基于四能级结构原子的干涉和非经典激发
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摘要
光和原子的相互作用是量子光学实验一个重要的方向。光和原子相互作用,在共振附近会产生电磁感应透明现象。电磁感应透明是当前原子系统里的相干光学实验的理论基础,基于相干介质里的电磁感应透明的物理过程有非常丰富的实验现象和重要的应用。
原子系综在量子信息领域里有很多潜在的用途,例如:利用电磁感应透明实现光脉冲延迟的控制;利用原子系综产生具有非经典关联的窄带光子对。光脉冲延迟的有效控制可以保证波包的重合度.量子信息里最重要的一个方向就是实现远距离量子通信。由于光场随传播距离是指数衰减,所以实现远距离量子通信中量子中继的使用是必须的,Duan et al.提出使用原子系综做为量子中继。而要使用原子系综做为量子中继就要求连接中继的光子对必须是窄带光子对,能跟原子系综有效耦合。传统的光子对产生都是基于非线性晶体中的参量下转换,这种方法产生的光子对有很宽的线宽,不能有效跟原子系综耦合。用原子系综产生的光子对是窄带光子对,可以跟原子系综有效耦合,所以原子系综产生的窄带光子对在量子通信中可能会起到很重要的作用.
这篇论文的主题是利用远失谐拉曼峰进行光速控制和利用热原子系综产生具有非经典关联的窄带光子对。这篇论文的主要研究内容如下:
1.基于双拉曼峰结构的光速控制。对光速的控制在最近的几年里非常受关注。我们提出一种利用四能级系统里的双远失谐拉曼峰进行光速控制的方案。在四能级系统中这种拉曼峰具有很好的频率对称性,在光泵的作用下可以保持形状地从很强的吸收峰变成很强的增益峰。我们在理论上证明.这种方案可以将光场的群速度从远慢于光速一直变到远快于光速,并且在这个过程中波包不会经历大的形变。这个方案可以有效地控制光脉冲从正延迟到负延迟。
2.利用非简并四波混频过程实现光学轨道角动量合成.光场的轨道角动量是光场一种很有意思的特性,在近年来吸引了很多人的兴趣。在实验中我们验证在四波混频过程中光场的轨道角动量守恒,利用四波混频可以实现光场的轨道角动量合成。
3.在热原子系综里利用自发四波混频过程产生具有非经典关联的窄带光子对。关联光子对在量子信息领域里有很大的作用,很多年来基于非线性晶体的参量下转换一直是产生关联光子对的标准方法,但这种方法产生的光子对具有很大的线宽,不能跟原子有效耦合。用原子系综可以产生窄线宽光子对。国际上已经有一些实验小组在冷原子里产生窄带关联光子对,并给出光子对的时间分辨的二阶关联函数。在热原子系综里虽然也有产生关联光子的报导,但是从来没给出产生的光子对的时间分辨二阶关联函数.在这里我们首次给出热原子系综产生的关联光子对的时间分辨关联计数.验证了产生的关联光子的二阶关联函数违背了Cauchy-schwarz不等式,具有量子关联特性。
4.验证热原子系综产生的光子对的轨道角动量纠缠。纠缠是量子力学里特有的一种奇妙的现象,是量子信息过程中一种重要的资源。光子的轨道角动量可以用来产生高维纠缠,使得某些量子信息过程有更高的效率。这里我们验证用热原子系综产生的光子对具有轨道角动量纠缠,这种光子对间的轨道角动量纠缠间接验证了热原子系综跟系统产生的光子具有轨道角动量纠缠。
The interaction between the light and the atomic system is one of the most important aspect in quantum optics, which provides us abundant of interesting phenomenon and application. The electromagnetically induced transparency(EIT) occurred when the lasers are arranged in the near resonant region of a coherent medium. The EIT is the basis of many optical experiments in atomic system.
There are many possible usage of atomic ensemble in the quantum information. For example, the EIT effect can be used to control the delay of the wave packets; the atomic ensemble can be used to generate the nonclassical correlated photon pairs. The controllable delay between the wave packets can keep the wave packets overlapped well. Long distant quantum communication is one of the most important aspect in quantum information. Photons are decayed exponentially as the increment of the distance, therefore quantum repeaters are needed in the long distance quantum communication. Duan et al. have shown us that the atomic ensemble can be used as the quantum repeater. Narrow bandwidth photon pairs are needed in order to use the atomic ensemble as the quantum repeater. The spontaneous parametric down conversion(SPDC) in the nonlinear crystal can generate photon pairs effectively. However the photon pairs generated by SPDC have very broad bandwidth, and can not couple with atomic ensemble effectively. The photon pairs generated in the atomic system have a very narrow bandwidth, and can couple with atomic ensemble effectively. Therefore narrow bandwidth photon pairs generated in the atomic ensemble may be very useful in the quantum communication.
In this dissertation we give a scheme which can be used to control the delay of the wave packet from positive delay to negative delay effectively, and experimentally demonstrate the generation of nonclassical correlated photon pairs using spontaneous four-wave-mixing process in hot atomic ensemble. The works presented in this dissertation are listed as follows,
1. Control of light speed: from slow light to superluminal light. Control of light speed has attracted much attention in the past years. We give a scheme which can be used to change the group velocity of probe field from slower-than-c to faster- than-c continuously by controlling the strength of an optical pump. We used a far detuning double-coupling structure, which will lead to two Raman absorptive peaks, and when an optical pump is added to the system the absorptive peaks will change into enhanced peaks, and the normal dispersion between the two peaks change into anomalous dispersion. Therefore the probe field can change from slow light to superluminal propagation. This scheme can control the delay of the pulse from positive to negative delay effectively.
2. Computation of topological charges of optical vortex via non-degenerate four-wave-mixing. Orbital angular momentum (OAM) of light, which has many interesting property, was quite unfamiliar to the researchers until very recently. In this experiment we show that the OAM will be preserved in the four-wave-mixing process. Therefore the four-wave-mixing process can be used for computation of topological charges of optical vortex.
