光力学腔中的正交模劈裂、非线性多稳与量子纠缠特性
|
摘要
随着半导体材料学与实验工艺的快速发展，人们已经将光力学系统微型化到微纳尺度，这使得纳米力学振子的量子效应越来越明显。为了考察纳米力学振子的量子效应，人们尝试着利用各种方法将纳米力学振子冷却，目前已经能将纳米力学振子冷却到105K。纳米力学振子冷却以后，为了给出量子世界到经典世界过渡的清晰图像和出于对量子计算和量子信息以及量子非破坏性测量的重要意义的考虑，人们又把工作重点转移到操控纳米力学振子量子态的研究上。本文针对三个不同的腔光力学系统分别研究了系统的正交模劈裂，非线性多稳和量子纠缠特性。
首先，基于微磁盘—波导光力学系统，当系统处于稳态时，我们研究了反作用耦合的二次项对正交模劈裂的影响。通过数值模拟我们发现，当泵浦场较弱时，反作用耦合的二次项对正交模劈裂几乎没有影响。此时，反作用耦合的二次项可以被安全的忽略。当泵浦场足够强时，我们发现随着反作用耦合的二次项系数的增大，正交模劈裂产生的低频模斯托克斯场会向更低频率方向移动，而正交模劈裂产生的高频模斯托克斯场几乎不发生改变。另外，我们也发现，发生在泵浦场，正交模劈裂产生的低频模斯托克斯场和纳米量级的波导振子之间的四波混频过程更加高效。当泵浦场足够强并有较大的反作用耦合的二次项系数出现时，我们发现，由于四波混频过程泵浦场的能量能够有效地转移给正交模劈裂产生的低频模斯托克斯场和混频产生的反斯托克斯场，所以正交模劈裂产生的低频模斯托克斯场和混频产生的反斯托克斯场可以获得相对较大的振幅。
其次，基于原子辅助光力学系统，在非弱腔场近似下，我们研究了构成系统的纳米力学振子，量子化腔场和被束缚在腔内的原子的稳态行为。通过数值模拟我们发现，当最初的腔频大于原子的跃迁频率而其它相关参数确定时，系统存在三个分支的稳态解。相反，则系统仅有一个分支的稳态解。另外，当腔内含大量光子（少量光子）时，在系统三个分支的稳态解同时存在的区域内，弱腔场近似会导致第一个分支和第二个分支的稳态解出现较大的偏差（偏差可以忽略）。有趣的是，在最初的腔频大于原子的跃迁频率的区域内，系统的第一个分支的稳态解（不包含原子的极化率）将表现出双稳行为。当相关参量确定时，通过改变驱动场的功率和泵浦场与原子间的耦合强度，可以控制第一个分支的稳态解的双稳行为。造成系统存在多个分支的稳态和第一个分支的稳态具有双稳行为的根本原因是在量子化的腔场—原子—纳米力学振子间存在有效的反馈。
最后，基于量子阱辅助光力学系统，在系统处于稳态时，我们研究了构成系统的三个子系统量子阱内激子，腔场和纳米力学振子中任意两个子系统之间的两体纠缠，并重点考察了构成系统的非直接相互作用的量子阱内激子和纳米力学振子之间的两体纠缠。通过数值模拟我们发现，当相关参数确定腔场与驱动场的反斯托克斯边带共振以及量子阱內激子与驱动场的斯托克斯边带共振时，三个可能的两体纠缠同时存在，其中激子—纳米力学振子两体纠缠是最大的。随着环境温度的升高，激子—纳米力学振子两体纠缠的最大值将逐渐变小，在温度达到T≈20K时，纠缠将会消失。随着纳米力学振子质量的增加，激子—纳米力学振子两体纠缠的最大值将先增大然后再逐渐减小，在纳米力学振子质量m≈100ng时，纠缠将会消失。随着驱动场输入功率的增加，纳米力学振子—激子两体纠缠的最大值也先增大然后再减小。另外，当相关参数确定腔场与驱动场的反斯托克斯边带近共振以及量子阱內激子与驱动场的斯托克斯边带近共振时，在由失谐形成的椭圆面区域内，激子—纳米力学振子两体纠缠保持同一最大值。当相关参数确定腔场与驱动场的反斯托克斯边带共振以及量子阱內激子与驱动场的斯托克斯边带共振时，在由最佳质量附近变化的纳米力学振子质量和最佳功率附近变化的驱动场功率形成的梯形面区域内，激子—纳米力学振子两体纠缠保持同一最大值。
我们预期关于正交模劈裂的相关结果对纳米力学振子冷却方案的设计和深入的理解纳米力学振子的冷却机制将有重要意义。非线性多稳的相关结果对利用光学方法探测纳米力学振子的稳态和基于光力学系统的非线性现象的研究将有潜在的应用价值。量子纠缠的相关结果对揭示量子世界到经典世界的过渡和对给量子计算和量子信息以及量子非破坏性测量提供特殊量子态的载体将会十分有益。
With the rapid development of semiconductor materials and experimentalprocess, the optomechanical system has been microminiaturized up to micrometeror nanometer scales, which makes the quantum effect of the nanomechanicalresonator more obvious. To observe the quantum effect of the nanomechanicalresonator, some people try to cool the nanomechanical resonator in various ways,and so far the lower temperature105Khas been reached. After cooling of thenanomechanical resonator, since the quantum state plays an important role in thequantum computation and quantum information and the quantum non-demolitionmeasurement, so that some people want to control the quantum state of thenanomechanical resonator in order to show the clear picture from the quantumworld to the classical world. In the context of the above expression, we study thenormal mode splitting, nonlinear multistability, and quantum entanglement basedon three different optomechanical systems in this paper, respectively.
First, we study the effect from the quadratic term of the reactive coupling onthe normal splitting when the microdisk-waveguide optomechanical system issteady state. With the help of the numerical simulation, we find that the normalmode splitting is not sensitive to the quadratic term for a weak pump field, so thequadratic term can be safely neglected. When the pump field is strong enough, wefind that the generated lower-frequency Stokes mode moves to the more lowerfrequency and the generated higher-frequency Stokes mode dose not almostchange with the coefficient of the quadratic term increasing. In addition, we alsofind that the four-wave-mixing process is more efficient among the pump field,the generated lower-frequency Stokes mode, and the waveguide-resonator. When the pump field is strong enough, we find the amplitudes of the generatedlower-frequency Stokes mode and the anti-Stokes field originating from thefour-wave-mixing will be amplified for the large coefficient of the quadratic termof the reactive coupling due to the efficient energy transfer from the pump field.
Second, beyond the weak cavity field approximation we study the steady-state behaviors for the nanomechanical resonator, the quantified cavity field, andthe cold atoms confined in the cavity, respectively. With the help of the numericalsimulation, under the relevant parameters determined we find that three branchesof steady-state solutions exist for the system when the original cavity frequency islarger than the transition frequency of the atom. On the contrary, only one branchof steady-state solutions emerges. In addition, when there are a lot of photonsinside the cavity the weak cavity field approximation will results in the largeerrors for the first and second branches of steady-state solutions in the regionswhere three branches of steady-state solutions simultaneously exist. In particular,the first branch of steady-state solutions will show the bistable behaviordepending critically on the coupling intensity between the pump field and theatom and the driving power. The above results should be attributed to an effectivefeedback mechanism originating from the strong coupling betweenatom-light-resonator interactions.
Finally, when the quantum-well-assisted optomechanical system is steadystate, we study the bipartite entanglement among the exciton in the quantum well,the cavity field, and the nanomechanical resonator, especially the bipartiteentanglement between the exciton and the nanomechanical resonator. And theinteraction between the exciton and the nanomechanical resonator is indirect.With the help of the numerical simulation, under the relevant parametersdetermined we find that three bipartite possible entanglements will together existand the bipartite entanglement between the exciton and the nanomechanical resonator reaches its maximal value when the cavity field resonates with theanti-Stokes sideband of the driving field and the exciton resonates with the Stokessideband of the driving field. And we also find that the maximal value for thebipartite entanglement between the exciton and the nanomechanical resonatorgradually decreases with the temperature increasing and finally vanishes whenT≈20K. Further, we also find that the maximal value for the bipartiteentanglement between the exciton and the nanomechanical resonator firstincreases then decreases with the nanomechanical resonator mass increasing andfinally vanishes when m≈100ng.The maximal value for the bipartiteentanglement between the exciton and the nanomechanical resonator depends onthe input power of the driving field in a similar way as the mass. In addition,under the relevant parameters determined, we find that the bipartite entanglementbetween the exciton and the nanomechanical resonator still remains the identicalmaximal value in the elliptic regions formed by the detunings, when the cavityfield approximately resonates with the anti-Stokes sideband of the driving fieldand the exciton approximately resonates with the Stokes sideband of the drivingfield. Under the relevant parameters determined, we also find that thenanomechanical resonator mass around the optimal mass and the driving poweraround the optimal driving power, make the maximal value of the bipartiteentanglement between the exciton and the nanomechanical resonator be equal toidentical maximal value, when the cavity field resonates with the anti-Stokessideband of the driving field and the exciton resonates with the Stokes sideband ofthe driving field.
