a r X i v :q u a n t -p h /0508075v 2 21 M a r 2007
Mechanical e?ects of optical resonators on driven trapped atoms:
Ground state cooling in a high ?nesse cavity
Stefano Zippilli 1and Giovanna Morigi 2
1
Abteilung f¨u r Quantenphysik,Universit¨a t Ulm,D-89069Ulm,Germany
2
Grup d’Optica,Departament de Fisica,Universitat Aut`o noma de Barcelona,08193Bellaterra,Spain
(Dated:February 1,2008)We investigate theoretically the mechanical e?ects of light on atoms trapped by an external potential,whose dipole transition couples to the mode of an optical resonator and is driven by a laser.We derive an analytical expression for the quantum center-of-mass dynamics,which is valid in presence of a tight external potential.This equation has broad validity and allows for a transparent interpretation of the individual scattering processes leading to cooling.We show that the dynamics are a competition of the mechanical e?ects of the cavity and of the laser photons,which may mutually interfere.We focus onto the good-cavity limit and identify novel cooling schemes,which are based on quantum interference e?ects and lead to e?cient ground state cooling in experimentally accessible parameter regimes.
I.
INTRODUCTION
Atom cooling by photon scattering is achieved by en-hancing the rate of scattering processes that dissipate motional energy,thereby exploiting the conservation of internal and mechanical energy in the interaction be-tween atoms and electromagnetic ?eld [1].The atomic scattering cross section can be signi?cantly modi?ed by the coupling to an optical resonator,which acts both on the internal as well as on the external degrees of freedom.Hence,the scattering properties can be tailored,allowing to achieve e?cient cooling also for atoms and molecules which may not o?er a convenient con?guration in free space [2,3].This principle is at the basis of cooling by means of an optical resonator.Indeed,the mechanical e?ects on atoms coupled to an optical resonator are ob-ject of several experimental [4,5,6,7,8,9,10,11,12]and theoretical [3,13,14,15,16,17,18,19,20,21,22]investigations,which aim at developing a systematic un-derstanding of these complex dynamics both for its fun-damental aspects,as well as for the perspective of a high degree of control of complex systems with scalable num-ber of degrees of freedom.
In this work we investigate the cooling dynamics of atoms inside optical resonators,when their center-of-mass motion is tightly con?ned by an external po-tential,like for instance a dipole [7,23]or an ion trap [11,24,25,26].We consider the situation where an atomic optical dipole transition is driven by a laser and by a cavity resonator,as sketched in Fig.1,and dis-cuss in detail the results presented in [27].In particular,we show the detailled derivation of the rate equation dis-cussed in [27].This equation has broad validity,which is supported by numerical checks,and allows for a transpar-ent interpretation of the individual scattering processes leading to cooling.Moreover,in the corresponding pa-rameter regimes it reproduces the results reported in [13]and [15].
In this manuscript we mostly focus onto the good-cavity limit.In this regime we discuss when e?cient
cooling into the potential ground state can be achieved.In particular,we show that in experimentally accessible parameter regimes one may obtain almost unit ground state occupation,even when the natural linewidth of the dipole transition would not allow for ground state cooling in free space.E?cient ground-state cooling is often found by exploiting interference e?ects,arising from phase cor-relation between the laser and the ?eld scattered by the atom into the resonator.Most of these interference ef-fects are due to the discrete nature of the spectrum of the center-of-mass motion,which is trapped by a harmonic potential.Hence,the dynamics here studied di?er sub-stantially from the ones of cooling of free atoms inside cavities [3,14,17,18,19].Such interference e?ects are at the basis of novel cooling schemes,some of which have been identi?ed in [27],and which are discussed in detail in the present work.
FIG.1:An atom is con?ned by an harmonic potential of frequency νinside an optical resonator.A mode of the res-onator couples with strength ?g to the dipole,which is driven transversally by a laser at Rabi frequency ?.The system dis-sipates by spontaneous emission of the atomic excited state at rate γand by cavity decay at rate κ.The other parameters are discussed in Sec.III.
This article is organized as follows.In Sec.II some pre-
2
liminary considerations are made.In Sec.
III the model
is introduced,and the basic equations for the motion are obtained.In Sec.IV we discuss the dynamics of cooling from the rate equation we obtain and review previous re-sults presented in the literature.In Sec.V novel cooling schemes are presented,whose dynamics are due to quan-tum correlations which are established in the good cavity limit.In Sec.VI the results are reported:The cooling ef-?ciencies in the various parameter regimes are discussed and compared.In Sec.VII the conclusions are drawn. The appendices report detailed calculations at the basis of the equations derived in Secs.III,IV and V.
II.MECHANICAL EFFECTS OF CA VITY AND LASER ON THE ATOMIC MOTION
FIG.2:Sketch of the internal levels|g and|e of the atomic dipole transition,driven by a laser and a cavity mode with coupling strengths?g and?,respectively.The arrows show the cavity and laser frequency with respect to the dipole fre-quency.Here,?andδc are the detunings of atom and cavity, respectively,from the laser frequency,?c is the detuning of the atomic transition from the cavity frequency.The fre-quency of the atomic transition(ω0),of the cavity mode(ωc) and of the laser?eld(ωL)are indicated in the vertical scale. In this section we make some physical considerations, in order to provide insight into the results presented in the rest of the manuscript.The scattering cross section of the bare atom is usually very informative about the cooling process[28].When the atomic transition is driven in saturation,this analysis is more conveniently done in the dressed state picture[19,29,30].At this purpose, we?rst assume that the atom is?xed at the position x,such that the coupling constant to the cavity mode is?g=g(x).The dipole level scheme and the relevant parameters are shown in Fig.2.We denote by|g,n c and|e,n c the states of the system,where|g ,|e are the ground and excited state of the atomic dipole and|n c the number of photons of the cavity mode.In the situation in which the atom is strongly coupled to the cavity mode and weakly pumped by the laser,the states which are relevantly involved into the dynamics are|g,0c and the dressed states
|+ =sin?|g,1c +cos?|e,0c (1)
|? =cos?|g,1c ?sin?|e,0c (2) with
tan?=?g/(??c/2+
?g2+?2c/4(3) and the respective linewidths areγ+～κsin2?+γcos2?,γ?～κcos2?+γsin2?,whereγis the linewidth of the dipole transition andκthe cavity decay rate.The weak laser probe couples the dressed states|g,0c and|e,0c . Signatures of the dressed states are for instance the resonances in the rate of photon scattering as obtained by scanning the probe laser through atomic resonance. This situation is depicted in Fig.3.Here,the curve has been evaluated for a good resonator,namelyκ?γ,?g and ?c=0.For these parameters the linewidth of one of the two resonances is narrower than the natural linewidth of the dipole.Moreover,when the probe laser is resonant with the cavity mode,the spectrum exhibits a minimum, which reaches zero forκ=0,namely no photons are scattered.This behaviour is due to an interference e?ect between laser and cavity resonator,such that there is no radiation scattered by the atom,as it is at a point where the two?elds,laser and cavity,mutually cancel[31,32, 33].
0 Ν 0 Ν
0.08
0.04
0 0 Ν 0 Ν
2
1
I
n
t
e
n
s
i
t
y
(
a
r
b
.
u
n
i
t
s
)
(b)
(a)
?
?
FIG.3:Excitation spectrum as a function of the laser detun-ing?in the reference frame of the atom.Here,?g=0.5γ,κ=0.01γ.In(a)?c=?10γand(b)?c=1.2γ.The vertical bars indicate the frequency?0of the carrier(central line)and of the red and blue sideband transitions,?0+νand ?0?ν,respectively,when the laser is set at?=?0and the trap frequencyν=0.2γ.In(a)?0～?c?ν;In(b)?0=?c, namely cavity mode and laser are resonant.See text.
We now consider the center-of-mass motion of an atom in a harmonic oscillator,and?rst assume that the me-chanical e?ects are only due to the laser,while the cavity wave vector is orthogonal to the motional axis.In this regime,the motion gives rise to a modulation of the laser
3
frequency at the trap frequencyν.In the regime of strong con?nement(Lamb-Dicke regime)this gives rise to two sidebands of the carrier,i.e.the laser frequency.The car-rier and sideband positions are indicated by the vertical bars in Fig.3in the reference frame of the atom.The cen-tral bar is the carrier.The bar at the right(left)of the carrier corresponds to a transition which lowers(rises) the atomic vibrational excitation by one phonon,namely the so-called red(blue)sideband transition.These two components are out of phase with respect to the carrier. In the limit in which the atomic motion weakly perturbs the internal and cavity dynamics,the scattering along the sidebands is proportional to the corresponding value of the excitation spectrum.Cooling is thus obtained by realizing a large gradient between scattering rates along the sidebands.Figures3(a)and(b)show two possible scenarios,which are discussed in this paper.Case(a) corresponds to use the narrow resonance for implement-ing sideband cooling with the dressed states[15].This scenario is obtained by choosing a large value of|?c|and setting the detuning between the cavity and the laser equal to the trap frequency,such that the red sideband absorption falls at the center of the narrow resonance. This case has been studied in[15].In case(b)a large gradient is achieved by exploiting the interference pro?le arising when laser and cavity are resonant.
The dressed state picture,as obtained by neglecting the motion of the atom,can be also applied to get some insight into the cooling dynamics when cooling is due only to the resonator forces or to both laser and res-onator.Nevertheless,it does not explain other cooling dynamics,which we discuss in this article,and which are due to correlations in the gradients of the?elds over the atomic wave packet.At this purpose one has to consider also the quantum motion.
Figure4summarizes the basic scattering processes de-termining the cooling dynamics in the basis|g,0c;n , |±;n ,where n is the number of excitations of the center-of-mass harmonic oscillator.The process shown in Fig.4(a)describes absorption of a laser photon and spontaneous emission,whereby the change in the center-of-mass state is due to the recoil induced by the sponta-neously emitted photon.The scattering rate is scaled by the geometric factorαand is found after averaging over the solid angle of photon emission into free space.This contribution is di?usive,as the motion can be scattered into a higher or lower vibrational state with probabilities depending on the overlap integrals between the initial and the?nal motional states after a photon recoil.In section V we discuss the parameter regime in which this contribution can be suppressed by an interference e?ect in the dressed states absorption.
The processes depicted in Figs.4(b)and(c)describe scattering of a laser photon by spontaneous emission where the motion is changed by mechanical coupling to the laser,(b),and to the cavity,(c),?eld.Since the?nal state of the two scattering processes is the same,they interfere.In addition,each term is composed by multi-ple excitation paths,and can vanish in some parameter regimes.In section V we discuss interference e?ects in these two terms.
The processes depicted in Figs.4(d)and(e)describe scattering of a laser photon by cavity decay,where the motion is changed by mechanical coupling to the laser,(d),and to the cavity,(e),?eld.The scattered pho-ton is transmitted through the cavity mirrors into the external modes,and therefore these two processes do not interfere with the ones above discussed,but add up co-herently with one another.In section IV C we discuss parameter regimes where interference e?ects in these two terms relevantly a?ect the dynamics.The general dy-namics are a competition of all these processes,and will be discussed in detail in the following sections.