3. Generation of nonclassical photon pairs in a hot atomic ensemble. Correlated photon pairs are very important in quantum information field. Usually, spontaneous parametric down-conversion in nonlinear crystal is used in the generation of the correlated photon pairs. However the photon pairs generated using this method have a very broad bandwidth. Narrow band photon pairs can be generated by atomic system. Although previous works had demonstrated the non-classical correlation between the Stokes and anti-Stokes photons generated in the hot atomic ensemble, there is not any previous work in the hot atomic ensemble which gives a clear picture of the time-resolved second order correlation function between the photon pairs. In the cold atomic system such a relation between the Stokes and anti-Stokes photons has been given out since the first experiment. This experiment gives the time-resolved second order correlation function between the photon pairs generated in a hot rubidium cell, and the violation of the Cauchy-Schwarz inequality intuitively. The scheme we used in this experiment is spontaneous four-wave-mixing.
4. Entanglement of the orbital angular momentum states of the photons generated in a hot atomic ensemble. Quantum protocols will be more efficient with high-dimensional entangled states. Photons carrying orbital angular momenta can be used to create a high-dimensional entangled state. In this paper we experimentally demonstrate the entanglement of the orbital angular momentum between the Stokes and anti-Stokes photons generated in a hot atomic ensemble using spontaneous four- wave-mixing. This experiment also demonstrates the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.
原子系综在量子信息领域里有很多潜在的用途,例如:利用电磁感应透明实现光脉冲延迟的控制;利用原子系综产生具有非经典关联的窄带光子对。光脉冲延迟的有效控制可以保证波包的重合度.量子信息里最重要的一个方向就是实现远距离量子通信。由于光场随传播距离是指数衰减,所以实现远距离量子通信中量子中继的使用是必须的,Duan et al.提出使用原子系综做为量子中继。而要使用原子系综做为量子中继就要求连接中继的光子对必须是窄带光子对,能跟原子系综有效耦合。传统的光子对产生都是基于非线性晶体中的参量下转换,这种方法产生的光子对有很宽的线宽,不能有效跟原子系综耦合。用原子系综产生的光子对是窄带光子对,可以跟原子系综有效耦合,所以原子系综产生的窄带光子对在量子通信中可能会起到很重要的作用.
这篇论文的主题是利用远失谐拉曼峰进行光速控制和利用热原子系综产生具有非经典关联的窄带光子对。这篇论文的主要研究内容如下:
1.基于双拉曼峰结构的光速控制。对光速的控制在最近的几年里非常受关注。我们提出一种利用四能级系统里的双远失谐拉曼峰进行光速控制的方案。在四能级系统中这种拉曼峰具有很好的频率对称性,在光泵的作用下可以保持形状地从很强的吸收峰变成很强的增益峰。我们在理论上证明.这种方案可以将光场的群速度从远慢于光速一直变到远快于光速,并且在这个过程中波包不会经历大的形变。这个方案可以有效地控制光脉冲从正延迟到负延迟。
2.利用非简并四波混频过程实现光学轨道角动量合成.光场的轨道角动量是光场一种很有意思的特性,在近年来吸引了很多人的兴趣。在实验中我们验证在四波混频过程中光场的轨道角动量守恒,利用四波混频可以实现光场的轨道角动量合成。
3.在热原子系综里利用自发四波混频过程产生具有非经典关联的窄带光子对。关联光子对在量子信息领域里有很大的作用,很多年来基于非线性晶体的参量下转换一直是产生关联光子对的标准方法,但这种方法产生的光子对具有很大的线宽,不能跟原子有效耦合。用原子系综可以产生窄线宽光子对。国际上已经有一些实验小组在冷原子里产生窄带关联光子对,并给出光子对的时间分辨的二阶关联函数。在热原子系综里虽然也有产生关联光子的报导,但是从来没给出产生的光子对的时间分辨二阶关联函数.在这里我们首次给出热原子系综产生的关联光子对的时间分辨关联计数.验证了产生的关联光子的二阶关联函数违背了Cauchy-schwarz不等式,具有量子关联特性。
4.验证热原子系综产生的光子对的轨道角动量纠缠。纠缠是量子力学里特有的一种奇妙的现象,是量子信息过程中一种重要的资源。光子的轨道角动量可以用来产生高维纠缠,使得某些量子信息过程有更高的效率。这里我们验证用热原子系综产生的光子对具有轨道角动量纠缠,这种光子对间的轨道角动量纠缠间接验证了热原子系综跟系统产生的光子具有轨道角动量纠缠。
The interaction between the light and the atomic system is one of the most important aspect in quantum optics, which provides us abundant of interesting phenomenon and application. The electromagnetically induced transparency(EIT) occurred when the lasers are arranged in the near resonant region of a coherent medium. The EIT is the basis of many optical experiments in atomic system.
There are many possible usage of atomic ensemble in the quantum information. For example, the EIT effect can be used to control the delay of the wave packets; the atomic ensemble can be used to generate the nonclassical correlated photon pairs. The controllable delay between the wave packets can keep the wave packets overlapped well. Long distant quantum communication is one of the most important aspect in quantum information. Photons are decayed exponentially as the increment of the distance, therefore quantum repeaters are needed in the long distance quantum communication. Duan et al. have shown us that the atomic ensemble can be used as the quantum repeater. Narrow bandwidth photon pairs are needed in order to use the atomic ensemble as the quantum repeater. The spontaneous parametric down conversion(SPDC) in the nonlinear crystal can generate photon pairs effectively. However the photon pairs generated by SPDC have very broad bandwidth, and can not couple with atomic ensemble effectively. The photon pairs generated in the atomic system have a very narrow bandwidth, and can couple with atomic ensemble effectively. Therefore narrow bandwidth photon pairs generated in the atomic ensemble may be very useful in the quantum communication.