We expect that the relevant results for normal mode splitting is significant todesign the proposal used to cool the nanomechanical resonator and to understandthe mechanism of nanomechanical cooling deeply. And, we also think that therelevant results for nonlinear multistability is potentially valuable to detect thesteady state of nanomechanical resonator by optical method and to study the nonlinear phenomenon based on the optomechanical system. Further, weanticipate that the relevant results for quantum entanglement is instructive toreveal the process from the quantum world to classical world and to provide thecarrier of quantum state for the quantum computation and quantum informationand quantum non-demolition measurement.
首先，基于微磁盘—波导光力学系统，当系统处于稳态时，我们研究了反作用耦合的二次项对正交模劈裂的影响。通过数值模拟我们发现，当泵浦场较弱时，反作用耦合的二次项对正交模劈裂几乎没有影响。此时，反作用耦合的二次项可以被安全的忽略。当泵浦场足够强时，我们发现随着反作用耦合的二次项系数的增大，正交模劈裂产生的低频模斯托克斯场会向更低频率方向移动，而正交模劈裂产生的高频模斯托克斯场几乎不发生改变。另外，我们也发现，发生在泵浦场，正交模劈裂产生的低频模斯托克斯场和纳米量级的波导振子之间的四波混频过程更加高效。当泵浦场足够强并有较大的反作用耦合的二次项系数出现时，我们发现，由于四波混频过程泵浦场的能量能够有效地转移给正交模劈裂产生的低频模斯托克斯场和混频产生的反斯托克斯场，所以正交模劈裂产生的低频模斯托克斯场和混频产生的反斯托克斯场可以获得相对较大的振幅。
其次，基于原子辅助光力学系统，在非弱腔场近似下，我们研究了构成系统的纳米力学振子，量子化腔场和被束缚在腔内的原子的稳态行为。通过数值模拟我们发现，当最初的腔频大于原子的跃迁频率而其它相关参数确定时，系统存在三个分支的稳态解。相反，则系统仅有一个分支的稳态解。另外，当腔内含大量光子（少量光子）时，在系统三个分支的稳态解同时存在的区域内，弱腔场近似会导致第一个分支和第二个分支的稳态解出现较大的偏差（偏差可以忽略）。有趣的是，在最初的腔频大于原子的跃迁频率的区域内，系统的第一个分支的稳态解（不包含原子的极化率）将表现出双稳行为。当相关参量确定时，通过改变驱动场的功率和泵浦场与原子间的耦合强度，可以控制第一个分支的稳态解的双稳行为。造成系统存在多个分支的稳态和第一个分支的稳态具有双稳行为的根本原因是在量子化的腔场—原子—纳米力学振子间存在有效的反馈。
最后，基于量子阱辅助光力学系统，在系统处于稳态时，我们研究了构成系统的三个子系统量子阱内激子，腔场和纳米力学振子中任意两个子系统之间的两体纠缠，并重点考察了构成系统的非直接相互作用的量子阱内激子和纳米力学振子之间的两体纠缠。通过数值模拟我们发现，当相关参数确定腔场与驱动场的反斯托克斯边带共振以及量子阱內激子与驱动场的斯托克斯边带共振时，三个可能的两体纠缠同时存在，其中激子—纳米力学振子两体纠缠是最大的。随着环境温度的升高，激子—纳米力学振子两体纠缠的最大值将逐渐变小，在温度达到T≈20K时，纠缠将会消失。随着纳米力学振子质量的增加，激子—纳米力学振子两体纠缠的最大值将先增大然后再逐渐减小，在纳米力学振子质量m≈100ng时，纠缠将会消失。随着驱动场输入功率的增加，纳米力学振子—激子两体纠缠的最大值也先增大然后再减小。另外，当相关参数确定腔场与驱动场的反斯托克斯边带近共振以及量子阱內激子与驱动场的斯托克斯边带近共振时，在由失谐形成的椭圆面区域内，激子—纳米力学振子两体纠缠保持同一最大值。当相关参数确定腔场与驱动场的反斯托克斯边带共振以及量子阱內激子与驱动场的斯托克斯边带共振时，在由最佳质量附近变化的纳米力学振子质量和最佳功率附近变化的驱动场功率形成的梯形面区域内，激子—纳米力学振子两体纠缠保持同一最大值。
我们预期关于正交模劈裂的相关结果对纳米力学振子冷却方案的设计和深入的理解纳米力学振子的冷却机制将有重要意义。非线性多稳的相关结果对利用光学方法探测纳米力学振子的稳态和基于光力学系统的非线性现象的研究将有潜在的应用价值。量子纠缠的相关结果对揭示量子世界到经典世界的过渡和对给量子计算和量子信息以及量子非破坏性测量提供特殊量子态的载体将会十分有益。
With the rapid development of semiconductor materials and experimentalprocess, the optomechanical system has been microminiaturized up to micrometeror nanometer scales, which makes the quantum effect of the nanomechanicalresonator more obvious. To observe the quantum effect of the nanomechanicalresonator, some people try to cool the nanomechanical resonator in various ways,and so far the lower temperature105Khas been reached. After cooling of thenanomechanical resonator, since the quantum state plays an important role in thequantum computation and quantum information and the quantum non-demolitionmeasurement, so that some people want to control the quantum state of thenanomechanical resonator in order to show the clear picture from the quantumworld to the classical world. In the context of the above expression, we study thenormal mode splitting, nonlinear multistability, and quantum entanglement basedon three different optomechanical systems in this paper, respectively.
First, we study the effect from the quadratic term of the reactive coupling onthe normal splitting when the microdisk-waveguide optomechanical system issteady state. With the help of the numerical simulation, we find that the normalmode splitting is not sensitive to the quadratic term for a weak pump field, so thequadratic term can be safely neglected. When the pump field is strong enough, wefind that the generated lower-frequency Stokes mode moves to the more lowerfrequency and the generated higher-frequency Stokes mode dose not almostchange with the coefficient of the quadratic term increasing. In addition, we alsofind that the four-wave-mixing process is more efficient among the pump field,the generated lower-frequency Stokes mode, and the waveguide-resonator. When the pump field is strong enough, we find the amplitudes of the generatedlower-frequency Stokes mode and the anti-Stokes field originating from thefour-wave-mixing will be amplified for the large coefficient of the quadratic termof the reactive coupling due to the efficient energy transfer from the pump field.
Second, beyond the weak cavity field approximation we study the steady-state behaviors for the nanomechanical resonator, the quantified cavity field, andthe cold atoms confined in the cavity, respectively. With the help of the numericalsimulation, under the relevant parameters determined we find that three branchesof steady-state solutions exist for the system when the original cavity frequency islarger than the transition frequency of the atom. On the contrary, only one branchof steady-state solutions emerges. In addition, when there are a lot of photonsinside the cavity the weak cavity field approximation will results in the largeerrors for the first and second branches of steady-state solutions in the regionswhere three branches of steady-state solutions simultaneously exist. In particular,the first branch of steady-state solutions will show the bistable behaviordepending critically on the coupling intensity between the pump field and theatom and the driving power. The above results should be attributed to an effectivefeedback mechanism originating from the strong coupling betweenatom-light-resonator interactions.
Finally, when the quantum-well-assisted optomechanical system is steadystate, we study the bipartite entanglement among the exciton in the quantum well,the cavity field, and the nanomechanical resonator, especially the bipartiteentanglement between the exciton and the nanomechanical resonator. And theinteraction between the exciton and the nanomechanical resonator is indirect.With the help of the numerical simulation, under the relevant parametersdetermined we find that three bipartite possible entanglements will together existand the bipartite entanglement between the exciton and the nanomechanical resonator reaches its maximal value when the cavity field resonates with theanti-Stokes sideband of the driving field and the exciton resonates with the Stokessideband of the driving field. And we also find that the maximal value for thebipartite entanglement between the exciton and the nanomechanical resonatorgradually decreases with the temperature increasing and finally vanishes whenT≈20K. Further, we also find that the maximal value for the bipartiteentanglement between the exciton and the nanomechanical resonator firstincreases then decreases with the nanomechanical resonator mass increasing andfinally vanishes when m≈100ng.The maximal value for the bipartiteentanglement between the exciton and the nanomechanical resonator depends onthe input power of the driving field in a similar way as the mass. In addition,under the relevant parameters determined, we find that the bipartite entanglementbetween the exciton and the nanomechanical resonator still remains the identicalmaximal value in the elliptic regions formed by the detunings, when the cavityfield approximately resonates with the anti-Stokes sideband of the driving fieldand the exciton approximately resonates with the Stokes sideband of the drivingfield. Under the relevant parameters determined, we also find that thenanomechanical resonator mass around the optimal mass and the driving poweraround the optimal driving power, make the maximal value of the bipartiteentanglement between the exciton and the nanomechanical resonator be equal toidentical maximal value, when the cavity field resonates with the anti-Stokessideband of the driving field and the exciton resonates with the Stokes sideband ofthe driving field.
