下载文档原格式
宇宙“紫外线”;探寻宇宙最高能量粒子
宇宙是一个神秘而又令人着迷的世界，我们人类一直在探索它的奥妙和秘密。
最近，科学家们发现了一种新的宇宙“紫外线”，这是一种高能量粒子，可能是从宇宙中传来的。
这种宇宙“紫外线”被称为“极超高能宇宙线”，简称UHECRs。
这些粒子具有极高的能量，比我们已知的任何粒子都要高。
事实上，这些粒子的能量已经超过了我们所能制造出的任何粒子加速器的最高能量。
由于它们的能量如此之高，科学家们认为这些粒子可能是从宇宙中最遥远和最强大的天体中产生的。
这些天体包括超新星、黑洞、星系碰撞等。
但是，要捕捉到这些高能量粒子并不容易。
它们在穿越宇宙时会与宇宙微波背景辐射相互作用，并被散射和吸收。
因此，只有当它们与大气层相互作用时，才能被探测器捕捉到。
目前，世界各地已经建立了许多UHECRs探测器。
其中一种探测器是位于阿根廷的皮埃尔·奥古斯特·阿格里奇科斯天文台的阿格里奇科斯探测器，它是迄今为止最大和最灵敏的UHECRs探测器之一。
这些探测器会记录下来这些高能量粒子的轨迹和能量，以帮助科学家们更好地理解宇宙的起源和演化。
研究UHECRs也有助于了解宇宙中的磁场和物质分布等重要问题。
虽然我们还有很多问题需要解决，但这是一个非常令人激动的时刻。
通过探测UHECRs，我们可以更深入地了解宇宙，并探寻宇宙中最高能量粒子的奥秘。
中微子综述及未来应用展望摘要：中微子是1930年奥地利物理学家泡利为了解释β衰变中能量似乎不守恒而提出的，1933年正式命名为中微子。
中微子只参与非常微弱的弱相互作用，具有最强的穿透力。
因此中微子的检测非常困难，1956年才被观测到。
大多数粒子物理和核物理过程都伴随着中微子的产生，而且中微子具有微小的质量。
欧洲科学家在实验中发现，中微子速度超过光速，中微子可以直透地球，它在穿过地球时损耗很小，因此在通信中有广阔的应用前景。
Abstract：Neutrino is the 1930 Austria physicist Pauli to explain beta decay energy does not seem to conservation and put forward, 1933 was officially named as the neutrino. Neutrino involved only very weak weak interactions, with the strongest penetration. Therefore the neutrino detection is difficult to be observed, 1956. The majority of the particle physics and nuclear physics processes are accompanied by neutrino production, and neutrinos have tiny quality. European scientists found in experiments, neutrino faster than the speed of light, neutrinos can into earth, which crosses over the earth when the loss is very small, so the communication has the extensive application prospect关键词：中微子、中微子的质量、中微子速度、通讯目录综述中微子的发现历程中微子的质量中微子通信的展望结束语一、综述19世纪末20世纪初对放射性的研究，科学家们发现，在量子世界中，能量的吸收和发射是不连续的。
a r X i v :a s t r o -p h /0508141v 2 29 M a y 2006Gravitino,Axino,Kaluza-Klein Graviton Warm and MixedDark Matter and ReionizationKarsten Jedamzik a ,Martin Lemoine b ,Gilbert MoultakaaaLaboratoire de Physique Th´e orique et Astroparticules,CNRS UMR 5825,Universit´e Montpellier II,F-34095Montpellier Cedex 5,FrancebGReCO,Institut d’Astrophysique de Paris,CNRS,98bis boulevard Arago,F-75014Paris,FranceStable particle dark matter may well originate during the decay of long-lived relic particles,as recently extensively examined in the cases of the axino,gravitino,and higher-dimensional Kaluza-Klein (KK)graviton.It is shown that in much of the viable parameter space such dark matter emerges naturally warm/hot or mixed.In particular,decay produced gravitinos (KK-gravitons)may only be considered cold for the mass of the decaying particle in the several TeV range,unless the decaying particle and the dark matter particle are almost degenerate.Such dark matter candidates are thus subject to a host of cosmological constraints on warm and mixed dark matter,such as limits from a proper reionization of the Universe,the Lyman-αforest,and the abundance of clusters of galaxies..It is shown that constraints from an early reionsation epoch,such as indicated by recent observations,may potentially limit such warm/hot components to contribute only a very small fraction to the dark matter.The nature of the ubiquitous dark matter is still un-known.Dark matter in form of fundamental,and as yet experimentally undiscovered,stable particles predicted to exist in extensions of the standard model of parti-cle physics may be particularly promising.For a scale of the new physics around 1TeV,as preferred by the-oretical arguments,such dark matter abundances pro-duced either during freeze-out of stable particles from equilibrium,or freeze-out of meta-stable particles and their subsequent decay into stable particles,may come tantalizingly close to the abundance required by cosmol-ogy.For this reason,a number of candidate dark matter particles,including also stable axinos produced in decays of next-to-lightest supersymmetric particles (NLSP);bi-nos or staus [1,2,3,4],stable gravitinos produced via NLSP bino,stau,or sneutrino decays [5,6,7,8,9],or stable KK-gravitons produced via the decay of KK U (1)hypercharge gauge bosons [5],have been recently consid-ered/reconsidered.For details and the theoretical moti-vation for the possible existence of such particles we refer the reader to the orginal literature.In this note we consider the fact that particle dark matter (DM)produced by the decay of a relic popula-tion of metastable particles is often warm or even hot.This has been known for some time [10],but has escaped entering into the conlusions of some recent studies.This effect is also known to exist in the context of dark matter production by cosmic string evaporation [11].Neverthe-less,very recently the very same observation has been rediscovered in the studies by Cembranos et al.[12]and Kaplinghat [13].These latter papers concentrate on the possible resolution of a number of alleged deviations be-tween the observed sub-structure of galactic halos and structure of dwarf galaxies and that predicted in struc-ture formation with a purely cold DM particle,whereas our study focusses mostly on constraining such warm-or mixed-dark matter models by reionization.In any case,for a complete view the reader is referred to the abovestudies as well.Decay produced particle dark matter is often warm/hot,i.e.is endowed with primordial free-streaming velocities leading to the early erasure of small-scale per-turbations [14],due to the kinetic energy imparted on the decay product during the decay process itself.Since axi-nos,gravitinos,and KK-gravitons are superweakly inter-acting,they will not thermalise after decay,and inherit as kinetic energy a good fraction of the rest mass en-ergy of the mother particle.For decay χ→γ+˜Gof a massive particle χto an essentially massless particle γ(with m γ≪m χ)and the dark matter particle ˜G,with m χ>m ˜G one finds for the instantaneous post-decay mo-mentum of ˜Gp i˜G =(m 2χ−m 2˜G )2m χm ˜GT 0g d1/3,(2)where T and g are cosmic temperarture and statisticalweight of the plasma at the present ′0′and particle de-cay ′d ′epochs,respectively.It has been shown that a sudden decay approximation,approximating all particles to decay at the same T d ,is excellent [3],provided oneuses the relation t d ≃Γ−1d with t =(2H )−1in the early radiation dominated Universe,where t is cosmic time,Γd is the decay width of the particle,and H the Hubble constant,ing the above one findsv 0DM ≃4.57×10−5km 2m χm ˜G g −1/12d τd2 Free-streaming velocities may become appreciable for ei-ther light DM particles(i.e.m˜G ≪mχ)or late decay,acondition satisfied for much of the axino-,gravitino-,and KK-graviton-DM parameter space.Cosmological constraints on warm dark matter deriv-ing,for example,from the Lyman-αforest or cosmo-logical reionization,are often formulated as lower lim-its on the mass of a hypothetical gravitino DM parti-cle.Such limits assume a relativistically freezing out gravitino,leading thereby to a well-specified relationv rms≃0.044kms−1(Ω˜G h2/0.15)0.34(m˜G/1keV)−1.34[15]between gravitino mass and root-mean-square present day gravitino velocity(cf.e.g.to[16,17]).However, it is rather the latter quantity,v rms,which is,without further assumptions about the nature and production mechanism of the dark matter,constrained by cosmol-ogy.Free-streaming particles erase primordial dark mat-ter perturbations between very early times and the epoch of matter-radiation equality(EQ),after which further erasure becomes inefficient.Up to which scale pertur-bations have been erased than depends essentially only on v rms and the time of EQ(determined itself byΩm, the total non-relativistic matter density),such that one finds[17]R0c≃0.226Mpc Ωm0.05km/s 0.86,(4)by detailed Boltzman-equation simulations[18].Here R0c≡1/k c defines the wave vector k c for which the pri-mordial power spectrum is suppressed by a factor two[19] when compared to the same cosmological model,but with cold dark matter.Armed with a relation between v rms and gravitino mass,as well as Eq.