冷原子介质中超慢光的非线性传播特性研究
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摘要
激光的发明导致了非线性光学的诞生。非线性光学的研究大大扩展了传统光学的研究领域,促进了非线性和精密光谱学等新型光学技术的产生和发展,提供了产生新波段高强度相干辐射的强有力手段。光与物质相互作用过程中呈现的丰富多彩的非线性现象,是非线性物理学最为重要的研究对象之一。
传统的非线性光学存在以下困难:由于普通的非共振介质只能提供微弱的非线性响应,因此必须使用很强的光源才能得到足够的非线性效应。为了在较弱的输入光强下得到较强的非线性响应,必须使入射光场的频率接近介质的共振频率。但是由于共振,介质对入射光场的吸收达到峰值,从而使光场受到很大的损耗。由于这一原因,长期以来人们一直认为利用光与介质的共振效应来实现非线性效应的增强是非常困难的。
近年来,由于电磁感应透明(EIT)效应的研究,相干介质的弱光非线性光学的研究引起了人们的极大关注。EIT的基本原理是利用控制光场所诱导的原子量子态的之间的干涉效应消除介质对入射探测光场的吸收。EIT可使介质的色散特性产生重大改变,从而为人工调控介质的线性与非光学性质开辟了新途经。利用EIT导致的群速度减慢可制作新型的光学延迟器件,实现冷原子介质中的量子信息的存储与读取等。利用EIT也可使介质的非线性效应大为增强,从而开创了低光强甚至单光子水平下的非线性光学研究的新领域。利用EIT效应还可极大地增强介质的交叉相位调制,为研制新型的全光量子相位门和实现全光量子计算与量子通信提供了重要的技术支持。
尽管EIT可消除光吸收,但介质的色散效应会使光脉冲在传播过程中产生很大的变形,对光信息的传输和处理十分不利。如何使EIT介质的色散效应和非线性效应保持平衡从而使光脉冲在传播的过程中保持波形不变是本文的主要研究内容。通过引入和发展非线性波动理论中的奇异摄动理论,特别是多重尺度方法,我们对多能级EIT介质中超慢光的非线性传播特性进行了系统深入的研究。本文的工作主要包括以下几个方面:
1.研究了N-型四能级EIT介质中高阶超慢光孤子的形成与传播。从薛定谔方程以和麦克斯韦方程出发,用多重尺度方法导出了探测光包络函数满足的高阶非线性薛定谔方程。研究发现,与光纤等通常介质不同,EIT介质的高阶色散和非瞬时Kerr非线性效应对探测光脉宽的改变十分敏感。在脉宽变短时这些高阶效应明显增强,因而不能作为非线性薛定谔方程的微扰项加以处理。我们给出了高阶非线性薛定谔方程的严格孤子解,发现这种光孤子的传播速度可比光在真空及通常介质中的传播速度低5个数量级。我们还通过数值模拟研究了孤子之间的相互作用,并检验了高阶超慢光孤子稳定性。
2.研究了A-型三能级EIT介质中(2+1)维弱光空间孤子。在探测光场的包络具有较大的时间长度但较小的空间宽度的情况下,从薛定谔方程以和麦克斯韦方程导出了描述探测光包络函数满足的具有衍射和饱和非线性项的非线性薛定谔方程,用变分法得到了稳定传播的(2+1)维的空间弱光孤子解。研究发现EIT介质中空间孤子的产生只需要很低的输入功率。另外,通过数值模拟进一步验证了空间孤子的稳定性并研究了它们之间的碰撞。最后,探讨了如何通过改变控制光的空间分布实现对弱光空间孤子物理特性的操控。
3.研究了M-型五能级EIT介质中的弱光超慢矢量孤子的形成与传播。利用多重尺度方法导出了描述探测光两个不同偏振分量的包络函数所满足的耦合非线性薛定谔方程组,给出了各种超慢矢量光孤子解。研究结果表明,利用EIT介质物理特性的可调控性和通过调节系统参数可以很容易地得到标准的Manakov方程组。研究发现,与光纤等通常介质不同,在EIT介质中产生超慢Manakov矢量孤子不仅只需要很低的输入功率,而且通过改变外加磁场强度可以方便地实现对矢量孤子偏振方向的主动操控。
4.研究了六能级EIT介质中的三光子纠缠及三比特量子相位门的构造。从密度矩阵运动方程出发,导出了体系的线性光学极化率与各阶非线性光学极化率的表达式。研究表明,由于EIT效应体系的五阶完全交叉非线性光学极化率得到很大的增强,因而可用来实现很强的五阶完全交叉相位调制。另外由于体系的易调控性,探测、信号和触发光场之间的群速度匹配条件很容易得到满足。利用体系所具有的这些十分有趣的物理性质,我们设计了一种新型的实验框架,用以实现三光子的量子纠缠和构造三比特量子相位门。研究发现该三比特相位门可转化为Toffoli门,因而有可能在量子计算中得到重要和广泛的应用。
EIT介质的非线性光学性质的研究是一个方兴未艾,倍受关注的研究领域。以上所述的关于多能级EIT介质中超慢光的非线性传播特性的研究结果不仅对于揭示EIT介质的非线性光学特性具有重要的物理意义,而且对于弱光条件下的光信息处理和传输也具有潜在的应用价值。
The invention of lasers leads to the naissance of nonlinear optics which has greatly extended the research region of conventional optics in the past half century. The novel nonlinear phenomena presented by interaction between light and matter are the main subjects of nonlinear optics.