We expect that the relevant results for normal mode splitting is significant todesign the proposal used to cool the nanomechanical resonator and to understandthe mechanism of nanomechanical cooling deeply. And, we also think that therelevant results for nonlinear multistability is potentially valuable to detect thesteady state of nanomechanical resonator by optical method and to study the nonlinear phenomenon based on the optomechanical system. Further, weanticipate that the relevant results for quantum entanglement is instructive toreveal the process from the quantum world to classical world and to provide thecarrier of quantum state for the quantum computation and quantum informationand quantum non-demolition measurement.
引文
[1] NICHOLS EF，HULL GF. A preliminary communication on the pressure ofheat and light radiation [J]. Physical Review (Series I),1901,13:307-320.
[2] NICHOLS EF，HULL GF. The pressure due to radiation [J]. AstrophysicalJournal,1903,17:315-351.
[3] ASHKIN A. Applications of laser radiation pressure [J]. Science,1980,210:1081-1088.
[4] ASHKIN A, DZIEDZICJ M, BJORKHOLM J E, et al. Observation of a singlebeam gradient force optical trap for dielectric particles [J]. Optics Letters,1986,11:288-290.
[5] DORSEL A, MCCULLEN J D, MEYSTRE P, et al. Optical bistability andmirror confinement induced by radiation pressure [J]. Physical ReviewLetters,1983,51:1550-1553.
[6] ABRAMOVICI A, ALTHOUSE W E, DREVER R W P, et al. The laserinterferometer gravitational wave observatory [J]. Science,1992,256:325-333.
[7] CLELAND A N, ROUKES M L. Fabrication of high frequency nanometerscale mechanical resonators from bulk Si crystals [J]. Applied PhysicsLetters,1996,69:3653-2655.
[8] GUPTA A, AKIN D, BASHIR R. Single virus particle mass detection usingmicroresonators with nanoscale thickness [J]. Applied Physics Letters,2004,84:1976-1978.
[9] MARQUARDT F, HARRIS J G E, GIRVIN S M. Dynamical multistabilityinduced by radiation pressure in high finesse micromechanical opticalcavities [J]. Physical Review Letters,2006,96:103901-1-4.
[10] CARMON T, ROKHSARI H, YANG L, et al. Temporal behavior of radiation66pressure induced vibrations of an optical microcavity phonon mode [J].Physical Review Letters,2005,94:223902-1-4.
[11] CARMON T, CROSS M C, VAHALA KERRY J. Chaotic quivering ofmicron scaled on chip resonators excited by centrifugal optical pressure [J].Physical Review Letters,2007,98:167203-1-4.
[12] GONG Z R, IAN H, LIU YU X, et al. Kerr nonlinearity induced by anoscillating mirror in an optical cavity [J]. ArXiv,2011,0805.4102:1-10.
[13] HUANG S, AGARWAL G S. Reactive coupling can beat the motionalquantum limit of nanowaveguides coupled to a microdisk resonator [J].Physical Review A,2010,82:033811-1-5.
[14] SRINIVASAN K, STINTZ A, KRISHNA S, et al. Photoluminescencemeasurements of quantum dot containing semiconductor microdiskresonators using optical fiber taper waveguides [J]. Physical Review B,2005,72:205318-1-9.
[15] DUMEIGE Y, FéRON P. Whispering gallery mode analysis of phasematched doubly resonant second harmonic generation [J]. PhysicalReview A,2006,74:063804-1-7.
[16] CLELAND A N, GELLER M R. Superconducting qubit storage andentanglement with nanomechanical resonators [J]. Physical Review Letters,2004,93:070501-1-4.
[17] SABOONI M, LI Q, KR LL S, et al. Efficient quantum memory using aweakly absorbing sample [J]. Physical Review Letters,2013,110:133604-1-5.
[18] CHEN Y H, LEE M J, WANG I C, et al. Coherent optical memory with highstorage efficiency and large fractional delay [J]. Physical Review Letters,2013,110:083601-1-5.
[19] DING D S, WU J H, ZHOU Z Y, et al. Multimode image memory based on acold atomic ensemble [J]. Physical Review A,2013,87:013835-1-6.
[20] ZHANG X, KALACHEV A, KOCHAROVSKAYA O. Quantum storagebased on control field angular scanning [J]. Physical Review A,2013,87:013811-1-9.
[21] SHIM J H, NIEMEYER I, ZHANG J, et al. Room temperature high speednuclear spin quantum memory in diamond [J]. Physical Review A,2013,87:012301-1-6.
[22] VISCOR D, AHUFINGER V, MOMPART J, et al. Two color quantummemory in double-Λ media [J]. Physical Review A,2012,86:053827-1-6.
[23] GRODECKA G A, ZEUTHEN E, S. S RENSEN A. High capacity spatialmultimode quantum memories based on atomic ensembles [J]. PhysicalReview Letters,2012,109:133601-1-5.
[24] HIGGINBOTTOM D B, SPARKES B M, RANCIC M, et al. Spatial modestorage in a gradient echo memory [J]. Physical Review A,2012,86:023801-1-10.
[25] BENSKY G, PETROSYAN D, MAJER J, et al. Optimizing inhomogeneousspin ensembles for quantum memory [J]. Physical Review A,2012,86:012310-1-7.
[26] REIM K F, NUNN J, JIN X M, et al. Multipulse addressing of a ramanquantum memory: configurable beam splitting and efficient readout [J].Physical Review Letters,2012,108:263602-1-5.
[27] DOBRINDT J M, WILSON R I, KIPPENBERG T J. Parametric normalmode splitting in cavity optomechanics [J]. Physical Review Letters,2008,101:263602-1-4.
[28] ASBóTH J K, RITSCH H, DOMOKOS P. Optomechanical coupling in a onedimensional optical lattice [J]. Physical Review A,2008,77:063424-1-25.
[29] MURCH W K, MOORE L K, GUPTA S, et al. Observation of quantummeasurement backaction with an ultracold atomic gas [J]. Nature Physics,2008,4:561-564.
[30] BRENNECKE F, RITTER S, DONNER T, et al. Cavity optomechanics witha Bose Einstein Condensate [J]. Science,2008,322:235-238.
[31] SMITH H S M, LEROUX D I, ZHANG H, et al. Optomechanical cavitycooling of an atomic ensemble [J]. Physical Review Letters,2011,107:143005-1-4.
[32] HUANG W M, IRWIN K, TSAI S W, et al. Possible quantum phasemanipulation of a two leg ladder in mixed dimensional fermionic coldatoms [J]. Physical Review A,2013,87:031603-1-4.
[33] ZOHAR E, CIRAC J I, REZNIK B. Cold atom quantum simulator for SU(2)yang mills lattice gauge theory [J]. Physical Review Letters,2013,110:125304-1-5.
[34] ZHOU L, PU H, ZHANG W P. Anderson localization of cold atomic gaseswith effective spin orbit interaction in a quasiperiodic optical lattice [J].Physical Review A,2013,87:023625-1-7.
[35] CHEN Y H, LEE M J, WANG I C, et al. Coherent optical memory with highstorage efficiency and large fractional delay [J]. Physical Review Letters,2013,110:083601-1-5.
[36] CLERK A A, DEVORET M H, GIRVIN S M, et al. Introduction to quantumnoise, measurement and amplification [J]. ArXiv,2010,0810.4729-1-96.
[37] MARQUARDT F, CHEN J P, CLERKAA, et al. Quantum theory of cavityassisted sideband cooling of mechanical motion [J]. Physical ReviewLetters,2007,99:093902-1-4.
[38] MANCINI S, VITALI D, TOMBESI P. Optomechanical cooling of amacroscopic oscillator by homodyne feedback [J]. Physical Review Letters,1998,80:688-691.
[39] POGGIO M, DEGEN C L, MAMIN H J, et al. Feedback cooling of acantilever’s fundamental mode below5mK [J]. Physical Review Letters,2007,99:017201-1-4.
[40] ASPELMEYER M, MEYSTRE P, SCHWAB K. Quantum optomechanics [J].Physics Today,2012,65:29-35.
[41] TEUFEL J D, DONNER T, LI D, et al. Sideband cooling of micromechanicalmotion to the quantum ground state [J].Nature,2011,475:359-363.
[42] CHAN J, MAYER A T P, H. SAFAVI-NAEINI A, et al. Laser cooling of ananomechanical oscillator into its quantum ground state [J]. Nature,2011,478:89-92.
