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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
[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 130401Google 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 140401Google Scholar
[5] Horodecki M, Oppenheim J 2013 Nat. Commun. 4 2059Google Scholar
[6] Brandão F, Horodecki M, Ng N, Oppenheim J, Wehner S 2015 Proc. Natl. Acad. Sci. USA 112 3275Google Scholar
[7] Rebentrost P, Mohseni M, Aspuru-Guzik A 2009 J. Phys. Chem. B 113 9942Google Scholar
[8] Shao L H, Xi Z, Fan H, Li Y 2015 Phys. Rev. A 91 042120Google Scholar
[9] Bromley T R, Cianciaruso M, Adesso G 2015 Phys. Rev. Lett. 114 210401Google Scholar
[10] Misra A, Singh U, Bhattacharya S, Pati A K 2016 Phys. Rev. A 93 052335Google Scholar
[11] Du S, Bai Z, Guo Y 2015 Phys. Rev. A 91 052120Google Scholar
[12] Narasimhachar V, Gour G 2015 Nat. Commun. 6 7689Google Scholar
[13] Girolami D 2014 Phys. Rev. Lett. 113 170401Google Scholar
[14] Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403Google Scholar
[15] Yao Y, Xiao X, Ge L, Sun C P 2015 Phys. Rev. A 92 022112Google Scholar
[16] Tan K C, Kwon H, Park C Y, Jeong H 2016 Phys. Rev. A 94 022329Google 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 052324Google Scholar
[19] de Vicente J I , Streltsov A 2017 J. Phys. A: Math. Theor. 50 045301Google Scholar
[20] Streltsov A, Adesso G, Plenio M B 2017 Rev. Mod. Phys. 89 041003Google Scholar
[21] Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122Google Scholar
[22] Scully M O, Zubairy M S, Agarwal G S, Walther H 2003 Science 299 862Google Scholar
[23] Liao J Q, Dong H, Sun C P 2010 Phys. Rev. A 81 052121Google Scholar
[24] Türkpençe D, Müstecaplıoğlu Ö E 2016 Phys. Rev. E 93 012145Google 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 244Google Scholar
[27] Poyatos J F, Cirac J I, Zoller P 1996 Phys. Rev. Lett. 77 4728Google Scholar
[28] Verstraete F, Wolf M M, Cirac J I 2009 Nat. Phys. 5 633Google Scholar
[29] Wang Y D, Clerk A A 2013 Phys. Rev. Lett. 110 253601Google Scholar
[30] Gelbwaser-Klimovsky D, Kurizki G 2015 Sci. Rep. 5 7809Google Scholar
[31] Engel G S et al. 2007 Nature. 446 782Google Scholar
[32] Lloyd S 2011 J. Phys.: Conf. Ser. 302 012037Google Scholar
[33] Åberg J 2014 Phys. Rev. Lett. 113 150402Google 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 143001Google Scholar
[36] Kammerlander P, Anders J 2016 Sci. Rep. 6 22174Google Scholar
[37] Watanabe G, Venkatesh B P, Talkner P, del Campo A 2017 Phys. Rev. Lett. 118 050601Google 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 032117Google 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 031105Google Scholar
[45] Levitin L B, Toffoli T 2011 Int. J. Theor. Phys. 50 3844Google 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 123Google Scholar
[48] Thomas G, Johal R S 2011 Phys. Rev. E 83 031135Google Scholar
[49] He J Z, He X, Zheng J 2012 Chin. Phys. B 21 050303Google Scholar
[50] Wang H, Liu S Q, He J Z 2009 Phys. Rev. E 79 041113Google Scholar
[51] 张英丽, 周斌 2011 物理学报 60 120301Google Scholar
Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301Google Scholar
[52] Correa L A, Palao J P, Adesso G, Alonso D 2013 Phys. Rev. E 87 042131Google Scholar
[53] Park J J, Kim K H, Sagawa T, Kim S W 2013 Phys. Rev. Lett. 111 230402Google Scholar
[54] 王涛, 黄晓理, 刘洋, 许欢 2013 物理学报 62 060301Google Scholar
Wang T, Huang X L, Liu Y, Xu H 2013 Acta Phys. Sin. 62 060301Google 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 115013Google Scholar
[57] Uzdin R 2016 Phys. Rev. Appl. 6 024004Google Scholar
[58] 赵丽梅, 张国锋 2017 物理学报 66 240502Google Scholar
Zhao L M, Zhang G F 2017 Acta Phys. Sin. 66 240502Google Scholar
[59] Dillenschneider R, Lutz E 2009 Europhys. Lett. 88 50003Google 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 083012Google 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 551Google 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 510Google 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 075015Google Scholar
[73] Campaioli F et al. 2017 Phys. Rev. Lett. 118 150601Google Scholar
[74] Ferraro D, Campisi M, Andolina G M, Pellegrini V, Polini M 2018 Phys. Rev. Lett. 120 117702Google 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 030605Google Scholar
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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
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.