In this dissertation we give a scheme which can be used to control the delay of the wave packet from positive delay to negative delay effectively, and experimentally demonstrate the generation of nonclassical correlated photon pairs using spontaneous four-wave-mixing process in hot atomic ensemble. The works presented in this dissertation are listed as follows,
1. Control of light speed: from slow light to superluminal light. Control of light speed has attracted much attention in the past years. We give a scheme which can be used to change the group velocity of probe field from slower-than-c to faster- than-c continuously by controlling the strength of an optical pump. We used a far detuning double-coupling structure, which will lead to two Raman absorptive peaks, and when an optical pump is added to the system the absorptive peaks will change into enhanced peaks, and the normal dispersion between the two peaks change into anomalous dispersion. Therefore the probe field can change from slow light to superluminal propagation. This scheme can control the delay of the pulse from positive to negative delay effectively.
2. Computation of topological charges of optical vortex via non-degenerate four-wave-mixing. Orbital angular momentum (OAM) of light, which has many interesting property, was quite unfamiliar to the researchers until very recently. In this experiment we show that the OAM will be preserved in the four-wave-mixing process. Therefore the four-wave-mixing process can be used for computation of topological charges of optical vortex.
3. Generation of nonclassical photon pairs in a hot atomic ensemble. Correlated photon pairs are very important in quantum information field. Usually, spontaneous parametric down-conversion in nonlinear crystal is used in the generation of the correlated photon pairs. However the photon pairs generated using this method have a very broad bandwidth. Narrow band photon pairs can be generated by atomic system. Although previous works had demonstrated the non-classical correlation between the Stokes and anti-Stokes photons generated in the hot atomic ensemble, there is not any previous work in the hot atomic ensemble which gives a clear picture of the time-resolved second order correlation function between the photon pairs. In the cold atomic system such a relation between the Stokes and anti-Stokes photons has been given out since the first experiment. This experiment gives the time-resolved second order correlation function between the photon pairs generated in a hot rubidium cell, and the violation of the Cauchy-Schwarz inequality intuitively. The scheme we used in this experiment is spontaneous four-wave-mixing.
4. Entanglement of the orbital angular momentum states of the photons generated in a hot atomic ensemble. Quantum protocols will be more efficient with high-dimensional entangled states. Photons carrying orbital angular momenta can be used to create a high-dimensional entangled state. In this paper we experimentally demonstrate the entanglement of the orbital angular momentum between the Stokes and anti-Stokes photons generated in a hot atomic ensemble using spontaneous four- wave-mixing. This experiment also demonstrates the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.
引文
Abram, I., R. K. Raj, J. L. Oudar, and G. Dolique, 1986, "Direct observation of the second-order coherence of parametrically generated light", Phys. Rev. Lett. 57(20), 2516.
Agarwal, G. S., T. N. Dey, and S. Menon, 2001, "Knob for changing light propagation from sublu-minal to superluminal", Phys. Rev. A 64(5), 053809.
Allen, L., M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, 1992, "Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes", Phys. Rev. A 45(11),8185.
Allen, L., M. J. Padgett, and M. Babiker, 1999, "The orbital angular momentum of light", volume 39 of PROGRESS IN OPTICS, pp. 291 - 372.
Arimondo, E., 1996, "Coherent population trapping in laser spectroscopy", volume 35 of PROGRESS IN OPTICS, pp. 257 - 354.
Arlt, J., K. Dholakia, L. Allen, and M. J. Padgett, 1998, "The production of multiringed laguerre-gaussian modes by computer-generated holograms", J. Mod. Opt. 45(6), 1231.
Autler, S. H., and C. H. Townes, 1955, "Stark effect in rapidly varying fields", Phys. Rev. 100(2),703.
Balic, V., 2005, Generation of narrow-bandwidth paired photons with electronically controllable waveforms, Ph.D. thesis, Stanford University.
Balic, V., D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, 2005, "Generation of paired photons with controllable waveforms", Phys. Rev. Lett. 94(18), 183601.
Barreiro, S., and J. W. R. Tabosa, 2003, "Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms", Phys. Rev. Lett. 90(13), 133001.
Barreiro, S., J. W. R. Tabosa, J. P. Torres, Y. Deyanova, and L. Torner, 2004, "Four-wave mixing of light beams with engineered orbital angular momentum in cold cesium atoms", Opt. Lett. 29( 13),1515.
Bechmann-Pasquinucci, H., and A. Peres, 2000, "Quantum cryptography with 3-state systems",Phys. Rev. Lett. 85(15), 3313.
Bergmann, K., H. Theuer, and B. W. Shore, 1998, "Coherent population transfer among quantum states of atoms and molecules", Rev. Mod. Phys. 70(3), 1003.
Berman, P. R., D. G. Steel, G. Khitrova, and J. Liu, 1988, "Effects of radiative decay in four-wave-mixing spectroscopy: Narrow resonances produced by nonconservation of population, alignment, and orientation", Phys. Rev. A 38(1), 252.
Bigelow, M. S., N. N. Lepeshkin, and R. W. Boyd, 2003, "Superluminal and Slow Light Propagation in a Room-Temperature Solid", Science 301(5630), 200.
Bigelow, M. S., N. N. Lepeshkin, and R. W. Boyd, 2004, "Ultra-slow and superluminal light propagation in solids at room temperature", JOURNAL OF PHYSICS-CONDENSED MATTER 16(46), R1321.
Bortman-Arbiv, D., A. D. Wilson-Gordon, and H. Friedmann, 2001, "Phase control of group velocity: From subluminal to superluminal light propagation", Phys. Rev. A 63(4), 043818.
Bourennane, M., A. Karlsson, and G. Bjork, 2001, "Quantum key distribution using multilevel encoding", Phys. Rev. A 64(1), 012306.
Boyd, R. W., M. G. Raymer, P. Narum, and D. J. Harter, 1981, "Four-wave parametric interactions in a strongly driven two-level system", Phys. Rev. A 24(1), 411.
