原子—腔系统透射谱的研究
|
摘要
腔量子电动力学是研究光与原子相互作用的有力工具,在低粒子数密度下,vacuum Rabi splitting,是实现强相互作用的重要特征。对于多粒子体系,则称为normal mode splitting。这种强相互作用显著地改变着原子的辐射特性,并且对于极高品质腔,可以实现系统的纠缠,因此也成为实现量子逻辑运算的潜在途径,而受到广泛研究。
本文首先回顾对原子-腔系统的研究发展,包括利用原子束、冷原子介质及Doppler-broaden介质和腔所构成的系统的研究工作。接下来,主要介绍我们利用原子介质与F-P腔构成的系统,在极高粒子数密度,和高probe光强下,二能级原子腔系统的透射谱的理论和实验研究;以及加入repump光后的抽运作用和非线性效应的实验研究。具体包括以下两方面:
1.研究了不同条件下,冷原子(或原子束)和Doppler-broaden原子介质和腔所构成的系统的透射谱。实验上(Doppler-broaden介质)观察到,系统在不同条件下,其透射谱会呈现出丰富、独特、新颖的特点。在粒子数较高及probe光较强时,因非谐振性,正交模劈裂峰会演化为一个单峰,但同时由于较强光强所导致的烧孔效应,而出现饱和吸收透明峰,因此这一单峰便演化成饱和透明峰伴随两个半圆形泡状峰的特殊结构。随着粒子数密度的增加,这种准三峰结构演化为五峰结构,同时由于吸收的增加,峰的高度会变矮。而随着粒子数的进一步增加,烧孔效应消失,饱和吸收透明峰和中心区域正交模劈裂峰随之消失。并且更为重要的是当耦合强度大于半个自由光谱区时,更多的正交模劈裂峰会随之出现。这种多正交模劈裂峰结构,是在耦合极大条件下,原子-腔系统的一个有趣的新的现象。本文就此及以上实验给出了系统的理论解释。
2.对repump光的抽运作用及加入repump光以后的一些非线性效应的研究。在实验中,为了增加粒子数密度,加入一束repump光,将处于另一基态F=3的原子抽运到激发态(所用原子介质为~(85)Rb蒸气,二能级为~(85)RbD2线能级),从而增加与probe光作用的粒子数目。还研究了不同条件下repump光的作用,观察到了两种完全不同的现象---其一,温度较低,repump光较弱条件下的repump光的光抽运效应;其二,温度较高、probe光和repump光光强较大时的非线性效应。当温度较低并将两束光的光强限定在较小范围内时,改变repump光强和改变温度具有相同的效果,这表明反抽运光将处于基态F=3上的原子激发到了激发态,而部分原子会回落到另一基态---F=2态。这对于probe光来说,相当于粒子数增加。而当提高系统温度时,粒子数密度增加,同时由于原子之间的随机碰撞作用的增强,原子回落到基态F=3上的概率也必然增多,所以此时repump光的抽运作用就越发明显,因此在这种粒子数密度极大,probe光强很强的条件下,一些非线性效应---自聚焦效应---就会发生,这是对内腔中自聚焦现象的一个重要的实验研究,这对于开展内腔中一些极强非线性效应研究具有重要意义。
创新性的工作包括以下两点:
Ⅰ.在不同条件下,研究了二能级原子腔系统的透射谱。尤其是在极强耦合强度下,对多正交模劈裂峰结构的进行了深入探讨。
Ⅱ.对加入repump光的热效应和非线性效应进行了研究。
In the low number density limit, the vacuum Rabi splitting is the important characteristic in the strong interaction in the cavity QED system as the powerful instrument in studying the interaction of the atom and the light. While for the multiple particles system, this is also called normal mode splitting. The strong interaction changes the characteristic of the atom emission remarkably. And in the good cavity system, the entanglement can be accomplished, so it is extensively investigated as the potential method for quantum logical calculus.
