Chin. Phys. Lett.  2018, Vol. 35 Issue (5): 050301    DOI: 10.1088/0256-307X/35/5/050301
Dynamical Evolution of an Effective Two-Level System with $\mathcal{PT}$ Symmetry
Lei Du1, Zhihao Xu1,2,3, Chuanhao Yin4, Liping Guo1,2,3**
1Institute of Theoretical Physics, Shanxi University, Taiyuan 030006
2Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006
3State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006
4Institute of Physics, Chinese Academy of Sciences, Beijing 100190
Cite this article:   
Lei Du, Zhihao Xu, Chuanhao Yin et al  2018 Chin. Phys. Lett. 35 050301
Download: PDF(1883KB)   PDF(mobile)(1560KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract We investigate the dynamics of parity- and time-reversal ($\mathcal{PT}$) symmetric two-energy-level atoms in the presence of two optical and one radio-frequency fields. The strength and relative phase of fields can drive the system from the unbroken to the broken $\mathcal{PT}$ symmetric regions. Compared with the Hermitian model, Rabi-type oscillation is still observed, and the oscillation characteristics are also adjusted by the strength and relative phase in the region of the unbroken $\mathcal{PT}$ symmetry. At the exception point, the oscillation breaks down. To better understand the underlying properties we study the effective Bloch dynamics and find that the emergence of the $z$ components of the fixed points is the feature of the $\mathcal{PT}$ symmetry breaking and the projections in the $x$–$y$ plane can be controlled with high flexibility compared with the standard two-level system with the $\mathcal{PT}$ symmetry. It helps to study the dynamic behavior of the complex $\mathcal{PT}$ symmetric model.
Received: 27 December 2017      Published: 30 April 2018
PACS:  03.65.Yz (Decoherence; open systems; quantum statistical methods)  
  03.75.Kk (Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow)  
  03.65.-w (Quantum mechanics)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11104171, 11404199, 11574187 and 11604188, the Youth Science Foundation of Shanxi Province of China under Grant No 2012021003-1, and the Natural Science Foundation for Youths of Shanxi Province under Grant Nos 201601D201027 and 1331KSC.
URL:       OR
E-mail this article
E-mail Alert
Articles by authors
Lei Du
Zhihao Xu
Chuanhao Yin
Liping Guo
[1]Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
Bender C M, Boettcher S and Meisinger P N 1999 J. Math. Phys. 40 2201
[2]Guo A, Salamo G J, Duchesne D, Morandotti R, Volatier-Ravat M, Aimez V, Siviloglou G A and Christodoulides D N 2009 Phys. Rev. Lett. 103 093902
[3]Rüter C E, Makris K G, EI-Ganainy R, Christodoulides D N, Segev M and Kip D 2010 Nat. Phys. 6 192
[4]Bittner S, Dietz B, Günther U, Harney H L, Miski-Oglu M, Richter A and Schäfer F 2012 Phys. Rev. Lett. 108 024101
[5]Chang L, Jiang X, Hua S, Yang C, Wen J, Jiang L, Li G, Wang G and Xiao M 2014 Nat. Photon. 8 524
[6]Feng L, Wong Z J, Ma R M, Wang Y and Zhang X 2014 Science 346 972
[7]Hodaei H, Miri M A, Heinrich M, Christodoulides D N and Khajavikhan M 2014 Science 346 975
[8]Hodaei H, Miri M A, Hassan A U, Hayenga W E, Heinrich M, Christodoulides D N and Khajavikhan M 2015 Opt. Lett. 40 4955
[9]Schindler J, Lie A, Zheng M C, Ellis F M and Kottos T 2011 Phys. Rev. A 84 040101
[10]Peng B, Ozdemir S K, Lei F, Monifi F, Gianfreda M, Long G L, Fan S, Nori F, Bender C M and Yang L 2014 Nat. Phys. 10 394
Jing H, Özdemir S K, Geng Z, Zhang J, Lü X Y, Peng B, Yang L and Nori F 2015 Sci. Rep. 5 9663
[11]Wimmer M, Miri M A, Christodoulides D and Peschel U 2016 Sci. Rep. 5 17760
[12]Ben-Aryeh Y, Mann A and Yaakov I 2004 J. Phys. A 37 12059
[13]Bender C M, Brody D C, Jones H F and Meister B K 2007 Phys. Rev. Lett. 98 040403
[14]Graefe E M 2012 J. Phys. A 45 444015
[15]Lian X, Zhong H, Xie Q, Zhou X, Wu Y and Liao W 2014 Eur. Phys. J. D 68 189
[16]Baradaran M and Panahi H 2017 Chin. Phys. B 26 060301
[17]Graefe E M, Korsch H J and Niederle A E 2008 Phys. Rev. Lett. 101 150408
[18]Graefe E M, Korsch H J and Niederle A E 2010 Phys. Rev. A 82 013629
[19]Zhu B G, Lü R and Chen S 2015 Phys. Rev. A 91 042131
Zhu B G, Lü R and Chen S 2016 Phys. Rev. A 93 032129
