Study on energy extraction assisted with quantum correlated coherence in bath

Li Hai; Zou Jian; Shao Bin; Chen Yu; Hua Zhen

doi:10.7498/aps.68.20181525

Abstract

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:

Authors and contacts

1.
School of Information and Electronic Engineering, Shandong Technology and Business Universiy, Yantai 264000, China
2.
School of Physics, Beijing Institute of Technology, Beijing 100081, China
3.
Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
4.
School of Physics and Electronic Sciences, Guizhou Normal College, Guiyang 550018, China

Corresponding author: Li Hai, shenghuo2003@126.com ; Zou Jian, zoujian@bit.edu.cn ;

Funds: Project supported by the National Science Foundation of China (Grants Nos. 11547036, 11775019, 11375025, 61472227), the Education Department Foundation of Guizhou Province of China (Grants No. 090122), and the Ph.D. Research Startup Foundation of Shandong Technology and Business University, China (Grant No. BS201418).

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References

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Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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 $m\in[1, 120]$.

DownLoad: Full-Size Img PowerPoint

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, $N$ = 200

Figure 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).

DownLoad: Full-Size Img PowerPoint

map

[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
[4]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401 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 Google Scholar
[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 Google Scholar
[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
[32]	Lloyd S 2011 J. Phys.: Conf. Ser. 302 012037 Google Scholar
[33]	Åberg J 2014 Phys. Rev. Lett. 113 150402 Google Scholar
[34]	Skrzypczyk P, Short A J, Popescu S 2014 Nat. Commun. 5 4185
[35]	Goold J, Huber M, Riera A, del Rio L, Skrzypczyk P 2016 J. Phys. A 49 143001 Google Scholar
[36]	Kammerlander P, Anders J 2016 Sci. Rep. 6 22174 Google Scholar
[37]	Watanabe G, Venkatesh B P, Talkner P, del Campo A 2017 Phys. Rev. Lett. 118 050601 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]
[42]	Çakmak B, Manatuly A, Müstecaplıoğlu Ö E 2017 Phys. Rev. A 96 032117 Google Scholar
[43]	Manzano G, Silva R, Parrondo J M R 2017 arXiv: 1709.00231v2[quant-ph]
[44]	Quan H T, Liu Y X, Sun C P, Nori F 2007 Phys. Rev. E 76 031105 Google Scholar
[45]	Levitin L B, Toffoli T 2011 Int. J. Theor. Phys. 50 3844 Google Scholar
[46]	Francica G, Goold J, Plastina F, Paternostro M 2017 npj Quantum Information 3 12
[47]	Zhang G F 2008 Eur. Phys. J. D 49 123 Google Scholar
[48]	Thomas G, Johal R S 2011 Phys. Rev. E 83 031135 Google Scholar
[49]	He J Z, He X, Zheng J 2012 Chin. Phys. B 21 050303 Google Scholar
[50]	Wang H, Liu S Q, He J Z 2009 Phys. Rev. E 79 041113 Google Scholar
[51]	张英丽, 周斌 2011 60 120301 Google Scholar Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 Google Scholar
[52]	Correa L A, Palao J P, Adesso G, Alonso D 2013 Phys. Rev. E 87 042131 Google Scholar
[53]	Park J J, Kim K H, Sagawa T, Kim S W 2013 Phys. Rev. Lett. 111 230402 Google Scholar
[54]	王涛, 黄晓理, 刘洋, 许欢 2013 62 060301 Google Scholar Wang T, Huang X L, Liu Y, Xu H 2013 Acta Phys. Sin. 62 060301 Google Scholar
[55]	Brunner N, et al. 2014 Phys. Rev. E 89 032115
[56]	Mitchison M T, Woods M P, Prior J, Huber M 2015 New J. Phys. 17 115013 Google Scholar
[57]	Uzdin R 2016 Phys. Rev. Appl. 6 024004 Google Scholar
[58]	赵丽梅, 张国锋 2017 66 240502 Google Scholar Zhao L M, Zhang G F 2017 Acta Phys. Sin. 66 240502 Google Scholar
[59]	Dillenschneider R, Lutz E 2009 Europhys. Lett. 88 50003 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
[67]	Kist T B L, Orszag M, Brun T A, Davidovich L 1999 J. Opt. B: Quantum Semiclass. Opt. 1 251
[68]	Deléglise et al. 2008 Nature 455 510 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
[73]	Campaioli F et al. 2017 Phys. Rev. Lett. 118 150601 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
[77]	Ito S 2018 Phys. Rev. Lett. 121 030605 Google Scholar

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Vol. 68, Issue 4 - 2019-02-20

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