[43] H. SAFAVI-NAEINI A, CHAN J, T. HILL J, et al. Observation of quantummotion of a nanomechanical resonator [J]. Physical Review Letters,2012,108:033602-1-5.
[44] WANG Z H, TAKAHASHI S. Spin decoherence and electron spin bath noiseof a nitrogen vacancy center in diamond [J]. Physical Review B,2013,87:115122-1-6.
[45] LAMBERT J, C TéR. Quantum Hall ferromagnetic phases in the Landaulevel N=0of a grapheme bilayer [J]. Physical Review B,2013,87:115415-1-20.
[46] KONG J, OU Z Y, ZHANG W P. Phase measurement sensitivity beyond thestandard quantum limit in an interferometer consisting of a parametricamplifier and a beam splitter [J]. Physical Review A,2013,87:023825-1-6.
[47] G. DALLA TORRE E, OTTERBACH J, DEMLER E, et al. Dissipativepreparation of spin squeezed atomic ensembles in a steady state [J].Physical Review Letters,2013,110:120402-1-5.
[48] BUCHMANN L F, JING H, RAMAN C, et al. Optical control of a quantumrotor [J]. Physical Review A,2013,87:031601(R)-1-4.
[49] J. BARTLEY T, J. D. CROWLEY P, DATTA A, et al. Strategies forenhancing quantum entanglement by local photon subtraction [J]. PhysicalReview A,2013,87:022313-1-11.
[50] HEESE R, FREYBERGER M. Entropic uncertainty relation for pointerbased simultaneous measurements of conjugate observables [J]. PhysicalReview A,2013,87:012123-1-7.
[51] SHARYPOV A V, HE B. Generation of arbitrary symmetric entangled stateswith conditional linear optical coupling [J]. Physical Review A,2013,87:032323-1-6.
[52] CHOI R H, FORTESCUE B, GOUR G, et al. Entanglement sharing protocolvia quantum error correcting codes [J]. Physical Review A,2013,87:032319-1-7.
[53] C. TICHY M, MINTERT F, BUCHLEITNER A. Limits to multipartiteentanglement generation with bosons and fermions [J]. Physical Review A,2013,87:022319-1-17.
[54]曾谨言.量子力学卷I与量子力学卷II [M].北京：科学出版社，2007.
[55]喀兴林.高等量子力学[M].北京：高等教育出版社，2001.
[56] ZUREK W H. Decoherence, einselection, and the quantum origins of theclassical [J]. Reviews of Modern Physics,2003,75:715-775.
[57] JOSHI C, LARSON J, JONSON M, et al. Entanglement of distant opto-mechanical systems [J]. Physical Review A,2012,85:033805-1-11.
[58] MARI A, EISERT J. Gently modulating optomechanical Systems [J].Physical Review Letters,2009,103:213603-1-4.
[59] A. NIELSEN M, L.CHUANG I.量子计算与量子信息[M].北京：高等教育出版社，2003.
[60] PARK K, LEE S W, JEONG H. Quantum teleportation between particle likeand field like qubits using hybrid entanglement under decoherence effects[J]. Physical Review A,2012,86:062301-1-9.
[61] BOURDON P S, GERJUOY E. Overcoming a limitation of deterministicdense coding with a nonmaximally entangled initial state [J]. PhysicalReview A,2010,81:022314-1-11.
[62] KUMAR A, ADHIKARI S, BANERJEE S, et al. Optimal quantumcommunication using multiparticle partially entangled states [J]. PhysicalReview A,2013,87:022307-1-6.
[63] IMOTO N, HAUS H A, YAMAMOTO Y. Quantum nondemolitionmeasurement of the photon number via the optical Kerr effect [J]. PhysicalReview A,1985,32:2287-2292.
[64] JACOBS K, TOMBESI P, COLLETT M J, et al. Quantum-nondemolitionmeasurement of photon number using radiation pressure [J]. PhysicalReview A,1994,49:1961-1966.
[65] O. SCULLY M, ZUBAIRY M S. Quantum optics [M]. Cambridge:Cambridge University Press,1997.
[66] H. LOUSISELL W. Quantum statistical properties of Radiation [M].California: A Wiley-Interscience publication,1973.
[67] WALLS D F, MILBURN G J. Quantum Optics [M]. Berlin: Springer-VerlagBerlin Heidelberg,1997.
[68] LAW C K. Interaction between a moving mirror and radiation pressure: aHamiltonian formulation [J]. Physical Review A,1995,51:2537-254.
[69] VITALI D, GIGAN S, FERREIRA A, et al. Optomechanical entanglementbetween a movable mirror and a cavity field [J]. Physical Review Letters,2007,98:030405-1-4.
[70] BONIFACIO R, LUGIATO L A. Optical bistability and cooperative effects inresonance fluorescence [J]. Physical Review A,1978,18:1129-1144.
[71] SANDLE W J, GALLAGHER A. Optical bistability by an atomic vapor in afocusing Fabry-Perot cavity [J]. Physical Review A,1981,24:2017-2028.
[72] GRANT D E, KIMBLE H J. Optical bistability for two-level atoms in astanding-wave cavity [J]. Optics Letters,1982,7:353-355.
[73] ROSENBERGER A T, OROZCO L A, KIMBLE H J. Observation ofabsorptive bistability with two-level atoms in a ring cavity [J]. PhysicalReview A,1983,28:2569-2572.
[74] OROZCO L A, KIMBLE H J, ROSENBERGER A T, et al. Single-modeinstability in optical bistability [J]. Physical Review A,1989,39:1235-1252.
[75] ACKEMANN T, HEUER A, LOGVIN YU A, et al. Light-shift-induced levelcrossing and resonator less optical bistability in sodium vapor [J]. PhysicalReview A,1997,56:2321-2326.
[76] GENES C, VITALI D, TOMBESI P, et al. Ground-state cooling of amicromechanical oscillator: comparing cold damping and cavity-assistedcooling schemes [J]. Physical Review A,2008,77:033804-1-9.
[77] GHOBADI R, BAHRAMPOUR A R, SIMON C. Quantum optomechanics inthe bistablere gime [J]. Physical Review A,2011,84:033846.
[78] ADESSO G, SERAFINI A, ILLUMINATI F. Determination of continuousvariable entanglement by purity measurements [J]. Physical Review Letters,2004,92:087901-1-4.
[79] GIEDKE G, WOLF M M, KRüGER O, et al. Entanglement of formation forsymmetric Gaussian states [J]. Physical Review Letters,2003,91:107901-1-4.
[80] WOLF M M, GIEDKE G, KRüGER O, et al. Gaussian entanglement offormation [J].Physical Review A,2004,69:052320-1-8.
[81] SERAFINI A, ADESSO G, ILLUMINATI F. Unitarily localizableentanglement of Gaussian states [J]. Physical Review A,2005,71:032349-1-11.
[82] VIDAL G, WERNERRF. Computable measure of entanglement [J]. PhysicalReview A,2002,65:032314-1-11.
[83] HOME R, JOHNSON C. Matrix A nalysis [M]. Cambridge: CambridgeUniversity Press,1985.
[84] BRAUN M. Differential Equations and Their Applications[M].New York:Springer-Verlag Press,1983.
[85] DEJESUS E X，KAUFMAN C. Non-periodic flow in the numericalintegration of a nonlinear differential equation of fluid dynamics [J].Physical Review A,1985,31:903-909.
[86] DEJESUS E X, KAUFMAN C. Routh Hurwitz criterion in the examinationof eigenvalues of a system of nonlinear ordinary differential equations [J].Physical Review A,1987,35:5288-5290.
[87] A. KORN C, M. KORN T. Mathematical hand book for scientists andengineers [M]. New York: McGraw-Hill,1968.
[88] CARMON T, ROKHSARI H, YANG L, et al. Temporal behavior of radiationpressure induced vibrations of an optical microcavity phonon mode [J].Physical Review Letters,2005,94:223902-1-4.
[89] KIPPENBERG T J, ROKHSARI H, CARMON T, et al. Analysis of radiationpressure induced mechanical oscillation of an optical microcavity [J].Physical Review Letters,2005,95:033901-1-4.
[90] TEUFEL J D, HARLOW J W, REGAL C A, et al. Dynamical backaction ofmicrowave fields on a nanomechanical oscillator [J]. Physical ReviewLetters,2008,101:197203-1-4.
[91] SCHLIESSER A, NOOSHI N, VAHALA K J, et al. Radiation pressurecooling of a micromechanical oscillator using dynamical backaction [J].Physical Review Letters,2006,97:243905-1-4.
[92] WILSON R I, ZOLLER P, IMAMOGLU A. Laser cooling of ananomechanical resonator mode to its quantum ground state [J]. PhysicalReview Letters,2004,92:075507-1-4.
[93] TIAN L, ZOLLER P. Coupled ion nanomechanical systems [J]. PhysicalReview Letters,2004,93:266403-1-4.