In this thesis, the development of the investigation on the cavity QED system is reviewed firstly, including the atom beam, cold atom and Doppler-broaden medium, etc. And then, our works on the two-level Doppler-broaden atom and FP cavity system under large number density and large power condition, are mainly described, including the experiments and theories. Additionally, we discuss the transport effect and the nonlinear effect when the repump laser is added in the system. As followed:
1. Investigating the spectrum of the atom and cavity system under different conditions. The abundant, unique and novel phenomenon under different conditions in the system, are observed. For the large number density and large probe power, the phenomena that the double normal mode splitting peaks will be inosculated into one peak owing to the anharmonicity does not occur, because of the hole-burning effect which causes the appearance of the saturated absorption transparent peak with two semicircular and vesicular peaks. And with the increasing of the number density, the quasi-three-peak structure evolves into five-peak structure. And at the same time, the height of the peaks is shortened due to the absorption. And further, as the atom number rising, the hole-burning effect disappears gradually, and the center peak and normal mode splitting peaks in the central range disappear, too. While the most important thing is that a novel structure-multiple normal mode splitting peaks—in the transmission spectrum appears when the coupling strength exceeds the half of the free spectrum range. The new and interesting structure occurs in the large coupling strength range, and here, we shall give a theoretical analysis.
2. Observing the transport effect of the repump laser and the nonlinear effect. In our experiment, in order to increase the atom number density, we add the repump laser which excites the atoms from the ground state F=3 to the excited state (the medium is the ~(85)Rb vapor, the two levels are the levels of the ~(85)Rb D2 line) . As a result, the number density is increased for the probe laser, and the system appears different behaviors under different conditions. That is to say, 1) under low temperature and low repump power, we have observed the transport effect of the repump laser. 2) the nonlinear effect under high temperature. As we limit the system temperature and the repump power, the result of changing repump power is same with the change of the temperature. This effect illuminates that the repump laser excites the ground state F=3 into the excited state, and the excited atoms are transferred to another ground state F=2. For the probe laser, this effect is same as increasing the temperature. When the temperature is increased, the atom number density rises accordingly. But at the same time, more atoms return to the ground state F=3 because of the strong collision among the atoms, so the role of the repump laser is more obvious. So under the strong probe power, the nonlinear effects-selif-fucusing effect-emerge. The is the first experiment finished in the atom-cavity system, and which will be important for the study in the field.
The characterized works are summarized as followed:
1. Discussing the spectrum of the two-level Doppler-broaden medium and cavity system under different conditions. Especially in the strong coupling range, the structure of the multiple normal mode splitting peaks is discussed in detail.
2. Investigating the transport effect and the nonlinear effect after adding the repump laser.
本文首先回顾对原子-腔系统的研究发展,包括利用原子束、冷原子介质及Doppler-broaden介质和腔所构成的系统的研究工作。接下来,主要介绍我们利用原子介质与F-P腔构成的系统,在极高粒子数密度,和高probe光强下,二能级原子腔系统的透射谱的理论和实验研究;以及加入repump光后的抽运作用和非线性效应的实验研究。具体包括以下两方面:
1.研究了不同条件下,冷原子(或原子束)和Doppler-broaden原子介质和腔所构成的系统的透射谱。实验上(Doppler-broaden介质)观察到,系统在不同条件下,其透射谱会呈现出丰富、独特、新颖的特点。在粒子数较高及probe光较强时,因非谐振性,正交模劈裂峰会演化为一个单峰,但同时由于较强光强所导致的烧孔效应,而出现饱和吸收透明峰,因此这一单峰便演化成饱和透明峰伴随两个半圆形泡状峰的特殊结构。随着粒子数密度的增加,这种准三峰结构演化为五峰结构,同时由于吸收的增加,峰的高度会变矮。而随着粒子数的进一步增加,烧孔效应消失,饱和吸收透明峰和中心区域正交模劈裂峰随之消失。并且更为重要的是当耦合强度大于半个自由光谱区时,更多的正交模劈裂峰会随之出现。这种多正交模劈裂峰结构,是在耦合极大条件下,原子-腔系统的一个有趣的新的现象。本文就此及以上实验给出了系统的理论解释。