III.THE MODEL
A.Basic Equations
We consider an atom of mass M,which is con?ned by a harmonic potential of frequencyνinside an optical res-onator.The relevant center-of-mass dynamics are along the x-axis,while the degrees of freedom of the transverse motion have been traced out,assuming that the trans-verse con?nement is much https://www.doczj.com/doc/fa1025980.html,ter on we discuss how the treatment can be generalized to three dimen-sional motion.The atom internal degrees of freedom, which are relevant to the dynamics,are the ground state |g and the excited state|e ,constituting a dipole transi-tion at frequencyω0and linewidthγ.The dipole couples with a cavity mode at frequencyωc and with a laser at frequencyωL,whose wave vectors k c and k L form the angleθc andθL,respectively,with the x-axis.The sys-tem is sketched in Fig.1and2.We denote byρthe density matrix for the atom and the resonator degrees of freedom in the reference frame rotating at the laser fre-quency.The density matrixρobeys the master equation ?
iˉh
[H,ρ]+L sρ+Kρ≡Lρ(4)
where L is the Liouvillian describing the total dynamics. Here,the Hamiltonian H is
H=H mec+H at+H cav+H at?cav+H L(5) where the terms describing the coherent dynamics in ab-sence of coupling with the e.m.-?eld are
H mec=
p2
2
Mν2x2(6)
H at=?ˉh?σ?σ(7)
H cav=?ˉhδc a?a(8) Here,x,p are position and momentum of the center of mass;σ=|g e|,andσ?its adjoint;a,a?are the annihilation and creation operators of a cavity photon;
4
FIG.4:Scattering processes leading to a change of the vibrational number by one phonon.The states |g,0c ;n ,|±;n are the cavity-atom dressed states at phonon number n .Processes (a),(b),(c)describe scattering of a laser photon by spontaneous emission.They prevail in good resonators,for κ??g ,γ.Processes (d)and (e)describe scattering of a laser photon by cavity decay.They prevail in
bad
resonators,for
γ?
?
g ,κ.The parameters α,?c ,?L emerge from the mechanical e?ects of light and are de?ned in Sec.III B.
?=ωL ?ω0and δc =ωL ?ωc are the detunings of the laser from the dipole and from the cavity frequency,respectively,such that
?c =??δc .
The terms
H at ?cav =ˉh g cos(kx cos θc +φ)(a ?σ+aσ?)(9)
H L =ˉh ?(e i kx cos θL σ?+H .c .)
(10)describe the radiative couplings of the dipole with the
cavity mode and the laser,respectively,where g is the cavity-mode vacuum Rabi frequency and ?the Rabi fre-quency for the coupling with the laser,φis a phase,and k is the modulus of the wave vector (|k L |≈|k c |≈ω0/c =k ).
The superoperators K and L s in Eq.(4)describe the cavity decay and dipole spontaneous emission into the modes external to the resonator,respectively,and are
K ρ=
κ2
2σ?ρσ??σ?σρ?ρσ?σ
(12)
where κis the cavity decay rate due to the ?nite trans-mission at the mirrors and
?ρ= 1?1
d cos θ0N (θ0)
e ?i k cos θ0x ρe i k cos θ0x (13)
describes the events in which the atomic motion recoils by emission of a photon at the angle θ0with the trap axis with probability N (θ0)d cos θ0.Note that N (θ0)must be evaluated taking into account the geometry of the setup.For later convenience we introduce the annihilation and creation operators b and b ?of a quantum of vibra-tional energy,such that
x =
ˉ
h Mν/2(b ??b ),(15)
and the Hamiltonian term (6)can be rewritten as
H mec =ˉh ν
b ?b +
1
ˉ
h iˉh
[H mec ,ρ](18)
5 L0Iρ=
1
2 2σρσ??σ?σρ?ρσ?σ (22)
appear at zero order in the expansion inη.The term
?g=g cosφ(23)
is the zero order atom–cavity coupling strength.
The spectrum of L0isλ=λI+λE,whereλI are the
eigenvalues of L0I andλE are the eigenvalues of L0E.
The stationary state is a right eigenstate at eigenvalue
zero,as it ful?lls the secular equation L0ρ=0[39].The
corresponding eigenspace is spanned,for instance,by the
eigenvectorsρn=ρSt?|n n|,whereρSt full?lls the equa-
tion
L0IρSt=0
while the operator|n n|is eigenvector of the superop-
erator L0E at eigenvalueλE=0.The corresponding
eigenspace is in?nitely degenerate.We denote by P the
projection operator over theλ=0eigenspace,de?ned as
Pρ=ρSt?
∞
n=0|n n|Tr I{ n|ρ|n }(24)
where Tr I is the trace over the dipole and cavity degrees of freedom.At second order inηone gets a closed equa-tion for the center of mass dynamics of the form
d
2
Tr I{σ?σρSt}(26)
S(ν)=1
dt
p n=η2[(n+1)A?p n+1
?((n+1)A++nA?)p n+nA+p n?1](33)
where
A±=2Re{S(?ν)+D}(34)
are the rate of heating(A+)and cooling(A?).The so-
lution of this type of equation is well known[34].The
average phonon number obeys the equation
˙ n =?η2(A
?
?A+) n +η2A+(35)
which,for A?>A+,has solution
n
t
= n
e?W t+ n
St 1?e?W t (36)
Here, n
is the initial average phonon number and
n
St
=
A+
D.Discussion
In Eq.(33)the internal dynamics enter through the coe?cients S(ν)and D,which determine the rates(34). The function S(ν)is the spectrum of the?uctuations of the radiative force on the atom,namely the Fourier transform of the autocorrelation function of the opera-tor V1in Eq.(28).For the atom coupled to an optical resonator and driven transversally by a laser,we use the de?nition(28)in Eq.(27),and obtain
S(ν)=?2L S L(ν)+?2c S c(ν)+?L?c S cL(ν) Here,
S L=?Tr I{V L(L0I+iν)?1V LρSt}
is the contribution of the mechanical e?ect due to the laser,the term
S c=?Tr I{V c(L0I+iν)?1V cρSt}
the contribution of the mechanical e?ect due to the res-onator,and
S cL=?Tr I{V c(L0I+iν)?1V LρSt}
?Tr I{V L(L0I+iν)?1V cρSt}
the contribution due to correlations between the mechan-ical e?ects of laser and resonator.Depending on the ge-ometry of the setup,one term can be dominant over the others.
The coe?cient D,Eq.(26),gives the di?usion in the dynamics of the center-of-mass motion.It is the prod-uct of two terms:the spontaneous emission rate of the excited state into the modes of the e.m.-?eld,and the stationary excited state population,which is determined by the overall dynamics at zero order in the Lamb-Dicke expansion.
IV.CA VITY COOLING OF TRAPPED ATOMS A.An explicit form of the rate equation for cooling An analytical form for the rates entering equation(33) can be derived in the limit of a weak laser drive.The main steps of the derivation are reported in Appendix A. In this limit the heating and cooling rates take the form
A±=γα|T S|2+γ|?L Tγ,±
L +?c Tγ,±
c
|2(39)
+κ|?L Tκ,±
L +?c Tκ,±
c
|2
with
T S=?
δc+iκ/2
f(?ν)(41)
Tκ,±
L
=i?
?g
f(0)f(?ν)
(43)
Tκ,±
c
=??
?g (??ν+iγ/2)(δc+iκ/2)+?g2
B.
Cooling in the bad cavity limit
Cooling in the bad cavity limit,as discussed in [13],is recovered
by maximizing
the
ratio
A ?/A +in the limit in which spontaneous emission is negligible.In Eq.(39)we set γ=0and take |δc |?ν.The equivalence with the cooling and heating rates reported in [13]is evident
by using the de?nitions ?δ=?g 2?c /(κ2/4+?2c )and ?γ
=?g 2κ/(κ2/4+?2c ),and imposing ?c =?L =1(namely,the cavity axes and the laser are parallel to the atomic motion).Below we use this notation but keep ?L and ?c ,thereby allowing for a more general geometry.From Eq.(39)we ?nd
A ±?
?2?
γ???δ?ν+i?γ/2
?i ?L
???δ+i?γ/2
?2
(α+?2L )γ+
?g 2κ(?2L +?2
c )
4
+(δc +ν)2
?g 2κ
α+?2L
4
+(δc ?ν)
2
(50)
In the following we do not discuss the solutions leading to
Doppler cooling,and focus onto the parameter regimes that lead to ground state cooling,assuming γ>ν.
For κ?νEq.(49)reaches the minimum value at δc =?ν,
n (?)St δc =?ν=κ24C 1 α+?2
L 16ν2 (51)
where
C 1=?g 2/γκ
(52)
is the one-atom cooperativity [41].The corresponding
cooling rate is W
δc =?ν
=η
2
4C 1(?2L
+
?2c
)?2
1+(4ν/κ)2
(53)
Therefore,large ground-state populations and large cool-ing rates can be achieved for ν?κand C 1?1,namely
for good cavities and in the limit in which the cavity linewidth is much smaller than the trap frequency.
Insight into these results can be found by using the dressed state picture discussed in Sec.II:For κ?ν,large ?and δc =?νthe excitation spectrum corre-sponds to the situation depicted in Fig 3(a),where the the red sideband transition is resonant with the narrow resonance at frequency λ+=ν,while the carrier and the blue sideband are driven far-o?resonance.Hence,this condition is analogous to sideband cooling,whereby now the narrow resonance is the dressed state of the system composed by cavity and atom.
The cavity loss rate sets the lower limit to the width of the narrow resonance,on which sideband cooling is made,and thus to the e?ciency of the process,as it is visible in Eqs.(51)and (53).From these equations it is also visible that large cooperativities ensure better e?ciencies.
The results reported in this section have been obtained from rate equation (33)with the coe?cients Eqs.(39)-(44)expanded at leading order in 1/?.Such expansion is valid in the limit where the detuning between atom and cavity (respectively,laser)is the largest physical pa-rameter.We remark that Eq.(51)is in agreement with the result reported in [15]in the corresponding parameter regime,whereby the di?erent numerical factors,as well as the dependence on the angles,are due to the di?erent laser con?guration there considered.
V.
COOLING BY QUANTUM CORRELATIONS
IN THE GOOD CA VITY LIMIT
In this section we present and discuss novel cooling
dynamics based on quantum interference e?ects,which are dominant in the good cavity limit,when
κ?ν,γ,?g .
8
In this regime we focus onto the?rst two terms of the rates(39),corresponding to the processes in Fig.4(a)-(c),and treat cavity decay,giving rise to the processes depicted in Fig.4(d),(e),as small perturbations.In the following we assume that
φ=
π
δc+ν
?ν(55)
where we assume?xed couplings and decay rates,hence also a?xed cooperativity.For instance,in the case of sideband cooling discussed in Sec.IV C,the optimal cool-ing conditions are reached forδc=?ν,corresponding to the solution of Eq.(54)for?→∞.In this limit,the linewidth of the dressed state resonance which is used for cooling is in?nitely small,and the steady state occupa-tion vanishes accordingly.
Below we discuss various regimes where ground-state cooling is e?cient and which may be identi?ed,for the corresponding parameter regimes,with an approximate solution of Eq.(54).
B.Suppression of di?usion by quantum
interference
In this section we discuss a cooling scheme based on the suppression of di?usion by quantum interference.The cooling dynamics are based on the suppression of the car-rier transition,and can be understood with the dressed state picture.As discussed in Sec.II,the carrier transi-tion can vanish in the regime in which laser and cavity are resonant.The sidebands due to the harmonic mo-tion,however,are weak perturbations in opposition of phase with respect to the carrier.Thus,they give rise to photon scattering with probability given by the cor-responding value of the excitation spectrum,depicted in Fig.3(b)for some parameter regime.The cooling strat-egy is thus to enhance the red sideband over the blue sideband absorption,thereby pro?ting of the suppression of carrier excitations,and thus of di?usion.This idea is reminiscent of cooling mechanisms based on quantum in-terference between atomic levels[30,37],whereby here the suppression of the carrier transition is due to the destructive interference between the laser and the light elastically scattered into the resonator by the atom.
