Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution

Sahar Alipour1, Aurelia Chenu2,3, Ali T. Rezakhani4, and Adolfo del Campo2,3,5

1QTF Center of Excellence, Department of Applied Physics, Aalto University, P. O. Box 11000, FI-00076 Aalto, Espoo, Finland
2Donostia International Physics Center, E-20018 San Sebastián, Spain
3IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
4Department of Physics, Sharif University of Technology, Tehran 14588, Iran
5Department of Physics, University of Massachusetts, Boston, MA 02125, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in this fashion can be implemented in two alternative physical scenarios: one characterized by the presence of balanced gain and loss, the other involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration, we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system, and provide a protocol for the fast thermalization of a quantum oscillator.

We introduce a universal scheme to engineer shortcut to adiabaticity (STA) in arbitrary open quantum systems. Our work provides a generalization of the counter-diabatic driving technique to open quantum processes. To this end, we consider the evolution of a quantum system described by a mixed state along a prescribed trajectory of interest. We then find the equation of motion that generates the desired dynamics. The latter can be recast in terms of the nonlinear evolution of a system in the presence of balanced gain and loss. Alternatively, the dynamics can be associated with a non-Markovian master equation with time-dependent Lindblad operators, whose explicit form is determined by the prescribed trajectory. We demonstrated this framework by discussing the controlled open quantum dynamics of a two-level system and a driven quantum oscillator.

► BibTeX data

► References

[1] Erik Torrontegui, Sara Ibáñez, Sofia Martínez-Garaot, Michele Modugno, Adolfo del Campo, David Guéry-Odelin, Andreas Ruschhaupt, Xi Chen, and Juan Gonzalo Muga. Chapter 2: Shortcuts to adiabaticity. In Ennio Arimondo, Paul R. Berman, and Chun C. Lin, editors, Advances in Atomic, Molecular, and Optical Physics, Vol. 62, pp. 117. Academic Press, 2013. 10.1016/​B978-0-12-408090-4.00002-5.

[2] Adolfo del Campo and Kihwan Kim. Focus on shortcuts to adiabaticity. New J. Phys., 21:050201, 2019. 10.1088/​1367-2630/​ab1437.

[3] D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga. Shortcuts to adiabaticity: Concepts, methods, and applications. Rev. Mod. Phys., 91:045001, 2019. 10.1103/​RevModPhys.91.045001.

[4] Xi Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga. Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity. Phys. Rev. Lett., 104:063002, 2010. 10.1103/​PhysRevLett.104.063002.

[5] Mustafa Demirplak and Stuart A Rice. Adiabatic population transfer with control fields. J. Phys. Chem. A, 107:9937, 2003. 10.1021/​jp030708a.

[6] Mustafa Demirplak and Stuart A Rice. Assisted adiabatic passage revisited. J. Phys. Chem. B, 109:6838, 2005. 10.1021/​jp040647w.

[7] Jiawen Deng, Qing-Hai Wang, Zhihao Liu, Peter Hänggi, and Jiangbin Gong. Boosting work characteristics and overall heat-engine performance via shortcuts to adiabaticity: Quantum and classical systems. Phys. Rev. E, 88:062122, 2013. 10.1103/​PhysRevE.88.062122.

[8] Adolfo del Campo, J Goold, and M Paternostro. More bang for your buck: Super-adiabatic quantum engines. Sci. Rep., 4:6208, 2014. 10.1038/​srep06208.

[9] Ken Funo, Jing-Ning Zhang, Cyril Chatou, Kihwan Kim, Masahito Ueda, and Adolfo del Campo. Universal work fluctuations during shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett., 118:100602, 2017. 10.1103/​PhysRevLett.118.100602.

[10] J.-F. Schaff, X.-L. Song, P. Vignolo, and G. Labeyrie. Fast optimal transition between two equilibrium states. Phys. Rev. A, 82:033430, 2010. 10.1103/​PhysRevA.82.033430.

[11] J.-F. Schaff, X.-L. Song, P. Capuzzi, P. Vignolo, and G. Labeyrie. Shortcut to adiabaticity for an interacting Bose-Einstein condensate. Europhys. Lett., 93:23001, 2011. 10.1209/​0295-5075/​93/​23001.

[12] M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch. High-fidelity quantum driving. Nat. Phys., 8:147, 2012. 10.1038/​nphys2170.

[13] W. Rohringer, D. Fischer, F. Steiner, I. E. Mazets, J. Schmiedmayer, and M. Trupke. Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas. Sci. Rep., 5:9820, 2015. 10.1038/​srep09820.