(3),we may now trans-late in the literature existing limits on relativistically freezing out gravitino warm dark matter,into limits on warm dark matter generated by particle decay.Here we employ decay widths as calculated in the original litera-ture[20].We note here that the equivalence between traditional warm dark matter,described by a Fermi-Dirac distribu-tion,and metastable particle decay produced dark mat-ter,with a velocity distribution given by exponential de-cay,is not entirely perfect.This is due to the differing ve-locity distributions.Kaplinghat[13]computes the tans-fer function for decay produced dark matter andfinds differences in the damping tails between decay produced dark matter and warm dark matter.Nevertheless,given current measurement and theoretical uncertainties in cos-mology,such as for example in the determination of the epoch of reionization,both types of DM should be consid-ered as having equivalent effects on structure formation as long as they have an identical second moment of the distribution,i.e.an identical root-mean-square velocity. There exists a large number of observable cosmologi-cal differences between scenarios with warm-(WDM)and cold-dark matter(CDM).It has even been argued that WDM has phenomelogical advantages over CDM,poten-tially resolving possible difficulties of CDM scenarios in explaining a scarce of substructure in Milky-Way typehalos or the existence of cores in dwarf galaxies.Nev-ertheless,counterarguments in favor of CDM have also been presented,such that the situation is not resolved. We will here only focus on three cosmological implica-tions of WDM or mixed dark matter(MDM)scenarios; namely the optical depth in the Lyman-αforest of mildly non-linearfluctuations on smaller scales∼1Mpc[21], the successful reionization of the Universe at high red-shift(probing perturbations on the smallest scales∼10−100kpc)[17,22],and for the case of MDM,the abundance of clusters at close to the present epoch[23].A recent analysis of the matter power spectrum as im-plied by observations of the Lyman-αforest and the cosmic microwave background anisotropies(CMBR)by the WMAP mission has yielded a2σlower limit on the WDM gravitino mass of550eV[21].Using the above this may be translated to a limit v0rms<∼0.1km s−1.One year of observations of polarization of the CMBR by the WMAP sattelite have revealed a high optical depth τ≈0.17±0.04[24]for Thomson scatterings of CMBR photons on electrons.The recently presented three year WMAP analysis has led to a downward revision of this value toτ≈0.09±0.03[25],where error bars are one sigma and aΛCDM concordance model has been as-sumed.This implies a fairly complete reionization of the Universe at redshift8.5<∼z<∼15(at95%confidence level)seemingly consistent with CDM scenarios.Such scenarios predict an early reionization of the Universe due to the early formation of sub-galactic halos and massive stars therein.The situation is different in WDM scenar-ios due to the lack of small-scale power and the concomi-tant late formation of thefirst stars.If the fairly high optical depth is indeed due to thefirst stars,rather than due to some’exotic’mechanism,reionization places very stringent limits on the warmness of the DM.In particu-lar,Yoshida et al.[22]have shown that even for WDM with m˜G≈10keV reionization is far from substantial at redshift z∼17(appropriate to theτcentral value of the one year WMAP analysis).This corresponds to v0rms<∼0.002km s−1.In the numerically expansive studyof Yoshida et al WDM scenarios with m˜G>10keV havenot been considered.As the case m˜G=10keV fails,evenlarger m˜Gcould potentially fail.Nevertheless,uncertain-ties in these calculations exist due to the modeling of the physics of gas cooling,radiation transport,and star for-mation.We thus regard such limits as preliminary. Scenarios of DM due to decaying metastable particles often may come in theflavor of mixed dark matter when only a component of the DM is due to decay,with the other component possibly due to thermal scatterings at high temperature.Such scenarios of MDM scenarios may also be constrained by the abundance of clusters of galax-ies[23].Nevertheless,MDM may only be constrained by these means,in case the warm component is warm/hot enough to erase primordial perturbations on the scale of a cluster of galaxies.Forλc≡2π/k≈20Mpc wefind that a half wavelength roughly encompasses1014M⊙,the1101001000100000.010.1110100100010000100000m G ∆m v = 0.002 km/s v = 0.1v = 1FIG.1:Contour plots of constant present-day free-streamingvelocities in a variety of scenarios where the dark matter ˜Gis generated by the late decay of a non-relativistic primaryχ→˜G +γ(cf.Eq.1).Results are shown in the plane of m ˜Gand ∆m ≡m χ−m ˜G (all in GeV).The scenarios are bino-decay into gravitinos (red-solid),slepton decay into gravitinos (blue-dotted),and B 1decays into KK-gravitons (green-dashed).Shown are the contours of velocities (from top to bottom)v =0.002,0.1,and 1km s −1,respectively.Also shown,by the thin dotted lines,are the contours where the effects of small-scale suppression due to the coupling of a charged slep-ton to the CMBR decaying later into a gravitino are similar to warm dark matter with v =0.002,0.1,and 1km s −1,re-spectively (see text for details).approximate mass of a typical cluster.In order to erase perturbations on the scale λc the present day DM ve-locity has to exceed v 0rms >∼1km s−1.If this is the case,however,only a fraction between 10−20%of all the DM may be warm/hot [23](cf.also to [21]for similar limits from the Lyman-αforest).In Fig.1WDM limits on gravitino DM produced by metastable particle decay are shown in the param-eter space spanned by the mass splitting between the gravitino and the NLSP ∆m ≡m NLSP −m ˜G and thegravitino mass itself.The respective limits of v 0rms=0.002,0.1,and 1kms −1,as discussed above,are indicated as heavy lines for the cases when either the bino (long-dashed)or the stau or sneutrino (solid)is the NLSP.The order of the lines is such that v 0rms exceeds the limit in the parameter space below the lines,with lines athigher ∆m corresponding to a limit with lower v 0rms .It is seen that most of the parameter space results in WDM,potentially already in conflict with,at least,the high optical depth as inferred by WMAP.In particular,only for excessively large m NLSP >∼5TeV decay produced gravitino dark matter may be considered almost cold.The limit may be less stringent when only a small com-ponent <∼10%of the gravitino DM is due to decay,as then masses m NLSP >∼100GeV ascertain that the decay-produced component is not too hot to delay the formation of clusters of galaxies.We note here,however,that for gravitino masses nottoo small (m ˜G <∼0.1GeV for a bino NLSP and m ˜G <∼10GeV for a stau NLSP [7,8])very stringent constraintson such scenarios apply from a disruption of Big Bang nucleosynthesis (BBN)with smaller mass splittings ∆m preferentially constrained by the effects of electromag-netic energy injection after the epoch of BBN and distor-tion of the CMBR blackbody spectrum and larger ∆m by hadronic three-body decays during and after BBN.In particular,6Li [26]production as well as significant per-turbations of the 3He/D [27]ratio potentially rule out much of the parameter space