2.对repump光的抽运作用及加入repump光以后的一些非线性效应的研究。在实验中,为了增加粒子数密度,加入一束repump光,将处于另一基态F=3的原子抽运到激发态(所用原子介质为~(85)Rb蒸气,二能级为~(85)RbD2线能级),从而增加与probe光作用的粒子数目。还研究了不同条件下repump光的作用,观察到了两种完全不同的现象---其一,温度较低,repump光较弱条件下的repump光的光抽运效应;其二,温度较高、probe光和repump光光强较大时的非线性效应。当温度较低并将两束光的光强限定在较小范围内时,改变repump光强和改变温度具有相同的效果,这表明反抽运光将处于基态F=3上的原子激发到了激发态,而部分原子会回落到另一基态---F=2态。这对于probe光来说,相当于粒子数增加。而当提高系统温度时,粒子数密度增加,同时由于原子之间的随机碰撞作用的增强,原子回落到基态F=3上的概率也必然增多,所以此时repump光的抽运作用就越发明显,因此在这种粒子数密度极大,probe光强很强的条件下,一些非线性效应---自聚焦效应---就会发生,这是对内腔中自聚焦现象的一个重要的实验研究,这对于开展内腔中一些极强非线性效应研究具有重要意义。
创新性的工作包括以下两点:
Ⅰ.在不同条件下,研究了二能级原子腔系统的透射谱。尤其是在极强耦合强度下,对多正交模劈裂峰结构的进行了深入探讨。
Ⅱ.对加入repump光的热效应和非线性效应进行了研究。
In the low number density limit, the vacuum Rabi splitting is the important characteristic in the strong interaction in the cavity QED system as the powerful instrument in studying the interaction of the atom and the light. While for the multiple particles system, this is also called normal mode splitting. The strong interaction changes the characteristic of the atom emission remarkably. And in the good cavity system, the entanglement can be accomplished, so it is extensively investigated as the potential method for quantum logical calculus.
In this thesis, the development of the investigation on the cavity QED system is reviewed firstly, including the atom beam, cold atom and Doppler-broaden medium, etc. And then, our works on the two-level Doppler-broaden atom and FP cavity system under large number density and large power condition, are mainly described, including the experiments and theories. Additionally, we discuss the transport effect and the nonlinear effect when the repump laser is added in the system. As followed:
1. Investigating the spectrum of the atom and cavity system under different conditions. The abundant, unique and novel phenomenon under different conditions in the system, are observed. For the large number density and large probe power, the phenomena that the double normal mode splitting peaks will be inosculated into one peak owing to the anharmonicity does not occur, because of the hole-burning effect which causes the appearance of the saturated absorption transparent peak with two semicircular and vesicular peaks. And with the increasing of the number density, the quasi-three-peak structure evolves into five-peak structure. And at the same time, the height of the peaks is shortened due to the absorption. And further, as the atom number rising, the hole-burning effect disappears gradually, and the center peak and normal mode splitting peaks in the central range disappear, too. While the most important thing is that a novel structure-multiple normal mode splitting peaks—in the transmission spectrum appears when the coupling strength exceeds the half of the free spectrum range. The new and interesting structure occurs in the large coupling strength range, and here, we shall give a theoretical analysis.
2. Observing the transport effect of the repump laser and the nonlinear effect. In our experiment, in order to increase the atom number density, we add the repump laser which excites the atoms from the ground state F=3 to the excited state (the medium is the ~(85)Rb vapor, the two levels are the levels of the ~(85)Rb D2 line) . As a result, the number density is increased for the probe laser, and the system appears different behaviors under different conditions. That is to say, 1) under low temperature and low repump power, we have observed the transport effect of the repump laser. 2) the nonlinear effect under high temperature. As we limit the system temperature and the repump power, the result of changing repump power is same with the change of the temperature. This effect illuminates that the repump laser excites the ground state F=3 into the excited state, and the excited atoms are transferred to another ground state F=2. For the probe laser, this effect is same as increasing the temperature. When the temperature is increased, the atom number density rises accordingly. But at the same time, more atoms return to the ground state F=3 because of the strong collision among the atoms, so the role of the repump laser is more obvious. So under the strong probe power, the nonlinear effects-selif-fucusing effect-emerge. The is the first experiment finished in the atom-cavity system, and which will be important for the study in the field.