As we know, the nonlinearity of a conventional optical medium is very weak when working far from resonant regime, or there is a very large optical absorption when working near resonant regime where nonlinear effect is strong. Thus people are used to consider that it was difficult to enhance nonlinearity without suffering serious absorption.
The proposal of electromagnetically induced transparency (EIT) solves the above difficulty. Due to the quantum interference induced by a coupling laser field, the absorption of a probe laser field can be largely suppressed even it is tuned to a strong one-photon resonance. The wave propagation in an optical medium under EIT configuration displays many striking features such as a significant reduction of the group velocity of the probe field which can be used to optical buffers and storage of the probe pulse. A great enhancement of Kerr nonlinearity in EIT media is beneficial to certain nonlinear processes under weak driving conditions. A great enhancement of cross-Kerr nonlinearity in EIT media can be use to construct effective all-optical quantum phase gates which supports quantum information and computation.
Although absorption is suppressed, the dispersion effect in such media is still very strong and hence the wave shape of the probe pulse will suffer a serious deformation during the propagation which is harmful to the information transmission. How to balance the dispersion with nonlinearity to get a distortion free propagation of the probe wave packet is a main subject of the present dissertation. In this dissertation, we have adopted a strange perturbation method, i. e. the multiple-scale method, to investigate the nonlinear properties of the wave propagation in cold atomic media under EIT configurations. Our work includes the following aspects:
1. We have investigated the influence of high order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a four-state atomic system under EIT configuration. We have derived a high-order nonlinear Schrodinger equation and showed that for short pulse duration these high-order effects may be significant and therefore must be treated from a nonperturbative viewpoint. The exact soliton solutions of the high-order nonlinear Schrodinger equation have been given which may travel with an extremely slow velocity. We have also carried out numerical simulations on the stability and interaction of these high-order ultraslow optical solitons.
2. We have studied the formation and propagation of stable (2+1)-D spatial optical solitons in a resonant three-level atomic system. We have obtained a NLS equation with a saturation nonlinearity, which governs the dynamics of the envelope of the probe field and support stable (2+1)-D spatial optical solitons. We have demonstrated that the spatial optical soliton in such a system can be generated by using an extremely weak probe-light intensity. We have also made a detailed numerical study on the interaction between two (2+1)-D spatial optical solitons. The controllability of the spatial optical soliton has also been studied by manipulating the coupling laser field.
3. We have proposed a scheme to create temporal vector optical solitons in a coherent five-level atomic system. Such solitons can have ultraslow propagating velocity and may be produced with extremely low input power. We have demonstrated both analytically and numerically that it is easy to realize Manakov temporal vector optical solitons by actively manipulating the dispersion and nonlinear effects of the system. The system proposed can be also used to realize a complete control over the polarization of the probe field.
4. We have investigated the three-way entanglement and three-qubit phase gates based on a coherent six-level atomic system. From the density matrix equations, we have shown that the completely cross fifth-order optical susceptibilities are greatly enhanced with other susceptibilities being simultaneously suppressed in our system. Based on such important feature we have demonstrated that the system can produce
efficient three-way entanglement and implement a robust three-qubit quantum phase gate which can be further transferred to a Toffoli gate.
The nonlinear optical properties of the EIT media have attracted more and more attentions in recent years. The investigations on nonlinear propagation properties of ultraslow light in EIT media not only make sense in exploring the nonlinear optical properties of the EIT media, but also have a potential application in modern optical information processing and transmission at a low light level.
