熵压缩·振幅平方压缩·量子相位
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摘要
压缩是量子光场的一种非经典效应。由于压缩态光场中某正交分量的量子噪声低于相干态光场中相应分量的量子涨落，若用此分量传递信息，则可得到比相干态光场更高的保真度，所以压缩态光场在弱信号探测、低噪声光通讯等方面具有广泛的应用前景。因此。压缩态光场引起人们极大的关注。
另外，在量子光学中，光强比例于光子数，那么相位是什么?能不能也定义一个与经典电磁场相位相应的相位算符?如何定义?等等。这些自然是很有趣的问题。
本论文：首先，研究了叠加相干态的方差压缩与熵压缩，讨论了方差压缩、熵压缩与相干参数的幅角δ的关系，并对两者进行比较。从而证明了熵压缩实现了光场压缩效应的高灵敏量度。其次，研究了真空态与相干态的叠加态振幅平方压缩，讨论了叠加参数p、相干参数(R，θ)对真空态与相干态的叠加态振幅平方压缩的影响。最后，详细地分析了Dirac相位算符、S—G相位算符、P—B相位算符，并对它们的一些性质作出比较，系统地论述它们的优点和不足之处。
Squeezing is a non-classical effect of quantum field. The quantum noise of one of the quadrature components of the squeezed state is less than the noise corresponding to the coherent state, if the squeezed state is used to transmit information,we shall receive higher fidelity than the coherent state.So the squeezed state will have extensive applications in the detection of weak signal in the modern low-noise optical communication systems ,and so on.They draw an increasing amount of attention.
Moreover,in quantum optics, the intensity of light is direct proportion to photon numbers,then what is phase?Can we define a phase operator that is corresponding to the phase of classical radiation field?How should it be defined?etc..All these are naturally interesting problems.
In this thesis, first, quadrature squeezing and entropic squeezing of superposition coherent states are studied.The relations between quadrature squeezing or entropic squeezing and angle 8 of coherent parameter are discussed and compared.The results show the entropic squeezing is a high sensitive measure for the squeezing effect of the field.Second,amplitude-squared squeezing for the superposition state of the vacuum state and the coherent state is studied.The effects of superposition parameter and coherent parameters on the amplitude-squared squeezing are discussed.Finally,Dirac phase operator, S-G phase operator and P-B phase operator are analyzed in detail. Some properties of these operators are compared. Meanwhile, strong and weak points of these operators are showed more systematically.
另外，在量子光学中，光强比例于光子数，那么相位是什么?能不能也定义一个与经典电磁场相位相应的相位算符?如何定义?等等。这些自然是很有趣的问题。
本论文：首先，研究了叠加相干态的方差压缩与熵压缩，讨论了方差压缩、熵压缩与相干参数的幅角δ的关系，并对两者进行比较。从而证明了熵压缩实现了光场压缩效应的高灵敏量度。其次，研究了真空态与相干态的叠加态振幅平方压缩，讨论了叠加参数p、相干参数(R，θ)对真空态与相干态的叠加态振幅平方压缩的影响。最后，详细地分析了Dirac相位算符、S—G相位算符、P—B相位算符，并对它们的一些性质作出比较，系统地论述它们的优点和不足之处。
Squeezing is a non-classical effect of quantum field. The quantum noise of one of the quadrature components of the squeezed state is less than the noise corresponding to the coherent state, if the squeezed state is used to transmit information,we shall receive higher fidelity than the coherent state.So the squeezed state will have extensive applications in the detection of weak signal in the modern low-noise optical communication systems ,and so on.They draw an increasing amount of attention.
Moreover,in quantum optics, the intensity of light is direct proportion to photon numbers,then what is phase?Can we define a phase operator that is corresponding to the phase of classical radiation field?How should it be defined?etc..All these are naturally interesting problems.
In this thesis, first, quadrature squeezing and entropic squeezing of superposition coherent states are studied.The relations between quadrature squeezing or entropic squeezing and angle 8 of coherent parameter are discussed and compared.The results show the entropic squeezing is a high sensitive measure for the squeezing effect of the field.Second,amplitude-squared squeezing for the superposition state of the vacuum state and the coherent state is studied.The effects of superposition parameter and coherent parameters on the amplitude-squared squeezing are discussed.Finally,Dirac phase operator, S-G phase operator and P-B phase operator are analyzed in detail. Some properties of these operators are compared. Meanwhile, strong and weak points of these operators are showed more systematically.
引文
[1] Gea-Banacloche J, Leuchs G. Squeezed states for interferometric gravitational-wave detectors [J]. J Mod Opt, 1987, 34(6,7): 793-811.