[94] BROWN K R, BRITTON J, EPSTEIN R J, et al. Passive cooling of amicromechanical oscillator with a resonant electric circuit [J]. PhysicalReview Letters,2007,99:137205-1-4.
[95] BLAIR D G, IVANOV E N, TOBAR M E, et al. High sensitivitygravitational wave antenna with parametric transducer readout [J]. PhysicalReview Letters,1995,74:1908-1911.
[96] ARMOUR A D, BLENCOWE M P, SCHWAB K C. Entanglement anddecoherence of a micromechanical resonator via coupling to a Cooper pairbox [J]. Physical Review Letters,2002,88:148301-1-4.
[97] MARTIN I, SHNIRMAN A, TIAN L, et al. Ground state cooling ofmechanical resonators [J]. Physical Review B,2004,69:125339-1-12.
[98] BHATTACHARYA M, MEYSTRE P. Trapping and cooling a mirror to itsquantum mechanical ground state [J]. Physical Review Letters,2007,99:073601-1-4.
[99] BHATTACHARYA M, UYS H, MEYSTRE P. Optomechanical trapping andcooling of partially reflective mirrors [J]. Physical Review A,2008,77:033819-1-12.
[100] HUANG S, AGARWALG S. Normal mode splitting in a coupled systemofananomechanical oscillator and a parametric amplifier cavity [J]. PhysicalReview A,2009,80:033807-1-7.
[101] HUANG S, AGARWALG S. Normal mode splitting and antibunching inStokes and anti-Stokes processes in cavity optomechanics: radiationpressure induced four-wave-mixing cavity optomechanics [J]. PhysicalReview A,2010,81:033830-1-6.
[102] HUANG S, AGARWALG S. Reactive-coupling-induced normal modesplittings in microdisk resonators coupled to waveguides [J]. PhysicalReview A,2010,81:053810-1-4.
[103] LI M, PERNICE W H P, TANG H X. Reactive cavity optical force onmicrodisk-coupled nanomechanical beam waveguides [J]. Physical ReviewLetters,2009,103:223901-1-4.
[104] JAYICH A M, SANKEY J C, ZWICKL B M, et al. Dispersiveoptomechanics: a membrane inside a cavity [J]. New Journal of Physics,2008,10:095008.
[105] SANKEY J C, YANG C, ZWICKL B M, et al. Strong and tunable nonlinearoptomechanicalc oupling in a low-loss system [J]. Nature Physics,2010,6:707-712.
[106] HUANG S, AGARWAL G S. Electromagnetically induced transparencyfrom two phonon processes in quadratically coupled membranes [J].Physical Review A,2011,83:023823-1-5.
[107] IAN H, GONG Z R, LIU Y X, et al. Cavity optomechanical couplingassisted by an atomic gas [J]. Physical Review A,2008,78:013824-1-7.
[108] HAMMERER K, WALLQUIST M, GENES C, et al. Strong coupling of amechanical oscillator and a single atom [J]. Physical Review Letters,2009,103:063005-1-4.
[109] CAMERER S, KORPPI M, J CKEL A, et al. Realization of anoptomechanical interface between ultracold atoms and a membrane [J].Physical Review Letters,2011,107:223001-1-5.
[110] MEISER D, MEYSTRE P. Coupled dynamics of atoms and radiationpressure driven interferometers [J]. Physical Review A,2006,73:033417-1-10.
[111] FLEISCHHAUER M, IMAMOGLU A, MARANGOSP J. Electrom-agnetically induced transparency: Optics in coherent media [J]. Reviews ofModern Physics,2005,77:633-673.
[112] CHANG YUE, SHI T, LIU Y X, et al. Multistability of electromagneticallyinduced transparency in atom-assisted optomechanical cavities [J]. PhysicalReview A,2011,83:063826-1-10.
[113] QIN L, ZHANG K, PENG R W, et al. Optical magnetism inducedtransparency in a metamaterial [J]. Physical Review B,2013,87:125136-1-6.
[114] HE Z S, TSAI J H, CHANG Y Y, et al. Ladder-type electromagneticallyinduced transparency with optical pumping effect [J]. Physical Review A,2013,87:033402-1-7.
[115] YOSHIDA I, HAYASHI N, FUJITA K, et al. Line-shape comparison ofelectromagnetically induced transparency and Raman Ramsey fringes insodium vapor [J]. Physical Review A,2013,87:023836-1-6.
[116] HEINZE G, RENTZSCH N, HALFMANN T. Multiplexed image storage byelectromagnetically induced transparency in a solid [J]. Physical Review A,2012,86:053837-1-8.
[117] BERMAN P R, RAYMOND OOIC H. Pulse propagation in a medium ofΛ-type atoms [J]. Physical ReviewA,2012,86:053812-1-9.
[118] BROWN A C, HART H. Influence of multiple ionization thresholds onharmonic generation from Ar+[J]. Physical Review A,2012,86:063416-1-5.
[119] LAUPRêTRE T, KUMAR S, BERGER P, et al. Ultranarrow resonance dueto coherent population oscillations in a Λ-type atomic system [J]. PhysicalReview A,2012,85:051805-1-5.
[120] KAWAMORI E, SYUGU W J, HSIEH T Y, et al. Experimentalidentification of electromagnetically induced transparency in magnetizedplasma [J]. Physical Review Letters,2012,108:075003-1-5.
[121] EILAM A, SHAPIRO M. Strong field adiabatic passage in the continuum:electromagnetically induced transparency and stimulated Raman adiabaticpassage [J]. Physical Review A,2012,85:012520-1-6.
[122] ABDUMALIKOV. JR AA, ASTAFIEV O, ZAGOSKIN A M, et al.Electromagnetically induced transparency on a single artificial atom [J].Physical Review Letters,2010,104:193601-1-4.
[123] EISERT J, PLENIO M B, BOSE S, et al. Towards quantum entanglement innanoelectromechanical devices [J]. Physical Review Letters,2004,93:190402-1-4.
[124] BARZANJEH S, VITALI D, TOMBESI P, et al. Entangling optical andmicrowave cavity modes by means of a nanomechanical resonator [J].Physical Review A,2011,84:042342-1-6.
[125] GENES C, VITALI D, TOMBESI P. Emergence of atom light mirrorentanglement inside an optical cavity [J]. Physical Review A,2008,77:050307-1-4.
[126] TAN H, LI G, MEYSTRE P. Dissipation driven two mode mechanicalsqueezed states in optomechanical systems [J]. Physical Review A,2013,87:033829-1-7.
[127] XUEREB A, PATERNOSTRO M. Selectable linear or quadratic coupling inan optomechanical system [J].Physical Review A,2013,87:023830-1-7.
[128] SETE E A, ELEUCH H. Controllable nonlinear effects in anoptomechanical resonator containing a quantum well [J]. Physical ReviewA,2012,85:043824-1-8.
[129] AHN D, CHUANG S L. High optical gain of I–VII semiconductor quantumwells for efficient light emitting devices [J]. Applied Physics Letters,2013,102:121114-1-4.
[130] GU Y, ZHANG Y G, CHEN X Y, et al. InAs/In0.83Al0.17As quantum wellson GaAs substrate with type-I emission at2.9μm [J]. Applied PhysicsLetters,2013,102:121110-1-4.
[131] SCHIAVON D, BINDER M, LOEFFLER A, et al. Optically pumpedGaInN/GaN multiple quantum wells for the realization of efficient greenlight-emitting devices [J]. Applied Physics Letters,2013,102:113509-1-4.
[132] HSU H C, HUANG H Y, O. ERIKSSON M, et al. Surface related andintrinsic exciton recombination dynamics in ZnO nanoparticlessynthesized by a sol-gel method [J]. Applied Physics Letters,2013,102:013109-1-4.
[133] LI H J, KANG J J, LI PP, et al. Enhanced performance of GaN based lightemitting diodes with a low temperature p-GaN hole injection layer [J].Applied Physics Letters,2013,102:011105-1-4.
[134] ZHOU L, GONSCHOREK M, GIRAUD E, et al. Measurement ofpolarization induced electric fields in GaN/AlInN quantum wells [J].Applied Physics Letters,2012,101:251902-1-3.
[135] Chen D, Han J. High reflectance membrane-based distributed Braggreflectors for GaN photonics [J]. Applied Physics Letters,2012,101:221104-1-4.
[136] CHEN T F, WANG Y Q, XIANG P, et al. Crack-free InGaN multiplequantum wells light emitting diodes structures transferred from Si (111)substrate onto electroplating copper submount with embedded electrodes[J]. Applied Physics Letters,2012,100:241112-1-4.
[137] BAAS A, KARR J P, ELEUCH H, et al. Optical bistability insemiconductor microcavities [J]. Physical Review A,2004,69:023809-1-8.