[14] Shujin Deng, Pengpeng Diao, Qianli Yu, Adolfo del Campo, and Haibin Wu. Shortcuts to adiabaticity in the strongly coupled regime: Nonadiabatic control of a unitary fermi gas. Phys. Rev. A, 97:013628, 2018a. 10.1103/​PhysRevA.97.013628.

[15] Shujin Deng, Aurélia Chenu, Pengpeng Diao, Fang Li, Shi Yu, Ivan Coulamy, Adolfo del Campo, and Haibin Wu. Superadiabatic quantum friction suppression in finite-time thermodynamics. Sci. Adv., 4:eaar5909, 2018b. 10.1126/​sciadv.aar5909.

[16] Pengpeng Diao, Shujin Deng, Fang Li, Shi Yu, Aurélia Chenu, Adolfo del Campo, and Haibin Wu. Shortcuts to adiabaticity in fermi gases. New J. Phys., 20:105004, oct 2018. 10.1088/​1367-2630/​aae45e.

[17] Jingfu Zhang, Jeong Hyun Shim, Ingo Niemeyer, T. Taniguchi, T. Teraji, H. Abe, S. Onoda, T. Yamamoto, T. Ohshima, J. Isoya, and Dieter Suter. Experimental implementation of assisted quantum adiabatic passage in a single spin. Phys. Rev. Lett., 110:240501, 2013. 10.1103/​PhysRevLett.110.240501.

[18] J. Kölbl, A. Barfuss, M. S. Kasperczyk, L. Thiel, A. A. Clerk, H. Ribeiro, and P. Maletinsky. Initialization of single spin dressed states using shortcuts to adiabaticity. Phys. Rev. Lett., 122:090502, 2019. 10.1103/​PhysRevLett.122.090502.

[19] Shuoming An, Dingshun Lv, Adolfo del Campo, and Kihwan Kim. Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space. Nat. Commun., 7:12999, 2016. 10.1038/​ncomms12999.

[20] Tenghui Wang, Zhenxing Zhang, Liang Xiang, Zhilong Jia, Peng Duan, Weizhou Cai, Zhihao Gong, Zhiwen Zong, Mengmeng Wu, Jianlan Wu, Luyan Sun, Yi Yin, and Guoping Guo. The experimental realization of high-fidelity `shortcut-to-adiabaticity' quantum gates in a superconducting xmon qubit. New J. Phys., 20:065003, 2018. 10.1088/​1367-2630/​aac9e7.

[21] Tenghui Wang, Zhenxing Zhang, Liang Xiang, Zhilong Jia, Peng Duan, Zhiwen Zong, Zhenhai Sun, Zhangjingzi Dong, Jianlan Wu, Yi Yin, and Guoping Guo. Experimental realization of a fast controlled-$Z$ gate via a shortcut to adiabaticity. Phys. Rev. Applied, 11:034030, 2019. 10.1103/​PhysRevApplied.11.034030.

[22] H.-P. Breuer and P. Petruccione. The Theory of Open Quantum Systems. Oxford University Press, Oxford, 2007.

[23] M. B. Plenio and P. L. Knight. The quantum-jump approach to dissipative dynamics in quantum optics. Rev. Mod. Phys., 70:101, 1998. 10.1103/​RevModPhys.70.101.

[24] Carl M. Bender and Stefan Boettcher. Real spectra in non-Hermitian Hamiltonians having $\mathcal{PT}$ symmetry. Phys. Rev. Lett., 80:5243, 1998. 10.1103/​PhysRevLett.80.5243.

[25] Christian E. Rüter, Konstantinos G. Makris, Ramy El-Ganainy, Demetrios N. Christodoulides, Mordechai Segev, and Detlef Kip. Observation of parity-time symmetry in optics. Nat. Phys., 6:192, 2010. 10.1038/​nphys1515.

[26] Alois Regensburger, Christoph Bersch, Mohammad-Ali Miri, Georgy Onishchukov, Demetrios N. Christodoulides, and Ulf Peschel. Parity-time synthetic photonic lattices. Nature (London), 488:167, 2012. 10.1038/​nature11298.

[27] Liang Feng, Ye-Long Xu, William S. Fegadolli, Ming-Hui Lu, José E. B. Oliveira, Vilson R. Almeida, Yan-Feng Chen, and Axel Scherer. Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. Nat. Mater., 12:108, 2012. 10.1038/​nmat3495.

[28] Bo Peng, Sahin Kaya Özdemir, Fuchuan Lei, Faraz Monifi, Mariagiovanna Gianfreda, Gui Lu Long, Shanhui Fan, Franco Nori, Carl M. Bender, and Lan Yang. Parity-time-symmetric whispering-gallery microcavities. Nat. Phys., 10:394, 2014. 10.1038/​nphys2927.