Braje, D. A., V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, 2004, "Frequency mixing using electro-magnetically induced transparency in cold atoms", Phys. Rev. Lett. 93(18), 183601.
Budker, D., D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, 1999, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation", Phys.Rev. Lett. 83(9), 1767.
Burnham, D. C., and D. L. Weinberg, 1970, "Observation of simultaneity in parametric production of optical photon pairs", Phys. Rev. Lett. 25(2), 84.
Calvo, G. F., A. Picon, and E. Bagan, 2006, "Quantum field theory of photons with orbital angular momentum", Phys. Rev. A 73(1), 013805.
Duan, L. M., J. I. Cirac, and P. Zoller, 2002, "Three-dimensional theory for interaction between atomic ensembles and free-space light", Phys. Rev. A 66(2), 023818.
Duan, L. M., M. D. Lukin, J. I. Cirac, and P. Zoller, 2001, "Long-distance quantum communication with atomic ensembles and linear optics", Nature 414(6862), 413 .
Eisaman, M. D., A. Andre, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, 2005, "Elec-tromagnetically induced transparency with tunable single-photon pulses", Nature 438(7069), 837
Fisher, R. A. (ed.), 1983, Optical phase conjugation (Academic Press, New York).
Fleischhauer, M., A. Imamoglu, and J. P. Marangos, 2005, "Electromagnetically induced transparency: Optics in coherent media", Rev. Mod. Phys. 77(2), 633 .
Fleischhauer, M., and M. D. Lukin, 2000, "Dark-state polaritons in electromagnetically induced transparency", Phys. Rev. Lett. 84(22), 5094.
Fleischhauer, M., and M. D. Lukin, 2002, "Quantum memory for photons: Dark-state polaritons",Phys. Rev. A 65(2), 022314.
Fleischhauer, M., M. D. Lukin, A. B. Matsko, and M. O. Scully, 2000, "Threshold and linewidth of a mirrorless parametric oscillator", Phys. Rev. Lett. 84(16), 3558 .
Fleischhauer, M., and M. O. Scully, 1994, "Quantum sensitivity limits of an optical magnetometer based on atomic phase coherence", Phys. Rev. A 49(3), 1973.
Galindo, A., and M. A. Martin-Delgado, 2002, "Information and computation: Classical and quantum aspects", Rev. Mod. Phys. 74(2), 347.
Gaubatz, U., P. Rudecki, S. Schiemann, and K. Bergmann, 1990, "Population transfer between molecular vibrational levels by stimulated raman-scattering with partially overlapping laserfields- a new concept and experimental results", J. Chem. Phys. 92(9), 5363 .
Goren, C, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, 2003, "Switching from positive to negative dispersion in transparent degenerate and near-degenerate systems", Phys. Rev. A 68(4), 043818.
Guedes, I., L. Misoguti, and S. C. Zilio, 2006, "Precise control of superluminal and slow light propagation by transverse phase modulation", Opt. Express 14(13), 6201.
Hakuta, K., M. Suzuki, M. Katsuragawa, and J. Z. Li, 1997, "Self-induced phase matching in parametric anti-stokes stimulated raman scattering", Phys. Rev. Lett. 79(2), 209.
Harris, S. E., 1997, "Electromagnetically induced transparency", Phys. Today 50(7), 36 .
Harris, S. E., J. E. Field, and A. Imamoglu, 1990, "Nonlinear optical processes using electromagnetically induced transparency.", Phys. Rev. Lett. 64(10), 1107.
Harris, S. E., J. E. Field, and A. Kasapi, 1992, "Dispersive properties of electromagnetically induced transparency", Phys. Rev. A 46(1), R29.
Harris, S. E., and L. V. Hau, 1999, "Nonlinear optics at low light levels", Phys. Rev. Leu. 82(23),4611.
Harris, S. E., and M. Jain, 1997, "Optical parametric oscillators pumped by population-trapped atoms", Opt. Lett. 22(9), 636 .
Harris, S. E., and A. V. Sokolov, 1997, "Broadband spectral generation with refractive index control", Phys. Rev. A 55(6), R4019.
Hau, L. V, S. E. Harris, 2. Dutton, and C. H. Behroozi, 1999, "Light speed reduction to 17 metres per second in an ultracold atomic gas", Nature 397(6720), 594 .
Heckenberg, N. R., R. Mcduff, C. P. Smith, and A. G. White, 1992, "Generation of optical-phase singularities by computer-generated holograms", Opt. Lett. 17(3), 221 .
Hemmer, P. R., D. P. Katz, J. Donoghue, M. Croningolomb, M. S. Shahriar, and P. Kumar, 1995,"Efficient low-intensity optical-phase conjugation based on coherent population trapping in sodium", Opt. Lett. 20(9), 982 .
Hong, C. K., Z. Y. Ou, and L. Mandel, 1987, "Measurement of subpicosecond time intervals between two photons by interference", Phys. Rev. Lett. 59(18), 2044.
Imamoglu, A., 1991, Ph.D. thesis (Stanford University).
Inoue, R., N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, 2006, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon", Phys.Rev. A 74(5), 053809.
Jain, M., H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, 1996, "Efficient nonlinear frequency conversion with maximal atomic coherence", Phys. Rev. Lett. 77(21), 4326.
James, D. F. V., P. G. Kwiat, W. J. Munro, and A. G. White, 2001, "Measurement of qubits", Phys.Rev. A 64(5), 052312.
Jiang, W., Q.-F. Chen, Y.-S. Zhang, and G.-C. Guo, 2006, "Computation of topological charges of optical vortices via nondegenerate four-wave mixing", Phys. Rev. A 74(4), 043811.
Jiang, W., Q.-F. Chen, Y.-S. Zhang, and G.-C. Guo, 2006, "Optical pumping-assisted electromag-netically induced transparency", Phys. Rev. A 73(5), 053804.
Kasapi, A., M. Jain, G. Y. Yin, and S. E. Harris, 1995, "Electromagnetically induced transparency:Propagation dynamics", Phys. Rev. Lett. 74(13), 2447.