Di?usion is suppressed when T S=0in Eqs.(39), leading to the vanishing of the di?usion coe?cient D, Eq.(26).From Eq.(39)this occurs whenδc=0and, ideally,forκ=0.Let us?rst consider the ideal condition of a lossless resonator.In this case,forδc=0the steady state average phonon number is given by
n (0)
St
=
[ν(ν+?)??g2]2+γ2ν2/4
16?opt(0)2
=
γ2ν2
γ 1?1
9 Case(ii)can be ful?lled in the so-called weak con-
?nement regime[28],namely when the linewidth of the
dipole transition is much larger than the trap frequency.
Result(57)shows that ground state cooling can be e?-
ciently achieved.This is to our knowledge a novel regime.
Here,?～?g2/ν,so that we can rewrite the cooling limit
as
n (0)St ?opt(0)≈γ2ν2/16?g4.(59)
We now discuss how the e?ciency is modi?ed forδc=0
butκ?nite.At?rst order inκthe di?usion coe?cient
D=0.In fact,D=O(κ2),being the stationary pop-
ulation of the excited state of second order inκin this
regime[32,33].At?rst order in this expansion the steady
state average phonon number is
n
St = n (0)
St
(1+F)(60)
where the term
F=κ2
2
A??2
κ
A??A+
?L?c
[ν(ν??)??g2]2+ν2γ2/4
(62)
Cavity decay increases the linewidth of the dressed-state resonances,and it thus detrimental.Nevertheless,for high cooperativities the result we?nd in Eq.(60)ap-proaches the result of the ideal case,Eq.(59).In partic-ular,for?g?νits value at?=?opt(0)takes the simple form
n
St ?opt(0)≈ n (0)St ?opt(0)+1
16?g4?2c
(65)
It reaches a minimum for?=?opt(ν/2),namely ?opt(ν/2)=2?g2/3ν?ν,that has the form
n (0)St ?opt(ν/2)=9α16?g4(66) with the corresponding cooling rate
W ?opt(ν/2)=16η2?2(1+3ν2/4?g2)2+(3γν/8?g2)2(67)
To our knowledge,this is a novel cooling regime.Insight into these dynamics cannot be simply gained by inspec-tion of the excitation rate at zero order in the Lamb-Dicke parameter.In fact,the disappearance of the blue side-band transition is due to a quantum interference e?ect between the paths of mechanical excitation driven by the https://www.doczj.com/doc/fa1025980.html,paring this case with cooling by suppres-sion of di?usion,see Sec.V B,one?nds that forδc=ν/2 one can reach lower temperatures in a faster time,as it is evident from a comparison of Eqs.(66)and(67)with Eqs.(58),(63)and with the results reported in Sec.IV C. A?nite,but small,value ofκleads to the corrected average excitation
n St= n (0)St(1+κF)+κG(68)
where
F=
1
9γ2ν2/16+(?g2?3ν(?+ν)/2)2
+ γ2/4+(?+ν)2 γν (69) G=
9γ2ν2/16+ ?g2?3ν(?+ν)/2 2
10 are the corrections at?rst order inκ.They lower the
e?ciency of the mechanism.In particular,the optimal
?nal occupation number becomes
n
St ?opt(ν/2)= 1+1
64C1
(71)
while the corrections to the cooling rate scale with1/C1. Therefore,for large cooperativities this interference e?ect is relevant to the cooling dynamics.We remark,that as forδc=ν/2the heating transition vanishes,similarly for δc=?ν/2the cooling transition cancels out.
D.Suppression of di?usion and heating by
quantum interference
We?nally discuss a cooling scheme based on the sup-pression of both di?usion and heating transitions by quantum interference.Let us?rst consider suppression of the carrier excitation,that leads to a vanishing di?usion coe?cient.This can be achieved by using a standing-wave drive,such that the trap center is at one of its nodes.Therefore,at zero order in the Lamb-Dicke ex-pansion the atom does not scatter any photon and the cavity is thus empty.Photon scattering originates from the dynamics due to the?nite size of the atomic wave packet,and it is thus a process of second order in the Lamb-Dicke expansion.In order to investigate these dy-namics,we evaluate the heating and cooling rate entering the rate equation(33)by considering a new Hamiltonian, which is given by operator(5)with the new laser-dipole coupling
H L=ˉh?cos(kx cosθL+φL)(σ?+σ)(72) The condition for which the trap is at a node of the laser standing wave corresponds to choose
φL=π/2,
For this value,the interaction with the laser vanishes at zero order in the Lamb-Dicke expansion and the steady state is the empty cavity?eld and the atom in the ground state,namelyρ′St=|g,0c g,0c|.Note that no assump-tion has been made on the value of the Rabi frequency?. By expanding Eq.(72)at?rst order in the Lamb-Dicke parameter,we obtain in place of the operator(28)the new interaction term
V L=?ˉh??L(σ?+σ)
In the rest of this section we will consider?L=1. Following the lines of the derivation as in section III B with the new de?nitions,we obtain the equation for the external dynamics,Eq.(25),where now
D=0and
S(ν)=?Tr I{V L(L′0I+iν)?1V Lρ′St}(73) Here,L′0I has the same form as L0I in Eq.(19),with H0L=0.Clearly,the disappearance of the di?usion term is due to the fact that there is no?eld at zero order in the Lamb-Dicke expansion.
The term(73),giving the mechanical action on the atomic motion,originates solely from scattering of laser photons.In fact,the mechanical e?ects of the resonator ?eld appear at higher order in the Lamb-Dicke expansion. The cooling and heating rates A′±=2Re{S(?ν)}take the form
A′±=γ|Tγ±
1L
|2+κ|Tκ±
1L
|2(74) where now
Tγ,±
1L
=?
(δc?ν+iκ/2)
f(?ν)
(76)
(77) and
f(x)=(x+δc+iκ/2)(x+?+iγ/2)??g2(78) Hence,the transition amplitudes do not relevantly di?er from the ones in Eqs.(40)-(44).However,no low satura-tion limit is needed in the derivation of these results. We study now the cooling dynamics in an exemplary limit,namely in the case of a very good resonator.We ?rst consider an ideal resonator,namelyκ=0.We ob-tain
A′±|κ=0=
?2(δc?ν)2γ
γ
.
This result is exact forκ=0.
Finite values ofκintroduce corrections to the heating rate,which takes the form
A′+?κ?2/?g2=
?2
C1 Correspondingly,the average number of phonon at steady state is
n
St
?
[2ν(?+ν)??g2]2+γ2ν2
C1
(80)
11
the minimum value of the number of excitations at steady state is found at?=?opt(ν)and is given by
n
St ?opt(ν)=1/4C1,
These cooling dynamics are novel,and correspond to the situation in which the excitation pathways of the com-bined multilevel atom–cavity system interfere destruc-tively,thereby suppressing the blue sideband excitation. They are reminiscent of cooling schemes for multilevel atoms discussed in[42],where suppression of the carrier and blue sideband transitions is achieved by quantum in-terference between atomic excitations.In the case stud-ied here,however,the mechanism which leads to suppres-sion of the carrier transition is di?erent from the one that leads to the suppression of the blue sideband transition, and both are due to the composite e?ect of cavity and laser on the atom.Moreover,the parameter regime here considered is one of several possible,that can be identi-?ed by imposing the disappearance of the blue sidebands transition.
VI.RESULTS
In this section we compare the cooling e?ciencies in the various regime,as evaluated from the analytical re-sults,and check the range of validity of the analytical calculations with a quantum Monte-Carlo wavefunction method,where the full quantum dynamics of master equation(4)is simulated.We focus onto the good cavity limit,in particular onto the parametersκ?ν?γ.
A.Plot of the analytical results
The plots in Figure5show the phonon number at steady state and the cooling rate for di?erent geometries of the setup.In particular,the plots of the?rst row de-pict the situation in which the mechanical e?ects on the atom are due to both laser and cavity?eld,the plots of the second row show the dynamics when the e?ects are solely due to the resonator,and the ones in the third row when the e?ects are solely due to the laser.The contour plots show most evidently the parameter regions where cooling is e?ective.Here,the dashed line represents the function(55)which determines the parameters minimiz-ing the steady state temperature.Clearly,in the neigh-bourhood of this line the lowest temperature is achieved in all three cases.We note that the parameter regimes where cooling occurs may di?er depending on whether the dipole forces are due to the resonator or to the laser. We now discuss the dynamics in detail.Due to the wealth of behaviours,we focus onto the parameter re-gions where ground-state cooling appears e?cient. Figures5(b),(f),and(j)display the value of the average phonon number as a function ofδc and ?opt(δc),namely its value along the function(55).Fig-ures5(d),(h),and(l)show the corresponding cooling rates.Each plot displays two curves,which have been evaluated for two di?erent values of the cavity decay rate κ(solid curve:κ=0.01ν,dashed curve:κ=0.1ν). From these curves it is visible that,as the cavity decay rate increases,the cooling e?ciency decreases,namely the temperature gets higher and the cooling rate lower. Nevertheless,for the parameter here considered the cool-ing dynamics remains e?cient.Let us now discuss the behaviour as we varyδc and keep?=?opt(δc).
In all cases the function n
St
exhibits a minimum at δc=?νat very large values of?.This is the sideband cooling regime,discussed in Sec.IV C.The cooling rate at these points is very small,since it scales as??2,as vis-ible from Eq.(53)[43].This cooling scheme exploits the dressed states of the system at zero order in the Lamb-Dicke expansion,see Sec.II,and its e?ciency is thus relatively independent of whether the cavity or the laser forces determine cooling.Here,the cooling e?ciency is very sensitive to variation ofδc,as visible from the con-tour plots.This sensitiveness is due to the narrowness of the linewidth of the dressed-state resonance which is used for cooling the motion.
The curves in Figures5(b),(f)show also a minimum atδc=ν/2.This is due to cooling by suppression of the resonator’s mechanical coupling to the blue sideband transition,see Sec.V C.Clearly,this minimum is more enhanced in Fig.5(f),where cooling is solely due to the mechanical e?ects of the cavity,and does not appear in Fig.5(j),where the resonator?eld has no mechanical e?ects on the atom.The corresponding cooling rate is relatively large,being the atom driven close to resonance in this regime.An interesting characteristic,emerging from the contour plots,is that these cooling dynamics are relatively robust to?uctuations of the parameters, showing that ground-state cooling is e?cient even in the regime in which suppression of the heating transition is partial.
The heating region atδc=?ν/2,appearing in the case in which the mechanical e?ects of the cavity solely contribute to cooling,Figs.5(e)-(h),is originated from the same interference e?ects that give rise to cooling at the valueδc=ν/2,and that forδc=?ν/2leads to suppression of the cooling transition,see Sec.V C. Another regime where cooling is e?ective is found at δc=0when the mechanical e?ects are solely due to the laser.This parameter regime is characterized by small temperatures and large cooling rates,as visible from Figs.5(i)-(l).This is the regime in which the carrier transition is suppressed by an interference phenomenon at zero order in the motion,see Secs.II and V B.Cooling e?ciency is robust against?uctuations of the parameters, and appear to be relatively stable as the value ofκis in-creased,as compared with the sideband cooling case,see Fig.5(j).