[2] Buzek V, Keitel H, Knight P L. Sampling entropies and operational phase-space measurement [J]. Phys Rev (A), 1995, 5(3): 2575-2593.
[3] Meystre P, Zubairy M S. Squeezed states in the Jaynes-Cumings model[J]. Phys Lett (A), 1982, 89A(8):390-392.
[4] 吴龙泉，李洪才．关于几种叠加态的压缩性质的讨论[J]．福建师范大学学报(自然科学版)，2002．18(1)：24-28．
[5] 李洪才，吴龙泉．在腔场与可移动镜子系统中对镜子位置的测理[J]．光子学报．2002，31(10)：1169-1173．
[6] 李洪才，吴龙泉．利用简并Λ型三能级原子与单模腔场的Raman相互作用制备压缩态的叠加态[J]．光子学报，2001，30(9)：1060-1063．
[7] Arkadiusz Orlowski. Information entropy and squeezing of quantum fluctuations[J]. Phys Rev (A), 1997, 56(4): 2545-2548.
[8] 方卯发，陈菊梅．熵测不准关系与熵压缩[J]．光学学报，2001，21(1)：8-11．
[9] B.L.Schumaker. Quantum mechanical pure states with gaussian wave function[J]. Phys Rep, 1986, 135(6): 342-343.
[10] C.E.shannon, W.Weaver, The Mathematical theory of communication.[J]. Urbana: The University of Illinois Press, 1963.81-96.
[11] A.Wehrl. Rev.Mod.Phys., 1978, 50:221.
[12] 闫珂柱，孔祥和，夏云杰．奇偶相干态的Wehrl熵和shannon熵[J]．光学学报，1998，18(6)：717-721．
[13] 于国臣，屈爱存，王连水．叠加相干态的Wehrl熵和shannon熵[J]．量子电子学
报，2000，17(1)：26-30．
[14] 夏云杰，闫珂柱，孔祥和，等．光场量子态的信息熵和保真度[J]．量子光学学报，1996，2(1)：24-30．
[15] Uffink J B M, Ililgevoord J. Uncertainty principle and uncertainty relation [J]. Found.Phys., 1975, 15(9):925-944.
[16] Beckner W. Inequalities in Fourier analysis[J]. Ann.Math., 1975, 102(2): 159-182.
[17] Bialyncki-Birula I, Mycielski J. Uncertainty relations for information entropy in wave mechanics [J].Commun.Math.Phys., 1975,44(2): 129-132.
[18] Jorge S R.Position-momentum entropic uncertainty relation and complementarity in single-slit and double-slit experiments[J].Phys Rev (A),1998,57(3):1519-1525.
[19] 黄春佳，周明，历江帆，等．单模辐射场与耦合双原子相互作用系统中场熵的压缩特性[J]．物理学报，2002，51(4)：805-808．
[20] 李永平，柳永亮，贺金玉．单模辐射场与级联三能级原子相互作用场熵的压缩特性[J]．量子光学学报，2002，8(4)：161-165．
[21] 郭光灿．量子光学[M]．北京：高等教育出版社，1990．60．
[22] Dirac P A M. The quantum theory of the emission and absorption of radiation[J]. Proc.R.Soc.A, 1927, 114 (2): 243.
[23] Susskind L, Glogower J. Quantum mechanical phase and time operator[J]. Physics, 1964, 1 (1): 49.
[24] 彭金生，李高翔．近代量子光学导论[M]．北京：科学出版社，1996．67．
[25] Barnett S M, Pegg D T. Phase in quantum optics[J]. J.Phys.A, 1986, 19 (18): 3849-3562.
[26] Buzek V, Wilson-Gordon A D, Knight P L, et al. Coherent states in a finite-dimensional basis: Their phase properties and relationship to coherent states of light[J]. Phys.Rev.A, 1992, 45 (11): 8079-8094.
[27] Pegg D T, Barnett S M. Phase properties of the quantized single-mode electromagnetic
field[J]. Phys.Rev.A, 1989, 39 (4): 1665-1675.
[28] 周本汉．量子相位算符的不确定关系及其演化方程[J]．光电子·激光，1998，9(1)：54-57．
[29] Barnett S M, Pegg D T. On the Hermitian optical phase operator[J]. J.Mod.Optics, 1989, 36 (1): 7-19.
[30] 田永红，徐大海，韩立波．量子光场相位研究的进展[J]．荆州师范学院学报，2000，23(5)：41-43．
[31] Mark Hillery. Amplitude-squared squeezing of the electromagnetic field[J]. Phys.Rev.A, 1987,36(8): 3796-3802.
[32] Mark Hillery. Squeezing of the field amplitude in second harmonic generation[J]. Opt.Commun., 1987, 62(2): 135-138.