[29] Bo Zhen, Chia Wei Hsu, Yuichi Igarashi, Ling Lu, Ido Kaminer, Adi Pick, Song-Liang Chua, John D. Joannopoulos, and Marin Soljačić. Spawning rings of exceptional points out of dirac cones. Nature (London), 525:354, 2015. 10.1038/​nature14889.

[30] A Ruschhaupt, Xi Chen, D Alonso, and J G Muga. Optimally robust shortcuts to population inversion in two-level quantum systems. New J. Phys., 14: 093040, 2012. 10.1088/​1367-2630/​14/​9/​093040.

[31] Anthony Kiely and Andreas Ruschhaupt. Inhibiting unwanted transitions in population transfer in two-and three-level quantum systems. J. Phys. B: At. Mol. Opt. Phys., 47:115501, 2014. 10.1088/​0953-4075/​47/​11/​115501.

[32] D. A. Lidar, I. L. Chuang, and K. B. Whaley. Decoherence-free subspaces for quantum computation. Phys. Rev. Lett., 81:2594, 1998. 10.1103/​PhysRevLett.81.2594.

[33] S. L. Wu, X. L. Huang, H. Li, and X. X. Yi. Adiabatic evolution of decoherence-free subspaces and its shortcuts. Phys. Rev. A, 96:042104, 2017. 10.1103/​PhysRevA.96.042104.

[34] Amikam Levy, A. Kiely, J. G. Muga, R. Kosloff, and E. Torrontegui. Noise resistant quantum control using dynamical invariants. New J. Phys., 20:025006, 2018. 10.1088/​1367-2630/​aaa9e5.

[35] A. B. Boyd, A. Patra, C. Jarzynski, and J. P. Crutchfield. Shortcuts to thermodynamic computing: The cost of fast and faithful erasure. arXiv:1812.11241, 2018. URL https:/​/​​abs/​1812.11241.

[36] Adolfo del Campo, Aurélia Chenu, Shujin Deng, and Haibin Wu. Friction-Free Quantum Machines. In F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso, editors, Thermodynamics in the Quantum Regime, pp. 127. Springer International Publishing, Cham, 2018. 10.1007/​978-3-319-99046-0_5.

[37] S. Ibáñez, S. Martínez-Garaot, Xi Chen, E. Torrontegui, and J. G. Muga. Shortcuts to adiabaticity for non-Hermitian systems. Phys. Rev. A, 84:023415, 2011. 10.1103/​PhysRevA.84.023415.

[38] Guan-Qiang Li, Guang-De Chen, Ping Peng, and Wei Qi. Non-Hermitian shortcut to adiabaticity of two-and three-level systems with gain and loss. Eur. Phys. J. D, 71:1, 2017. 10.1140/​epjd/​e2016-70525-6.

[39] Ye-Hong Chen, Qi-Cheng Wu, Bi-Hua Huang, Jie Song, Yan Xia, and Shi-Biao Zheng. Improving shortcuts to non-Hermitian adiabaticity for fast population transfer in open quantum systems. Ann. Phys. (Berlin), 530: 1700247, 2018. 10.1002/​andp.201700247.

[40] François Impens and David Guéry-Odelin. Fast quantum control in dissipative systems using dissipationless solutions. Sci. Rep., 9:1, 2019. 10.1038/​s41598-019-39731-z.

[41] G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral. Transitionless quantum driving in open quantum systems. New J. Phys., 16:053017, 2014. 10.1088/​1367-2630/​16/​5/​053017.

[42] M. S. Sarandy and D. A. Lidar. Adiabatic approximation in open quantum systems. Phys. Rev. A, 71:012331, 2005. 10.1103/​PhysRevA.71.012331.

[43] Roie Dann, Ander Tobalina, and Ronnie Kosloff. Shortcut to equilibration of an open quantum system. Phys. Rev. Lett., 122:250402, 2019. 10.1103/​PhysRevLett.122.250402.

[44] L. Dupays, I. L. Egusquiza, A. del Campo, and A. Chenu. Superadiabatic thermalization of a quantum oscillator by engineered dephasing. Phys. Rev. Research, 2:033178, 2020. 10.1103/​PhysRevResearch.2.033178.

[45] Tamiro Villazon, Anatoli Polkovnikov, and Anushya Chandran. Swift heat transfer by fast-forward driving in open quantum systems. Phys. Rev. A, 100:012126, 2019. 10.1103/​PhysRevA.100.012126.