In general,we can conclude that in the range of values ofδc around the interval[0,ν/2],and close to atomic
12
FIG.5:Average phonon number at steady state n
St and corresponding cooling rate W,in units ofν,in the good cavity limit,
forκ?ν?γand for three possible geometries:in(a)-(d)(?rst row)both cavity and laser?elds contribute to the cooling: HereθL=θc=π/4.In(e)-(h)(second row)the mechanical e?ects of the cavity solely determine cooling:HereθL=π/2and θc=π/4.In(i)-(l)(last row)the mechanical e?ects of the laser solely determine cooling:HereθL=π/4andθc=π/2.The
contour plots show n
St and W as a function ofδc and?in units ofν.The gradation of grey follows the scale where darkest
region corresponds to the smallest values,the lightest region to the largest values.The corresponding values are reported at the bottom of the?gure.The heating regions are not coded and explicitly indicated by the label H.The dashed curve appearing in each contour plot represents the curve?opt(δc),Eq.(55).The parameters areη=0.1,θL=π/4,?=ν,?g=7ν,γ=10ν,κ=0.01ν.The other plots display n St and W as a function ofδc and?opt(δc),for the same parameters as of the contour plot andκ=0.01ν(solid line),κ=0.1ν(dashed line).
resonance,the cooling e?ciency is relatively high.We remark that the?nal temperature is limited by the ratio κ/ν.This is understood in the dressed state picture,as the?nal limit to the narrow dressed state resonance is set by the cavity decay rateκ.
B.Numerical simulations
The curves reported in Fig.5have been obtained from the analytical equations,which have been evaluated as-suming that dipole and cavity dynamics reach the steady state on a much faster time scale than the center-of-mass dynamics.In Fig.6we verify these results by compar-ing them with a full quantum Monte Carlo wave function
13
simulation of Master Equation (4).We see that in general the analytical predictions are in agreement with the nu-merical results for a vast range of parameters,which are experimentally accessible.The discrepancies are small and are due to parameter regimes where the adiabatic evolution is not ful?lled.The discrepancies a?ect mostly the cooling rate,which varies by an overall factor,while the ?nal average excitations of the center-of-mass oscil-lator are in agreement.
5
10
15
10 3
10 210 1100
05
10
10 3
10 210 11000
15
30
45
10 3
10 210
1
1000
25
50
10 3
10 210
1
1000
5
10
15
10 3
10 210 1
100
20
40
10 3
10 210 1100ν?1
time (in units of 10 )
2
ν?1
time (in units of 10 )
2ν?1ν?1
ν?1
ν?1time (in units of 10 )4time (in units of 10 )
time (in units of 10 )
3time (in units of 10 )
3
5n
n
n
n
n
n
(d)
(a)
(b)
(e)
(c)
(f)
FIG.6:Comparison between the analytical equations,
Eqs.(33)and (39),and a full quantum Monte Carlo simu-lation of Eq.(4).The curves show the evolution of the aver-age phonon number as the function of time in units of ν?1,the dashed lines correspond to the analytical predictions,the solid lines to the quantum Monte Carlo simulation.The pa-rameters are η=0.1,θL =θc =φ=π/4,?=ν,γ=10ν,κ=0.1νand (a)g =10ν,δc =?1.1ν;(b)g =10ν,δc =0;(c)g =10ν,δc =0.5ν;(d)g =50ν,δc =?1.1ν;(e)g =50ν,δc =0;(f)g =50ν,δc =0.5ν;
VII.
CONCLUSIONS
We have presented an extensive study of the cooling dynamics of trapped atoms in optical resonators.Our study is based on a rate equation,which we derive from
the master equation of the system composed by atom and cavity,and whose validity is supported by numerical sim-ulations taking into account the full quantum dynamics.Our analytical results are valid in the Lamb-Dicke regime and when the center-of-mass potential is independent of the internal state,like in [7,25,26].
The equations we derive reproduce the results reported in [13,15]in their speci?c parameter regimes.Moreover,they allow us to identify new parameter regimes where the dynamics of the atomic center-of-mass,coupled to a laser and a cavity ?eld,results from a non-trivial com-petition of the laser and of the resonator dipole forces,which can mutually interfere.These interference e?ects are at the basis of novel cooling schemes,which we iden-tify in this paper and which allow to reach very large ground-state occupations.The corresponding dynamics are reminescent of cooling schemes exploiting interference in multi-level atomic transitions [30,42,44].
It must be remarked that the interference e?ects dis-cussed in this work base themselves on the discreteness of the spectrum of the mechanical excitations,which is the same for the dipolar ground and the excited states.Dy-namics will be substantially modi?ed when the external potential depends on the internal state,as the spectro-scopic properties of the atom are changed and with it the scattering cross section.Preliminary considerations are in [37]for the case of trapped multilevel atoms,while the e?ects of state-dependent mechanical potentials on the cavity ?eld have been discussed in [45].
In this paper we have focussed onto the case of dipole transitions,which in free space do not allow one for ap-plying sideband cooling.Here,ground-state cooling can be obtained in good resonators,whereby the ?nal cooling e?ciency is limited by the cavity decay rate.The bad-cavity case is contained in the analytical equations we have derived.In this limit the e?ect of the laser seems to be predominant and for a general con?guration the optimal cooling corresponds to standard cavity sideband cooling [46].This di?ers strikingly with the good cav-ity limit,where correlations between atom and resonator can lead to very e?cient cooling.We remark that these dynamics are largely modi?ed when the drive is set on the resonator.
To conclude,this work considers the cooling dynam-ics to the potential ground state of a single atom inside a resonator.In the future we will investigate how the collective dynamics of several atoms,con?ned in a res-onator,in?uence the cooling e?ciency,and how these can be used to prepare quantum states of the system in a controlled way.
Acknowledgments
The authors wish to thank Helmut Ritsch and Axel Kuhn for several stimulating discussions.Support from the IST-network QGATES and of the Spanish Ministe-rio de Educaci′o n y Ciencia (Ramon-y-Cajal fellowship
14 129170)is acknowledged.
APPENDIX A:LIMIT OF WEAK DRIVING
FIELD
We consider the limit when the atom is weakly driven,
namely when the Rabi frequency?is much smaller than
all the other physical parameters that characterize the
internal dynamics.We study the dynamics of the motion
in perturbation theory in second order in?andη,and
neglect the terms of orderη4?2,η2?4and higher.
At zero order in?the laser?eld is zero.Hence,at
steady state the cavity is empty and the atom is in the
ground state.The state of dipole and cavity is described
by the density matrix
ρ?St=|g,0c g,0c|,
which is the solution of the equation L?0Iρ?St=0,with
L?0Iρ=L0I ?=0ρ(A1)
=
1
?g m
L n,m(A3)
=η2?2
?g2 +O
η2?4?g2
L2,2(A5)
=?2L L L+?2c L c+?c?L L cL+L di?(A6) The subscripts L,c and cL label the terms describing processes in which the mechanical e?ect on the atoms are due respectively to the laser,the cavity,and to the cooperative action of laser and cavity.They have the form
L L=?P L1L L??1
L1L(A7)
L c=?P L1c L??1
L1c L??1
L0L L??1
L0L
?P L1c L??1
L0L L??1
L1c L??1
L0L(A8)
L cL=P L1L L??1
L1c L??1
L0L
+P L1c L??1
L0L L??1
L1L
+P L1c L??1
L1L L??1
L0L(A9) where the terms which trivially vanish have been omitted. Here,
L0Lρ=?
i
ˉh
[(b?+b)V L,ρ](A11)
L1cρ=?η
i
2
σ 2(b+b?)ρ(b+b?)
?(b+b?)2ρ?ρ(b+b?)2 σ?(A15) is the Liouvillian at second order inηfor the atomic spontaneous emission.
Tracing over the internal degree of freedom we obtain an equation for the density matrixμ=Tr I{Pρ}for the center-of-mass variables,
T r I{L di?Pρ}=η2[D(bμb??b?bμ+b?μb?bb?μ)+H.c.] T r I{L j Pρ}=η2[S j(ν)(bμb??b?bμ)
+S j(?ν)(b?μb?bb?μ)+H.c.](A16) with j={L,c,cL}.The coe?cients D and S j are de?ned as
D=
γα
15 Setting S(ν)=?2L S L(ν)+?2c S c(ν)+?c?L S cL(ν)we?nd
an equation of the same form as Eq.(25).The real part
of these terms are
Re{D}=γα|T S|2/2(A19)
Re{S L(?ν)}= γ|Tγ,±L|2+κ|Tκ,±L|2 /2(A20)
Re{S c(?ν)}= γ|Tγ,±c|2+κ|Tκ,±c|2 /2(A21)
Re{S cL(?ν)}= γTγ,±L Tγ,±c?+κTκ,±L Tκ,±c? /2
+c.c.(A22)
where the coe?cients T j are given explicitly in Eqs.(40)-
(44).Finally,heating and cooling rates are given by
A±=2Re{S(?ν)+D}and their explicit dependence
on the physical parameters are reported in Eq.(39).
APPENDIX B:LIMIT OF SMALL CA VITY LOSS
RATE
In this appendix we discuss the derivation of the rate
equation,in the limit of small cavity loss andδc=0,by
making no assumption over the laser Rabi frequency?,
which may saturate the atomic transition.The results
we obtain in this appendix are valid provided that?g=0.
In order to derive the rate equation for the atomic
motion we closely follow the general approach described
in section III B,where here we expand at second order
inηand at?rst order inκ.The limit of applications
of the perturbative expansion are found after identifying
the smallest rate determining the internal dynamics for
κ=δc=0.This is the width of the narrow resonance
γ?,which for su?ciently large values of|?|takes the
form
γ?～γ
iˉh
[H at+H0at?cav+H0L,ρ]+L0sρ
and the steady state,which is solution of L00Iρ0St=0,
is given by Eq.(64).The superoperator at zero order in ηandκis given by
L00=L00I+L0E(B3) and the corresponding projector over the
eigenspace at eigenvalue zero is Pρ=|g,βc g,βc|? n|n n|Tr I{ n|ρ|n }.The dynamics of this sub-space at the lowest relevant order inηandκ/γ?are P˙ρ=L P Pρwhere
L P=
∞
n=0,m=0ηnκm
γ?
L2,1(B5) where
η2L2,0=?P L1L?100L1(B6)η2
κ
ˉh
[(b?+b)V1,ρ](B8)
Liouvillian at?rst order inηfor the coupling be-tween atom and electromagnetic?eld,and V1given by Eqs.(28).Note that we have omitted to write the terms which trivially vanish.Tracing over the internal degree of freedom we obtain the equation
˙μ=Tr I{L Pρ0SS?μ}
for the center-of-mass variables density matrixμ= T r I{Pρ},whereby
Tr I{L2,?Pρ}=η2[S?(ν)(bμb??b?bμ)
+S?(?ν)(b?μb?bb?μ)+H.c.](B9) Here the index?={0,1}indicate the order of the ex-pansion inκ.From this equation we can identify the coe?cients of Eq.(25),and thus
D=0
and
S(ν)=S0(ν)+S1(ν)
where
S0(ν)=?Tr I{V1(L00I+iν)?1V1ρ0SS}
S1(ν)=Tr I{V1(L00I+iν)?1
V1L?100I K+K(L00I+iν)?1V1 ρ0SS}
(B10) Note that D=o(κ2),as in this system the population of the atomic excited state grows quadratically withκ[32, 33].
