implicitly assumefor the classical pulse a slowly varying envelope such thatit arrives at z=0at t=0and is then constant fora time bining this expression for thefield withexpressions(A2)and(A3)for the atomic polarizability inequation(A1)yieldsV=−i κ4πJTbdω d zj(z) a(ω)e−i[(k c−k)z−ωc t]−h.c.where we defined a dimensionless coupling constant κ=N ph Ja1σΓ/2A∆withσthe scattering cross sec-tion on resonance.We now definefield quadratures for spatially localized modes[24,25]asx(z)=14πbdω a(ω)e−i(k c−k)z+h.c. ,(A4a)p(z)=−i4πbdω a(ω)e−i(k c−k)z−h.c. (A4b)with commutation relations[x(z),p(z′)]=icδ(z−z′) where the delta function has to be understood to have a width on the order of c/b.Since we assumed thatΩ≪b, the time it takes for such a fraction of the pulse to cross the ensemble is much smaller than the Larmor period 1/Ω.During the interaction with one of these spatiallylocalized modes the atomic state does not change appre-ciable and we can simplify the interaction operator to V= κ(JT)−1/2J z p(0)where J z= i F(i)z and we as-sumed that the ensemble is located at z=0and changedto a frame rotating at the carrier frequencyωc.A last approximation concerns the description of theatomic spin state.Initially the sample is prepared in acoherent spin state with maximal polarization along x, i.e.in the eigenstate of J x with maximal eigenvalue J. We can thus make use of the Holstein-Primakoffapprox-imation[23]which allows to describe the spin state as a Gaussian state of a single harmonic oscillator.The first step is to express collective step up/down operators (along x),J±=J y±iJ z,in terms of bosonic creation and annihilation operators,[b,b†]=11,asJ+=√11−b†b/2J b,J−=√11−b†b/2J. It is easily checked that these operators satisfy the correct commutation relations[J+,J−]=2J x if one identifies J x=J−b†b.The fully polarized initial state thus corresponds to the ground state of the harmonic oscillator.Note that this map-ping is exact.Under the condition that b†b ≪J one can approximate J+≃√2Jb†and therefore J z≃−i 2and P=−i(b−b†)/√。
光学效应英语作文The Optical Effect。
Introduction。
The optical effect is a fascinating phenomenon that occurs when light interacts with various materials, resulting in the manipulation of light waves and the creation of stunning visual effects. From the iridescence of a soap bubble to the shimmering colors of a peacock's feathers, the optical effect is all around us, and its beauty and complexity never fail to captivate our imagination.Explanation of the Optical Effect。
The optical effect is a result of the interaction between light and matter. When light waves encounter a material, they can be reflected, refracted, or diffracted, leading to a variety of visual effects. One of the mostcommon optical effects is iridescence, which occurs whenlight waves are scattered by the microstructures on the surface of a material, creating a rainbow-like display of colors. Another well-known optical effect is the shimmering of a mirage, which is caused by the refraction of light asit passes through layers of air with different temperatures. Applications of the Optical Effect。
光学效应英语作文In the realm of physics, optical phenomena are thecaptivating interactions between light and matter that shape our visual experiences. These phenomena are not only fundamental to our understanding of the world but also play a crucial role in various technologies and applications we encounter daily.Reflection and Refraction: The most common optical effects are reflection and refraction. Reflection occurs when light bounces off a surface, as seen in mirrors that create images. Refraction, on the other hand, happens when light passes through a medium with a different density, causing it to change direction. This is the principle behind lenses used in eyeglasses and cameras.Dispersion: Dispersion is the separation of light into its constituent colors when it passes through a prism. Thiseffect is responsible for the beautiful rainbows we see after a rain shower, as sunlight is refracted and dispersed by raindrops.Diffraction: Diffraction is the bending of light around obstacles or through slits. It is the reason why we can see shadows with sharp edges and why light can spread out to illuminate areas behind an object, even though the object blocks a direct line of sight.Polarization: Polarization is the alignment of light waves in a specific direction. It is used in sunglasses to reduce glare from reflective surfaces like water or glass, making it easier to see in bright conditions.Total Internal Reflection: This occurs when light traveling from a denser medium to a less dense medium hits the boundary at an angle greater than the critical angle. Instead of passing through, the light is completely reflected back into the denser medium. This is the principle behind fiber optics, which is used for high-speed data transmission.Lenses and Optical Instruments: Lenses are the heart of many optical devices, from microscopes to telescopes. They use refraction to magnify, focus, or disperse light, allowing us to see objects at different scales and distances.Laser Technology: Lasers, which produce highly concentrated beams of light, are a product of optical phenomena. They have a wide range of applications, from medical procedures to industrial manufacturing and even in everyday items likelaser pointers.Optical Illusions: Optical illusions exploit the way our eyes and brain process visual information, often playing with perspective, contrast, and color to create images that trick our senses.Conclusion: Optical phenomena are not just scientific curiosities; they are integral to our daily lives. From the way we see the world around us to the technologies thatenhance our experiences, the study of light and its interactions with matter is a fascinating field that continues to inspire innovation and discovery.。