Kash, M. M., V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev,E. S. Fry, and M. O. Scully, 1999, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas", Phys. Rev. Lett. 82(26), 5229.
Kolchin, P., 2007, "Electromagnetically-induced-transparency-based paired photon generation",Phys. Rev. A 75(3).
Korsunsky, E. A., and D. V. Kosachiov, 1999, "Phase-dependent nonlinear optics with double-λ atoms", Phys. Rev. A 60(6), 4996.
Korsunsky, E. A., N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, 1999, "Phase-dependent electromagnetically induced transparency", Phys. Rev. A 59(3), 2302 .
Kuklinski, J. R., U. Gaubatz, F. T. Hioe, and K. Bergmann, 1989, "Adiabatic population transfer in a three-level system driven by delayed laser pulses", Phys. Rev. A 40(11), 6741.
Kuzmich, A., W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble,2003, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles", Nature 423(6941), 731 .
Langford, N. K., R. B. Dalton, M. D. Harvey, J. L. O'Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett,and A. G. White, 2004, "Measuring entangled qutrits and their use for quantum bit commitment",Phys. Rev. Lett. 93(5), 053601.
Lin, J., A. I. Rubiera, and Y. Zhu, 1995, "Nearly degenerate four-wave mixing with bichromatic laser fields in a rb atomic system", Phys. Rev. A 52(6), 4882.
Liu, C., Z. Dutton, C. H. Behroozi, and L. V. Hau, 2001, "Observation of coherent optical information storage in an atomic medium using halted light pulses", Nature 409(6819), 490 .
Liu, J., and D. G. Steel, 1988, "High-resolution four-wave-mixing spectroscopy of collision-induced narrow resonances in doppler-broadened systems",.Phys. Rev. A 38(9), 4639.
Longhi, S., 2005, "Group delay tuning in active fiber bragg gratings: From superluminal to subluminal pulse reflection", Phys. Rev. E 72(5), 056614.
Lu, Y. J., and Z. Y. Ou, 2000, "Optical parametric oscillator far below threshold: Experiment versus theory", Phys. Rev. A 62(3), 033804.
Lukin, M. D., M. Fleischhauer, M. O. Scully, and V. L. Velichansky, 1998, "Intracavity electromagnetically induced transparency", Opt. Lett. 23(4), 295 .
Lukin, M. D., A. B. Matsko, M. Fleischhauer, and M. O. Scully, 1999, "Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence", Phys. Rev. Lett. 82(9),1847.
Mair, A., A. Vaziri, G. Weihs, and A. Zeilinger, 2001, "Entanglement of the orbital angular momentum states of photons", Nature 412(6844), 313 .
Mandel, L., and E. Wolf, 1995, Optical coherence and quantum optics (Cambridge University Press).
Matsukevich, D. N., T. Chaneliere, M. Bhattacharya, S. Y. Lan, S. D. Jenkins, T. A. B. Kennedy,and A. Kuzmich, 2005, "Entanglement of a photon and a collective atomic excitation", Phys.Rev. Lett. 95(4), 040405.
Mazets, I. E., and B. G. Matisov, 1996, "Adiabatic raman polariton in a bose condensate", JETP Lett. 64(7), 515.
Merriam, A. J., S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, 2000, "Efficient nonlinear frequency conversion in an all-resonant double-lambda system", Phys. Rev. Lett.84(23), 5308 .
Merriam, A. J., S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, 1999, "Efficientgas-phase generation of coherent vacuum ultraviolet radiation", Opt. Lett. 24(9), 625 .
Nielsen, M. A., and I. L. Chuang, 2000, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England).
Nye, J. F., and M. V. Berry, 1974, "Dislocations in wave trains", Proc. R. Soc. London A 336(1605),165.
Ooi, C. H. R., M. O. Scully, Q. Q. Sun, and M. S. Zubairy, 2007, "Correlation of photon pairs from the double raman amplifier: Generalized analytical quantum langevin theory", Phys. Rev. A 75.
Oreg, J., F. T. Hioe, and J. H. Eberly, 1984, "Adiabatic following in multilevel systems", Phys. Rev.A 29(2), 690.
Ou, Z. Y., and Y. J. Lu, 1999, "Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons", Phys. Rev. Lett. 83(13), 2556.
Phillips, D. F., A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, 2001, "Storage of light in atomic vapor", Phys. Rev. Lett. 86(5), 783 .
Reinties, J. F., 1984, Nonlinear optical parametric processes in liquids and gases (New York :Academic Press).
Schmidt, O., R. Wynands, Z. Hussein, and D. Meschede, 1996, "Steep dispersion and group velocity below c/3000 in coherent population trapping", Phys. Rev. A 53( 1), R27 .
Scully, M. O., and M. Fleischhauer, 1992, "High-sensitivity magnetometer based on index-enhanced media", Phys. Rev. Lett. 69(9), 1360.
Scully, M. O., E. S. Fry, C. H. R. Ooi, and K. Wodkiewicz, 2006, "Directed spontaneous emission from an extended ensemble of n atoms: Timing is everything", Phys. Rev. Lett. 96(1), 010501.
Steck, D. A., 2003, "Alkali d line data", URL http: //steck .us/alkalidata.
Steel, D. G., and J. T. Remillard, 1987, "Resonant nearly degenerate backward four-wave mixing in open and closed systems", Phys. Rev. A 36(9), 4330.
Tabosa, J. W. R., and D. V. Petrov, 1999, "Optical pumping of orbital angular momentum of light in cold cesium atoms", Phys. Rev. Lett. 83(24), 4967.
Turukhin, A. V., V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, 2001, "Observation of ultraslow and stored light pulses in a solid", Phys. Rev. Lett. 88(2),023602.
Turukhin, A. V., V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer,2002, "Observation of ultraslow and stored light pulses in a solid.", Phys. Rev. Lett. 88(2).
Vaziri, A., J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, 2003, "Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum", Phys. Rev. Lett. 91(22),227902.