Heating and cooling rates are found from the relation A±=2Re{S0(?ν)+S1(?ν)},and take the form
A±=?2A± ?2L+?2c+ξ±κ (B11)
16
whereby |ξ±
κ|?1.In particular,
A ±=
ν2γ
ν
2C 1 1?γ2C 1
+κ
?g 2
?1
?L ?c (B13)
Result (B11)coincides with the one obtained from ex-panding Eq.(39)to the ?rst order in κand with δc =0,
from which the results in Eqs.(58)and (60)have been obtained.Nevertheless,in deriving rates (B11)we have made no assumption on the strength of the laser inten-sity.
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[43]Ideally,forδc=?νwe should take?→∞.Here,we
have taken a large but?nite value,consistent with the
expansion in1/?presented in Sec.IV C.
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企业环保标语大全 企业环保标语大全 1．保护中发展，发展中保护 2．落实环保责任，完善环保制度 3．环境与人类共存，开发与保护同步 4．垃圾混置是垃圾，垃圾分类是资源 5．建设绿色企业，坚持绿色经营 6．降低生产成本，节约地球资源 7．生产绿色产品，节约地球资源 8．珍惜资源、永续利用 9．依靠科技进步、促进环境保护 10．合理利用资源、保护生态平衡、促进经济持续发展11．保护环境山河美、持续发展事业兴 12．发展经济不能以牺牲环境为代价 13．使用环保材料，减少环境污染 14．推行清洁生产，促进经济社会可持续发展15．推行清洁生产，实现碧水蓝天 16．推行循环经济，提高资源利用水平 17．依靠科技进步，推行清洁生产 18．环境与人类共存，发展与环保同步
19．贯彻环境教育，宣导环保资讯 20．全员参与改善，持续环保社区 21．提高环保意识，争做环保公民 22．让地球远离污染，让绿色走进家园23．有限的资源，无限的循环 24．降低损耗齐用心，开源节流增效益25．节约的是利润，损耗的是财富 26．树立节约意识，倡导节约行为 27．浪费不因量小而为之，节约不因细微而不为28．保护环境降污染，千方百计增效益29．资源节约齐参加，珍惜使用靠大家30．改变观念，废物利用，资源回收，持续发展31．保护环境、就是保护生产力 32．既要金山银山、更要青山绿水 33．提倡绿色生活、实施清洁生产 34．树立节水意识、反对浪费水源 35．提高环境道德水平、建设文明小康城区36．保护环境、造福后代 37．全面建设小康社会、同心共创美好家园38．当环保卫士、做时代公民 39．让大气清新、让天空蔚蓝、让河山碧绿40．企业求发展、环保须先行
高中数学新课标学习心得体会 通过对新课标的学习，本人有一些心得体会，现汇报如下： 一、课程的基本理念 总体目标中提出的数学知识（包括数学事实、数学活动经验）本人认为可以简单的这样表述：数学知识是“数与形以及演绎”的知识。 1、基本的数学思想 基本数学思想可以概括为三个方面：即“符号与变换的思想”、“集全与对应的思想”和“公理化与结构的思想”，这三者构成了数学思想的最高层次。基于这些基本思想，在具体的教学中要注意渗透，从低年级开始渗透，但不必要进行理论概括。而所谓数学方法则与数学思想互为表里、密切相关，两者都以一定的知识为基础，反过来又促进知识的深化及形成能力。 2、重视数学思维方法 高中数学应注重提高学生的数学思维能力。数学思维的特性：概括性、问题性、相似性。数学思维的结构和形式：结构是一个多因素的动态关联系统，可分成四个方面：数学思维的内容（材料与结果）、基本形式、操作手段（即思维方法）以及个性品质（包括智力与非智力因互素的临控等）；其基本形式可分为逻辑思维、形象思维和直觉思维三种类型。 3、应用数学的意识 增强应用数学的意识主要是指在教与学观念转变的前提下，突出主动学习、主动探究。 4、注重信息技术与数学课程的整合 高中数学课程应提倡实现信息技术与课程内容的有机整合，整合的基本原则是有利于学生认识数学的本质。在保证笔算训练的全体细致，尽可能的使用科学型计算器、各种数学教育技术平台，加强数学教学与信息技术的结合，鼓励学生运用计算机、计算器等进行探索和发现。 5、建立合理的科学的评价体系 高中数学课程应建立合理的科学的评价体系，包括评价理念、评价内容、评价形式评价体制等方面。既要关注学生的数学学习的结果，也要关注他们学习的过程；既要关注学生数学学习的水平，也要关注他们在数学活动中表现出来的情感态度的变化，在数学教育中，评价应建立多元化的目标，关注学生个性与潜能的发展。 二、课程设置
第三单元生物圈中的绿色植物 第一章生物圈中有哪些绿色植物 ?1、绿色植物分为四大类群：藻类、苔藓、蕨类、种子植物 一、藻类、苔藓、蕨类植物 ?2、藻类、苔藓、蕨类植物的区别： ?3、藻类，苔藓，蕨类植物的共同点：藻类，苔藓，蕨类植物都不结种子，它们的叶片背面 有孢子囊群，可产生孢子，称为孢子植物，孢子是一种生殖细胞，在温暖潮湿的地方才能萌发和生长，所以说孢子植物的生活离不开水。 4.藻类植物：“春水绿于染” 5.藻类植物既有单细胞，也有多细胞。既有生活在淡水中，也有海水中。 6.多细胞藻类植物整个身体浸没在水中，几乎全身都可以吸收水和无机盐。可以进行光合作用，但没有专门吸收和运输养料以及进行光合作用的器官。 7.藻类植物没有根茎叶的分化。 8.苔藓植物生存在阴湿环境中。有类似根和茎的分化，但是茎中没有导管，叶中没有叶脉，根很简单，称为假根，具有固定作用。 9.苔藓植物可作为监测空气污染程度的指示植物。 10.蕨类植物：有根茎叶的分化，具有输导组织。有些蕨类植物比较高大。 11.蕨类植物用处：①卷柏、贯众可药用②满江红是一种优良绿肥和饲料③蕨类植物遗体层层堆积，经过漫长年代、复杂变化，逐渐变成了煤。 12.藻类植物，苔藓植物，蕨类植物，生殖依靠孢子，所以也被统称为孢子植物。 第二节 二、种子植物 ? 1.、种子的结构 菜豆种子：种皮、胚(胚芽、胚轴、胚根、2片子叶)【双子叶植物，网状叶脉】
玉米种子：果皮和种皮、胚(胚芽、胚轴、胚根、1片子叶)、胚乳【单子叶植物，平行叶脉】种皮：保护里面幼嫩的胚。 胚：新植物体的幼体，由胚芽（发育成茎和叶）、胚轴（发育成连接根和茎的部位）、胚根（发育成根）和子叶组成。胚乳不是胚的结构。 ?2、子叶和胚乳里有营养物质，供给胚发育成幼苗。 ?3、菜豆种子中与子叶相连的结构是胚轴，玉米种子中滴加碘液变蓝的结构是胚乳，说明胚 乳中含有淀粉。 菜豆种子（双子叶植物）： 胚轴：发育成根和茎的连接部 胚芽：发育成茎叶芽 胚根：发育成根 子叶（两片）：贮存营养物质 种皮：保护 玉米种子（单子叶植物）： 果皮和种皮：保护胚 胚乳：贮存营养物质（含有淀粉，遇碘变蓝） 子叶（一片）：转运营养物质 胚芽：发育成茎叶芽 胚轴：发育成茎和根的连接部 胚根：发育成根 ?4、菜豆种子和玉米种子的异同 （严格意义来说，一粒玉米就是一个果实） ?5、种子植物比苔藓、蕨类更适应陆地的生活，其中一个重要的原因是能产生种子。 ?6、种子植物包括两大类群：裸子植物和被子植物。 裸子植物：种子裸露着，不能形成果实，常见的裸子植物有松、杉、柏、苏铁、银杏； 被子植物（绿色开花植物）：种子外面有果皮包被着，是陆地上分布最广泛的植物类群。（苹果，梨，葡萄，水稻） 第二章被子植物的一生
环保企业文化标语 导读：本文是关于环保企业文化标语，如果觉得很不错，欢迎点评和分享！ 1、维护社会公德，保护生态环境。 2、环保时代，健康生活。自由追逐，财富就在咱们手中。 3、引领环保新时尚，创造自由新生活。 4、你环保健康，一起财富自由。 5、改善环境，保护家园；净化环境，美化家园。 6、百业要兴，环保先行。 7、给你“更环保、更健康、更成功”的选择。 8、低碳生活，自由财富。 9、环保新主义，财富由你创，健康自然来！ 10、拯救地球，一起动手。 11、人类若不能与其他物种共存，便不能与这个星球共存。 12、做世界一流环保产品，让地球人都身体康健，给财富自由的翅膀。 13、节能环保缔造健康生活，健康生活成就财富自由。 14、环保进万家，财富赢天下。 15、改善环境，创建美好未来是我们共同的愿望。 16、尽环保力量，谋健康财富。 17、蓝天白云，绿水青山；咱们的发奋，自然的美丽。
18、绿色环保，引领时尚。 19、咱们所拥有的不仅仅是财富，还有干净的水滋养身体。 20、一草一木要爱惜，环境生活创佳绩。 21、落实环境职责，完善环保制度。 22、既要金山银山，更要青山绿水。 23、树立企业形象，协调人与自然。 24、我们期待世界更蓝的天空，期待你灿烂的微笑，期待社会自由的财富。 25、悠然一心，财富自由。 26、争做环保使者，共创绿色礼貌。 27、改善生态环境，营造绿色家园。 28、节能为环保，财富又自由。 29、环保创造健康，财富携手自由。 30、我们所拥有的不仅是财富，还有干净的水滋养身体。 31、财富我创造，自由交给你，享受健康，享受绿色，享受美好生活。 32、绿色与生命共存，健康与财富共进。 33、环保又健康，财富享自由。 34、你我环保，一齐健康，共创财富，共享自由。 35、树环保意识，创健康财富。 36、创意节能环保，缔造健康生活，共创幸福财富，分享快乐自由。