传统的非线性光学存在以下困难:由于普通的非共振介质只能提供微弱的非线性响应,因此必须使用很强的光源才能得到足够的非线性效应。为了在较弱的输入光强下得到较强的非线性响应,必须使入射光场的频率接近介质的共振频率。但是由于共振,介质对入射光场的吸收达到峰值,从而使光场受到很大的损耗。由于这一原因,长期以来人们一直认为利用光与介质的共振效应来实现非线性效应的增强是非常困难的。
近年来,由于电磁感应透明(EIT)效应的研究,相干介质的弱光非线性光学的研究引起了人们的极大关注。EIT的基本原理是利用控制光场所诱导的原子量子态的之间的干涉效应消除介质对入射探测光场的吸收。EIT可使介质的色散特性产生重大改变,从而为人工调控介质的线性与非光学性质开辟了新途经。利用EIT导致的群速度减慢可制作新型的光学延迟器件,实现冷原子介质中的量子信息的存储与读取等。利用EIT也可使介质的非线性效应大为增强,从而开创了低光强甚至单光子水平下的非线性光学研究的新领域。利用EIT效应还可极大地增强介质的交叉相位调制,为研制新型的全光量子相位门和实现全光量子计算与量子通信提供了重要的技术支持。
尽管EIT可消除光吸收,但介质的色散效应会使光脉冲在传播过程中产生很大的变形,对光信息的传输和处理十分不利。如何使EIT介质的色散效应和非线性效应保持平衡从而使光脉冲在传播的过程中保持波形不变是本文的主要研究内容。通过引入和发展非线性波动理论中的奇异摄动理论,特别是多重尺度方法,我们对多能级EIT介质中超慢光的非线性传播特性进行了系统深入的研究。本文的工作主要包括以下几个方面:
1.研究了N-型四能级EIT介质中高阶超慢光孤子的形成与传播。从薛定谔方程以和麦克斯韦方程出发,用多重尺度方法导出了探测光包络函数满足的高阶非线性薛定谔方程。研究发现,与光纤等通常介质不同,EIT介质的高阶色散和非瞬时Kerr非线性效应对探测光脉宽的改变十分敏感。在脉宽变短时这些高阶效应明显增强,因而不能作为非线性薛定谔方程的微扰项加以处理。我们给出了高阶非线性薛定谔方程的严格孤子解,发现这种光孤子的传播速度可比光在真空及通常介质中的传播速度低5个数量级。我们还通过数值模拟研究了孤子之间的相互作用,并检验了高阶超慢光孤子稳定性。
2.研究了A-型三能级EIT介质中(2+1)维弱光空间孤子。在探测光场的包络具有较大的时间长度但较小的空间宽度的情况下,从薛定谔方程以和麦克斯韦方程导出了描述探测光包络函数满足的具有衍射和饱和非线性项的非线性薛定谔方程,用变分法得到了稳定传播的(2+1)维的空间弱光孤子解。研究发现EIT介质中空间孤子的产生只需要很低的输入功率。另外,通过数值模拟进一步验证了空间孤子的稳定性并研究了它们之间的碰撞。最后,探讨了如何通过改变控制光的空间分布实现对弱光空间孤子物理特性的操控。
3.研究了M-型五能级EIT介质中的弱光超慢矢量孤子的形成与传播。利用多重尺度方法导出了描述探测光两个不同偏振分量的包络函数所满足的耦合非线性薛定谔方程组,给出了各种超慢矢量光孤子解。研究结果表明,利用EIT介质物理特性的可调控性和通过调节系统参数可以很容易地得到标准的Manakov方程组。研究发现,与光纤等通常介质不同,在EIT介质中产生超慢Manakov矢量孤子不仅只需要很低的输入功率,而且通过改变外加磁场强度可以方便地实现对矢量孤子偏振方向的主动操控。
4.研究了六能级EIT介质中的三光子纠缠及三比特量子相位门的构造。从密度矩阵运动方程出发,导出了体系的线性光学极化率与各阶非线性光学极化率的表达式。研究表明,由于EIT效应体系的五阶完全交叉非线性光学极化率得到很大的增强,因而可用来实现很强的五阶完全交叉相位调制。另外由于体系的易调控性,探测、信号和触发光场之间的群速度匹配条件很容易得到满足。利用体系所具有的这些十分有趣的物理性质,我们设计了一种新型的实验框架,用以实现三光子的量子纠缠和构造三比特量子相位门。研究发现该三比特相位门可转化为Toffoli门,因而有可能在量子计算中得到重要和广泛的应用。
EIT介质的非线性光学性质的研究是一个方兴未艾,倍受关注的研究领域。以上所述的关于多能级EIT介质中超慢光的非线性传播特性的研究结果不仅对于揭示EIT介质的非线性光学特性具有重要的物理意义,而且对于弱光条件下的光信息处理和传输也具有潜在的应用价值。
The invention of lasers leads to the naissance of nonlinear optics which has greatly extended the research region of conventional optics in the past half century. The novel nonlinear phenomena presented by interaction between light and matter are the main subjects of nonlinear optics.