at larger m ˜G .If such con-straints are combined with the requirement of having thesupersymmetric potential bounded from below,only very little parameter space remains,at least in the constrainedminimal supersymmetric standard model (CMSSM)and for small tri-linear couplings A [28].These limits are notshown in Fig.1.Fig.1shows also analogous results for a KK-B 1decay-ing into a photon and KK-graviton,with constraints indi-cated by the dotted line.It is seen that constraints from the warmness are not quite as stringent as in the gravitino case,yet,for m G 1around the weak scale,m B 1>∼1TeV is still required for a sucessful reionization by star for-mation.Only for much smaller m G 1<∼1GeV may decayof lighter m B 1<∼300GeV result in CDM.However,it is rather expected for the mass difference between the KK-B 1and KK-graviton to be small,since it should be only due to radiative corrections.Almost degenerate B 1and G 1are then constrained by limits from BBN.It has re-cently been pointed out that a generation of dark mat-ter by particle decay may lead to an additional suppres-sion of small-scale power provided the decaying particle is charged [29].Since the charged ’primary’is coupled to the CMBR sub-horizon perturbations in the primary-photon fluid are below the Jeans mass.Perturbations may thus only start growing by the gravitational instabil-ity when decoupled from the CMBR,i.e.after the decay of the primary.In particular,it was found in Ref.[29,30]that for a charged particle decay time of τd =3.5yr the wavevector k d where the power is reduced by half,when compared to a CDM scenario,is approximately k d ≈3Mpc −1(assuming h =0.7).Comparing thisto Eq.(4)one may infer a velocity v 0rms≈0.078km s −1which would yield a similar erasure of small-scale power due to finite DM velocities.An analogy between the net result of these two physically different small-scale power suppression mechanism may be established by not-ing that the damping scale due to charged particle de-cay is approximately the horizon scale at decay [29],λd ∼0.265Mpc(τ/yrs)1/paring this scale toEq.(4)the above limits of v 0rms=0.002,0.1,and 1kms −1translate to decay times τd ∼3×10−3,2,and 125yr,re-spectively.In Fig.1the light lines are lines of constantdecay time for the decay ˜τ→τ+˜Gwith values as given above.Here shorter decay times are at higher ∆m .It is seen that in the scenarios considered here the effects of free-streaming are generally more important than thoseof charged particle decay,though this may be different when other scenarios are considered[30].We now investigate the resulting free-streaming veloci-ties in axino DM generation due to stau-(˜τ→τ+˜a)and bino-(˜B→γ+˜a)decays as proposed by Ref.[1,2,3,4]. Taking the decay widths of the literature[31]wefind present root-mean-square velocities ofv0≈14.7km1MeV−1 m˜τ100GeV−1 f as m˜a100GeV−1 f aFIG.4:As Fig.2,but for a spectral index for the adiabatic primordial perturbations of n s=1.when larger halos,with virial temperatures T vir>∼104K, may collapse as in such halos cooling is possible due to atomic hydrogen.The typical UV-radiation produc-tion for a star cluster at low metallicity and for an ini-tial mass function close to that observed locally is es-timated around Nγ=4000ionising photons per stellar proton.Since normally only a small fraction f⋆∼10% of the gas forms stars and moreover only a small fraction f esc∼10%is capable of leaving the host galaxy,one may estimate around40ionising photons per collapsed and cooled baryon.This implies that the fraction of halos F(T vir>104)with virial temperature larger than104K has to be rather large,>∼1/(Nγf⋆f esc)=2.5×10−2. Note that this conservatively neglects further recombi-nations.A virial temperature of104K corresponds to a mass scale of M104≈3×107M⊙[(1+z)/11]−3/2where z is redshift.We have utilised CMBFAST in order tofind the trans-fer function in models of mixed dark matter with vary-ing warm/hot dark matter fractionsΩx and root-mean-square velocity v x.The transfer function allowed us to compute the collapsed mass fraction F(M)as a function of redshift.Our models assumeΩx+Ωc+Ωb=0.3, whereΩc is the cold dark matter density parameter andΩb is the baryonic density parameter,and we as-sumedΩb=0.04and a Hubble parameter of h=0.65. Most of our calculations assume a red spectral index for scalar adiabatic perturbations n s=0.951correspond-ing to the central value of the by the after three years ofWMAP observations determined n s=0.951+0.015−0.019withintheΛCDM concordance model.This model assumes a negligible contribution of primordial gravitational waves to the CMBR anisotropies.Gravitational waves due to an inflationary epoch mostly contribute to the CMBR anisotropies on large scales.If present,they may therfore also describe the WMAP data well,albeit with a lower normalisation of scalar perturbations on the largest scales and a larger spectral index n s.As the two sigma upper limit on n s from a combination of WMAP observations and large-scale structure surveys(and in the absence of a running spectral index)is close to one,we have also utilised a Harrison-Zeldovich spectrum n s=1for one particular computation.This may be indicative of vari-ations of our results with respect to the assumed cosmo-logical model.All models are normalized on the present horizon scale(taking COBE-DMR results,i.e.Eq.(30) in Ref.[35]),irrespective of if gravitational waves are present or not.Finally,the warm component was sim-ulated by adding a massive“neutrino”to thefluid with a root-mean-square velocity of v x,while keeping also the three massless standard model neutrinos.In Fig.2we show the redshifts at which in a particular mixed model(defined byΩx and v x)a fraction>10−2of all baryons have collapsed within halos exceeding a virial temperature of104K.Assuming an essentially instanta-neous baryon cooling and star formation[36],and given the required F(T vir>104)>2.5×10−2as inferred in a “standard”reionization scenario,this redshift z may be approximately indentified with the epoch of reionization. It is seen that even for warm/hot dark matter fractions as small asΩx∼10−3−10−2reionization with standard efficiencies may be problematic for redshifts larger than z>10.This should be compared to the current estimate of z reion≈8.5−15as inferred by WMAP,indicating the potentially stringent nature of limits one could poten-tially derive on very small warm/hot dark matter frac-tions from reionization.Such limits,if holding up againts future observational tests,could severely constrain the nature of particle dark matter,by requiring it to be es-sentially exclusively cold.However,it needs to be stressed here,that the results as shown in Fig.2(as well as in thefigures which fol-low)are not intended by the authors to be employed to derive limits on mixed dark matter models.This is due to a variety of reasons,such as uncertainties in the reion-ization process and cosmological model(see below),but also due to the fact that we have not marginalized over all cosmological parameters entering the analysis.Fur-thermore,different constraints,not shown in thefigures, may be of importance.For example,models with rela-tively large v X andΩX,corresponding to a significant hot dark matter component,may potentially be ruled out simply by a relative mismatch between the predicted and observed powers on8Mpc h−1and the present hori-zon scale3000Mpc h−1,respectively.This is due to the hot component erasing power on8Mpc h−1due to free-streaming.Intrinsic uncertainties about the reionization process during