[46] N. Pancotti, M. Scandi, M. T. Mitchison, and M. Perarnau-Llobet. Speed-ups to isothermality: Enhanced quantum heat engines through control of the system-bath coupling. arXiv:1911.12437, 2019. URL https:/​/​​abs/​1911.12437. URL https:/​/​​10.1103/​PhysRevX.10.031015.

[47] L. Dupays and A. Chenu. Dynamical engineering of squeezed thermal states, 2020. URL https:/​/​​abs/​2008.03307.

[48] M. V. Berry. Transitionless quantum driving. J. Phys. A: Math. Theor., 42:365303, 2009. 10.1088/​1751-8113/​42/​36/​365303.

[49] Tosio Kato. On the adiabatic theorem of quantum mechanics. J. Phys. Soc. Jpn., 5:435, 1950. 10.1143/​JPSJ.5.435.

[50] J. E. Avron, R. Seiler, and L. G. Yaffe. Adiabatic theorems and applications to the quantum Hall effect. Commun. Math. Phys., 110:33, 1987. 10.1007/​BF01209015.

[51] Dorje C. Brody and Eva-Maria Graefe. Mixed-state evolution in the presence of gain and loss. Phys. Rev. Lett., 109:230405, 2012. 10.1103/​PhysRevLett.109.230405.

[52] Jiangbin Gong and Qing-Hai Wang. Time-dependent $\mathcal{PT}$-symmetric quantum mechanics. J. Phys. A: Math. Theor., 46:485302, 2013. 10.1088/​1751-8113/​46/​48/​485302.

[53] S. Alipour, A. T. Rezakhani, A. P. Babu, K. Mølmer, M. Möttönen, and T. Ala-Nissila. Correlation-Picture Approach to Open-Quantum-System Dynamics. arXiv:1903.03861 (to appear in PRX), 2020. URL https:/​/​​abs/​1903.03861.

[54] K. Funo, N. Shiraishi, and K. Saito. Speed limit for open quantum systems. New J. Phys., 21:013006, 2019. 10.1088/​1367-2630/​aaf9f5.

[55] A. T. Rezakhani, D. F. Abasto, D. A. Lidar, and P. Zanardi. Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions. Phys. Rev. A, 82:012321, 2010. 10.1103/​PhysRevA.82.012321.

[56] S. Alipour and A. T. Rezakhani. Extended convexity of quantum Fisher information in quantum metrology. Phys. Rev. A, 91:042104, 2015. 10.1103/​PhysRevA.91.042104.

[57] S. Alipour, F. Benatti, F. Bakhshinezhad, M. Afsary, S. Marcantoni, and A. T. Rezakhani. Correlations in quantum thermodynamics: Heat, work, and entropy production. Sci. Rep., 6:35568, 2016. 10.1103/​PhysRevX.4.031042.

[58] R. W. Rendell and A. K. Rajagopal. Revivals and entanglement from initially entangled mixed states of a damped jaynes-cummings model. Phys. Rev. A, 67:062110, 2003. 10.1103/​PhysRevA.67.062110.

[59] H. Carmichael. An Open Systems Approach to Quantum Optics. Springer, Berlin, 1993.

[60] J. G. Muga, X. Chen, S. Ibáñez, I. Lizuain, and A. Ruschhaupt. Transitionless quantum drivings for the harmonic oscillator. J. Phys. B: At. Mol. Opt. Phys., 43: 085509, 2010. 10.1088/​0953-4075/​43/​8/​085509.

[61] Christopher Jarzynski. Generating shortcuts to adiabaticity in quantum and classical dynamics. Phys. Rev. A, 88:040101, 2013. 10.1103/​PhysRevA.88.040101.

[62] Adolfo del Campo. Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett., 111:100502, 2013. 10.1103/​PhysRevLett.111.100502.

[63] S. Ibáñez, Xi Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt. Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity. Phys. Rev. Lett., 109:100403, 2012. 10.1103/​PhysRevLett.109.100403.

[64] Andrew Smith, Yao Lu, Shuoming An, Xiang Zhang, Jing-Ning Zhang, Zongping Gong, H. T. Quan, Christopher Jarzynski, and Kihwan Kim. Verification of the quantum nonequilibrium work relation in the presence of decoherence. New J. Phys., 20:013008, 2018. 10.1088/​1367-2630/​aa9cd6.

[65] L. Amico et al. Roadmap on atomtronics. arXiv:2008.04439, 2020. URL http:/​/​​abs/​2008.04439.

[66] A. del Campo and M. G. Boshier. Shortcuts to adiabaticity in a time-dependent box. Sci. Rep., 2:648, 2012. 10.1038/​srep00648.