[20]Jin L and Song Z 2009 Phys. Rev. A 80 052107
Yuce C 2015 Phys. Lett. A 379 1213
Joglekar Y N, Scott D, Babbey M and Saxena A 2010 Phys. Rev. A 82 030103(R)
[21]Bergmann K, Theuer H and Shore B W 1998 Rev. Mod. Phys. 70 1003
[22]Alexanian M and Bose S K 1995 Phys. Rev. A 52 2218
[23]Sun X L, Zhang J W, Cheng P F, Zuo Y N and Wang L J 2018 Chin. Phys. B 27 023101
[24]Shahriar M S and Hemmer P R 1990 Phys. Rev. Lett. 65 1865
[25]Li H, Sautenkov V A, Rostovtsev Y V, Welch G R, Hemmer P R and Scully M O 2009 Phys. Rev. A 80 023820
[26]Luo B, Tang H and Guo H 2009 J. Phys. B 42 235505
[27]Basler C, Grzesiak J and Helm H 2015 Phys. Rev. A 92 013809
[28]Novikov S, Sweeney T, Robinson J E, Premaratne S P, Suri B, Wellstood F C and Palmer B S 2016 Nat. Phys. 12 75
[29]Peng P, Cao W, Shen C, Qu W, Wen J, Jiang L and Xiao Y 2016 Nat. Phys. 12 1139
[30]Bender C M, Brody D C and Jones H F 2002 Phys. Rev. Lett. 89 270401
[31]Milburn T J, Doppler J, Holmes C A, Portolan S, Rotter S and Rabl P 2015 Phys. Rev. A 92 052124
[32]Menke H, Klett M, Cartarius H, Main J and Wunner G 2016 Phys. Rev. A 93 013401
[33]Hang C, Huang G and Konotop V V 2013 Phys. Rev. Lett. 110 083604
[34]Li H, Dou J and Huang G 2013 Opt. Express 21 32053
[35]Lee T E and Chan C K 2014 Phys. Rev. X 4 041001
[36]Hao Y and Gu Q 2011 Phys. Rev. A 83 043620
Related articles from Frontiers Journals
[1] Changhao Zhao, Yongcheng He, Xiao Geng, Kaiyong He, Genting Dai, Jianshe Liu, and Wei Chen. Multi-Mode Bus Coupling Architecture of Superconducting Quantum Processor[J]. Chin. Phys. Lett., 2023, 40(1): 050301
[2] Chen Wang, Lu-Qin Wang, and Jie Ren. Managing Quantum Heat Transfer in a Nonequilibrium Qubit-Phonon Hybrid System with Coherent Phonon States[J]. Chin. Phys. Lett., 2021, 38(1): 050301
[3] Guobin Chen, Yang Hui, Junci Sun, Wenhao He, and Guanxiang Du. Rapid Measurement and Control of Nitrogen-Vacancy Center-Axial Orientation in Diamond Particles[J]. Chin. Phys. Lett., 2020, 37(11): 050301
[4] Liwei Duan, Yan-Zhi Wang, and Qing-Hu Chen. $\mathcal{PT}$ Symmetry of a Square-Wave Modulated Two-Level System[J]. Chin. Phys. Lett., 2020, 37(8): 050301
[5] Xiao-Lan Zong, Wei Song, Ming Yang, Zhuo-Liang Cao. Influence of Quantum Feedback Control on Excitation Energy Transfer *[J]. Chin. Phys. Lett., 0, (): 050301
[6] Xiao-Lan Zong, Wei Song, Ming Yang, Zhuo-Liang Cao. Influence of Quantum Feedback Control on Excitation Energy Transfer[J]. Chin. Phys. Lett., 2020, 37(6): 050301
[7] Zi Cai, Yizhen Huang, W. Vincent Liu. Imaginary Time Crystal of Thermal Quantum Matter[J]. Chin. Phys. Lett., 2020, 37(5): 050301
[8] Bing-Bing Chai, Jin-Liang Guo. Distillability of Sudden Death in Qutrit-Qutrit Systems under Global Mixed Noise[J]. Chin. Phys. Lett., 2019, 36(5): 050301
[9] Yang Yang, An-Min Wang, Lian-Zhen Cao, Jia-Qiang Zhao, Huai-Xin Lu. Frozen Quantum Coherence for a Central Two-Qubit System in a Spin-Chain Environment[J]. Chin. Phys. Lett., 2018, 35(8): 050301
[10] Jun Wen, Guan-Qiang Li. Preservation of Quantum Coherence for Gaussian-State Dynamics in a Non-Markovian Process[J]. Chin. Phys. Lett., 2018, 35(6): 050301
[11] Kang-Kang Ju, Cui-Xian Guo, Xiao-Yin Pan. Initial-Slip Term Effects on the Dissipation-Induced Transition of a Simple Harmonic Oscillator[J]. Chin. Phys. Lett., 2017, 34(1): 050301
[12] H. A. Zad. Total Pairwise Quantum Correlation and Entanglement in a Mixed-Three-Spin Ising-$XY$ Model with Added Dzyaloshinskii–Moriya Interaction under Decoherence[J]. Chin. Phys. Lett., 2016, 33(09): 050301
[13] Hong-Mei Zou, Mao-Fa Fang. Controlling Entropic Uncertainty in the Presence of Quantum Memory by Non-Markovian Effects and Atom–Cavity Couplings[J]. Chin. Phys. Lett., 2016, 33(07): 050301
[14] Wei-Ting Zhu, Qing-Bao Ren, Li-Wei Duan, Qing-Hu Chen. Entanglement Dynamics of Two Qubits Coupled Independently to Cavities in the Ultrastrong Coupling Regime: Analytical Results[J]. Chin. Phys. Lett., 2016, 33(05): 050301
[15] Da-Chuang Li, Xian-Ping Wang, Hu Li, Xiao-Man Li, Ming Yang, Zhuo-Liang Cao. Effects of Pure Dzyaloshinskii–Moriya Interaction with Magnetic Field on Entanglement in Intrinsic Decoherence[J]. Chin. Phys. Lett., 2016, 33(05): 050301
Full text