the dark ages are still large enough to evade dras-tic conclusions.It may be that either the effiency of star forming regions to produce UV-radiation(by a top-heavy initial mass function,for example)or the escape fraction/star formation effiency are substantially larger at early times than at the current epoch.Most of suchevolutionary effects should be testable,by,for example searches for very high redshift galaxies or heavy element abundances in the high redshift gas,by the NGST(next-generation space telescope).In Fig.3we show the red-shifts where a much smaller fraction of10−4of the gas was able to collapse in virial halos with T vir>104K. This corresponds to a factor100increase in“reioniza-tion”efficiency.It is seen that fairly early z∼16reion-sation epochs are possible except whenΩx becomes large>∼10−2and free-streaming velocities are not too smallv x>∼0.1km s−1.It is evident,that even with a factor ∼100higher efficiency reionization than expected,and provided the reionization redshift is found to be larger than z>∼12,limits from reionization on warm/mixed dark matter may be more stringent than those derived from the CMBR-Lyman-αforest.This conclusion is also in accord with the numerical simulations recently per-formed in Ref.[22].Both plots show by the star and the lines also the re-cently derived limit[21]on a small thermal warm/hot gravitino component from a combination of WMAP-CMBR data(probing perturbations on larger scales∼10−3000Mpc)and the Lyman-αforest(probing pertur-bations on smaller scales∼1−40Mpc).The models considered in Ref.[21]are lying on the diagonal dotted line and are ruled out because of a too severe suppression of the power spectrum at small scales,at odds with obser-vations of the Lyman-αforest.Models with the sameΩX but even larger v X than that indicated by the star,mov-ing the power spectrum supression to even larger scales, should also be at odds with the observations.We have therefore added a vertical dotted line,such that the re-gion in the right upper hand corner of the star(bounded by these dotted lines)should be ruled out.Similarly,uncertainties in the prediction of the reion-ization redshift in mixed dark matter models are also due to uncertainties in the cosmological model and/or scalar spectral index n s.In Fig.4we show the reionization redshift in our simple reionization model for the same re-quired collapse fraction and virial halo temperatureas as in Fig.2,but for a model which has a Harrison-Zeldovich n s spectral index.It is seen that the requirement of early reionization is more easily satisfied for n s=1 than for n s=0.951.Nevertheless,the change is not big and amounts only to∆z reion≈2.We have also varied the COBE normalization,moving it approximately two sigma upwards(resulting in a factor1.14larger pertur-bations)and have obtained very similar results to those shown in Fig.4,i.e.approximately∆z reion≈2.We con-clude that the proper reionization of the Universe seems a promising alley in constraining warm and mixed dark matter scenarios.Finally we note that the potentially strong constraints on warm/mixed dark matter possible from a determination of the reionsation redshift have also been noted in the two very recent papers of Refs.[12,13][1]K.Rajagopal,M.S.Turner and F.Wilczek,Nucl.Phys.B358,447(1991).[2]L.Covi,J.E.Kim and L.Roszkowski,Phys.Rev.Lett.82,4180(1999).[3]L.Covi,H.B.Kim,J.E.Kim and L.Roszkowski,JHEP0105,033(2001).[4]L.Covi,L.Roszkowski and M.Small,JHEP0207,023(2002);L.Covi,L.Roszkowski,R.Ruiz de Austri and M.Small,JHEP0406003(2004).[5]J.L.Feng,A.Rajaraman and F.Takayama,Phys.Rev.Lett.91,011302(2003)[6]J.L.Feng,A.Rajaraman and F.Takayama,Phys.Rev.D68,063504(2003)[7]J.L.Feng,S.f.Su and F.Takayama,Phys.Rev.D70,063514(2004)[8]J.L.Feng,S.Su and F.Takayama,Phys.Rev.D70,075019(2004)[9]L.Roszkowski,R.Ruiz de Austri and K.-Y.Choi JHEP0508080(2005)[10]S.Borgani,A.Masiero and M.Yamaguchi,Phys.Lett.B386,189(1996)[11]W.B.Lin,D.H.Huang,X.Zhang and R.H.Branden-berger,Phys.Rev.Lett.86,954(2001)[12]J. A.Cembranos,J.L.Feng, A.Rajaraman,andF.Takayama,hep-ph/0507150[13]M.Kaplinghat,astro-ph/0507300[14]cf.R.Kolb.&M.Turner,in The Early Universe,Addison-Wesley1990.[15]HereΩ˜G is the gravitino contribution to the present crit-ical density and h is the Hubble constant in units of100km s−1Mpc−1.[16]P.Bode,J.P.Ostriker and N.Turok,Astrophys.J.556,93(2001)[17]R.Barkana,Z.Haiman and J.P.Ostriker,arXiv:astro-ph/0102304.[18]C.P.Ma and E.Bertschinger,Astrophys.J.455,7(1995)[19]The linear power spectrum for warm dark matter(WDM)is given by the power spectrum for cold dark mat-ter(CDM)multiplied by a transfer function T WDM=(1+(ǫkR0c)2ν)−η/νwhich accounts for the additional free-streaming in WDM scenarios.In the above,k is wavevector and the valuesη=5,ν=1.2,andǫ=0.361arefrequently used.[20]For decaying sleptons into leptons and gravitinos˜l→l+˜G we employ Eq.(6)of Ref[8],whereas for decayingbinos(KK-U(1)gauge bosons)into photons(Z-bosons)and gravitinos(KK-gravitons)˜B→γ(Z)+˜G(B1→γ(Z)+G1)we employ Eq.(1)(Eq.(2))of Ref.[5].[21]M.Viel,J.Lesgourgues,M.G.Haehnelt,S.Matarreseand A.Riotto,arXiv:astro-ph/0501562.[22]N.Yoshida,A.Sokasian,L.Hernquist and V.Springel,Astrophys.J.591,L1(2003)[23]T.Kahniashvili, E.von Toerne,N.A.Arhipova andB.Ratra,arXiv:astro-ph/0503328.[24]A.Kogut et al.,Astrophys.J.Suppl.148,161(2003).[25]D.N.Spergel et al.,arXiv:astro-ph/0603449.[26]K.Jedamzik,Phys.Rev.Lett.84,3248(2000)K.Jedamzik,Phys.Rev.D70,063524 (2004)M.Kawasaki,K.Kohri and T.Moroi, arXiv:astro-ph/0402490.[27]G.Sigl,K.Jedamzik,D.N.Schramm and V.S.Berezin-sky,Phys.Rev.D52,6682(1995)M.Kawasaki,K.Kohri and T.Moroi,arXiv:astro-ph/0408426.[28]D.Cerdeno et al,in preparation[29]K.Sigurdson and M.Kamionkowski,Phys.Rev.Lett.92,171302(2004)[30]S.Profumo,K.Sigurdson,P.Ullio andM.Kamionkowski,Phys.Rev.D71,023518(2005) [31]For decay of binos into photons and axinos˜B→γ+˜a weuse Eq.(4.3)from Ref.[3]and for decay of right-handedstaus into taus and axinos˜τR→τ+˜a we use Eq.(3)of Ref.[32].[32]A.Brandenburg,L.Covi,K.Hamaguchi,L.Roszkowskiand F.D.Steffen,arXiv:hep-ph/0501287.[33]A.Brandenburg and F.D.Steffen,JCAP0408,008(2004)[34]Z.Haiman,T.Abel,and M.J.Rees,Astrophys.J.534,11(2000)[35]E.F.Bunn and M.White,Astrophys.J.480,6(1997).[36]We have further conservatively neglected a potential de-lay in halo formation due to an increase of the effective dark matter Jeans mass[17].。
Stabilized high-power laser system forthe gravitational wave detector advancedLIGOP.Kwee,1,∗C.Bogan,2K.Danzmann,1,2M.Frede,4H.Kim,1P.King,5J.P¨o ld,1O.Puncken,3R.L.Savage,5F.Seifert,5P.Wessels,3L.Winkelmann,3and B.Willke21Max-Planck-Institut f¨u r Gravitationsphysik(Albert-Einstein-Institut),Hannover,Germany2Leibniz Universit¨a t Hannover,Hannover,Germany3Laser Zentrum Hannover e.V.,Hannover,Germany4neoLASE GmbH,Hannover,Germany5LIGO Laboratory,California Institute of Technology,Pasadena,California,USA*patrick.kwee@aei.mpg.deAbstract:An ultra-stable,high-power cw Nd:Y AG laser system,devel-oped for the ground-based gravitational wave detector Advanced LIGO(Laser Interferometer Gravitational-Wave Observatory),was comprehen-sively ser power,frequency,beam pointing and beamquality were simultaneously stabilized using different active and passiveschemes.The output beam,the performance of the stabilization,and thecross-coupling between different stabilization feedback control loops werecharacterized and found to fulfill most design requirements.The employedstabilization schemes and the achieved performance are of relevance tomany high-precision optical experiments.