[2] Buzek V, Keitel H, Knight P L. Sampling entropies and operational phase-space measurement [J]. Phys Rev (A), 1995, 5(3): 2575-2593.
[3] Meystre P, Zubairy M S. Squeezed states in the Jaynes-Cumings model[J]. Phys Lett (A), 1982, 89A(8):390-392.
[4] 吴龙泉，李洪才．关于几种叠加态的压缩性质的讨论[J]．福建师范大学学报(自然科学版)，2002．18(1)：24-28．
[5] 李洪才，吴龙泉．在腔场与可移动镜子系统中对镜子位置的测理[J]．光子学报．2002，31(10)：1169-1173．
[6] 李洪才，吴龙泉．利用简并Λ型三能级原子与单模腔场的Raman相互作用制备压缩态的叠加态[J]．光子学报，2001，30(9)：1060-1063．
[7] Arkadiusz Orlowski. Information entropy and squeezing of quantum fluctuations[J]. Phys Rev (A), 1997, 56(4): 2545-2548.
[8] 方卯发，陈菊梅．熵测不准关系与熵压缩[J]．光学学报，2001，21(1)：8-11．
[9] B.L.Schumaker. Quantum mechanical pure states with gaussian wave function[J]. Phys Rep, 1986, 135(6): 342-343.
[10] C.E.shannon, W.Weaver, The Mathematical theory of communication.[J]. Urbana: The University of Illinois Press, 1963.81-96.
[11] A.Wehrl. Rev.Mod.Phys., 1978, 50:221.
[12] 闫珂柱，孔祥和，夏云杰．奇偶相干态的Wehrl熵和shannon熵[J]．光学学报，1998，18(6)：717-721．
[13] 于国臣，屈爱存，王连水．叠加相干态的Wehrl熵和shannon熵[J]．量子电子学
报，2000，17(1)：26-30．
[14] 夏云杰，闫珂柱，孔祥和，等．光场量子态的信息熵和保真度[J]．量子光学学报，1996，2(1)：24-30．
[15] Uffink J B M, Ililgevoord J. Uncertainty principle and uncertainty relation [J]. Found.Phys., 1975, 15(9):925-944.
[16] Beckner W. Inequalities in Fourier analysis[J]. Ann.Math., 1975, 102(2): 159-182.
[17] Bialyncki-Birula I, Mycielski J. Uncertainty relations for information entropy in wave mechanics [J].Commun.Math.Phys., 1975,44(2): 129-132.
[18] Jorge S R.Position-momentum entropic uncertainty relation and complementarity in single-slit and double-slit experiments[J].Phys Rev (A),1998,57(3):1519-1525.
[19] 黄春佳，周明，历江帆，等．单模辐射场与耦合双原子相互作用系统中场熵的压缩特性[J]．物理学报，2002，51(4)：805-808．
[20] 李永平，柳永亮，贺金玉．单模辐射场与级联三能级原子相互作用场熵的压缩特性[J]．量子光学学报，2002，8(4)：161-165．
[21] 郭光灿．量子光学[M]．北京：高等教育出版社，1990．60．
[22] Dirac P A M. The quantum theory of the emission and absorption of radiation[J]. Proc.R.Soc.A, 1927, 114 (2): 243.
[23] Susskind L, Glogower J. Quantum mechanical phase and time operator[J]. Physics, 1964, 1 (1): 49.
[24] 彭金生，李高翔．近代量子光学导论[M]．北京：科学出版社，1996．67．
[25] Barnett S M, Pegg D T. Phase in quantum optics[J]. J.Phys.A, 1986, 19 (18): 3849-3562.
[26] Buzek V, Wilson-Gordon A D, Knight P L, et al. Coherent states in a finite-dimensional basis: Their phase properties and relationship to coherent states of light[J]. Phys.Rev.A, 1992, 45 (11): 8079-8094.
[27] Pegg D T, Barnett S M. Phase properties of the quantized single-mode electromagnetic
field[J]. Phys.Rev.A, 1989, 39 (4): 1665-1675.
[28] 周本汉．量子相位算符的不确定关系及其演化方程[J]．光电子·激光，1998，9(1)：54-57．
[29] Barnett S M, Pegg D T. On the Hermitian optical phase operator[J]. J.Mod.Optics, 1989, 36 (1): 7-19.
[30] 田永红，徐大海，韩立波．量子光场相位研究的进展[J]．荆州师范学院学报，2000，23(5)：41-43．
[31] Mark Hillery. Amplitude-squared squeezing of the electromagnetic field[J]. Phys.Rev.A, 1987,36(8): 3796-3802.
[32] Mark Hillery. Squeezing of the field amplitude in second harmonic generation[J]. Opt.Commun., 1987, 62(2): 135-138.