The characterized works are summarized as followed:
1. Discussing the spectrum of the two-level Doppler-broaden medium and cavity system under different conditions. Especially in the strong coupling range, the structure of the multiple normal mode splitting peaks is discussed in detail.
2. Investigating the transport effect and the nonlinear effect after adding the repump laser.
引文
[1]E M Purcell, Spontaneous emission probabilities at radio frequencies, Phys. Rev. 1946, 69,681.
[2]Pellizzari T, Gardiner S A, Cirac Ji, Zoller P, Decoherence, Continuous Observation, and quantum Computation: A Cavity QED Model, Phys. Rev. Lett. 1995,75, 3788.
[3]Turchette Q A, Hood C J, Lange H J W, Measurement of Conditional Phase Shifts for Quantum Logic, Phys. Rev. Lett, 1995, 75,4710.
[4]Parkins A S, Marte P, Zoller P, Kimble H J, Synthesis of Arbitrary Quantum State via Adiabatic Transfer of Zeeman Coherence, Phys. Rev. Lett. 1993, 71, 3095.
[5]Law C K, Kimble H J, Determinstic Generation of Abit-Stream of Single-Photon Pulses, Journal of Modern Optics, 1997,44,2067.
[6]Ciriac J I, Zoller P, Kimble J H, Mabuchi, Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network, Phys. Rev. Lett, 1997, 78, 3221.
[7]Y. Kaluzny, P Goy, M Gross, J M Raimond, and S Haroche, Observation of self- Induced Rabi Oscillations in Two-Level Atoms Excited Inside a Resonant Cavity: The Ringing Regime of Superradiance, Phys. Rev. Lett, 1983, 51, 1175.
[8]R J Thompson, R J Brecha, H J Kimble, and H J Carmichael, Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity, Phys. Rev. Lett., 1989, 63,240.
[9]J E Field, Vacuum-Rabi-splitting-induced transparency, Phys. Rev. A, 1993, 47, 5064.
[10]R J Thompson, G Rempe, and H J Kimble, Observation of normal-mode splitting for an atom in an optical cavity, Phys. Rev. Lett., 1992, 68, 1132.
[11]Gessler Hernandez, Jiepeng Zhang, and Yifu Zhu, Vacuum Rabi splitting and intracavity dark state in a cavity-atom system, Phys. Rev. A, 2007, 76, 053814.
[12]Haibin Wu, J Gea-Banacloche, and Min Xiao, Observation of Intracavity electromagnetically Induced Transparency and Polariton Resonances in a Doppler- Broadened Medium, Phys. Rev. Lett., 2008, 100, 173602.
[13]Hai Wang, D J Goorskey, W H Burkett, and Min Xiao, Cavity-Linewidth Narrowing by Means of Electromagnetically Induced Transparency, Opt. Lett., 2000, 25, 1732.
[14]T Opatrny and D G Welsch, Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency, Phys. Rev. A, 2001, 64,023805.
[15]Cleo L Bentley, Jiaren Liu, and Yan Liao, Cavity electromagnetically induced transparency of driven-three-level atoms: A transparent window narrowing below a natural width, Phys. Rev. A, 2000,61,023811.
[16]G S Agarwal and Surya P Tewari, Optical Instability with dispersion, Phys. Rev. A, 1980,21,1638.
[17]L Gammaitoni, F Marchesoni, E Menichella-Saetta, and S Santucci, Stochastic Resonance in Bistable Systems, Phys. Rev. Lett., 1989, 62,349.
[18]G Broggi and L A Lugiato, Transient noise-induced optical bistability, Phys. Rev. A, 1984,29,2949.
[19]Andrew J Irwin, Simon J Fraser, and Raymond Kapral, Stochastically induced coherence in bistable systems, Phys. Rev. Lett., 1990,64,2343.
[20]Amitabh Joshi, Andy Brown, Hai Wang, and Min Xiao, Controlling Optical Bistability in a Three-Level Atomic System, Phys. Rev. A, 2003, 83,1301.