龙源期刊网 https://www.doczj.com/doc/fa1025980.html, 乡村小学语文小班化教学策略研究 作者：仇家凤 来源：《文理导航》2020年第06期 【摘要】随着城镇化进程加快，大量农民向城镇转移，农村学生数减少，小班化教学成为现实。本文针对这一背景，就语文小班化教学的策略进行探讨，希望促进小学语文教学效果的提升。 【关键词】乡村小学;小班化教学;教学策略 近年来国内经济的快速发展吸引越来越多的农村劳动力进入城市谋取工作和发展机会。与此同时，农村学校的生源在逐渐减少，造成这种情况的原因一方面是由于国内长期以来施行的计划生育政策，另一方面务工人员将自己的子女带入城市，以此可以让他们享受到城市里良好的教育条件和环境。上述情况从客观上导致农村学校的适龄学生流失率越来越高，原来的大班在容量上逐渐缩减为小班，甚至是几名学生。农村教师在适应了之前的大班授课后，不得不面对目前农村学校这种急剧变化的教育情况，尤其是作为小学教育主课程的语文科目，其教学人员更需要考虑如何及时应对这些变化。 一、树立小班化教学理念 小班化给教育教学带来了新的契机。语文教学中的小班教学在表面上是指在学生数量较少的班级中进行的语文教学活动，而从更深层次的内容上来说，这种语文教学小班化其实是一种教育方式和方法的发展趋势，更是一种教学理念的演进。为了真正实现学生在语文课堂中能够以主体地位来参与到语文教学活动的各个环节，语文教师要在这里充当好教学引导者的角色。要重视学生在教学中的个性化发展，多阅读一些有利于提升语文阅读能力的文章，同时还要去积极探索有益的教学方法和策略，多赋予孩子学习的主动性，以此激发学生在小班化语文教学活动中的想象力和创造力，实现教育对人的引领和改造作用。 二、增强学生学习自信，发掘学生潜能 课堂教学是师生互动最重要的舞台，“在教学互动中提升质量”是关键，“充分挖掘每一个孩子的潜能”是目标。要努力实现这一目标，必须做到充分尊重每个学生的能力差异。抓住学生的闪光点，在同学、家长面前表扬。讲究语言艺术，让学生感受被赏识的快乐，用真诚的微笑和期待的目光面对每一个孩子，帮助学生树立信心。 三、尊重差异，实施“分层教学”
第三专题 生物圈中的绿色植物 一、绿色植物与生物圈的水循环 [知识网络结构] 水就是植物体的重要组成成分 原因 水保持植物直立的姿态,有利于进行光合作用 1、绿色植物的生活需要水 无机盐只有溶解在水中,才能被吸收与运输 水影响植物的分布:降水量大的地方,植被茂密 根吸水的部位:主要就是根尖成熟区, 吸水 成熟区的特点:生有大量根毛,增大根吸水的表面积 2、水分进入植物体内的途径 途径:木质部的导管 水分的运输 方向:自下而上 树皮:韧皮部中有筛管,输导有机物 茎的结构 形成层:细胞能分裂(木本植物有此结构) 木质部:有导管,输导水分与无机盐 实验:观察叶片的结构(练习徒手切片) 表皮(上、下表皮) 叶片的结构 叶肉 叶脉 重要结构:气孔,就是植物蒸腾失水的门户,也就是气体交换的窗口,由成对的保卫细 胞围成,气孔的开闭由保卫细胞控制。当保卫细胞吸水膨胀时,气孔张开, 当保卫细胞失水收缩时,气孔关闭。 概念:水分以气态从植物体内散发到体外的过程。 蒸腾作用 主要部位:叶片 降低了叶表面的温度 意义 促进对水与无机盐的运输 促进对水的吸收 绿色植物促进了生物圈中的水循环 绿色植物参与生物圈的水循环 提高大气湿度,增加降水量 保持水土 [课标考点解读] 绿色植物促进了生物圈中的水循环,因此保护森林与植被有非常重要的意义。本章重点阐明水就是绿色 植物生存的必要条件,水对植被的影响,植物吸水的主要部位及特点,水运输的途径,蒸腾作用的意义。在能力培养方面,通过解读数据,培养学生的探究能力。 [典型例题剖析] 例1、把发蔫的菠菜泡在清水中,菠菜又重新挺起来,这说明( ) A 、水就是光合作用的原料 B 、水就是溶解与运输物质的溶剂 C 、水能保持植物体固有的姿态 D 、水就是植物体重要的组成成分 [解析]:植物体内只有水分充足时,才能保持挺立的姿态,叶片才能舒展,有利于光合作用。本题没有数据说明水就是植物体的重要组成成分,也没有说明水就是如何作为溶剂来溶解无机盐的。本题考察学生对植物需水原因的分析与理解。答案:C 例2、下图所示,植物吸收水分的主要部位就是( ) [解析]:根尖成熟区就是吸水的主要部位,表皮细胞突起,形成大量根毛,大大增加了吸水的面积。本题主要考察学生识图的能力。答案:A 例3、3月12日就是我国的全民植树节,之所以选择这个时候,就是因为( ) A 、正值农闲时节 B 、土壤松散 C 、雨水较多 D 、叶没长出,蒸腾作用很弱 3、绿色植物参与生物圈的水循环
市生态环境绿色标杆企业创建 实施方案（试行） 为深入贯彻落实生态环境部《关于加强重污染天气应对夯实应急减排措施的指导意见》和《市打赢蓝天保卫战作战方案暨2018-2020年大气污染防治攻坚行动实施方案》，激励企业积极创建环保绿色标杆，主动减排，制定本方案。 一、总体要求 全面贯彻落实党的十九大精神和绿色发展理念，坚持“污染排放空间换时间”原则，鼓励企业切实承担污染治理主体责任，强化企业自我监管，积极落实各项减排措施。对达到绿色标杆标准的企业，在错峰生产和重污染天气应急（红色应急除外）期间，实行差别化管理，准予不停产、不限产，实现生产经营和污染减排的双赢。 二、实施范围 钢铁、焦化、炭素、陶瓷、玻璃、石灰窑、铸造、炼油与石油化工、制药、农药、涂料、油墨、工业锅炉、页岩砖、木业加工、表面涂装、家具、印刷（限书报刊、本册平板印刷、无VOCs排放的数字印刷）。（其他行业绿色标杆创建标准根据污染治理进程补充制定。） 三、创建要求 （一）基本要求 企业建设和运行有合法手续，上年度亩产效益评级为良好以上、 - 1 -
无重大环境投诉及群体性上访、未发生重大环境事故、没有被国家和省各类督察巡查发现问题并通报、无环境违法排污行为，按要求实现废气污染物排放在线监控，开展自行监测并实现信息公开，有完善的环保管理制度并有专职环保管理人员。 （二）行业创建标准 各行业创建标准见附件1。 四、豁免政策 对于列入错峰生产、重污染应急减排清单企业，达到绿色标杆企业创建标准要求的，在错峰生产、重污染应急（红色除外）期间免予停产、限产（国家和省明确规定必须执行停限产要求的除外）。 五、实施程序 采用企业自愿申报、县区审核、社会公示、市级核发的工作方式，开展生态环境绿色标杆企业认定工作。 （一）企业申报。按照企业自愿参与的原则，由企业向所在县区大气办提交绿色标杆企业申请表（见附件2，纸质版，A4纸打印并装订成册，一式三份）和电子版。 （二）县区审核。各县区大气办依据绿色标杆企业创建标准和豁免政策对申请表进行复核，筛选出符合条件、综合评价较高的绿色标杆企业。 （三）社会公示。对遴选出的绿色标杆企业，各县区大气办在官方网站和主流媒体进行公示，公示时间不少于5个工作日。对公示无异议的企业，报市大气办备案。 - 2 -
小学语文小班化教学案例 -----培养学生自主与合作学习能力的协调发展 一、案例背景 语文课程标准中指出：“倡导自主、合作、探究的学习方式”，由此可见，自主学习与合作探究的学习方式已成为课程改革的目标之一。那么，如何使自主学习与合作探究的学习方式在我们小班化课堂教学中有用地进行呢？通过自己的教学实践，我感到，教师要善于根据学生特点，为他们创设自主与合作学习的条件，才能确实使自主与合作学习落到实处，而不会是“看似课堂上热热闹闹，实则只是摆摆花架子而无实效性”的局面。下面，我就《我为你骄慢》一课的教学作了尝试。《我为你骄慢》是二年级下册一篇叙事性的文章，故事中的小男孩不小心打碎了老奶奶家的玻璃，当时害怕逃跑了，但后来用自己的行动取得老奶奶的原谅，老奶奶为小男孩感到骄慢。教学时，我给他们充分地自读自悟的机会，给他们个性化表达的机会，同时充分利用小班化小组学习的条件，进行组内合作学习，学会讨论、交流。 二、案例描述 1、解放读课文，要求读准字音、读通句子。 2、旁桌互认生字。 3、组长检查词语。 4、想想小男孩和老奶奶之间发生了什么事。根据下面的提示说一说：送报的小男孩，后来。老奶奶为小男孩感到。 （学生从自主学习到组内合作、交流，参与的主动性、积极性很高，学习气氛非常浓重。） 片段二：叙说故事情节； 1、默读课文1、2自然段，然后试着用自己的话向大家介绍“我打碎玻璃”的详尽经过。小组内练说，指名说。 2、引读第三自然段。
说话：我觉得很不自在，是因为。 生1：我觉得很不自在，是因为我打碎了老奶奶家的玻璃，难以为情见老奶奶。 生2：我觉得很不自在，是因为我担心老奶奶知道。 生3：我觉得很不自在，是因为我做了错事，老奶奶却还微笑着对我。 生4：我觉得很不自在，是因为我很后悔逃跑，感到良心不安。 3、默读四、五自然段，说说我是如何向老奶奶道歉的。 提供词语帮助说话： 三个星期过去了攒钱便条信封 xx悄悄地信箱松弛 小组内练说、指名说。 （通过叙说故事情节，让学生将课文的语言有用地迁移于自己的言语实践，这个要求对于中下层次的学生来说有难度，但是先让学生在小组内练习，让小组里会说的同学先说，能为中下层次的同学提供互助学习的机会，形成了一个优良的学习小环境。） 片段三：说话训练； 师：老奶奶为小男孩的什么而骄慢呢？ 生1：为他的厚道。 生2：为他的英勇。 师引导：这叫敢于承担责任。 生3：为他的知错就改。 师：当小男孩看到“我为你骄慢”的便条时是什么样的心情？
初中生物《生物圈中的绿色植物》单元教学设计以及思维导图1 《生物圈中的绿色植物》主题单元教学设计适用年级六年级 所需时间课内共用7课时，每周3课时 主题单元学习概述 本单元是山东科技出版社五四制，生物学六年级下册。本教材改变了以前教材过分强调学科体系完整性的状况，对分类学知识不再详细描述，降低了知识的难度，注重从学 生的生活经验出发，把提高学生的生物科学素养放在首位,重点是植物和生活环境相适应 的特征及在生物圈和人类的关系。 教材的知识编排结构是从生活环境、基本特征、在生物圈中的作用以及与人类的关系等几个方面进行讲述的，既可以对前面生物与环境相互影响的知识进一步巩固和深化， 又可以为后面学习绿色植物对生物圈的重大意义打下基础。本章节安排三节内容，“藻类、苔藓和蕨类植物和种子子植物，”这些植物放在一章内有利于学生对这三类植物的 特征进行横向的比较。 主题单元规划思维导图 主题单元学习目标 知识目标: (1)概述藻类、苔藓和蕨类植物的形态特征与生活环境。(2)了解藻类、苔藓和蕨类植物对生物圈的作用及与人类的关系。(3)知道种子的结构，明白玉米种子和菜豆种子的区别。(4)了解种子植物分为被子植物和裸子植物的依据并能够举例。能力目标: (1)通过对图片的观看、实物的观察，培养和训练观察能力和思维能力。 (2)通过讨论交流和展示，培养团队协作和归纳表达能力。情感态度与价值观: (1)关注生物圈中各种绿色植物及其生存状况，增强同学们的环保意识。 (2)通过展示交流，树立自信自强心。 对应课标:
1.初步具有收集、鉴别和利用课内外的图文资料及其他信息的能力。 2.关注绿色植物的生存状况，形成环保意识。 3.描述细胞分裂的基本过程。 4.描述各类植物的主要特征和生活环境。 5.说出植物在自然界的作用和人类的关系。 主题单元问题设 生物圈中有哪些绿色植物, 计 专题一:藻类植物 (2课时) 专题二:苔藓和蕨类植物 专题划分 (2课时) 专题三:种子植物 (3课时) 专题一专题一藻类植物 所需课时本专题使用2课时 专题一概述 本专题内容在整个单元中起到引导的作用。通过本专题的学习，学生能够知道藻类植物的基本特征和生活环境，明白藻类植物在自然界中的作用及人类对藻类植物的利用。 专题学习目标 知识目标: 概述藻类植物的主要特征和生活环境。 能力目标: 说出藻类植物在自然界中的作用和与人类的关系。 情感态度价值观: 关注藻类植物的生存现状，形成环保意识。
绿色企业行动宣传标语 标语，绿色企业行动宣传标语 1、绿色发展，有你才有意义，绿色建设，有你才更完美。 2、环保不分民族，生态没有国界。 3、绿色环保构建美好家园，优质服务打造精致企业。 4、碧水蓝天是我家，绿色生产靠大家。 5、青山绿水要靠你我他共同来维护。 6、打造一流绿色企业，为美好生活加油。 7、美丽油田，我是行动者。 8、落实绿色发展，央企责无旁贷。 9、树立水务形象，协调生产与水。 10、绿色企业，绿色家园，绿色企业，绿色中国。 11、做好环保每一处，携手共护水乡缘。 12、山不言，默背负；水不语，静容纳；绿水青山美石化。 13、树立绿色形象，协调生产与水。 14、保护环境光荣，污染环境可耻。 15、少开车，多步走，活到九十九。 16、石化应有自己的色彩。 17、践行绿色发展理念，守护美丽水乡油田。 18、守护水乡油田，奉献绿色能源。 19、绿色科技，人文内涵——中石化，可持续发展的践行者 20、倡低碳减排之风，走持续发展之路。 21、绿化美化净化看石化，靠你靠我靠他靠大家。 22、让我们与绿色同行，让绿色与我们共生。 23、绿色采购绿色供应，转型发展新愿景。 24、做好维护保养，杜绝跑冒滴漏。 25、垃圾分类，达标排放；保护环境，造福人民。 26、坚持企业优化，促进环境保护。
27、与绿色拥抱，生活更美好。 28、回家吧，回到绿色生产的美好。 29、环保是健康之基，绿色是和谐之源 30、坚持水务发展，促进环境保护。 31、用我们的双手，描绘绿色的家园。 32、绿色成就石化。 33、绿色环保低碳行，节能创效做先锋。 34、低碳环保，绿色生产，我们一直在行动。 35、保护石化环境，共建绿色家园。 36、守护蓝天白云，碧水青山，绿色石化等你回家。 37、万绿丛中一点“石化”。 38、汽油柴油，不如绿水长流；春风十里，不如绿色有你。 39、足下留一寸，换来四时春。 40、让中国石化阳光普照，让绿色企业神圣美妙。 41、水乡油田我的家，绿色生产人人夸。 42、绿色石化福社会，青山绿水笑开颜。 43、建优美环境，筑优良业绩，做优秀社管人。 44、让家园更美，让生活更好。 45、绿色发展，科技创新——中石化，带您畅享低碳生活。 46、垃圾分类回收是物有价值，分类投放是人有素质。 47、共建青山绿水，共享幸福安康。 48、聚焦碧水蓝天净土心动，攻关安全环保节能技术。 49、爱的魔力转圈圈，绿色生产让人心花怒放不知疲倦。 50、手牵手维护绿色家园，心连心构筑和谐石化。 51、爱护环境，是我们每一位石油人应尽的责任。 52、发展诚可贵，效益价更高；若为环保故，两者皆可抛。 53、开发资源立足绿色生态，油气稳产呵护碧水蓝天。 54、石化实说：我喜欢绿色。 55、将绿色进行到底，让绿荫遍布天下。
小班化语文教学案例——《清平乐村居》 【设计理念】 在课程标准的理念指导下，结合小班化教学的特点，本课的教学设计力求体现：1、师生、生生的互动。2、教学与活动相结合。3、面向全体，异质教学。4、针对个体，同质活动。 【教学内容】 《清平乐村居》是小学语文五年级上册的一篇课文。课文描绘了一幅充满农村生活气息的田园图景。词的上阕长短句相间，而下阕句式整齐，每句韵脚相同，节奏感强。全词描绘了南方一户农家生活劳动的场景：二老融洽，孩子孝顺，老有所养，少有所事，温馨、淳朴，自然。 【学习目标】 １．正确、流利、在感情地朗读课文，在读中感悟田园生活的意境。使学生从中受到美的熏陶；背诵课文。 ２．学会本课５个生字。理解由生字组成的词语。 ３．初步了解词的有关知识。 ４．理解这首词的意思。想象这首词所描绘的情景，并在说的基础上写下来。 【学习小组的建构】 本课的学习小组先采用异质组合的分组法，再采用异质组队的分组法。根据各项语文学习能力（思维能力、朗读能力、书写能力、口语表达能力等）的强弱进行组合。本班共有24人，分为6组，每组4人，分别为1,2,3,4号。把1、2、3、4号同学，在异质组合的分组法中1、2、3、4号同学作为学习伙伴，其中1号为本小组组长，语文阅读，书写等综合能力较强，2号为本小组中相对较弱的同学，3,4号属于中等水平。在异质组队的分组法所有1号的同学座位一组，所有2号的同学也作为一组，所有3号一组，所有4号一组为一组。 【教学过程】 一．导入新课 1.、师：读读我们以前学过的课文，也有一种情趣，我们二年级学过词串： 金秋烟波水乡 芦苇菱藕荷塘 夕阳归舟渔歌 枫叶灯火月光
《新课标下高中数学概念教学的实践与研究》 课题开题报告 浙江温州第二十二中学高洪武325000 一、课题提出的背景及现实意义 新一轮课程改革已经在全国部分省市如火如荼地开展，为了进一步扩大普通高中新课程实验范围，教育部决定从2006年秋季起，福建、浙江、辽宁和安徽4省将全面进入普通高中新课程实验。这将意味着我省教师将真正意义上进入新课程教学的实践与研究了。作为高中数学教师，理所当然将在这一实验过程中扮演着重要的角色。在新课程理念下，对构建数学理论大厦的数学概念如何实施教学是摆在每一位老师面前的一个严峻的课题。 高中数学课程标准指出：数学教学中应加强对基本概念和基本思想的理解和掌握，对一些核心概念和基本思想要贯穿高中数学教学的始终，帮助学生逐步加深理解。长期以来，由于受应试教育的影响，不少数学教师重解题、轻概念造成数学解题与概念脱节、学生对概念含混不清，一知半解，不能很好地理解和运用概念。数学课堂变成了教师进行学生解题技能培训的场所；而学生成了解题的机器，整天机械地按照老师灌输的“程序”进行简单的重复劳作。严重影响了学生思维的发展，能力的提高。这与新课程大力倡导的培养学生探究能力与创新精神已严重背离。那么在新课标下如何才能帮助学生更好、更加深刻地理解数学概念；如何才能灵活地应用数学概念解决数学问题，我想关键的环节还是在于教师如何实施数学概念教学，为此“新课标下高中数学概念教学的实践与研究”课题在这样的背景下应运而生。 二、国内外关于同类课题的研究综述和课题研究的理论依据 1.国内外关于同类课题的研究综述： 国内外关于数学概念教学理论研究是比较多的，对于一些概念课授课方法也是有研究的。但是那些理论的得出和经验的总结都是特定教育环境下的产物；而对于今天所推进的新课程实验（特别是在我国刚刚开始实施阶段），高中数学概念教学理论研究还几乎是一片空白。对于实践研究就更不足为谈了。 2. 课题研究的理论依据: 2-1 一般来说，数学概念要经历感知、理解、保持和应用四种心理过程。数学概念教学主要依据有如下理论： （1）联结理论、媒介理论：联结理论把概念的掌握过程解释为各种特征的重叠过程，尤如用照相机拍摄下来的事物在底片上的重叠，能够冲洗出照片一样。即接受外界刺激然后做出相应的反应。而媒介理论认为内部过程存在一种媒介因素，并用它来解释复杂的人类行动。 （2）同化、顺应理论：皮亚杰认为，概念的掌握过程无非是经历了一个同化与顺应的过程；所谓同化，就是把新概念、新知识接纳入到一个已知的认知结构中去；所谓顺应，就是当原有的认知结构不能纳入新概念时，必须改变已有的认知结构，以适应新概念。 （3）假设理论：假设理论不同于联结理论把概念掌握的过程看成是一个消极被动的过程，并认为学生掌握概念是一个积极制造概念的过程。所谓积极制造概念的过程，就是根据事实进行抽象、推理、概括、提出假设，并将这一假设应用于日后遇到的事例中加以检验的
初中生物生物圈中的绿 色植物知识点 Company number【1089WT-1898YT-1W8CB-9UUT-92108】
第三单元 生物圈中的绿色植物 第一章 生物圈中有哪些绿色植物 1、绿色植物分为四大类群：藻类、苔藓、蕨类、种子植物 一、藻类、苔藓、蕨类植物 2、藻类、苔藓、蕨类植物的区别： 3、藻类，苔藓，蕨类植物的共同点：藻类，苔藓，蕨类植物都不结种子， 它们的叶片背面有孢子囊群，可产生孢子，称为孢子植物，孢子是一种生殖细胞，在温暖潮湿的地方才能萌发和生长，所以说孢子植物的生活离不开水。 4.藻类植物：“春水绿于染” 5.藻类植物既有单细胞，也有多细胞。既有生活在淡水中，也有海水中。 6.多细胞藻类植物整个身体浸没在水中，几乎全身都可以吸收水和无机盐。可以进行光合作用，但没有专门吸收和运输养料以及进行光合作用的器官。 藻类植物 苔藓植物 蕨类植物 生活环境 大多数生活在水中 阴湿陆地上 阴湿陆地上 形态结构特征 没有根、茎、叶的分化 矮小，有茎和叶的分化（茎中无导管，叶中无叶脉），根是假根 有根茎叶的分化，有输导组 织 与人类关 系 释放氧气 监测空气污染的指示植物 遗体形成煤 矿 常见种类 水绵，衣藻，海带等 墙藓，葫芦藓等 肾蕨，满江红等
7.藻类植物没有根茎叶的分化。 8.苔藓植物生存在阴湿环境中。有类似根和茎的分化，但是茎中没有导管，叶中没有叶脉，根很简单，称为假根，具有固定作用。 9.苔藓植物可作为监测空气污染程度的指示植物。 10.蕨类植物：有根茎叶的分化，具有输导组织。有些蕨类植物比较高大。 11.蕨类植物用处：①卷柏、贯众可药用②满江红是一种优良绿肥和饲料③蕨类植物遗体层层堆积，经过漫长年代、复杂变化，逐渐变成了煤。 12.藻类植物，苔藓植物，蕨类植物，生殖依靠孢子，所以也被统称为孢子植物。 第二节 二、种子植物 1.、种子的结构 菜豆种子：种皮、胚(胚芽、胚轴、胚根、2片子叶)【双子叶植物，网状叶脉】 玉米种子：果皮和种皮、胚(胚芽、胚轴、胚根、1片子叶)、胚乳【单子叶植物，平行叶脉】 种皮：保护里面幼嫩的胚。 胚：新植物体的幼体，由胚芽（发育成茎和叶）、胚轴（发育成连接根和茎的部位）、胚根（发育成根）和子叶组成。胚乳不是胚的结构。 2、子叶和胚乳里有营养物质，供给胚发育成幼苗。 3、菜豆种子中与子叶相连的结构是胚轴，玉米种子中滴加碘液变蓝的结构 是胚乳，说明胚乳中含有淀粉。
