-
基于单模微腔与二能级原子系综(库)构成的混合动力学模型, 探索了非平衡库中量子关联相干(quantum correlated coherence, QCC) [Tan K C, et al. 2016 Phys. Rev. A 94, 022329])对系统动力学的影响. 推导了量子关联相干库下系统演化的动力学方程. 借助于含QCC的类GHZ库及其对应的参考库, 清晰地揭示了非平衡库中QCC扮演着热力学资源的角色——能够有效辅助系统从库中提取更多能量. 同时, 结合解析与数值模拟方法研究了类GHZ库的有效温度和系统与库间的耦合参数对QCC能量效应的影响. 研究发现, QCC对腔场的能量贡献不仅依赖于库的有效温度, 而且也和系统与库间的耦合参数有关. 这与二能级原子构成的传统的热库的情况(腔场从热库中提取的能量仅仅依赖于库的有效温度即二能级原子的热布局)完全不同. 此外, 研究发现QCC可视作一类优质的热力学资源, 在特定条件下其对系统的能量贡献远大于原子热布局的贡献. 因此, QCC将是高输出功率或高效率量子热机设计中的一类重要燃料.Based on a hybrid model of a single-mode microcavity system plus an ensemble of two-level atoms (TLAs), we investigate the effect of quantum correlated coherence (QCC) [Tan K C, et al. 2016 Phys. Rev. A 94, 022329] of bath on the dynamic behaviors of system. The dynamic equations of system for a general bath with QCC have been derived. With the help of the GHZ-like state with QCC and its reference state, the role of QCC as a thermodynamic resource has been clearly shown where QCC could be used to enhance the system's energy. Meanwhile, combining with the analytical and numerical simulation methods, the influences of effective temperature of
$ GHZ $ -like bath and the coupling strength between the system and the bath on the energy effect of QCC have been studied. We find that the energy contribution of QCC to the cavity field relies not only on the effective temperature of bath but also on the coupling strength. That is completely different from the case of traditional thermal bath where the energy captured by the cavity from the bath only depends on the bath temperature, i.e., the thermal distribution of TLAs. Moreover, several interesting phenomena, in the paper, have been shown: 1) the higher of the effective temperature of bath, the larger of the cavity's energy extracted from the QCC of bath; 2) under the fixed effective temperature of bath, the smaller of the coupling strength the larger of the maximal extractable energy from QCC of bath; 3) there exists the trade-off between the cavity's energy and the capability of cavity capturing the energy of TLAs entering the cavity, i.e., the cavity's energy extracted from each TLA crossing the cavity always decreases as the energy of cavity increases; 4) the energy contribution of QCC of bath to cavity is beyond the one of the thermal distribution of TLAs in bath, and it could become more prominent when the coupling strength is taken the smaller value, which also means that in the case of weak coupling strength it is the QCC of bath not the thermal distribution of bath dominating the cavity's energy. Thus, the QCC of bath could be viewed as a kind of high quality thermodynamic resource. It has the potential applications in the design of a quantum engine with high output power or efficiency, and the enhancement of charging speed of quantum battery. Our investigation is beneficial to the further understanding of quantum coherence in quantum thermodynamic regime.-
Keywords:
- quantum entanglement /
- quantum correlated coherence /
- energy extraction /
- thermodynamics resource
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-
图 1 单模微腔与一系列二能级原子组成的原子库相互作用示意图 (a)处于QCC库中的二能级原子顺次穿过微腔; (b)库中无QCC情况下, 二能级原子顺次穿过微腔
Fig. 1. Schematic diagram of a single-mode microcavity interacting with a TLA-bath consisting of a series of two-level atoms: (a) The atoms of bath with QCC passing through the cavity one by one; (b) the atoms of bath without QCC crossing the cavity.