[21]G P Agrawal and H J Carmichael, Optical bistability through nonlinear dispersion and absorption, Phys. Rev. A, 1979, 19,2074.
[22]C Boden, I Roloff, and F Mitschke, Transition from deterministic to stochastic behavior in bistable systems, Phys. Rev. A, 1991,43,6558.
[23]H M Gibbs, S L McCall, and T N C Venkatesan, Differential Gain and Bistability Using a Sodium-Filled Fabry-Perot Interferometer, Phys. Rev. Lett., 1976, 36,1135.
[24] L A Orozco, M G Raizen, Xiao Min, R J Brecha, H J Kimble, Squeezed-state generation in optical bistability, JOSA B, 1987, B7,1490.
[25]Jaynes, Cummings, Comparison of quantum and semi-classical radiation theories with application to the beam maser, IEEE, 1963, 58, 89294.
[26]Changxin Wang and Reeta Vyas, Cavity-modified Maxwell-Bloch equations for the vacuum Rabi splitting, Phys. Rev. A, 1997, 55, 823.
[27]Yifu Zhu, Daniel J. Gauthier, S. E. Morin, Qilin Wu, H. J. Carmichael, and T. W. Mossberg, Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations, Phys. Rev. Lett., 1990,64,2499.
[28]J. Gripp, S. L. Mielke, and L. A. Orozco, Anharmonicity of the vacuum Rabi peaks in a many-atom system, Phys. Rev. A, 1996, 54, R3747.
[29] D. Grischkowsky, Self-Focusing of Light by Potassium Vapor, Phys. Rev. Lett., 1970, 24, 866.
[30] Vincent Wong, Robert W. Boyd, C. R. Stroud, Ryan S. Bennink, David L. Aronstein, and Q-Han Park, Honeycomb Pattern Formation by Laser-Beam Filamentation in Atomic Sodium Vapor, Phys. Rev. Lett., 2002, 88,113901.
[31] J. Gea-Banacloche, Haibin Wu, and Min Xiao, Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime, Phys. Rev. A, 2008,78,023828.
[32]Julio Gea-Banacloche, Yong-qing Li, Shao-zheng Jin, and Min Xiao, Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment, Phys. Rev. A, 1995, 51, 576.
[33]A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, Normal -mode splitting with large collective cooperativity, Phys. Rev. A, 2006, 74, 053821.
[34]H. J. Carmichael, Quantum fluctuations in absorptive bistability without adiabatic elimination, Phys. Rev. A, 1986, 33, 3262.
[35]J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly, Theory of Spontaneous Emission Line Shape in an Ideal Cavity, Phys. Rev. Lett., 1983, 51, 550.
[36]Day T, Luecke F, Brownell M, Continiously tunable diode laser, Laser and Optronics, 1993,6,15.
[37]Arnold A. S., Wilson J. S., Boshier M. G., A simple extended-cavity diode laser, Rev. Sci. Instrum. 1998,69, 1236.
[38]Hawthorn C. J., Weber K. P. Scholtena R. E., Littrow configuration tunable external cavity diode laser with fixed direction output beam, Rev. Sci. Intrum, 2001, 72, 4477.
[39]Affolderbacha C., Milletib G., A compact laser head with high frequency stability for Rb atomic clocks and optical instrumentation, Rev. Sci. Instruum., 2005, 76, 073108.
[40]Petridis C., Lindsay I. D., Stothard D. J. M., et al, Mode-hop-free tuning over 80GHz of an extended cavity diode laser without antireflection coating, Rev. Sic. Instrum. 2001, 72,3811.
[41]卫栋,熊德智,陈海霞,张靖,基于降温技术的宽范围外腔光栅可调半导体激光器,量子光学学报,2007,13,56.
[42]R.Ludeke,E.P.Harris,Tunable GaAs laser in an external dispersion cavity,Appl.Phys.Lett.,1972,20,499.
[43]K.C.Harvey,C.J.Myatt,External-cavity diode laser using a grazing-incidence diffraction grating,Opt.Lett.1991,16,910.
[44]Zhang J.,Wei D.Xie C D,Peng K C,Characteristics of absorption and dispersion for rubidium D2 lines with the modulation transfer spectrum,Opt.Express,2003,11,1338.