企业环保标语口号 导读：本文是关于标语大全的文章，如果觉得很不错，欢迎点评和分享！ 1、节能为环保，财富为健康。 2、争做环保使者，共创绿色文明。 3、环保创造健康，财富携手自由。 4、支持环保，别让你的健康与财富自由流失。 5、为环保献力，为自己添富。 6、环保进万家，财富赢天下。 7、绿色的，健康的；节能的，世界的。 8、环保障，自然情，人康健，子孙福。 9、以美与人，用善待己。 10、人与自然需要和谐共存。 11、保护生态环境，倡导礼貌新风。 12、践行环保理念，扞卫健康生活。 13、保护环境，保存希望。 14、环保新主义，财富由你创，健康自然来。 15、健康环保，畅享自由财富。 16、青山常在，绿水常流。 17、生态环保，节能先锋，享受生活。 18、共创绿色世界，自由追寻梦想。
19、保护环境，持续发展。 20、这天节约一滴水，留给后人一滴血。 21、守护健康人生，畅享财富自由。 22、产品买环保，处理少烦恼。 23、全面建设小康社会，同心共创完美家园。 24、需求无限，资源有限；善用有限，发展无限。 25、有限的资源，无限的循环。 26、以法保护自然环境，以德建立社会礼貌。 27、环保生活，健康财富。 28、做良心企业，为您的完美生活的保驾护航。 29、改善环境，创建美好未来是我们共同的愿望。 30、欣赏荒野、回归自然。 31、天蓝水清，地绿居佳。 32、心飞翔，身康健，天下一片绿色。 33、与环保同行，与财富共进。 34、用心迎接挑战，实现持续发展。 35、环保畅享绿色人生，健康乐活财富自由。 36、做世界一流环保产品，让地球人都身体康健，给财富自由的翅膀。 37、环保健康手牵手，财富自由心连心。 38、绿色是性命之源，绿色是人类之根。 39、美好的环境来自我们每个人的珍惜和维护。
姓名 __________ 班级 _____________________ 一、选择题 3.春季玉米播种后，接着下了一场大雨，土壤长时间浸水结果玉米出苗很少，其 原因主要是 A. 土壤中养分流失 B. 土壤的派度过低 C. 土壤中水分不足 D. 土壤中空气不足 9. 百色市右江河谷是全国着名的亚热带水果基地、 南菜北运基地和“芒果之乡”， 盛产芒果、荔枝等名优水果。芒果、甜美多汁的芒果肉和芒果种子分别是由花的 哪些结构发育而来的 4.一粒小小的种子能长成参天大树，主要是因为种子中具有 A. 胚芽 B .胚 C.胚乳 7?图1为桃花的结构示意图，图中④ 在受精作用完成后，将发育成 A .种子 B .种皮 C. 果实 D.果皮 9. 农业生产中的施肥，主要为农作物的生长提供 A .有机物 B .水 C.无机盐 D. 氧气 10. 呼吸作用的实质是 A .分解有机物，释放能量 B .合成有机物，释放能量 C.分解有机物，贮存能量 D.合成有机物，贮存能量 11. 自然界中，被称为“天然的碳氧平衡器”的生物是 A .植物 B .动物 C.病毒 D.细菌和真菌 13. 植物体吸收和运输水分的主要结构分别是 A .根毛、导管 B .导管、根毛 C.根毛、根毛 D.导管、导管 14. “芒果、龙眼、荔枝”是百色市右江河谷盛产的名优水果，按植物的类群来分，它们都属于 A.子房、子房壁、胚珠 B. 子房壁、子房、胚珠 C. 子房、胚珠、子房壁 D. 胚珠、子房、子房壁 D.子叶 两 1
A.藻类植物 B.蕨类植物 C.裸子植物 D.被子植物 15. “人间四月芳菲尽，山寺桃花始盛开”。造成这一差异的非生物因素主要是
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小班化小学语文课堂教学模式 凤凰镇何田小学朱建平 小班化教学是建立在素质教育高标准，高要求的教育质量观和现代办学效益观基础上，充分发发挥“小班”本质特征的教学模式。现就有关教学策略方面浅谈几点体会。 一、教学方式的重组 在小班化教学模式中，师生之间的互动关系应得到增强和增加。 1、建立和谐的师生关系。教学是师生间交流沟通的过程，教师要和学生共同分享对教材的理解、课堂给予的快乐。教师的责任就是要成为学生学习的引导者、帮扶者和促进者。教师要转变教育观念，关心学生的心理需求，尊重学生的个性表达，营造一种平等宽容、健康和谐的课堂教学氛围。 2、营造浓郁学习氛围的教室环境。学生是课堂教学的主体，小班化教室环境的布置要以学生为本位，从有利于学生学习成长、有利于教师实施个别化教学去考虑。要把教室布置成为一个学习中心，营造浓郁的书香氛围。如可以在教室内悬挂励志格言、经典名句，张贴学生优秀作品，设立班级小书库，在课桌椅的排列上采取个体独立式或小组组合式，摆放成圆形、方框形、辩论型式、等等，以方便学生开展自学思考、课堂练习和进行一些互动沟通、讨论交流。 3、创设科学的教学情境。教师要注意采取各种方法激发学生强烈的求知欲望，引导学生迅速进入最佳语文学习状态，使他们在兴趣盎然的心理气氛中，跟着教师进入新知识的探索过程中。从教学需要出发，营造或创设与教学内容相适应的场景，力求生动、形象、有趣，以激发他们学习的兴趣，引起学生的情感体验，帮助学生迅速而正确地理解教材内容，促进儿童知识的、能力的、智力的、情感意志的尽可能大的发展。 二、自主探究策略 尊重和落实学生在课堂教学中的主体地位，注重学生在课堂内的自主探究，还学生以学习主动权，让学生有独立认知、思考的过程，是新课改的重要理念之
新课标下如何进行高中数学概念教学 发表时间：2011-01-26T17:01:56.810Z 来源：《少年智力开发报》2010年第9期供稿作者：杨昆 [导读] 如何在这一要求下进行数学概念教学？我认为抓好概念教学是提高数学教学质量的最关键的一环。 贵州省平塘民族中学杨昆 教师应该准确地提示概念的内涵与外延，使学生深刻理解概念，并在解决各类问题时灵活应用数学概念是新课标下数学概念的教学要求。因此正确理解数学概念，是掌握数学基础知识的前提。如何在这一要求下进行数学概念教学？我认为抓好概念教学是提高数学教学质量的最关键的一环。下面我从引入概念、解析概念、巩固概念三个方面谈谈对概念教学。 一、引入概念 概念教学中要引导学生经历从具体的实例抽象出数学概念的过程．因此引入数学概念就要以具体的典型材料和实例为基础，揭示概念形成的实际背景，要创设好的问题情境，帮助学生完成由材料感知到理性认识的过渡，并引导学生把背景材料与原有认知结构建立实质性联系．下面介绍几种引入数学概念的方法： 1.从实际生活中，引入新概念。 新课标强调“数学教学要紧密联系学生的生活实际”．在数学概念的引入上，尽可能地选取学生日常生活中熟悉的事例． 2.创设问题情境，引入新概念。 教师要善于恰当地创设趣味性、探索性的问题情境，激发学生概念学习的兴趣，使学生能够从问题分析中，归纳和抽象出概念的本质特征，这样形成的概念才容易被学生理解和接受。 3. 从最近概念引入新概念。 数学概念具有很强的系统性。数学概念往往是“抽象之上的抽象”，先前的概念往往是后续概念的基础，从而形成了数学概念的系统。公理化体系就是这种系统性的最高反映。教学中充分利用学生头脑中已有的知识与相关的经验引入概念，使相应的具体经验升华为理性认识，不仅能使学生准确地理解概念的形式定义，而且有利于建立起关于概念的恰当心理表征。使学生对知识的积累变成对知识的融合。 二、解析概念 生动恰当的引入概念，只是概念教学的第一步，，要使学生真正掌握新概念，还必须多角度、多方位的解析概念。对概念理解不深刻，解题时就会出现这样或那样的错误，要正确而深刻地理解一个概念并不是一件容易的事，教师要根据学生的知识结构和能力特点，从多方面着手，适当地引导学生正确地分析解剖概念，充分认识概念的科学性，抓住概念的本质。因此，教师要充分利用概念课，培养学生的能力，训练学生的思维，使学生认识到数学概念，既是进一步学习数学的理论基础，又是进行再认识的工具。为此，我们可以从以下几个方面努力，加深对概念的理解。 1.用数学符号语言解析概念。数学教学体现了数学语言的特点，数学语言无非是文字叙述、符号表示、图形表示三者之间的转换，当然要会三者的翻译，同时更重要的是强调符号感。引进数学符号以后，应当引导学生把符号与它所代表的实质内容联系起来，使学生在看到符号时就能够联想起符号所代表的概念及其本质特征。事实上，如果概念的符号能够与概念的实质内容建立起内在联系，那么，符号的掌握可以提高学生的抽象能力、概括能力。数学中的逻辑推理关键就在于能够合理、恰当地应用符号，而这又要依靠对符号的实质意义的把握。在概念学习中，形式地掌握符号而不懂得符号的本质涵义的情况是经常发生的，这时符号将使知识学习产生困难，导致数学推理的错误。 2.用图形语言解析概念。数与形的结合是使学生正确理解和深刻体会概念的好方法，数形结合妙用无穷，教学中凡是“数”与“形”能够结合起来讲的，一定要尽量结合起来讲。 3.逆向分析，加深对概念的理解。人的思维是可逆的，但必须有意识地去培养这种逆向思维活动的能力。对某些概念还应从多方面设问并思考。 4.讲清数学概念之内涵和外延，沟通知识的内在联系。概念反映的所有对象的共同本质属性的总和，叫做这个概念的内涵，又称涵义。适合于概念所指的对象的全体，叫做这个概念的外延，又称范围。 5.揭示概念与概念之间的区别与联系,使新概念与已有认知结构中的有关概念建立联系,把新概念纳入到已有概念体系中,同化新概念。教学中，应将相近、相反或容易混淆的概念放到一块来对比讲解，从定义、图形、性质等各方面进行分析对比，从而正确理解把握概念.。 三、巩固概念 学生认识和形成概念，理解和掌握之后，巩固概念是一个不可缺少的环节。巩固的主要手段是多练习、多运用，只有这样才能沟通概念、定理、法则、性质、公式之间的内存联系。我们可以选择概念性、典型性的习题，加强概念本质的理解，使学生最终理解和掌握数学思想方法。例如，当学习完“向量的坐标”这一概念之后，进行向量的坐标运算，提出问题：已知平行四边形ABCD的三个顶点ABC的坐标分别是(1,2),(2,4),(0,2),试求顶点D的坐标。学生展开充分的讨论，不少学生运用平面解析几何中学过的知识（如两点间的距离公式、斜率、直线方程、中点坐标公式等），结合平行四边形的性质，提出了各种不同的解法，有的学生应用共线向量的概念给出了解法，还有一些学生运用所学过向量坐标的概念，把点D的坐标和向量CD的坐标联系起来，巧妙地解答了这一问题。学生通过对问题的思考，尽快地投入到新概念的探索中去，从而激发了学生的好奇以及探索和创造的欲望，使学生在参与的过程中产生内心的体验和创造。除此之外，教师通过反例、错解等进行辨析，也有利于学生巩固概念。 总之，在中学数学概念的教学中，只要针对学生实际和概念的具体特点，注重引入，加强分析，重视训练，辅以灵活多样的教法，使学生准确地理解和掌握概念，才能更好地完成数学概念的教学任务，从而有效地提高数学教学质量。