[67] Seth Lloyd. Universal quantum simulators. Science, 273:1073, 1996. 10.1126/​science.273.5278.1073.

[68] Julio T. Barreiro, Markus Müller, Philipp Schindler, Daniel Nigg, Thomas Monz, Michael Chwalla, Markus Hennrich, Christian F. Roos, Peter Zoller, and Rainer Blatt. An open-system quantum simulator with trapped ions. Nature (London), 470:486, 2011. 10.1038/​nature09801.

[69] Markus Müller, Sebastian Diehl, Guido Pupillo, and Peter Zoller. Engineered open systems and quantum simulations with atoms and ions. In Paul Berman, Ennio Arimondo, and Chun Lin, editors, Advances in Atomic, Molecular, and Optical Physics, Vol. 61 of Advances in Atomic, Molecular, and Optical Physics, pp. 1. Academic Press, 2012. 10.1016/​B978-0-12-396482-3.00001-6.

[70] I. M. Georgescu, S. Ashhab, and Franco Nori. Quantum simulation. Rev. Mod. Phys., 86:153, 2014. 10.1103/​RevModPhys.86.153.

[71] R. Sweke, M. Sanz, I. Sinayskiy, F. Petruccione, and E. Solano. Digital quantum simulation of many-body non-Markovian dynamics. Phys. Rev. A, 94:022317, 2016. 10.1103/​PhysRevA.94.022317.

Cited by

[1] Agniva Roychowdhury and Sebastian Deffner, "Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals", Entropy 23 1, 81 (2021).

[2] Andreas Hartmann, Victor Mukherjee, Glen Bigan Mbeng, Wolfgang Niedenzu, and Wolfgang Lechner, "Multi-spin counter-diabatic driving in many-body quantum Otto refrigerators", Quantum 4, 377 (2020).

[3] Anthony Kiely, "Generalised Counterdiabatic Driving in Open Systems", Quantum Views 4, 45 (2020).

[4] J. G. Muga, S. Martínez-Garaot, M. Pons, M. Palmero, and A. Tobalina, "Time-dependent harmonic potentials for momentum or position scaling", Physical Review Research 2 4, 043162 (2020).

[5] Roie Dann, Ander Tobalina, and Ronnie Kosloff, "Fast route to equilibration", Physical Review A 101 5, 052102 (2020).

[6] Andreas Hartmann, Victor Mukherjee, Wolfgang Niedenzu, and Wolfgang Lechner, "Many-body quantum heat engines with shortcuts to adiabaticity", Physical Review Research 2 2, 023145 (2020).

[7] S. Zakavati, F. T. Tabesh, and S. Salimi, "Bounds on charging power of open quantum batteries", arXiv:2003.09814.

[8] L. Dupays, I. L. Egusquiza, A. del Campo, and A. Chenu, "Superadiabatic thermalization of a quantum oscillator by engineered dephasing", Physical Review Research 2 3, 033178 (2020).

[9] S. Alipour, A. T. Rezakhani, A. Chenu, A. del Campo, and T. Ala-Nissila, "Unambiguous Formulation for Heat and Work in Arbitrary Quantum Evolution", arXiv:1912.01939.

[10] Nicola Pancotti, Matteo Scandi, Mark T. Mitchison, and Martí Perarnau-Llobet, "Speed-Ups to Isothermality: Enhanced Quantum Thermal Machines through Control of the System-Bath Coupling", Physical Review X 10 3, 031015 (2020).

[11] Domingos S. P. Salazar, "Work distribution in thermal processes", Physical Review E 101 3, 030101 (2020).

[12] Obinna Abah, Ricardo Puebla, Anthony Kiely, Gabriele De Chiara, Mauro Paternostro, and Steve Campbell, "Energetic cost of quantum control protocols", arXiv:1906.07201.

[13] Inés de Vega, "The quantum dynamical map of the spin boson model", arXiv:2001.04236.

[14] Esteban Calzetta, "The importance of being measurement", arXiv:1909.13178.

[15] Léonce Dupays and Aurélia Chenu, "Dynamical engineering of squeezed thermal states", arXiv:2008.03307.

The above citations are from Crossref's cited-by service (last updated successfully 2021-01-19 05:29:44) and SAO/NASA ADS (last updated successfully 2021-01-19 05:29:46). The list may be incomplete as not all publishers provide suitable and complete citation data.

1 thought on “Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution

  1. Pingback: Perspective in Quantum Views by Anthony Kiely "Generalised Counterdiabatic Driving in Open Systems"