[45]Zhang J,Zhang T C,Dong R F,et al,Rb原子饱和吸收稳频半导体激光器系统,Acta Optica Sin.2003,23,197.
[2]Pellizzari T, Gardiner S A, Cirac Ji, Zoller P, Decoherence, Continuous Observation, and quantum Computation: A Cavity QED Model, Phys. Rev. Lett. 1995,75, 3788.
[3]Turchette Q A, Hood C J, Lange H J W, Measurement of Conditional Phase Shifts for Quantum Logic, Phys. Rev. Lett, 1995, 75,4710.
[4]Parkins A S, Marte P, Zoller P, Kimble H J, Synthesis of Arbitrary Quantum State via Adiabatic Transfer of Zeeman Coherence, Phys. Rev. Lett. 1993, 71, 3095.
[5]Law C K, Kimble H J, Determinstic Generation of Abit-Stream of Single-Photon Pulses, Journal of Modern Optics, 1997,44,2067.
[6]Ciriac J I, Zoller P, Kimble J H, Mabuchi, Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network, Phys. Rev. Lett, 1997, 78, 3221.
[7]Y. Kaluzny, P Goy, M Gross, J M Raimond, and S Haroche, Observation of self- Induced Rabi Oscillations in Two-Level Atoms Excited Inside a Resonant Cavity: The Ringing Regime of Superradiance, Phys. Rev. Lett, 1983, 51, 1175.
[8]R J Thompson, R J Brecha, H J Kimble, and H J Carmichael, Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity, Phys. Rev. Lett., 1989, 63,240.
[9]J E Field, Vacuum-Rabi-splitting-induced transparency, Phys. Rev. A, 1993, 47, 5064.
[10]R J Thompson, G Rempe, and H J Kimble, Observation of normal-mode splitting for an atom in an optical cavity, Phys. Rev. Lett., 1992, 68, 1132.
[11]Gessler Hernandez, Jiepeng Zhang, and Yifu Zhu, Vacuum Rabi splitting and intracavity dark state in a cavity-atom system, Phys. Rev. A, 2007, 76, 053814.
[12]Haibin Wu, J Gea-Banacloche, and Min Xiao, Observation of Intracavity electromagnetically Induced Transparency and Polariton Resonances in a Doppler- Broadened Medium, Phys. Rev. Lett., 2008, 100, 173602.
[13]Hai Wang, D J Goorskey, W H Burkett, and Min Xiao, Cavity-Linewidth Narrowing by Means of Electromagnetically Induced Transparency, Opt. Lett., 2000, 25, 1732.
[14]T Opatrny and D G Welsch, Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency, Phys. Rev. A, 2001, 64,023805.
[15]Cleo L Bentley, Jiaren Liu, and Yan Liao, Cavity electromagnetically induced transparency of driven-three-level atoms: A transparent window narrowing below a natural width, Phys. Rev. A, 2000,61,023811.
[16]G S Agarwal and Surya P Tewari, Optical Instability with dispersion, Phys. Rev. A, 1980,21,1638.
[17]L Gammaitoni, F Marchesoni, E Menichella-Saetta, and S Santucci, Stochastic Resonance in Bistable Systems, Phys. Rev. Lett., 1989, 62,349.
[18]G Broggi and L A Lugiato, Transient noise-induced optical bistability, Phys. Rev. A, 1984,29,2949.
[19]Andrew J Irwin, Simon J Fraser, and Raymond Kapral, Stochastically induced coherence in bistable systems, Phys. Rev. Lett., 1990,64,2343.
[20]Amitabh Joshi, Andy Brown, Hai Wang, and Min Xiao, Controlling Optical Bistability in a Three-Level Atomic System, Phys. Rev. A, 2003, 83,1301.
[21]G P Agrawal and H J Carmichael, Optical bistability through nonlinear dispersion and absorption, Phys. Rev. A, 1979, 19,2074.
[22]C Boden, I Roloff, and F Mitschke, Transition from deterministic to stochastic behavior in bistable systems, Phys. Rev. A, 1991,43,6558.
