Invariant operator theory for the single-photon energy in time-varying media

doi:10.1088/1674-1056/19/1/010306

Abstract After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis--Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions, $\varepsilon(t)=\varepsilon(0)$, $\mu(t)=\mu(0)$, and $\sigma(t)=0$ simultaneously. The use of the Lewis--Riesenfeld invariant operator method in quantum optics leads to a marvelous result:the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.

Keywords: single-photon energy invariant operator theory time-varying media

Accepted manuscript online:

PACS:	42.50.-p	(Quantum optics)
	02.30.Tb	(Operator theory)
	32.80.-t	(Photoionization and excitation)

Fund: This work was supported by National Research Foundation of Korea Grant funded by the Korean Government (No.~2009-0077951).

Cite this article:

Choi Jeong-Ryeol Invariant operator theory for the single-photon energy in time-varying media 2010 Chin. Phys. B 19 010306

[1]	Stowe K 1984 Introduction to Statistical Mechanics and Thermodynamics (New York: John Wiley and Sons) p445
[2]	Choi J R 2003 Chinese J. Phys. 41 257
[3]	Lewis H R Jr 1967 Phys. Rev. Lett. 18 510
[4]	Lewis H R Jr and Riesenfeld W B 1969 J. Math. Phys. 10 1458
[5]	Ermakov V P 1880 Univ. Izv. Kiev Series III 9 1
[6]	Remaud B and Hernandez E S 1980 Physica A 103 35
[7]	Yeon K H, Kim S S, Moon Y M, Hong S K, Um C I and George T F 2001 J. Phys. A: Math. Gen. 34 7719
[8]	Takayama K 1982 Phys. Lett. A 88 57
[9]	Malkin I A and Man'ko V I 1970 Phys. Lett. A 32 243
[10]	Pedrosa I A, Serra G P and Guedes I 1997 Phys. Rev. A 56 4300
[11]	Dodonov V V, Malkin I A and Man'ko V I 1974 Physica 72 597
[12]	Zhang S, Choi J R, Um C I and Yeon K H 2001 Phys. Lett. A 289 257
[13]	Choi J R 2006 Phys. Scr. 73 587
[14]	Song D Y 2000 Phys. Rev. Lett. 85 1141
[15]	Kim H C and Yee J H 2008 Ann. Phys. 323 1424
[16]	Um C I, Yeon K-H and George T F 2002 Phys. Rep. 362 63
[17]	Choi J R 2003 J. Optics B: Quantum Semiclass. Opt. 5 409
[18]	Choi J R 2004 Int. J. Theor. Phys. 43 2113
[19]	Choi J R 2004 Int. J. Mod. Phys. B 18 317
[20]	Choi J R and Yeon K H 2005 Int. J. Mod. Phys. B 19 2213
[21]	Choi J R 2006 J. Phys. B: At. Mol. Opt. Phys. 39 669
[22]	Felsen L B and Whitman G M 1970 IEEE Trans. on Antennas and Propagation 18 242
[23]	Zhang Y and Gao B-Q 2005 Chin. Phys. Lett. 22 446
[24]	Dodonov A V and Dodonov V V 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S47
[25]	Cirone M, Rz??ewski K and Mostowski J 1997 Phys. Rev. A 55 62
[26]	Crocce M, Dalvit D A R, Lombardo F C and Mazzitelli F D 2004 Phys. Rev. A 70 033811
[27]	Rezende S M and Morgenthaler F R 1969 J. Appl. Phys. 40 524
[28]	Kozaki S 1978 Electron. Lett. 14 826
[29]	Morgenthaler F R 1958 IRE Trans. Microwave Theory and Techniques MTT-6 167
[30]	Marchiolli M A and Mizrahi S S 1997 J. Phys. A: Math. Gen. 30 2619
[31]	Choi J R and Oh J-Y 2008 Int. J. Mod. Phys. B 22 267
[32]	Scully M O and Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge Univ. Press) Chaps. 8 and 9
[33]	Louisell W H 1973 Quantum Statistical Properties of Radiation (New York: John Wiley and Sons) Chaps. 6 and 7
[34]	Popp F A and Li K H 1993 Int. J. Theor. Phys. 32 1573
[35]	Caldirola P 1941 Nuovo Cimento 18 393
[36]	Kanai E 1948 Prog. Theor. Phys. 3 440
[37]	Edwards I K 1979 Am. J. Phys. 47 153
[38]	Gzyl H 1983 Phys. Rev. A 27 2297