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$m\in[1, 120]$ .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,$N$ = 200Figure 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 130401Google 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 140401Google Scholar
[5] Horodecki M, Oppenheim J 2013 Nat. Commun. 4 2059Google Scholar
[6] Brandão F, Horodecki M, Ng N, Oppenheim J, Wehner S 2015 Proc. Natl. Acad. Sci. USA 112 3275Google Scholar
[7] Rebentrost P, Mohseni M, Aspuru-Guzik A 2009 J. Phys. Chem. B 113 9942Google Scholar
[8] Shao L H, Xi Z, Fan H, Li Y 2015 Phys. Rev. A 91 042120Google Scholar
[9] Bromley T R, Cianciaruso M, Adesso G 2015 Phys. Rev. Lett. 114 210401Google Scholar
[10] Misra A, Singh U, Bhattacharya S, Pati A K 2016 Phys. Rev. A 93 052335Google Scholar
[11] Du S, Bai Z, Guo Y 2015 Phys. Rev. A 91 052120Google Scholar
[12] Narasimhachar V, Gour G 2015 Nat. Commun. 6 7689Google Scholar
[13] Girolami D 2014 Phys. Rev. Lett. 113 170401Google Scholar
[14] Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403Google Scholar
[15] Yao Y, Xiao X, Ge L, Sun C P 2015 Phys. Rev. A 92 022112Google Scholar
[16] Tan K C, Kwon H, Park C Y, Jeong H 2016 Phys. Rev. A 94 022329Google 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 052324Google Scholar
[19] de Vicente J I , Streltsov A 2017 J. Phys. A: Math. Theor. 50 045301Google Scholar
[20] Streltsov A, Adesso G, Plenio M B 2017 Rev. Mod. Phys. 89 041003Google Scholar
[21] Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122Google Scholar
[22] Scully M O, Zubairy M S, Agarwal G S, Walther H 2003 Science 299 862Google Scholar
[23] Liao J Q, Dong H, Sun C P 2010 Phys. Rev. A 81 052121Google Scholar
[24] Türkpençe D, Müstecaplıoğlu Ö E 2016 Phys. Rev. E 93 012145Google 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 244Google Scholar
[27] Poyatos J F, Cirac J I, Zoller P 1996 Phys. Rev. Lett. 77 4728Google Scholar
[28] Verstraete F, Wolf M M, Cirac J I 2009 Nat. Phys. 5 633Google Scholar
[29] Wang Y D, Clerk A A 2013 Phys. Rev. Lett. 110 253601Google Scholar
[30] Gelbwaser-Klimovsky D, Kurizki G 2015 Sci. Rep. 5 7809Google Scholar
[31] Engel G S et al. 2007 Nature. 446 782Google Scholar
[32] Lloyd S 2011 J. Phys.: Conf. Ser. 302 012037Google Scholar
[33] Åberg J 2014 Phys. Rev. Lett. 113 150402Google 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 143001Google Scholar
[36] Kammerlander P, Anders J 2016 Sci. Rep. 6 22174Google Scholar
[37] Watanabe G, Venkatesh B P, Talkner P, del Campo A 2017 Phys. Rev. Lett. 118 050601Google 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 032117Google 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 031105Google Scholar
[45] Levitin L B, Toffoli T 2011 Int. J. Theor. Phys. 50 3844Google 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 123Google Scholar
[48] Thomas G, Johal R S 2011 Phys. Rev. E 83 031135Google Scholar
[49] He J Z, He X, Zheng J 2012 Chin. Phys. B 21 050303Google Scholar
[50] Wang H, Liu S Q, He J Z 2009 Phys. Rev. E 79 041113Google Scholar
[51] 张英丽, 周斌 2011 物理学报 60 120301Google Scholar
Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301Google Scholar
[52] Correa L A, Palao J P, Adesso G, Alonso D 2013 Phys. Rev. E 87 042131Google Scholar
[53] Park J J, Kim K H, Sagawa T, Kim S W 2013 Phys. Rev. Lett. 111 230402Google Scholar
[54] 王涛, 黄晓理, 刘洋, 许欢 2013 物理学报 62 060301Google Scholar
Wang T, Huang X L, Liu Y, Xu H 2013 Acta Phys. Sin. 62 060301Google 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 115013Google Scholar
[57] Uzdin R 2016 Phys. Rev. Appl. 6 024004Google Scholar
[58] 赵丽梅, 张国锋 2017 物理学报 66 240502Google Scholar
Zhao L M, Zhang G F 2017 Acta Phys. Sin. 66 240502Google Scholar
[59] Dillenschneider R, Lutz E 2009 Europhys. Lett. 88 50003Google 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 083012Google 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 551Google 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 510Google 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 075015Google Scholar
[73] Campaioli F et al. 2017 Phys. Rev. Lett. 118 150601Google Scholar
[74] Ferraro D, Campisi M, Andolina G M, Pellegrini V, Polini M 2018 Phys. Rev. Lett. 120 117702Google 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 030605Google Scholar
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