[138] GENES C, MARI A, TOMBESI P, et al. Robust entanglement of amicromechanical resonator with output optical fields [J]. Physical ReviewA,2008,78:032316-1-14.
[139] CAMPMAN K L, SCHMIDT H, IMAMOGLU A, et al. Interface roughnessand alloy disorder scattering contributions to intersubband transitionlinewidths [J]. Applied Physics Letters,1996,69:2554-2556.
[140] SCHMIDT H, CAMPMAN K L, GOSSARD A C, et al.Tunneling inducedtransparency: Fano interference in intersubband transitions [J]. AppliedPhysics Letters,1997,70:3455-3457.
[2] NICHOLS EF，HULL GF. The pressure due to radiation [J]. AstrophysicalJournal,1903,17:315-351.
[3] ASHKIN A. Applications of laser radiation pressure [J]. Science,1980,210:1081-1088.
[4] ASHKIN A, DZIEDZICJ M, BJORKHOLM J E, et al. Observation of a singlebeam gradient force optical trap for dielectric particles [J]. Optics Letters,1986,11:288-290.
[5] DORSEL A, MCCULLEN J D, MEYSTRE P, et al. Optical bistability andmirror confinement induced by radiation pressure [J]. Physical ReviewLetters,1983,51:1550-1553.
[6] ABRAMOVICI A, ALTHOUSE W E, DREVER R W P, et al. The laserinterferometer gravitational wave observatory [J]. Science,1992,256:325-333.
[7] CLELAND A N, ROUKES M L. Fabrication of high frequency nanometerscale mechanical resonators from bulk Si crystals [J]. Applied PhysicsLetters,1996,69:3653-2655.
[8] GUPTA A, AKIN D, BASHIR R. Single virus particle mass detection usingmicroresonators with nanoscale thickness [J]. Applied Physics Letters,2004,84:1976-1978.
[9] MARQUARDT F, HARRIS J G E, GIRVIN S M. Dynamical multistabilityinduced by radiation pressure in high finesse micromechanical opticalcavities [J]. Physical Review Letters,2006,96:103901-1-4.
[10] CARMON T, ROKHSARI H, YANG L, et al. Temporal behavior of radiation66pressure induced vibrations of an optical microcavity phonon mode [J].Physical Review Letters,2005,94:223902-1-4.
[11] CARMON T, CROSS M C, VAHALA KERRY J. Chaotic quivering ofmicron scaled on chip resonators excited by centrifugal optical pressure [J].Physical Review Letters,2007,98:167203-1-4.
[12] GONG Z R, IAN H, LIU YU X, et al. Kerr nonlinearity induced by anoscillating mirror in an optical cavity [J]. ArXiv,2011,0805.4102:1-10.
[13] HUANG S, AGARWAL G S. Reactive coupling can beat the motionalquantum limit of nanowaveguides coupled to a microdisk resonator [J].Physical Review A,2010,82:033811-1-5.
[14] SRINIVASAN K, STINTZ A, KRISHNA S, et al. Photoluminescencemeasurements of quantum dot containing semiconductor microdiskresonators using optical fiber taper waveguides [J]. Physical Review B,2005,72:205318-1-9.
[15] DUMEIGE Y, FéRON P. Whispering gallery mode analysis of phasematched doubly resonant second harmonic generation [J]. PhysicalReview A,2006,74:063804-1-7.
[16] CLELAND A N, GELLER M R. Superconducting qubit storage andentanglement with nanomechanical resonators [J]. Physical Review Letters,2004,93:070501-1-4.
[17] SABOONI M, LI Q, KR LL S, et al. Efficient quantum memory using aweakly absorbing sample [J]. Physical Review Letters,2013,110:133604-1-5.
[18] CHEN Y H, LEE M J, WANG I C, et al. Coherent optical memory with highstorage efficiency and large fractional delay [J]. Physical Review Letters,2013,110:083601-1-5.
[19] DING D S, WU J H, ZHOU Z Y, et al. Multimode image memory based on acold atomic ensemble [J]. Physical Review A,2013,87:013835-1-6.
[20] ZHANG X, KALACHEV A, KOCHAROVSKAYA O. Quantum storagebased on control field angular scanning [J]. Physical Review A,2013,87:013811-1-9.
[21] SHIM J H, NIEMEYER I, ZHANG J, et al. Room temperature high speednuclear spin quantum memory in diamond [J]. Physical Review A,2013,87:012301-1-6.
[22] VISCOR D, AHUFINGER V, MOMPART J, et al. Two color quantummemory in double-Λ media [J]. Physical Review A,2012,86:053827-1-6.
[23] GRODECKA G A, ZEUTHEN E, S. S RENSEN A. High capacity spatialmultimode quantum memories based on atomic ensembles [J]. PhysicalReview Letters,2012,109:133601-1-5.
[24] HIGGINBOTTOM D B, SPARKES B M, RANCIC M, et al. Spatial modestorage in a gradient echo memory [J]. Physical Review A,2012,86:023801-1-10.
[25] BENSKY G, PETROSYAN D, MAJER J, et al. Optimizing inhomogeneousspin ensembles for quantum memory [J]. Physical Review A,2012,86:012310-1-7.
[26] REIM K F, NUNN J, JIN X M, et al. Multipulse addressing of a ramanquantum memory: configurable beam splitting and efficient readout [J].Physical Review Letters,2012,108:263602-1-5.
[27] DOBRINDT J M, WILSON R I, KIPPENBERG T J. Parametric normalmode splitting in cavity optomechanics [J]. Physical Review Letters,2008,101:263602-1-4.
[28] ASBóTH J K, RITSCH H, DOMOKOS P. Optomechanical coupling in a onedimensional optical lattice [J]. Physical Review A,2008,77:063424-1-25.
[29] MURCH W K, MOORE L K, GUPTA S, et al. Observation of quantummeasurement backaction with an ultracold atomic gas [J]. Nature Physics,2008,4:561-564.
[30] BRENNECKE F, RITTER S, DONNER T, et al. Cavity optomechanics witha Bose Einstein Condensate [J]. Science,2008,322:235-238.
[31] SMITH H S M, LEROUX D I, ZHANG H, et al. Optomechanical cavitycooling of an atomic ensemble [J]. Physical Review Letters,2011,107:143005-1-4.
[32] HUANG W M, IRWIN K, TSAI S W, et al. Possible quantum phasemanipulation of a two leg ladder in mixed dimensional fermionic coldatoms [J]. Physical Review A,2013,87:031603-1-4.
[33] ZOHAR E, CIRAC J I, REZNIK B. Cold atom quantum simulator for SU(2)yang mills lattice gauge theory [J]. Physical Review Letters,2013,110:125304-1-5.
[34] ZHOU L, PU H, ZHANG W P. Anderson localization of cold atomic gaseswith effective spin orbit interaction in a quasiperiodic optical lattice [J].Physical Review A,2013,87:023625-1-7.
[35] CHEN Y H, LEE M J, WANG I C, et al. Coherent optical memory with highstorage efficiency and large fractional delay [J]. Physical Review Letters,2013,110:083601-1-5.
[36] CLERK A A, DEVORET M H, GIRVIN S M, et al. Introduction to quantumnoise, measurement and amplification [J]. ArXiv,2010,0810.4729-1-96.
[37] MARQUARDT F, CHEN J P, CLERKAA, et al. Quantum theory of cavityassisted sideband cooling of mechanical motion [J]. Physical ReviewLetters,2007,99:093902-1-4.
[38] MANCINI S, VITALI D, TOMBESI P. Optomechanical cooling of amacroscopic oscillator by homodyne feedback [J]. Physical Review Letters,1998,80:688-691.
[39] POGGIO M, DEGEN C L, MAMIN H J, et al. Feedback cooling of acantilever’s fundamental mode below5mK [J]. Physical Review Letters,2007,99:017201-1-4.
[40] ASPELMEYER M, MEYSTRE P, SCHWAB K. Quantum optomechanics [J].Physics Today,2012,65:29-35.
[41] TEUFEL J D, DONNER T, LI D, et al. Sideband cooling of micromechanicalmotion to the quantum ground state [J].Nature,2011,475:359-363.
[42] CHAN J, MAYER A T P, H. SAFAVI-NAEINI A, et al. Laser cooling of ananomechanical oscillator into its quantum ground state [J]. Nature,2011,478:89-92.
[43] H. SAFAVI-NAEINI A, CHAN J, T. HILL J, et al. Observation of quantummotion of a nanomechanical resonator [J]. Physical Review Letters,2012,108:033602-1-5.
[44] WANG Z H, TAKAHASHI S. Spin decoherence and electron spin bath noiseof a nitrogen vacancy center in diamond [J]. Physical Review B,2013,87:115122-1-6.
[45] LAMBERT J, C TéR. Quantum Hall ferromagnetic phases in the Landaulevel N=0of a grapheme bilayer [J]. Physical Review B,2013,87:115415-1-20.