图 2 腔场在不同耦合参数
$\xi=0.1$ (蓝色点线),$\xi=0.3$ (红色点线)和$\xi=0.5$ (黑色点线)下, 从不同库态中提取的能量随穿腔原子数 ($m\in[1, 2\times10^3]$ ) 的变化 (a)腔场从类GHZ态下QCC中提取能量$\langle n(m, N)\rangle^{\rm qcc}$ 随$m$ 的变化; (b)腔场从参考态(热态)下原子布局中提取的能量$\langle n(m, N)\rangle^{\rm ref}$ 随$m$ 的变化; 其他参数取为$\theta=3{\text{π}}/8$ ,$N=2\times$ 103; 内插图为$m$ 在区间$[1, 120]$ 的图形Fig. 2. The variations of cavity's energy,
$\langle n(m, N)\rangle^{\rm qcc}$ and$\langle n(m, N)\rangle^{\rm ref}$ , respectively captured from the QCC of GHZ-like state in (a) and the thermal distribution of reference state (thermal state) in (b) with the number of TLAs crossing the cavity$m$ ($m\in[1, 2\times10^3]$ ), with$\theta=3{\text{π}}/8$ and$N=2\times10^3$ for$\xi=0.1$ (blue dots),$\xi=0.3$ (red dots) and$\xi=0.5$ (black dots). In the inset$m\in[1, 120]$ .
图 3 腔场在不同有效温度参数
$\theta=3{\text{π}}/7$ (蓝色点线),$\theta=3{\text{π}}/8$ (红色点线)和$\theta={\text{π}}/3$ (黑色点线)下, 从不同库态中提取的能量随穿腔原子数$m$ ($m\in[1, 2\times10^3]$ ) 的变化 (a)腔场从类GHZ态下QCC中提取能量$\langle n(m, N)\rangle^{\rm qcc}$ 随$m$ 的变化; (b)腔场从参考态(热态)下原子布局中提取的能量$\langle n(m, N)\rangle^{ref}$ 随$m$ 的变化; 其他参数取为$\xi$ = 0.3,$N$ = 200Fig. 3. The variations of cavity's energy,
$\langle n(m, N)\rangle^{\rm qcc}$ and$\langle n(m, N)\rangle^{\rm ref}$ , respectively captured from the QCC of$GHZ$ -like state in (a) and the thermal distribution of reference state (thermal state) in (b) with the number of TLAs crossing the cavity$m$ ($m\in[1, 200]$ ) and$\xi$ = 0.3 and$N=200$ for$\theta=3{\text{π}}/7$ (blue dots),$\theta=3{\text{π}}/8$ (red dots) and$\theta={\text{π}}/3$ (black dots). -
[1] García-Díaz M, Egloff D, Plenio M B 2016 Quant. Inf. Comput. 16 1282
[2] Linden N, Popescu S, Skrzypczyk P 2010 Phys. Rev. Lett. 105 130401
Google Scholar
[3] Ficek Z, Swain S 2005 Quantum Interference and Coherence: Theory and Experiments, Springer Series in Optical Sciences Vol. 100 (New York: Springer Science) p7
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Google Scholar
[5] Horodecki M, Oppenheim J 2013 Nat. Commun. 4 2059
Google Scholar
[6] Brandão F, Horodecki M, Ng N, Oppenheim J, Wehner S 2015 Proc. Natl. Acad. Sci. USA 112 3275
Google Scholar
[7] Rebentrost P, Mohseni M, Aspuru-Guzik A 2009 J. Phys. Chem. B 113 9942
Google Scholar
[8] Shao L H, Xi Z, Fan H, Li Y 2015 Phys. Rev. A 91 042120
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[9] Bromley T R, Cianciaruso M, Adesso G 2015 Phys. Rev. Lett. 114 210401
Google Scholar
[10] Misra A, Singh U, Bhattacharya S, Pati A K 2016 Phys. Rev. A 93 052335
Google Scholar
[11] Du S, Bai Z, Guo Y 2015 Phys. Rev. A 91 052120
Google Scholar
[12] Narasimhachar V, Gour G 2015 Nat. Commun. 6 7689
Google Scholar
[13] Girolami D 2014 Phys. Rev. Lett. 113 170401
Google Scholar
[14] Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403
Google Scholar
[15] Yao Y, Xiao X, Ge L, Sun C P 2015 Phys. Rev. A 92 022112
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[16] Tan K C, Kwon H, Park C Y, Jeong H 2016 Phys. Rev. A 94 022329
Google Scholar
[17] Wang X L, Yue Q L, Yu C H, Gao F, Qin S J 2017 arXiv: 1703.00648v1[quant-ph]
[18] Marvian I, Spekkens R W 2016 Phys. Rev. A 94 052324
Google Scholar
[19] de Vicente J I , Streltsov A 2017 J. Phys. A: Math. Theor. 50 045301
Google Scholar