©2012Optical Society of AmericaOCIS codes:(140.3425)Laser stabilization;(120.3180)Interferometry.References and links1.S.Rowan and J.Hough,“Gravitational wave detection by interferometry(ground and space),”Living Rev.Rel-ativity3,1–3(2000).2.P.R.Saulson,Fundamentals of Interferometric Gravitational Wave Detectors(World Scientific,1994).3.G.M.Harry,“Advanced LIGO:the next generation of gravitational wave detectors,”Class.Quantum Grav.27,084006(2010).4. B.Willke,“Stabilized lasers for advanced gravitational wave detectors,”Laser Photon.Rev.4,780–794(2010).5.P.Kwee,“Laser characterization and stabilization for precision interferometry,”Ph.D.thesis,Universit¨a t Han-nover(2010).6.K.Somiya,Y.Chen,S.Kawamura,and N.Mio,“Frequency noise and intensity noise of next-generationgravitational-wave detectors with RF/DC readout schemes,”Phys.Rev.D73,122005(2006).7. B.Willke,P.King,R.Savage,and P.Fritschel,“Pre-stabilized laser design requirements,”internal technicalreport T050036-v4,LIGO Scientific Collaboration(2009).8.L.Winkelmann,O.Puncken,R.Kluzik,C.Veltkamp,P.Kwee,J.Poeld,C.Bogan,B.Willke,M.Frede,J.Neu-mann,P.Wessels,and D.Kracht,“Injection-locked single-frequency laser with an output power of220W,”Appl.Phys.B102,529–538(2011).9.T.J.Kane and R.L.Byer,“Monolithic,unidirectional single-mode Nd:Y AG ring laser,”Opt.Lett.10,65–67(1985).10.I.Freitag,A.T¨u nnermann,and H.Welling,“Power scaling of diode-pumped monolithic Nd:Y AG lasers to outputpowers of several watts,”mun.115,511–515(1995).11.M.Frede,B.Schulz,R.Wilhelm,P.Kwee,F.Seifert,B.Willke,and D.Kracht,“Fundamental mode,single-frequency laser amplifier for gravitational wave detectors,”Opt.Express15,459–465(2007).#161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 1061712. A.D.Farinas,E.K.Gustafson,and R.L.Byer,“Frequency and intensity noise in an injection-locked,solid-statelaser,”J.Opt.Soc.Am.B12,328–334(1995).13.R.Bork,M.Aronsson,D.Barker,J.Batch,J.Heefner,A.Ivanov,R.McCarthy,V.Sandberg,and K.Thorne,“New control and data acquisition system in the Advanced LIGO project,”Proc.of Industrial Control And Large Experimental Physics Control System(ICALEPSC)conference(2011).14.“Experimental physics and industrial control system,”/epics/.15.P.Kwee and B.Willke,“Automatic laser beam characterization of monolithic Nd:Y AG nonplanar ring lasers,”Appl.Opt.47,6022–6032(2008).16.P.Kwee,F.Seifert,B.Willke,and K.Danzmann,“Laser beam quality and pointing measurement with an opticalresonator,”Rev.Sci.Instrum.78,073103(2007).17. A.R¨u diger,R.Schilling,L.Schnupp,W.Winkler,H.Billing,and K.Maischberger,“A mode selector to suppressfluctuations in laser beam geometry,”Opt.Acta28,641–658(1981).18. B.Willke,N.Uehara,E.K.Gustafson,R.L.Byer,P.J.King,S.U.Seel,and R.L.Savage,“Spatial and temporalfiltering of a10-W Nd:Y AG laser with a Fabry-Perot ring-cavity premode cleaner,”Opt.Lett.23,1704–1706 (1998).19.J.H.P¨o ld,“Stabilization of the Advanced LIGO200W laser,”Diploma thesis,Leibniz Universit¨a t Hannover(2009).20. E.D.Black,“An introduction to Pound-Drever-Hall laser frequency stabilization,”Am.J.Phys.69,79–87(2001).21.R.W.P.Drever,J.L.Hall,F.V.Kowalski,J.Hough,G.M.Ford,A.J.Munley,and H.Ward,“Laser phase andfrequency stabilization using an optical resonator,”Appl.Phys.B31,97–105(1983).22. A.Bullington,ntz,M.Fejer,and R.Byer,“Modal frequency degeneracy in thermally loaded optical res-onators,”Appl.Opt.47,2840–2851(2008).23.G.Mueller,“Beam jitter coupling in Advanced LIGO,”Opt.Express13,7118–7132(2005).24.V.Delaubert,N.Treps,ssen,C.C.Harb,C.Fabre,m,and H.-A.Bachor,“TEM10homodynedetection as an optimal small-displacement and tilt-measurement scheme,”Phys.Rev.A74,053823(2006). 25.P.Kwee,B.Willke,and K.Danzmann,“Laser power noise detection at the quantum-noise limit of32A pho-tocurrent,”Opt.Lett.36,3563–3565(2011).26. A.Araya,N.Mio,K.Tsubono,K.Suehiro,S.Telada,M.Ohashi,and M.Fujimoto,“Optical mode cleaner withsuspended mirrors,”Appl.Opt.36,1446–1453(1997).27.P.Kwee,B.Willke,and K.Danzmann,“Shot-noise-limited laser power stabilization with a high-power photodi-ode array,”Opt.Lett.34,2912–2914(2009).28. ntz,P.Fritschel,H.Rong,E.Daw,and G.Gonz´a lez,“Quantum-limited optical phase detection at the10−10rad level,”J.Opt.Soc.Am.A19,91–100(2002).1.IntroductionInterferometric gravitational wave detectors[1,2]perform one of the most precise differential length measurements ever.Their goal is to directly detect the faint signals of gravitational waves emitted by astrophysical sources.The Advanced LIGO(Laser Interferometer Gravitational-Wave Observatory)[3]project is currently installing three second-generation,ground-based detectors at two observatory sites in the USA.The4kilometer-long baseline Michelson inter-ferometers have an anticipated tenfold better sensitivity than theirfirst-generation counterparts (Inital LIGO)and will presumably reach a strain sensitivity between10−24and10−23Hz−1/2.One key technology necessary to reach this extreme sensitivity are ultra-stable high-power laser systems[4,5].A high laser output power is required to reach a high signal-to-quantum-noise ratio,since the effect of quantum noise at high frequencies in the gravitational wave readout is reduced with increasing circulating laser power in the interferometer.In addition to quantum noise,technical laser noise coupling to the gravitational wave channel is a major noise source[6].Thus it is important to reduce the coupling of laser noise,e.g.by optical design or by exploiting symmetries,and to reduce laser noise itself by various active and passive stabilization schemes.In this article,we report on the pre-stabilized laser(PSL)of the Advanced LIGO detector. The PSL is based on a high-power solid-state laser that is comprehensively stabilized.One laser system was set up at the Albert-Einstein-Institute(AEI)in Hannover,Germany,the so called PSL reference system.Another identical PSL has already been installed at one Advanced LIGO site,the one near Livingston,LA,USA,and two more PSLs will be installed at the second #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10618site at Hanford,WA,USA.We have characterized the reference PSL and thefirst observatory PSL.For this we measured various beam parameters and noise levels of the output beam in the gravitational wave detection frequency band from about10Hz to10kHz,measured the performance of the active and passive stabilization schemes,and determined upper bounds for the cross coupling between different control loops.At the time of writing the PSL reference system has been operated continuously for more than18months,and continues to operate reliably.The reference system delivered a continuous-wave,single-frequency laser beam at1064nm wavelength with a maximum power of150W with99.5%in the TEM00mode.The active and passive stabilization schemes efficiently re-duced the technical laser noise by several orders of magnitude such that most design require-ments[5,7]were fulfilled.In the gravitational wave detection frequency band the relative power noise was as low as2×10−8Hz−1/2,relative beam pointingfluctuations were as low as1×10−7Hz−1/2,and an in-loop measurement of the frequency noise was consistent with the maximum acceptable frequency noise of about0.1HzHz−1/2.The cross couplings between the control loops were,in general,rather small or at the expected levels.Thus we were able to optimize each loop individually and observed no instabilities due to cross couplings.This stabilized laser system is an indispensable part of Advanced LIGO and fulfilled nearly all design goals concerning the maximum acceptable noise levels of the different beam pa-rameters right after installation.Furthermore all or a subset of the implemented stabilization schemes might be of interest for many other high-precision optical experiments that are limited by laser noise.Besides gravitational wave detectors,stabilized laser systems are used e.g.in the field of optical frequency standards,macroscopic quantum objects,precision spectroscopy and optical traps.In the following section the laser system,the stabilization scheme and the characterization methods are described(Section2).Then,the results of the characterization(Section3)and the conclusions(Section4)are presented.ser system and stabilizationThe PSL consists of the laser,developed and fabricated by Laser Zentrum Hannover e.V.