Vaziri, A., G. Weihs, and A. Zeilinger, 2002a, "Experimental two-photon, three-dimensional entanglement for quantum communication", Phys. Rev. Lett. 89(24), 240401.
Vaziri, A., G. Weihs, and A. Zeilinger, 2002b, "Superpositions of the orbital angular momentum for applications in quantum experiments", J. Opt. B: Quantum Semiclass. Opt. 4(2), S47 .
van der Wai, C. H., M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M.D. Lukin, 2003, "Atomic memory for correlated photon states", Science 301(5630), 196 .
Wang, L. J., A. Kuzmich, and A. Dogariu, 2000, "Gain-assisted superluminal light propagation",Nature 406, 277.
Wootters, W. K., 1998, "Entanglement of formation of an arbitrary state of two qubits", Phys. Rev.Lett. 80(10), 2245.
Zhang, G. Z., K. Hakuta, and B. P. Stoicheff, 1993, "Nonlinear optical generation using electromag-netically induced transparency in atomic hydrogen", Phys. Rev. Lett. 71(19), 3099.
Zibrov, A. S., M. D. Lukin, and M. O. Scully, 1999, "Nondegenerate parametric self-oscillation viamultiwave mixing in coherent atomic media", Phys. Rev. Lett. 83(20), 4049 .
Agarwal, G. S., T. N. Dey, and S. Menon, 2001, "Knob for changing light propagation from sublu-minal to superluminal", Phys. Rev. A 64(5), 053809.
Allen, L., M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, 1992, "Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes", Phys. Rev. A 45(11),8185.
Allen, L., M. J. Padgett, and M. Babiker, 1999, "The orbital angular momentum of light", volume 39 of PROGRESS IN OPTICS, pp. 291 - 372.
Arimondo, E., 1996, "Coherent population trapping in laser spectroscopy", volume 35 of PROGRESS IN OPTICS, pp. 257 - 354.
Arlt, J., K. Dholakia, L. Allen, and M. J. Padgett, 1998, "The production of multiringed laguerre-gaussian modes by computer-generated holograms", J. Mod. Opt. 45(6), 1231.
Autler, S. H., and C. H. Townes, 1955, "Stark effect in rapidly varying fields", Phys. Rev. 100(2),703.
Balic, V., 2005, Generation of narrow-bandwidth paired photons with electronically controllable waveforms, Ph.D. thesis, Stanford University.
Balic, V., D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, 2005, "Generation of paired photons with controllable waveforms", Phys. Rev. Lett. 94(18), 183601.
Barreiro, S., and J. W. R. Tabosa, 2003, "Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms", Phys. Rev. Lett. 90(13), 133001.
Barreiro, S., J. W. R. Tabosa, J. P. Torres, Y. Deyanova, and L. Torner, 2004, "Four-wave mixing of light beams with engineered orbital angular momentum in cold cesium atoms", Opt. Lett. 29( 13),1515.
Bechmann-Pasquinucci, H., and A. Peres, 2000, "Quantum cryptography with 3-state systems",Phys. Rev. Lett. 85(15), 3313.
Bergmann, K., H. Theuer, and B. W. Shore, 1998, "Coherent population transfer among quantum states of atoms and molecules", Rev. Mod. Phys. 70(3), 1003.
Berman, P. R., D. G. Steel, G. Khitrova, and J. Liu, 1988, "Effects of radiative decay in four-wave-mixing spectroscopy: Narrow resonances produced by nonconservation of population, alignment, and orientation", Phys. Rev. A 38(1), 252.
Bigelow, M. S., N. N. Lepeshkin, and R. W. Boyd, 2003, "Superluminal and Slow Light Propagation in a Room-Temperature Solid", Science 301(5630), 200.
Bigelow, M. S., N. N. Lepeshkin, and R. W. Boyd, 2004, "Ultra-slow and superluminal light propagation in solids at room temperature", JOURNAL OF PHYSICS-CONDENSED MATTER 16(46), R1321.
Bortman-Arbiv, D., A. D. Wilson-Gordon, and H. Friedmann, 2001, "Phase control of group velocity: From subluminal to superluminal light propagation", Phys. Rev. A 63(4), 043818.
Bourennane, M., A. Karlsson, and G. Bjork, 2001, "Quantum key distribution using multilevel encoding", Phys. Rev. A 64(1), 012306.
Boyd, R. W., M. G. Raymer, P. Narum, and D. J. Harter, 1981, "Four-wave parametric interactions in a strongly driven two-level system", Phys. Rev. A 24(1), 411.
Braje, D. A., V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, 2004, "Frequency mixing using electro-magnetically induced transparency in cold atoms", Phys. Rev. Lett. 93(18), 183601.
Budker, D., D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, 1999, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation", Phys.Rev. Lett. 83(9), 1767.
Burnham, D. C., and D. L. Weinberg, 1970, "Observation of simultaneity in parametric production of optical photon pairs", Phys. Rev. Lett. 25(2), 84.
Calvo, G. F., A. Picon, and E. Bagan, 2006, "Quantum field theory of photons with orbital angular momentum", Phys. Rev. A 73(1), 013805.
Duan, L. M., J. I. Cirac, and P. Zoller, 2002, "Three-dimensional theory for interaction between atomic ensembles and free-space light", Phys. Rev. A 66(2), 023818.
Duan, L. M., M. D. Lukin, J. I. Cirac, and P. Zoller, 2001, "Long-distance quantum communication with atomic ensembles and linear optics", Nature 414(6862), 413 .
Eisaman, M. D., A. Andre, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, 2005, "Elec-tromagnetically induced transparency with tunable single-photon pulses", Nature 438(7069), 837
Fisher, R. A. (ed.), 1983, Optical phase conjugation (Academic Press, New York).
Fleischhauer, M., A. Imamoglu, and J. P. Marangos, 2005, "Electromagnetically induced transparency: Optics in coherent media", Rev. Mod. Phys. 77(2), 633 .