[20] Streltsov A, Adesso G, Plenio M B 2017 Rev. Mod. Phys. 89 041003
Google Scholar
[21] Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122
Google Scholar
[22] Scully M O, Zubairy M S, Agarwal G S, Walther H 2003 Science 299 862
Google Scholar
[23] Liao J Q, Dong H, Sun C P 2010 Phys. Rev. A 81 052121
Google Scholar
[24] Türkpençe D, Müstecaplıoğlu Ö E 2016 Phys. Rev. E 93 012145
Google Scholar
[25] Li H et al. 2014 Phys. Rev. E 89 052132
[26] Daǧ C B, Niedenzu W, Müstecaplıoğlu Ö E, Kurizki G 2016 Entropy 18 244
Google Scholar
[27] Poyatos J F, Cirac J I, Zoller P 1996 Phys. Rev. Lett. 77 4728
Google Scholar
[28] Verstraete F, Wolf M M, Cirac J I 2009 Nat. Phys. 5 633
Google Scholar
[29] Wang Y D, Clerk A A 2013 Phys. Rev. Lett. 110 253601
Google Scholar
[30] Gelbwaser-Klimovsky D, Kurizki G 2015 Sci. Rep. 5 7809
Google Scholar
[31] Engel G S et al. 2007 Nature. 446 782
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[38] Lostaglio M, Korzekwa K, Jennings D, Rudolph T 2015 Phys. Rev. X 5 021001
[39] Gour G, Müller M P, Narasimhachar V, Spekkens R W, Halpern N Y 2015 Phys. Rep. 583 1
[40] Santos J P, Céleri L C, Landi G T, Paternostro M 2017 arXiv: 1707.08946v2[quant-ph]
[41] Francica G, Goold J, Plastina F 2017 arXiv: 1707.06950v1[quant-ph]
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Google Scholar
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Google Scholar
[45] Levitin L B, Toffoli T 2011 Int. J. Theor. Phys. 50 3844
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[52] Correa L A, Palao J P, Adesso G, Alonso D 2013 Phys. Rev. E 87 042131
Google Scholar
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Google Scholar
[54] 王涛, 黄晓理, 刘洋, 许欢 2013 物理学报 62 060301
Google Scholar
Wang T, Huang X L, Liu Y, Xu H 2013 Acta Phys. Sin. 62 060301
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Zhao L M, Zhang G F 2017 Acta Phys. Sin. 66 240502
Google Scholar
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Google Scholar
[60] Huang X L, Wang T, Yi X X 2012 Phys. Rev. E 86 051105
[61] Niedenzu W, Gelbwaser-Klimovsky D, Kofman A G, Kurizki G 2016 New J. Phys. 18 083012
Google Scholar
[62] Manzano G, Galve F, Zambrini R, Parrondo J M R 2016 Phys. Rev. E 93 052120
[63] Manzano G 2018 Phys. Rev. E 98 042123
[64] Meschede D, Walther H, Müller G 1985 Phys. Rev. Lett. 54 551
Google Scholar
[65] Filipowicz P, Javanainen J, Meystre P 1986 Phys. Rev. A 34 3077
[66] Cresser J D 1992 Phys. Rev. A 46 5913
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Google Scholar
[69] (北京: 世界图书出版公司北京公司) p385
Scully M O, Zubairy M S 2011 Quantum Optics
[70] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[71] Hovhannisyan K V, Perarnau-Llobet M, Huber M, Acín A 2013 Phys. Rev. Lett. 111 240401
[72] Binder F C, Vinjanampathy S, Modi K, Goold J 2015 New J. Phys. 17 075015
Google Scholar
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Google Scholar
[74] Ferraro D, Campisi M, Andolina G M, Pellegrini V, Polini M 2018 Phys. Rev. Lett. 120 117702
Google Scholar
[75] Andolina G M, et al. 2018 arXiv: 1807.08656v2[quant-ph]
[76] Farina D, Andolina G M, Mari A, Polini M, Giovannetti V 2019 Phys. Rev. B 99 035421
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Google Scholar
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