(LZH) and neoLASE,and the stabilization,developed and integrated by AEI.The optical components of the PSL are on a commercial optical table,occupying a space of about1.5×3.5m2,in a clean,dust-free environment.At the observatory sites the optical table is located in an acoustically isolated cleanroom.Most of the required electronics,the laser diodes for pumping the laser,and water chillers for cooling components on the optical table are placed outside of this cleanroom.The laser itself consists of three stages(Fig.1).An almostfinal version of the laser,the so-called engineering prototype,is described in detail in[8].The primary focus of this article is the stabilization and characterization of the PSL.Thus only a rough overview of the laser and the minor modifications implemented between engineering prototype and reference system are given in the following.Thefirst stage,the master laser,is a commercial non-planar ring-oscillator[9,10](NPRO) manufactured by InnoLight GmbH in Hannover,Germany.This solid-state laser uses a Nd:Y AG crystal as the laser medium and resonator at the same time.The NPRO is pumped by laser diodes at808nm and delivers an output power of2W.An internal power stabilization,called the noise eater,suppresses the relaxation oscillation at around1MHz.Due to its monolithic res-onator,the laser has exceptional intrinsic frequency stability.The two subsequent laser stages, used for power scaling,inherit the frequency stability of the master laser.The second stage(medium-power amplifier)is a single-pass amplifier[11]with an output power of35W.The seed laser beam from the NPRO stage passes through four Nd:YVO4crys-#161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10619power stabilizationFig.1.Pre-stabilized laser system of Advanced LIGO.The three-staged laser(NPRO,medium power amplifier,high power oscillator)and the stabilization scheme(pre-mode-cleaner,power and frequency stabilization)are shown.The input-mode-cleaner is not partof the PSL but closely related.NPRO,non-planar ring oscillator;EOM,electro-optic mod-ulator;FI,Faraday isolator;AOM,acousto-optic modulator.tals which are longitudinally pumped byfiber-coupled laser diodes at808nm.The third stage is an injection-locked ring oscillator[8]with an output power of about220W, called the high-power oscillator(HPO).Four Nd:Y AG crystals are used as the active media. Each is longitudinally pumped by sevenfiber-coupled laser diodes at808nm.The oscillator is injection-locked[12]to the previous laser stage using a feedback control loop.A broadband EOM(electro-optic modulator)placed between the NPRO and the medium-power amplifier is used to generate the required phase modulation sidebands at35.5MHz.Thus the high output power and good beam quality of this last stage is combined with the good frequency stability of the previous stages.The reference system features some minor modifications compared to the engineering proto-type[8]concerning the optics:The external halo aperture was integrated into the laser system permanently improving the beam quality.Additionally,a few minor designflaws related to the mechanical structure and the optical layout were engineered out.This did not degrade the output performance,nor the characteristics of the locked laser.In general the PSL is designed to be operated in two different power modes.In high-power mode all three laser stages are engaged with a power of about160W at the PSL output.In low-power mode the high-power oscillator is turned off and a shutter inside the laser resonator is closed.The beam of the medium-power stage is reflected at the output coupler of the high power stage leaving a residual power of about13W at the PSL output.This low-power mode will be used in the early commissioning phase and in the low-frequency-optimized operation mode of Advanced LIGO and is not discussed further in this article.The stabilization has three sections(Fig.1:PMC,PD2,reference cavity):A passive resonator, the so called pre-mode-cleaner(PMC),is used tofilter the laser beam spatially and temporally (see subsection2.1).Two pick-off beams at the PMC are used for the active power stabilization (see subsection2.2)and the active frequency pre-stabilization,respectively(see subsection2.3).In general most stabilization feedback control loops of the PSL are implemented using analog electronics.A real-time computer system(Control and Data Acquisition Systems,CDS,[13]) which is common to many other subsystems of Advanced LIGO,is utilized to control and mon-itor important parameters of the analog electronics.The lock acquisition of various loops,a few #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10620slow digital control loops,and the data acquisition are implemented using this computer sys-tem.Many signals are recorded at different sampling rates ranging from16Hz to33kHz for diagnostics,monitoring and vetoing of gravitational wave signals.In total four real-time pro-cesses are used to control different aspects of the laser system.The Experimental Physics and Industrial Control System(EPICS)[14]and its associated user tools are used to communicate with the real-time software modules.The PSL contains a permanent,dedicated diagnostic instrument,the so called diagnostic breadboard(DBB,not shown in Fig.1)[15].This instrument is used to analyze two different beams,pick-off beams of the medium power stage and of the HPO.Two shutters are used to multiplex these to the DBB.We are able to measurefluctuations in power,frequency and beam pointing in an automated way with this instrument.In addition the beam quality quantified by the higher order mode content of the beam was measured using a modescan technique[16].The DBB is controlled by one real-time process of the CDS.In contrast to most of the other control loops in the PSL,all DBB control loops were implemented digitally.We used this instrument during the characterization of the laser system to measure the mentioned laser beam parameters of the HPO.In addition we temporarily placed an identical copy of the DBB downstream of the PMC to characterize the output beam of the PSL reference system.2.1.Pre-mode-cleanerA key component of the stabilization scheme is the passive ring resonator,called the pre-mode-cleaner(PMC)[17,18].It functions to suppress higher-order transverse modes,to improve the beam quality and the pointing stability of the laser beam,and tofilter powerfluctuations at radio frequencies.The beam transmitted through this resonator is the output beam of the PSL, and it is delivered to the subsequent subsystems of the gravitational wave detector.We developed and used a computer program[19]to model thefilter effects of the PMC as a function of various resonator parameters in order to aid its design.This