[1]	Non-Markovianity of an atom in a semi-infinite rectangular waveguide Jing Zeng(曾静), Yaju Song(宋亚菊), Jing Lu(卢竞), and Lan Zhou(周兰). Chin. Phys. B, 2023, 32(3): 030305.
[2]	Atomic optical spatial mode extractor for vector beams based on polarization-dependent absorption Hong Chang(常虹), Xin Yang(杨欣), Jinwen Wang(王金文), Yan Ma(马燕), Xinqi Yang(杨鑫琪), Mingtao Cao(曹明涛), Xiaofei Zhang(张晓斐), Hong Gao(高宏), Ruifang Dong(董瑞芳), and Shougang Zhang(张首刚). Chin. Phys. B, 2023, 32(3): 034207.
[3]	Ghost imaging based on the control of light source bandwidth Zhao-Qi Liu(刘兆骐), Yan-Feng Bai(白艳锋), Xuan-Peng-Fan Zou(邹璇彭凡), Li-Yu Zhou(周立宇), Qin Fu(付芹), and Xi-Quan Fu(傅喜泉). Chin. Phys. B, 2023, 32(3): 034210.
[4]	A 3-5 μm broadband YBCO high-temperature superconducting photonic crystal Gang Liu(刘刚), Yuanhang Li(李远航), Baonan Jia(贾宝楠), Yongpan Gao(高永潘), Lihong Han(韩利红), Pengfei Lu(芦鹏飞), and Haizhi Song(宋海智). Chin. Phys. B, 2023, 32(3): 034213.
[5]	In situ temperature measurement of vapor based on atomic speed selection Lu Yu(于露), Li Cao(曹俐), Ziqian Yue(岳子骞), Lin Li(李林), and Yueyang Zhai(翟跃阳). Chin. Phys. B, 2023, 32(2): 020602.
[6]	An all-optical phase detector by amplitude modulation of the local field in a Rydberg atom-based mixer Xiu-Bin Liu(刘修彬), Feng-Dong Jia(贾凤东), Huai-Yu Zhang(张怀宇), Jiong Mei(梅炅), Wei-Chen Liang(梁玮宸), Fei Zhou(周飞), Yong-Hong Yu(俞永宏), Ya Liu(刘娅), Jian Zhang(张剑), Feng Xie(谢锋), and Zhi-Ping Zhong(钟志萍). Chin. Phys. B, 2022, 31(9): 090703.
[7]	Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system Yuan-Yuan Liu(刘元元), Zhi-Ming Zhang(张智明), Jun-Hao Liu(刘军浩), Jin-Dong Wang(王金东), and Ya-Fei Yu(於亚飞). Chin. Phys. B, 2022, 31(9): 094203.
[8]	Photon blockade in a cavity-atom optomechanical system Zhong Ding(丁忠) and Yong Zhang(张勇). Chin. Phys. B, 2022, 31(7): 070304.
[9]	Heralded path-entangled NOON states generation from a reconfigurable photonic chip Xinyao Yu(于馨瑶), Pingyu Zhu(朱枰谕), Yang Wang(王洋), Miaomiao Yu(余苗苗), Chao Wu(吴超),Shichuan Xue(薛诗川), Qilin Zheng(郑骑林), Yingwen Liu(刘英文), Junjie Wu(吴俊杰), and Ping Xu(徐平). Chin. Phys. B, 2022, 31(6): 064203.
[10]	Nonreciprocal two-photon transmission and statistics in a chiral waveguide QED system Lei Wang(王磊), Zhen Yi(伊珍), Li-Hui Sun(孙利辉), and Wen-Ju Gu(谷文举). Chin. Phys. B, 2022, 31(5): 054206.
[11]	Time evolution law of a two-mode squeezed light field passing through twin diffusion channels Hai-Jun Yu(余海军) and Hong-Yi Fan(范洪义). Chin. Phys. B, 2022, 31(2): 020301.
[12]	Majorana fermions induced fast- and slow-light in a hybrid semiconducting nanowire/superconductor device Hua-Jun Chen(陈华俊), Peng-Jie Zhu(朱鹏杰), Yong-Lei Chen(陈咏雷), and Bao-Cheng Hou(侯宝成). Chin. Phys. B, 2022, 31(2): 027802.
[13]	Bright 547-dimensional Hilbert-space entangled resource in 28-pair modes biphoton frequency comb from a reconfigurable silicon microring resonator Qilin Zheng(郑骑林), Jiacheng Liu(刘嘉成), Chao Wu(吴超), Shichuan Xue(薛诗川), Pingyu Zhu(朱枰谕), Yang Wang(王洋), Xinyao Yu(于馨瑶), Miaomiao Yu(余苗苗), Mingtang Deng(邓明堂), Junjie Wu(吴俊杰), and Ping Xu(徐平). Chin. Phys. B, 2022, 31(2): 024206.
[14]	Brightening single-photon emitters by combining an ultrathin metallic antenna and a silicon quasi-BIC antenna Shangtong Jia(贾尚曈), Zhi Li(李智), and Jianjun Chen(陈建军). Chin. Phys. B, 2022, 31(1): 014209.
[15]	Anti-$\mathcal{PT}$-symmetric Kerr gyroscope Huilai Zhang(张会来), Meiyu Peng(彭美瑜), Xun-Wei Xu(徐勋卫), and Hui Jing(景辉). Chin. Phys. B, 2022, 31(1): 014215.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Invariant operator theory for the single-photon energy in time-varying media

Cite this article:

Online attention