Fleischhauer, M., and M. D. Lukin, 2000, "Dark-state polaritons in electromagnetically induced transparency", Phys. Rev. Lett. 84(22), 5094.
Fleischhauer, M., and M. D. Lukin, 2002, "Quantum memory for photons: Dark-state polaritons",Phys. Rev. A 65(2), 022314.
Fleischhauer, M., M. D. Lukin, A. B. Matsko, and M. O. Scully, 2000, "Threshold and linewidth of a mirrorless parametric oscillator", Phys. Rev. Lett. 84(16), 3558 .
Fleischhauer, M., and M. O. Scully, 1994, "Quantum sensitivity limits of an optical magnetometer based on atomic phase coherence", Phys. Rev. A 49(3), 1973.
Galindo, A., and M. A. Martin-Delgado, 2002, "Information and computation: Classical and quantum aspects", Rev. Mod. Phys. 74(2), 347.
Gaubatz, U., P. Rudecki, S. Schiemann, and K. Bergmann, 1990, "Population transfer between molecular vibrational levels by stimulated raman-scattering with partially overlapping laserfields- a new concept and experimental results", J. Chem. Phys. 92(9), 5363 .
Goren, C, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, 2003, "Switching from positive to negative dispersion in transparent degenerate and near-degenerate systems", Phys. Rev. A 68(4), 043818.
Guedes, I., L. Misoguti, and S. C. Zilio, 2006, "Precise control of superluminal and slow light propagation by transverse phase modulation", Opt. Express 14(13), 6201.
Hakuta, K., M. Suzuki, M. Katsuragawa, and J. Z. Li, 1997, "Self-induced phase matching in parametric anti-stokes stimulated raman scattering", Phys. Rev. Lett. 79(2), 209.
Harris, S. E., 1997, "Electromagnetically induced transparency", Phys. Today 50(7), 36 .
Harris, S. E., J. E. Field, and A. Imamoglu, 1990, "Nonlinear optical processes using electromagnetically induced transparency.", Phys. Rev. Lett. 64(10), 1107.
Harris, S. E., J. E. Field, and A. Kasapi, 1992, "Dispersive properties of electromagnetically induced transparency", Phys. Rev. A 46(1), R29.
Harris, S. E., and L. V. Hau, 1999, "Nonlinear optics at low light levels", Phys. Rev. Leu. 82(23),4611.
Harris, S. E., and M. Jain, 1997, "Optical parametric oscillators pumped by population-trapped atoms", Opt. Lett. 22(9), 636 .
Harris, S. E., and A. V. Sokolov, 1997, "Broadband spectral generation with refractive index control", Phys. Rev. A 55(6), R4019.
Hau, L. V, S. E. Harris, 2. Dutton, and C. H. Behroozi, 1999, "Light speed reduction to 17 metres per second in an ultracold atomic gas", Nature 397(6720), 594 .
Heckenberg, N. R., R. Mcduff, C. P. Smith, and A. G. White, 1992, "Generation of optical-phase singularities by computer-generated holograms", Opt. Lett. 17(3), 221 .
Hemmer, P. R., D. P. Katz, J. Donoghue, M. Croningolomb, M. S. Shahriar, and P. Kumar, 1995,"Efficient low-intensity optical-phase conjugation based on coherent population trapping in sodium", Opt. Lett. 20(9), 982 .
Hong, C. K., Z. Y. Ou, and L. Mandel, 1987, "Measurement of subpicosecond time intervals between two photons by interference", Phys. Rev. Lett. 59(18), 2044.
Imamoglu, A., 1991, Ph.D. thesis (Stanford University).
Inoue, R., N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, 2006, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon", Phys.Rev. A 74(5), 053809.
Jain, M., H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, 1996, "Efficient nonlinear frequency conversion with maximal atomic coherence", Phys. Rev. Lett. 77(21), 4326.
James, D. F. V., P. G. Kwiat, W. J. Munro, and A. G. White, 2001, "Measurement of qubits", Phys.Rev. A 64(5), 052312.
Jiang, W., Q.-F. Chen, Y.-S. Zhang, and G.-C. Guo, 2006, "Computation of topological charges of optical vortices via nondegenerate four-wave mixing", Phys. Rev. A 74(4), 043811.
Jiang, W., Q.-F. Chen, Y.-S. Zhang, and G.-C. Guo, 2006, "Optical pumping-assisted electromag-netically induced transparency", Phys. Rev. A 73(5), 053804.
Kasapi, A., M. Jain, G. Y. Yin, and S. E. Harris, 1995, "Electromagnetically induced transparency:Propagation dynamics", Phys. Rev. Lett. 74(13), 2447.
Kash, M. M., V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev,E. S. Fry, and M. O. Scully, 1999, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas", Phys. Rev. Lett. 82(26), 5229.
Kolchin, P., 2007, "Electromagnetically-induced-transparency-based paired photon generation",Phys. Rev. A 75(3).
Korsunsky, E. A., and D. V. Kosachiov, 1999, "Phase-dependent nonlinear optics with double-λ atoms", Phys. Rev. A 60(6), 4996.
Korsunsky, E. A., N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, 1999, "Phase-dependent electromagnetically induced transparency", Phys. Rev. A 59(3), 2302 .
Kuklinski, J. R., U. Gaubatz, F. T. Hioe, and K. Bergmann, 1989, "Adiabatic population transfer in a three-level system driven by delayed laser pulses", Phys. Rev. A 40(11), 6741.
Kuzmich, A., W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble,2003, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles", Nature 423(6941), 731 .
Langford, N. K., R. B. Dalton, M. D. Harvey, J. L. O'Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett,and A. G. White, 2004, "Measuring entangled qutrits and their use for quantum bit commitment",Phys. Rev. Lett. 93(5), 053601.
Lin, J., A. I. Rubiera, and Y. Zhu, 1995, "Nearly degenerate four-wave mixing with bichromatic laser fields in a rb atomic system", Phys. Rev. A 52(6), 4882.