As we know, the nonlinearity of a conventional optical medium is very weak when working far from resonant regime, or there is a very large optical absorption when working near resonant regime where nonlinear effect is strong. Thus people are used to consider that it was difficult to enhance nonlinearity without suffering serious absorption.
The proposal of electromagnetically induced transparency (EIT) solves the above difficulty. Due to the quantum interference induced by a coupling laser field, the absorption of a probe laser field can be largely suppressed even it is tuned to a strong one-photon resonance. The wave propagation in an optical medium under EIT configuration displays many striking features such as a significant reduction of the group velocity of the probe field which can be used to optical buffers and storage of the probe pulse. A great enhancement of Kerr nonlinearity in EIT media is beneficial to certain nonlinear processes under weak driving conditions. A great enhancement of cross-Kerr nonlinearity in EIT media can be use to construct effective all-optical quantum phase gates which supports quantum information and computation.
Although absorption is suppressed, the dispersion effect in such media is still very strong and hence the wave shape of the probe pulse will suffer a serious deformation during the propagation which is harmful to the information transmission. How to balance the dispersion with nonlinearity to get a distortion free propagation of the probe wave packet is a main subject of the present dissertation. In this dissertation, we have adopted a strange perturbation method, i. e. the multiple-scale method, to investigate the nonlinear properties of the wave propagation in cold atomic media under EIT configurations. Our work includes the following aspects:
1. We have investigated the influence of high order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a four-state atomic system under EIT configuration. We have derived a high-order nonlinear Schrodinger equation and showed that for short pulse duration these high-order effects may be significant and therefore must be treated from a nonperturbative viewpoint. The exact soliton solutions of the high-order nonlinear Schrodinger equation have been given which may travel with an extremely slow velocity. We have also carried out numerical simulations on the stability and interaction of these high-order ultraslow optical solitons.
2. We have studied the formation and propagation of stable (2+1)-D spatial optical solitons in a resonant three-level atomic system. We have obtained a NLS equation with a saturation nonlinearity, which governs the dynamics of the envelope of the probe field and support stable (2+1)-D spatial optical solitons. We have demonstrated that the spatial optical soliton in such a system can be generated by using an extremely weak probe-light intensity. We have also made a detailed numerical study on the interaction between two (2+1)-D spatial optical solitons. The controllability of the spatial optical soliton has also been studied by manipulating the coupling laser field.
3. We have proposed a scheme to create temporal vector optical solitons in a coherent five-level atomic system. Such solitons can have ultraslow propagating velocity and may be produced with extremely low input power. We have demonstrated both analytically and numerically that it is easy to realize Manakov temporal vector optical solitons by actively manipulating the dispersion and nonlinear effects of the system. The system proposed can be also used to realize a complete control over the polarization of the probe field.
4. We have investigated the three-way entanglement and three-qubit phase gates based on a coherent six-level atomic system. From the density matrix equations, we have shown that the completely cross fifth-order optical susceptibilities are greatly enhanced with other susceptibilities being simultaneously suppressed in our system. Based on such important feature we have demonstrated that the system can produce
efficient three-way entanglement and implement a robust three-qubit quantum phase gate which can be further transferred to a Toffoli gate.
The nonlinear optical properties of the EIT media have attracted more and more attentions in recent years. The investigations on nonlinear propagation properties of ultraslow light in EIT media not only make sense in exploring the nonlinear optical properties of the EIT media, but also have a potential application in modern optical information processing and transmission at a low light level.
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59、unpublished.
60、C. Hang and G. Huang, Chinese Optics Letters, 5, 47(2007).
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74、J. Wang, C. Hang, and G. Huang, Phys. Lett. A, (2007)in press.
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84、T. Hong, et al., Phys. Rev. Lett. 94,050801(2005).
85、R. Santra, et al., Phys. Rev. Lett. 94,173002(2005).
86、T. Zanon-Willette, et al., Phys. Rev. Lett. 97,233001(2006).
87、W. Yang, A. Joshi, and M. Xiao, Phys. Rev. Lett. 95, 093902 (2005).
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92、M. Shen, J. Shi, and Q. Wang, Phys. Rev. E 74,027601(2006).
93、S. Burger et al., Phys. Rev. Lett. 83, 5198(1999);
J. Denschlag et al., Science 287,97(2000);
L. Khaykovich et al., Science 296,1290(2002);
K. E. Strecker et al., Nature 417,150(2002).