[46] KONG J, OU Z Y, ZHANG W P. Phase measurement sensitivity beyond thestandard quantum limit in an interferometer consisting of a parametricamplifier and a beam splitter [J]. Physical Review A,2013,87:023825-1-6.
[47] G. DALLA TORRE E, OTTERBACH J, DEMLER E, et al. Dissipativepreparation of spin squeezed atomic ensembles in a steady state [J].Physical Review Letters,2013,110:120402-1-5.
[48] BUCHMANN L F, JING H, RAMAN C, et al. Optical control of a quantumrotor [J]. Physical Review A,2013,87:031601(R)-1-4.
[49] J. BARTLEY T, J. D. CROWLEY P, DATTA A, et al. Strategies forenhancing quantum entanglement by local photon subtraction [J]. PhysicalReview A,2013,87:022313-1-11.
[50] HEESE R, FREYBERGER M. Entropic uncertainty relation for pointerbased simultaneous measurements of conjugate observables [J]. PhysicalReview A,2013,87:012123-1-7.
[51] SHARYPOV A V, HE B. Generation of arbitrary symmetric entangled stateswith conditional linear optical coupling [J]. Physical Review A,2013,87:032323-1-6.
[52] CHOI R H, FORTESCUE B, GOUR G, et al. Entanglement sharing protocolvia quantum error correcting codes [J]. Physical Review A,2013,87:032319-1-7.
[53] C. TICHY M, MINTERT F, BUCHLEITNER A. Limits to multipartiteentanglement generation with bosons and fermions [J]. Physical Review A,2013,87:022319-1-17.
[54]曾谨言.量子力学卷I与量子力学卷II [M].北京：科学出版社，2007.
[55]喀兴林.高等量子力学[M].北京：高等教育出版社，2001.
[56] ZUREK W H. Decoherence, einselection, and the quantum origins of theclassical [J]. Reviews of Modern Physics,2003,75:715-775.
[57] JOSHI C, LARSON J, JONSON M, et al. Entanglement of distant opto-mechanical systems [J]. Physical Review A,2012,85:033805-1-11.
[58] MARI A, EISERT J. Gently modulating optomechanical Systems [J].Physical Review Letters,2009,103:213603-1-4.
[59] A. NIELSEN M, L.CHUANG I.量子计算与量子信息[M].北京：高等教育出版社，2003.
[60] PARK K, LEE S W, JEONG H. Quantum teleportation between particle likeand field like qubits using hybrid entanglement under decoherence effects[J]. Physical Review A,2012,86:062301-1-9.
[61] BOURDON P S, GERJUOY E. Overcoming a limitation of deterministicdense coding with a nonmaximally entangled initial state [J]. PhysicalReview A,2010,81:022314-1-11.
[62] KUMAR A, ADHIKARI S, BANERJEE S, et al. Optimal quantumcommunication using multiparticle partially entangled states [J]. PhysicalReview A,2013,87:022307-1-6.
[63] IMOTO N, HAUS H A, YAMAMOTO Y. Quantum nondemolitionmeasurement of the photon number via the optical Kerr effect [J]. PhysicalReview A,1985,32:2287-2292.
[64] JACOBS K, TOMBESI P, COLLETT M J, et al. Quantum-nondemolitionmeasurement of photon number using radiation pressure [J]. PhysicalReview A,1994,49:1961-1966.
[65] O. SCULLY M, ZUBAIRY M S. Quantum optics [M]. Cambridge:Cambridge University Press,1997.
[66] H. LOUSISELL W. Quantum statistical properties of Radiation [M].California: A Wiley-Interscience publication,1973.
[67] WALLS D F, MILBURN G J. Quantum Optics [M]. Berlin: Springer-VerlagBerlin Heidelberg,1997.
[68] LAW C K. Interaction between a moving mirror and radiation pressure: aHamiltonian formulation [J]. Physical Review A,1995,51:2537-254.
[69] VITALI D, GIGAN S, FERREIRA A, et al. Optomechanical entanglementbetween a movable mirror and a cavity field [J]. Physical Review Letters,2007,98:030405-1-4.
[70] BONIFACIO R, LUGIATO L A. Optical bistability and cooperative effects inresonance fluorescence [J]. Physical Review A,1978,18:1129-1144.
[71] SANDLE W J, GALLAGHER A. Optical bistability by an atomic vapor in afocusing Fabry-Perot cavity [J]. Physical Review A,1981,24:2017-2028.
[72] GRANT D E, KIMBLE H J. Optical bistability for two-level atoms in astanding-wave cavity [J]. Optics Letters,1982,7:353-355.
[73] ROSENBERGER A T, OROZCO L A, KIMBLE H J. Observation ofabsorptive bistability with two-level atoms in a ring cavity [J]. PhysicalReview A,1983,28:2569-2572.
[74] OROZCO L A, KIMBLE H J, ROSENBERGER A T, et al. Single-modeinstability in optical bistability [J]. Physical Review A,1989,39:1235-1252.
[75] ACKEMANN T, HEUER A, LOGVIN YU A, et al. Light-shift-induced levelcrossing and resonator less optical bistability in sodium vapor [J]. PhysicalReview A,1997,56:2321-2326.
[76] GENES C, VITALI D, TOMBESI P, et al. Ground-state cooling of amicromechanical oscillator: comparing cold damping and cavity-assistedcooling schemes [J]. Physical Review A,2008,77:033804-1-9.
[77] GHOBADI R, BAHRAMPOUR A R, SIMON C. Quantum optomechanics inthe bistablere gime [J]. Physical Review A,2011,84:033846.
[78] ADESSO G, SERAFINI A, ILLUMINATI F. Determination of continuousvariable entanglement by purity measurements [J]. Physical Review Letters,2004,92:087901-1-4.
[79] GIEDKE G, WOLF M M, KRüGER O, et al. Entanglement of formation forsymmetric Gaussian states [J]. Physical Review Letters,2003,91:107901-1-4.
[80] WOLF M M, GIEDKE G, KRüGER O, et al. Gaussian entanglement offormation [J].Physical Review A,2004,69:052320-1-8.
[81] SERAFINI A, ADESSO G, ILLUMINATI F. Unitarily localizableentanglement of Gaussian states [J]. Physical Review A,2005,71:032349-1-11.
[82] VIDAL G, WERNERRF. Computable measure of entanglement [J]. PhysicalReview A,2002,65:032314-1-11.
[83] HOME R, JOHNSON C. Matrix A nalysis [M]. Cambridge: CambridgeUniversity Press,1985.
[84] BRAUN M. Differential Equations and Their Applications[M].New York:Springer-Verlag Press,1983.
[85] DEJESUS E X，KAUFMAN C. Non-periodic flow in the numericalintegration of a nonlinear differential equation of fluid dynamics [J].Physical Review A,1985,31:903-909.
[86] DEJESUS E X, KAUFMAN C. Routh Hurwitz criterion in the examinationof eigenvalues of a system of nonlinear ordinary differential equations [J].Physical Review A,1987,35:5288-5290.
[87] A. KORN C, M. KORN T. Mathematical hand book for scientists andengineers [M]. New York: McGraw-Hill,1968.
[88] CARMON T, ROKHSARI H, YANG L, et al. Temporal behavior of radiationpressure induced vibrations of an optical microcavity phonon mode [J].Physical Review Letters,2005,94:223902-1-4.
[89] KIPPENBERG T J, ROKHSARI H, CARMON T, et al. Analysis of radiationpressure induced mechanical oscillation of an optical microcavity [J].Physical Review Letters,2005,95:033901-1-4.
[90] TEUFEL J D, HARLOW J W, REGAL C A, et al. Dynamical backaction ofmicrowave fields on a nanomechanical oscillator [J]. Physical ReviewLetters,2008,101:197203-1-4.
[91] SCHLIESSER A, NOOSHI N, VAHALA K J, et al. Radiation pressurecooling of a micromechanical oscillator using dynamical backaction [J].Physical Review Letters,2006,97:243905-1-4.
[92] WILSON R I, ZOLLER P, IMAMOGLU A. Laser cooling of ananomechanical resonator mode to its quantum ground state [J]. PhysicalReview Letters,2004,92:075507-1-4.
[93] TIAN L, ZOLLER P. Coupled ion nanomechanical systems [J]. PhysicalReview Letters,2004,93:266403-1-4.
[94] BROWN K R, BRITTON J, EPSTEIN R J, et al. Passive cooling of amicromechanical oscillator with a resonant electric circuit [J]. PhysicalReview Letters,2007,99:137205-1-4.
[95] BLAIR D G, IVANOV E N, TOBAR M E, et al. High sensitivitygravitational wave antenna with parametric transducer readout [J]. PhysicalReview Letters,1995,74:1908-1911.
[96] ARMOUR A D, BLENCOWE M P, SCHWAB K C. Entanglement anddecoherence of a micromechanical resonator via coupling to a Cooper pairbox [J]. Physical Review Letters,2002,88:148301-1-4.