Liu, C., Z. Dutton, C. H. Behroozi, and L. V. Hau, 2001, "Observation of coherent optical information storage in an atomic medium using halted light pulses", Nature 409(6819), 490 .
Liu, J., and D. G. Steel, 1988, "High-resolution four-wave-mixing spectroscopy of collision-induced narrow resonances in doppler-broadened systems",.Phys. Rev. A 38(9), 4639.
Longhi, S., 2005, "Group delay tuning in active fiber bragg gratings: From superluminal to subluminal pulse reflection", Phys. Rev. E 72(5), 056614.
Lu, Y. J., and Z. Y. Ou, 2000, "Optical parametric oscillator far below threshold: Experiment versus theory", Phys. Rev. A 62(3), 033804.
Lukin, M. D., M. Fleischhauer, M. O. Scully, and V. L. Velichansky, 1998, "Intracavity electromagnetically induced transparency", Opt. Lett. 23(4), 295 .
Lukin, M. D., A. B. Matsko, M. Fleischhauer, and M. O. Scully, 1999, "Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence", Phys. Rev. Lett. 82(9),1847.
Mair, A., A. Vaziri, G. Weihs, and A. Zeilinger, 2001, "Entanglement of the orbital angular momentum states of photons", Nature 412(6844), 313 .
Mandel, L., and E. Wolf, 1995, Optical coherence and quantum optics (Cambridge University Press).
Matsukevich, D. N., T. Chaneliere, M. Bhattacharya, S. Y. Lan, S. D. Jenkins, T. A. B. Kennedy,and A. Kuzmich, 2005, "Entanglement of a photon and a collective atomic excitation", Phys.Rev. Lett. 95(4), 040405.
Mazets, I. E., and B. G. Matisov, 1996, "Adiabatic raman polariton in a bose condensate", JETP Lett. 64(7), 515.
Merriam, A. J., S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, 2000, "Efficient nonlinear frequency conversion in an all-resonant double-lambda system", Phys. Rev. Lett.84(23), 5308 .
Merriam, A. J., S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, 1999, "Efficientgas-phase generation of coherent vacuum ultraviolet radiation", Opt. Lett. 24(9), 625 .
Nielsen, M. A., and I. L. Chuang, 2000, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England).
Nye, J. F., and M. V. Berry, 1974, "Dislocations in wave trains", Proc. R. Soc. London A 336(1605),165.
Ooi, C. H. R., M. O. Scully, Q. Q. Sun, and M. S. Zubairy, 2007, "Correlation of photon pairs from the double raman amplifier: Generalized analytical quantum langevin theory", Phys. Rev. A 75.
Oreg, J., F. T. Hioe, and J. H. Eberly, 1984, "Adiabatic following in multilevel systems", Phys. Rev.A 29(2), 690.
Ou, Z. Y., and Y. J. Lu, 1999, "Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons", Phys. Rev. Lett. 83(13), 2556.
Phillips, D. F., A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, 2001, "Storage of light in atomic vapor", Phys. Rev. Lett. 86(5), 783 .
Reinties, J. F., 1984, Nonlinear optical parametric processes in liquids and gases (New York :Academic Press).
Schmidt, O., R. Wynands, Z. Hussein, and D. Meschede, 1996, "Steep dispersion and group velocity below c/3000 in coherent population trapping", Phys. Rev. A 53( 1), R27 .
Scully, M. O., and M. Fleischhauer, 1992, "High-sensitivity magnetometer based on index-enhanced media", Phys. Rev. Lett. 69(9), 1360.
Scully, M. O., E. S. Fry, C. H. R. Ooi, and K. Wodkiewicz, 2006, "Directed spontaneous emission from an extended ensemble of n atoms: Timing is everything", Phys. Rev. Lett. 96(1), 010501.
Steck, D. A., 2003, "Alkali d line data", URL http: //steck .us/alkalidata.
Steel, D. G., and J. T. Remillard, 1987, "Resonant nearly degenerate backward four-wave mixing in open and closed systems", Phys. Rev. A 36(9), 4330.
Tabosa, J. W. R., and D. V. Petrov, 1999, "Optical pumping of orbital angular momentum of light in cold cesium atoms", Phys. Rev. Lett. 83(24), 4967.
Turukhin, A. V., V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, 2001, "Observation of ultraslow and stored light pulses in a solid", Phys. Rev. Lett. 88(2),023602.
Turukhin, A. V., V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer,2002, "Observation of ultraslow and stored light pulses in a solid.", Phys. Rev. Lett. 88(2).
Vaziri, A., J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, 2003, "Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum", Phys. Rev. Lett. 91(22),227902.
Vaziri, A., G. Weihs, and A. Zeilinger, 2002a, "Experimental two-photon, three-dimensional entanglement for quantum communication", Phys. Rev. Lett. 89(24), 240401.
Vaziri, A., G. Weihs, and A. Zeilinger, 2002b, "Superpositions of the orbital angular momentum for applications in quantum experiments", J. Opt. B: Quantum Semiclass. Opt. 4(2), S47 .
van der Wai, C. H., M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M.D. Lukin, 2003, "Atomic memory for correlated photon states", Science 301(5630), 196 .
Wang, L. J., A. Kuzmich, and A. Dogariu, 2000, "Gain-assisted superluminal light propagation",Nature 406, 277.
Wootters, W. K., 1998, "Entanglement of formation of an arbitrary state of two qubits", Phys. Rev.Lett. 80(10), 2245.
Zhang, G. Z., K. Hakuta, and B. P. Stoicheff, 1993, "Nonlinear optical generation using electromag-netically induced transparency in atomic hydrogen", Phys. Rev. Lett. 71(19), 3099.
Zibrov, A. S., M. D. Lukin, and M. O. Scully, 1999, "Nondegenerate parametric self-oscillation viamultiwave mixing in coherent atomic media", Phys. Rev. Lett. 83(20), 4049 .