led to a resonator with a bow-tie configuration consisting of four low-loss mirrors glued to an aluminum spacer. The optical round-trip length is2m with a free spectral range(FSR)of150MHz.The inci-dence angle of the horizontally polarized laser beam is6◦.Theflat input and output coupling mirrors have a power transmission of2.4%and the two concave high reflectivity mirrors(3m radius of curvature)have a transmission of68ppm.The measured bandwidth was,as expected, 560kHz which corresponds to afinesse of133and a power build-up factor of42.The Gaussian input/output beam had a waist radius of about568µm and the measured acquired round-trip Gouy phase was about1.7rad which is equivalent to0.27FSR.One TEM00resonance frequency of the PMC is stabilized to the laser frequency.The Pound-Drever-Hall(PDH)[20,21]sensing scheme is used to generate error signals,reusing the phase modulation sidebands at35.5MHz created between NPRO and medium power amplifier for the injection locking.The signal of the photodetector PD1,placed in reflection of the PMC, is demodulated at35.5MHz.This photodetector consists of a1mm InGaAs photodiode and a transimpedance amplifier.A piezo-electric element(PZT)between one of the curved mirrors and the spacer is used as a fast actuator to control the round-trip length and thereby the reso-nance frequencies of the PMC.With a maximum voltage of382V we were able to change the round-trip length by about2.4µm.An analog feedback control loop with a bandwidth of about 7kHz is used to stabilize the PMC resonance frequency to the laser frequency.In addition,the electronics is able to automatically bring the PMC into resonance with the laser(lock acquisition).For this process a125ms period ramp signal with an amplitude cor-responding to about one FSR is applied to the PZT of the PMC.The average power on pho-todetector PD1is monitored and as soon as the power drops below a given threshold the logic considers the PMC as resonant and closes the analog control loop.This lock acquisition proce-#161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10621dure took an average of about65ms and is automatically repeated as soon as the PMC goes off resonance.One real-time process of CDS is dedicated to control the PMC electronics.This includes parameters such as the proportional gain of the loop or lock acquisition parameters.In addition to the PZT actuator,two heating foils,delivering a maximum total heating power of14W,are attached to the aluminum spacer to control its temperature and thereby the roundtrip length on timescales longer than3s.We measured a heating and cooling1/e time constant of about2h with a range of4.5K which corresponds to about197FSR.During maintenance periods we heat the spacer with7W to reach a spacer temperature of about2.3K above room temperature in order to optimize the dynamic range of this actuator.A digital control loop uses this heater as an actuator to off-load the PZT actuator allowing compensation for slow room temperature and laser frequency drifts.The PMC is placed inside a pressure-tight tank at atmospheric pressure for acoustic shield-ing,to avoid contamination of the resonator mirrors and to minimize optical path length changes induced by atmospheric pressure variations.We used only low-outgassing materials and fabri-cated the PMC in a cleanroom in order to keep the initial mirror contamination to a minimum and to sustain a high long-term throughput.The PMCfilters the laser beam and improves the beam quality of the laser by suppress-ing higher order transverse modes[17].The acquired round-trip Gouy phase of the PMC was chosen in such a way that the resonance frequencies of higher order TEM modes are clearly separated from the TEM00resonance frequency.Thus these modes are not resonant and are mainly reflected by the PMC,whereas the TEM00mode is transmitted.However,during the design phase we underestimated the thermal effects in the PMC such that at nominal circu-lating power the round-trip Gouy-phase is close to0.25FSR and the resonance of the TEM40 mode is close to that of the TEM00mode.To characterize the mode-cleaning performance we measured the beam quality upstream and downstream of the PMC with the two independent DBBs.At150W in the transmitted beam,the circulating power in the PMC is about6.4kW and the intensity at the mirror surface can be as high as1.8×1010W m−2.At these power levels even small absorptions in the mirror coatings cause thermal effects which slightly change the mirror curvature[22].To estimate these thermal effects we analyzed the transmitted beam as a function of the circulating power using the DBB.In particular we measured the mode content of the LG10and TEM40mode.Changes of the PMC eigenmode waist size showed up as variations of the LG10mode content.A power dependence of the round-trip Gouy phase caused a variation of the power within the TEM40mode since its resonance frequency is close to a TEM00mode resonance and thus the suppression of this mode depends strongly on the Gouy phase.We adjusted the input power to the PMC such that the transmitted power ranged from100W to 150W corresponding to a circulating power between4.2kW and6.4kW.We used our PMC computer simulation to deduce the power dependence of the eigenmode waist size and the round-trip Gouy phase.The results are given in section3.1.At all circulating power levels,however,the TEM10and TEM01modes are strongly sup-pressed by the PMC and thus beam pointingfluctuations are reduced.Pointingfluctuations can be expressed tofirst order as powerfluctuations of the TEM10and TEM01modes[23,24].The PMC reduces thefield amplitude of these modes and thus the pointingfluctuations by a factor of about61according to the measuredfinesse and round-trip Gouy phase.To keep beam point-ingfluctuations small is important since they couple to the gravitational wave channel by small differential misalignments of the interferometer optics.Thus stringent design requirements,at the10−6Hz−1/2level for relative pointing,were set.To verify the pointing suppression effect of the PMC we used DBBs to measure the beam pointingfluctuations upstream and downstream #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10622Fig.2.Detailed schematic of the power noise sensor setup for thefirst power stabilizationloop.This setup corresponds to PD2in the overview in Fig.1.λ/2,waveplate;PBS,polar-izing beam splitter;BD,glassfilters used as beam dump;PD,single element photodetector;QPD,quadrant photodetector.of the PMC.The resonator design has an even number of nearly normal-incidence reflections.Thus the resonance frequencies of horizontal and vertical polarized light are almost identical and the PMC does not act as polarizer.Therefore we use a thin-film polarizer upstream of the PMC to reach the required purity of larger than100:1in horizontal polarization.Finally the PMC reduces technical powerfluctuations at radio frequencies(RF).A good power stability between9MHz and100MHz is necessary as the phase modulated light in-jected into the interferometer is used to sense several degrees of freedom of the interferometer that need to be controlled.Power noise around these phase modulation sidebands would be a noise source for the respective stabilization loop.The PMC has a bandwidth(HWHM)of about 560kHz and acts tofirst order as a low-passfilter for powerfluctuations with a-3dB corner frequency at this frequency.To verify that the suppression of RF powerfluctuations is suffi-cient to fulfill the design requirements,we measured the relative power