[97] MARTIN I, SHNIRMAN A, TIAN L, et al. Ground state cooling ofmechanical resonators [J]. Physical Review B,2004,69:125339-1-12.
[98] BHATTACHARYA M, MEYSTRE P. Trapping and cooling a mirror to itsquantum mechanical ground state [J]. Physical Review Letters,2007,99:073601-1-4.
[99] BHATTACHARYA M, UYS H, MEYSTRE P. Optomechanical trapping andcooling of partially reflective mirrors [J]. Physical Review A,2008,77:033819-1-12.
[100] HUANG S, AGARWALG S. Normal mode splitting in a coupled systemofananomechanical oscillator and a parametric amplifier cavity [J]. PhysicalReview A,2009,80:033807-1-7.
[101] HUANG S, AGARWALG S. Normal mode splitting and antibunching inStokes and anti-Stokes processes in cavity optomechanics: radiationpressure induced four-wave-mixing cavity optomechanics [J]. PhysicalReview A,2010,81:033830-1-6.
[102] HUANG S, AGARWALG S. Reactive-coupling-induced normal modesplittings in microdisk resonators coupled to waveguides [J]. PhysicalReview A,2010,81:053810-1-4.
[103] LI M, PERNICE W H P, TANG H X. Reactive cavity optical force onmicrodisk-coupled nanomechanical beam waveguides [J]. Physical ReviewLetters,2009,103:223901-1-4.
[104] JAYICH A M, SANKEY J C, ZWICKL B M, et al. Dispersiveoptomechanics: a membrane inside a cavity [J]. New Journal of Physics,2008,10:095008.
[105] SANKEY J C, YANG C, ZWICKL B M, et al. Strong and tunable nonlinearoptomechanicalc oupling in a low-loss system [J]. Nature Physics,2010,6:707-712.
[106] HUANG S, AGARWAL G S. Electromagnetically induced transparencyfrom two phonon processes in quadratically coupled membranes [J].Physical Review A,2011,83:023823-1-5.
[107] IAN H, GONG Z R, LIU Y X, et al. Cavity optomechanical couplingassisted by an atomic gas [J]. Physical Review A,2008,78:013824-1-7.
[108] HAMMERER K, WALLQUIST M, GENES C, et al. Strong coupling of amechanical oscillator and a single atom [J]. Physical Review Letters,2009,103:063005-1-4.
[109] CAMERER S, KORPPI M, J CKEL A, et al. Realization of anoptomechanical interface between ultracold atoms and a membrane [J].Physical Review Letters,2011,107:223001-1-5.
[110] MEISER D, MEYSTRE P. Coupled dynamics of atoms and radiationpressure driven interferometers [J]. Physical Review A,2006,73:033417-1-10.
[111] FLEISCHHAUER M, IMAMOGLU A, MARANGOSP J. Electrom-agnetically induced transparency: Optics in coherent media [J]. Reviews ofModern Physics,2005,77:633-673.
[112] CHANG YUE, SHI T, LIU Y X, et al. Multistability of electromagneticallyinduced transparency in atom-assisted optomechanical cavities [J]. PhysicalReview A,2011,83:063826-1-10.
[113] QIN L, ZHANG K, PENG R W, et al. Optical magnetism inducedtransparency in a metamaterial [J]. Physical Review B,2013,87:125136-1-6.
[114] HE Z S, TSAI J H, CHANG Y Y, et al. Ladder-type electromagneticallyinduced transparency with optical pumping effect [J]. Physical Review A,2013,87:033402-1-7.
[115] YOSHIDA I, HAYASHI N, FUJITA K, et al. Line-shape comparison ofelectromagnetically induced transparency and Raman Ramsey fringes insodium vapor [J]. Physical Review A,2013,87:023836-1-6.
[116] HEINZE G, RENTZSCH N, HALFMANN T. Multiplexed image storage byelectromagnetically induced transparency in a solid [J]. Physical Review A,2012,86:053837-1-8.
[117] BERMAN P R, RAYMOND OOIC H. Pulse propagation in a medium ofΛ-type atoms [J]. Physical ReviewA,2012,86:053812-1-9.
[118] BROWN A C, HART H. Influence of multiple ionization thresholds onharmonic generation from Ar+[J]. Physical Review A,2012,86:063416-1-5.
[119] LAUPRêTRE T, KUMAR S, BERGER P, et al. Ultranarrow resonance dueto coherent population oscillations in a Λ-type atomic system [J]. PhysicalReview A,2012,85:051805-1-5.
[120] KAWAMORI E, SYUGU W J, HSIEH T Y, et al. Experimentalidentification of electromagnetically induced transparency in magnetizedplasma [J]. Physical Review Letters,2012,108:075003-1-5.
[121] EILAM A, SHAPIRO M. Strong field adiabatic passage in the continuum:electromagnetically induced transparency and stimulated Raman adiabaticpassage [J]. Physical Review A,2012,85:012520-1-6.
[122] ABDUMALIKOV. JR AA, ASTAFIEV O, ZAGOSKIN A M, et al.Electromagnetically induced transparency on a single artificial atom [J].Physical Review Letters,2010,104:193601-1-4.
[123] EISERT J, PLENIO M B, BOSE S, et al. Towards quantum entanglement innanoelectromechanical devices [J]. Physical Review Letters,2004,93:190402-1-4.
[124] BARZANJEH S, VITALI D, TOMBESI P, et al. Entangling optical andmicrowave cavity modes by means of a nanomechanical resonator [J].Physical Review A,2011,84:042342-1-6.
[125] GENES C, VITALI D, TOMBESI P. Emergence of atom light mirrorentanglement inside an optical cavity [J]. Physical Review A,2008,77:050307-1-4.
[126] TAN H, LI G, MEYSTRE P. Dissipation driven two mode mechanicalsqueezed states in optomechanical systems [J]. Physical Review A,2013,87:033829-1-7.
[127] XUEREB A, PATERNOSTRO M. Selectable linear or quadratic coupling inan optomechanical system [J].Physical Review A,2013,87:023830-1-7.
[128] SETE E A, ELEUCH H. Controllable nonlinear effects in anoptomechanical resonator containing a quantum well [J]. Physical ReviewA,2012,85:043824-1-8.
[129] AHN D, CHUANG S L. High optical gain of I–VII semiconductor quantumwells for efficient light emitting devices [J]. Applied Physics Letters,2013,102:121114-1-4.
[130] GU Y, ZHANG Y G, CHEN X Y, et al. InAs/In0.83Al0.17As quantum wellson GaAs substrate with type-I emission at2.9μm [J]. Applied PhysicsLetters,2013,102:121110-1-4.
[131] SCHIAVON D, BINDER M, LOEFFLER A, et al. Optically pumpedGaInN/GaN multiple quantum wells for the realization of efficient greenlight-emitting devices [J]. Applied Physics Letters,2013,102:113509-1-4.
[132] HSU H C, HUANG H Y, O. ERIKSSON M, et al. Surface related andintrinsic exciton recombination dynamics in ZnO nanoparticlessynthesized by a sol-gel method [J]. Applied Physics Letters,2013,102:013109-1-4.
[133] LI H J, KANG J J, LI PP, et al. Enhanced performance of GaN based lightemitting diodes with a low temperature p-GaN hole injection layer [J].Applied Physics Letters,2013,102:011105-1-4.
[134] ZHOU L, GONSCHOREK M, GIRAUD E, et al. Measurement ofpolarization induced electric fields in GaN/AlInN quantum wells [J].Applied Physics Letters,2012,101:251902-1-3.
[135] Chen D, Han J. High reflectance membrane-based distributed Braggreflectors for GaN photonics [J]. Applied Physics Letters,2012,101:221104-1-4.
[136] CHEN T F, WANG Y Q, XIANG P, et al. Crack-free InGaN multiplequantum wells light emitting diodes structures transferred from Si (111)substrate onto electroplating copper submount with embedded electrodes[J]. Applied Physics Letters,2012,100:241112-1-4.
[137] BAAS A, KARR J P, ELEUCH H, et al. Optical bistability insemiconductor microcavities [J]. Physical Review A,2004,69:023809-1-8.
[138] GENES C, MARI A, TOMBESI P, et al. Robust entanglement of amicromechanical resonator with output optical fields [J]. Physical ReviewA,2008,78:032316-1-14.
[139] CAMPMAN K L, SCHMIDT H, IMAMOGLU A, et al. Interface roughnessand alloy disorder scattering contributions to intersubband transitionlinewidths [J]. Applied Physics Letters,1996,69:2554-2556.
[140] SCHMIDT H, CAMPMAN K L, GOSSARD A C, et al.Tunneling inducedtransparency: Fano interference in intersubband transitions [J]. AppliedPhysics Letters,1997,70:3455-3457.