[23]H M Gibbs, S L McCall, and T N C Venkatesan, Differential Gain and Bistability Using a Sodium-Filled Fabry-Perot Interferometer, Phys. Rev. Lett., 1976, 36,1135.
[24] L A Orozco, M G Raizen, Xiao Min, R J Brecha, H J Kimble, Squeezed-state generation in optical bistability, JOSA B, 1987, B7,1490.
[25]Jaynes, Cummings, Comparison of quantum and semi-classical radiation theories with application to the beam maser, IEEE, 1963, 58, 89294.
[26]Changxin Wang and Reeta Vyas, Cavity-modified Maxwell-Bloch equations for the vacuum Rabi splitting, Phys. Rev. A, 1997, 55, 823.
[27]Yifu Zhu, Daniel J. Gauthier, S. E. Morin, Qilin Wu, H. J. Carmichael, and T. W. Mossberg, Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations, Phys. Rev. Lett., 1990,64,2499.
[28]J. Gripp, S. L. Mielke, and L. A. Orozco, Anharmonicity of the vacuum Rabi peaks in a many-atom system, Phys. Rev. A, 1996, 54, R3747.
[29] D. Grischkowsky, Self-Focusing of Light by Potassium Vapor, Phys. Rev. Lett., 1970, 24, 866.
[30] Vincent Wong, Robert W. Boyd, C. R. Stroud, Ryan S. Bennink, David L. Aronstein, and Q-Han Park, Honeycomb Pattern Formation by Laser-Beam Filamentation in Atomic Sodium Vapor, Phys. Rev. Lett., 2002, 88,113901.
[31] J. Gea-Banacloche, Haibin Wu, and Min Xiao, Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime, Phys. Rev. A, 2008,78,023828.
[32]Julio Gea-Banacloche, Yong-qing Li, Shao-zheng Jin, and Min Xiao, Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment, Phys. Rev. A, 1995, 51, 576.
[33]A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, Normal -mode splitting with large collective cooperativity, Phys. Rev. A, 2006, 74, 053821.
[34]H. J. Carmichael, Quantum fluctuations in absorptive bistability without adiabatic elimination, Phys. Rev. A, 1986, 33, 3262.
[35]J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly, Theory of Spontaneous Emission Line Shape in an Ideal Cavity, Phys. Rev. Lett., 1983, 51, 550.
[36]Day T, Luecke F, Brownell M, Continiously tunable diode laser, Laser and Optronics, 1993,6,15.
[37]Arnold A. S., Wilson J. S., Boshier M. G., A simple extended-cavity diode laser, Rev. Sci. Instrum. 1998,69, 1236.
[38]Hawthorn C. J., Weber K. P. Scholtena R. E., Littrow configuration tunable external cavity diode laser with fixed direction output beam, Rev. Sci. Intrum, 2001, 72, 4477.
[39]Affolderbacha C., Milletib G., A compact laser head with high frequency stability for Rb atomic clocks and optical instrumentation, Rev. Sci. Instruum., 2005, 76, 073108.
[40]Petridis C., Lindsay I. D., Stothard D. J. M., et al, Mode-hop-free tuning over 80GHz of an extended cavity diode laser without antireflection coating, Rev. Sic. Instrum. 2001, 72,3811.
[41]卫栋,熊德智,陈海霞,张靖,基于降温技术的宽范围外腔光栅可调半导体激光器,量子光学学报,2007,13,56.
[42]R.Ludeke,E.P.Harris,Tunable GaAs laser in an external dispersion cavity,Appl.Phys.Lett.,1972,20,499.
[43]K.C.Harvey,C.J.Myatt,External-cavity diode laser using a grazing-incidence diffraction grating,Opt.Lett.1991,16,910.
[44]Zhang J.,Wei D.Xie C D,Peng K C,Characteristics of absorption and dispersion for rubidium D2 lines with the modulation transfer spectrum,Opt.Express,2003,11,1338.
[45]Zhang J,Zhang T C,Dong R F,et al,Rb原子饱和吸收稳频半导体激光器系统,Acta Optica Sin.2003,23,197.