noise up to100MHz downstream of the PMC with a dedicated experiment involving the optical ac coupling tech-nique[25].In addition the PMC serves the very important purpose of defining the spatial laser mode for the downstream subsystem,namely the input optics(IO)subsystem.The IO subsystem is responsible,among other things,to further stabilize the laser beam with the suspended input mode cleaner[26]before the beam will be injected into the interferometer.Modifications of beam alignment or beam size of the laser system,which were and might be unavoidable,e.g., due to maintenance,do not propagate downstream of the PMC tofirst order due to its mode-cleaning effect.Furthermore we benefit from a similar isolating effect for the active power and frequency stabilization by using the beams transmitted through the curved high-reflectivity mirrors of the PMC.2.2.Power stabilizationThe passivefiltering effect of the PMC reduces powerfluctuations significantly only above the PMC bandwidth.In the detection band from about10Hz to10kHz good power stability is required sincefluctuations couple via the radiation pressure imbalance and the dark-fringe offset to the gravitational wave channel.Thus two cascaded active control loops,thefirst and second power stabilization loop,are used to reduce powerfluctuations which are mainly caused by the HPO stage.Thefirst loop uses a low-noise photodetector(PD2,see Figs.1and2)at one pick-off port #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10623of the PMC to measure the powerfluctuations downstream of the PMC.An analog electronics feedback control loop and an AOM(acousto-optic modulator)as actuator,located upstream of the PMC,are used to stabilize the power.Scattered light turned out to be a critical noise source for thisfirst loop.Thus we placed all required optical and opto-electronic components into a box to shield from scattered light(see Fig.2).The beam transmitted by the curved PMC mirror has a power of about360mW.This beam isfirst attenuated in the box using aλ/2waveplate and a thin-film polarizer,such that we are able to adjust the power on the photodetectors to the optimal operation point.Afterwards the beam is split by a50:50beam splitter.The beams are directed to two identical photode-tectors,one for the control loop(PD2a,in-loop detector)and one for independent out-of-loop measurements to verify the achieved power stability(PD2b,out-of-loop detector).These pho-todetectors consist of a2mm InGaAs photodiode(PerkinElmer C30642GH),a transimpedance amplifier and an integrated signal-conditioningfilter.At the chosen operation point a power of about4mW illuminates each photodetector generating a photocurrent of about3mA.Thus the shot noise is at a relative power noise of10−8Hz−1/2.The signal conditioningfilter has a gain of0.2at very low frequencies(<70mHz)and amplifies the photodetector signal in the im-portant frequency range between3.3Hz and120Hz by about52dB.This signal conditioning filter reduces the electronics noise requirements on all subsequent stages,but has the drawback that the range between3.3Hz and120Hz is limited to maximum peak-to-peak relative power fluctuations of5×10−3.Thus the signal-conditioned channel is in its designed operation range only when the power stabilization loop is closed and therefore it is not possible to measure the free running power noise using this channel due to saturation.The uncoated glass windows of the photodiodes were removed and the laser beam hits the photodiodes at an incidence angle of45◦.The residual reflection from the photodiode surface is dumped into a glassfilter(Schott BG39)at the Brewster angle.Beam positionfluctuations in combination with spatial inhomogeneities in the photodiode responsivity is another noise source for the power stabilization.We placed a silicon quadrant photodetector(QPD)in the box to measure the beam positionfluctuations of a low-power beam picked off the main beam in the box.The beam parameters,in particular the Gouy phase,at the QPD are the same as on the power sensing detectors.Thus the beam positionfluctuations measured with the QPD are the same as the ones on the power sensing photodetectors,assuming that the positionfluctuations are caused upstream of the QPD pick-off point.We used the QPD to measure beam positionfluctuations only for diagnostic and noise projection purposes.In a slightly modified experiment,we replaced one turning mirror in the path to the power sta-bilization box by a mirror attached to a tip/tilt PZT element.We measured the typical coupling between beam positionfluctuations generated by the PZT and the residual relative photocurrent fluctuations measured with the out-of-the-loop photodetector.This coupling was between1m−1 and10m−1which is a typical value observed in different power stabilization experiments as well.We measured this coupling factor to be able to calculate the noise contribution in the out-of-the-loop photodetector signal due to beam positionfluctuations(see Subsection3.3).Since this tip/tilt actuator was only temporarily in the setup,we are not able to measure the coupling on a regular basis.Both power sensing photodetectors are connected to analog feedback control electronics.A low-pass(100mHz corner frequency)filtered reference value is subtracted from one signal which is subsequently passed through several control loopfilter stages.With power stabilization activated,we are able to control the power on the photodetectors and thereby the PSL output power via the reference level on time scales longer than10s.The reference level and other important parameters of these electronics are controlled by one dedicated real-time process of the CDS.The actuation or control signal of the electronics is passed to an AOM driver #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10624。
2022年新高考模拟卷语文5（原卷版）解析如果说高考是一场战役，那么头脑就是抢，学识就是子弹，铃声就是信号，考卷就是目标，答题就是拼杀，成绩就是胜利。
高考之战在即，让我们扛起抢，子弹上膛，聆听信号，冲向目标，英勇拼杀，多取最后的胜利！下面是高考店铺为大家编辑整理的“2022年高考语文模拟卷（新高考专用）（解析版）”此文本仅供参考，欢迎阅读。
一、非连续性文本阅读阅读下面的文字，完成各题材料一：“中国天眼”身在法地，但在科学家眼中，它心系深空，是一座“天空实验室”。
到现在为止，应该没有天文学家上过太空，但他们却是最了解宇宙的一群人，靠的是什么？不少人小时候索试过用曝光的胶片观看日食，还有动手能力更强的，用两个放大镜自制过光学望远镜。
望远镜就是天文学家了解宇宙的必备工具。
但射电望远镜不同于人们熟悉的光学望远镜、它不能直接成像，而是抓取目标的无线电信号，用数据说话。
天文学家利用“天眼”开展工作，有点类似移动靶射击运动，需要不断地选取目标、瞄准目标射击、分析结果。
据北京大学教授、中科院国家天文台研究员李柯伽介绍，第一步要考虑望远镜频率是否合适、灵敏度是否足够、目标是不是在可视范围内，以便确定观测源的坐标，形成观测列表。
第二步是望远镜控制部门执行观测。
如何精确控制“天眼”瞄准动辄光年之外的目标？简单地说，一是通过天体坐标计算出望远镜所需的“姿态”，二是驱动电机控制望远镜的“姿态”。
因为地球在不停自转和公转，这样的观测比移动靶射击复杂得多，要不断地修正望远镜的位置，不断地瞄准目标，并确保一直命中靶心。
第三步是通过编程来分析数据。
外表安静的“天眼”，内心澎湃，每秒最高传输数据38G。
海量的数据，基本没有手动分析的可能，所以天文学家都是“程序员”，用大数据手段实现天地“连线”。
前辈科学家发现的物理定律，我们在物理实验室里做实验，结果都能验证定律为真。
在“天空实验室”里呢？那可不一定。
天文学跟物理学密不可分，大尺度时空结构、宇宙演化、高能天体（如黑洞、脉冲星等）都是以广义相对论为重要理论基础的。
奇异粒子揭秘中微子的神秘面纱中微子，作为一种神秘的粒子，一直以来都让科学家们感到困惑。
它们的弱相互作用使得我们难以观测和研究，然而，通过对奇异粒子的揭秘，我们有望解开中微子的神秘面纱。
奇异粒子的特征奇异粒子是一类具有奇异夸克的粒子。
它们是由奇异夸克和反奇异夸克组成的，例如K子强子、Ω子强子等。
由于奇异夸克的存在，奇异粒子在衰变过程中会经历奇异改变，从而使得它们的衰变速率与其他粒子相比产生巨大的差异。
奇异粒子的衰变路径还可以通过K介子的弱相互作用进行研究。
实验证实，K介子在空气中的寿命只有数十亿分之一秒，而在低温低湿度的环境下，其寿命却可以达到几微秒。
这是因为低温低湿度条件下，空气中的水分分子无法与K介子发生反应，延长了其寿命。
奇异粒子与中微子的关系中微子是一类无电荷、几乎没有质量的基本粒子。
由于其极弱的相互作用，中微子可以穿过地球和各种物质而不受影响，因此很难被观测到。
奇异粒子与中微子之间存在着紧密的关系。
由于奇异粒子的衰变路径与中微子的生成密切相关，通过研究奇异粒子的衰变过程，我们可以间接地了解中微子的性质和行为。
奇异粒子的实验研究为了进一步研究奇异粒子和中微子的关系，科学家们进行了一系列精密的实验。
其中一项重要实验是在加速器中产生奇异粒子，并通过粒子探测器观测其衰变过程。
这些实验不仅提供了关于奇异粒子的重要信息，还揭示了中微子的一些性质。
例如，通过观测中微子的飞行距离和能量分布，科学家可以推断中微子的质量和振荡行为。
奇异粒子的研究进展随着技术的不断发展，对奇异粒子和中微子的研究取得了一系列重要进展。
在日本，超级神岗实验中心的超级K-Belle和BelleII实验是目前最具挑战性的实验之一。
通过这些实验，科学家们希望进一步研究奇异粒子的衰变规律和中微子的性质，从而进一步揭开宇宙的奥秘。
国际上还有许多其他实验项目，如超级LHC加速器和DUNE实验，致力于研究奇异粒子和中微子的各个方面。
这些实验的进行将为我们提供更多关于宇宙本质的重要信息。
