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Dynamical invariant based shortcut to equilibration in open quantum systems (2401.11659v3)
Published 22 Jan 2024 in quant-ph and cond-mat.stat-mech
Abstract: We propose using the dynamical invariant also known as the Lewis-Riesenfeld invariant, to speed-up the equilibration of a driven open quantum system. This allows us to reverse engineer the time-dependent master equation that describes the dynamics of the open quantum system and systematically derive a protocol that realizes a shortcut to equilibration. The method does not require additional constraints on the timescale of the dynamics beside the Born-Markov approximation and can be generically applied to boost single particle quantum engines significantly. We demonstrate it with the damped harmonic oscillator, and show that our protocol can achieve a high-fidelity control in shorter timescales than simple non-optimized protocols. We find that the system is heated during the dynamics to speed-up the equilibration, which can be considered as an analogue of the Mpemba effect in quantum control.
- S. Kallush, R. Dann, and R. Kosloff, Controlling the uncontrollable: Quantum control of open-system dynamics, Science Advances 8, eadd0828 (2022), https://www.science.org/doi/pdf/10.1126/sciadv.add0828 .
- R. Kosloff and A. Levy, Quantum Heat Engines and Refrigerators: Continuous Devices, Annual Review of Physical Chemistry 65, 365 (2014).
- S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemporary Physics 57, 545 (2016).
- N. M. Myers, O. Abah, and S. Deffner, Quantum thermodynamic devices: From theoretical proposals to experimental reality, AVS Quantum Science 4, 027101 (2022), https://pubs.aip.org/avs/aqs/article-pdf/doi/10.1116/5.0083192/16494008/027101_1_online.pdf .
- G. Kurizki and A. G. Kofman, Thermodynamics and Control of Open Quantum Systems (Cambridge University Press, 2022).
- R. Xu, Reinforcement learning approach to shortcuts between thermodynamic states with minimum entropy production, Phys. Rev. E 105, 054123 (2022).
- T. Villazon, A. Polkovnikov, and A. Chandran, Swift heat transfer by fast-forward driving in open quantum systems, Phys. Rev. A 100, 012126 (2019).
- R. Dann, A. Tobalina, and R. Kosloff, Shortcut to equilibration of an open quantum system, Phys. Rev. Lett. 122, 250402 (2019).
- R. Dann, A. Tobalina, and R. Kosloff, Fast route to equilibration, Phys. Rev. A 101, 052102 (2020).
- R. Dann and R. Kosloff, Quantum signatures in the quantum Carnot cycle, New J. Phys. 22, 013055 (2020).
- A. Das and V. Mukherjee, Quantum-enhanced finite-time Otto cycle, Phys. Rev. Research 2, 033083 (2020).
- H.-P. Breuer and F. Petruccione, The theory of Open Quantum Systems (Oxford University Press, 2002).
- R. Dann, A. Levy, and R. Kosloff, Time-dependent markovian quantum master equation, Phys. Rev. A 98, 052129 (2018).
- R. Dann and R. Kosloff, Inertial theorem: Overcoming the quantum adiabatic limit, Phys. Rev. Res. 3, 013064 (2021).
- H. R. Lewis and W. B. Riesenfeld, An exact quantum theory of the time‐dependent harmonic oscillator and of a charged particle in a time‐dependent electromagnetic field, J. Math. Phys. 10, 1458 (1969), https://doi.org/10.1063/1.1664991 .
- S. L. Wu, X. L. Huang, and X. X. Yi, Driven Markovian master equation based on the Lewis-Riesenfeld-invariant theory, Phys. Rev. A 106, 052217 (2022).
- V. Blickle and C. Bechinger, Realization of a micrometre-sized stochastic heat engine, Nature Physics 8, 143 (2012).
- R. Kosloff and Y. Rezek, The Quantum Harmonic Otto Cycle, Entropy 19, 136 (2017).
- A. Lampo, M. A. García March, and M. Lewenstein, eds., Quantum Brownian Motion Revisited (Springer Cham, 2019).
- T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113, 140401 (2014).
- E. B. Mpemba and D. G. Osborne, Cool?, Physics Education 4, 172 (1969).
- A. K. Chatterjee, S. Takada, and H. Hayakawa, Quantum Mpemba effect in a quantum dot with reservoirs, Phys. Rev. Lett. 131, 080402 (2023).
- P. Salamon and R. S. Berry, Thermodynamic length and dissipated availability, Phys. Rev. Lett. 51, 1127 (1983).
- M. Scandi and M. Perarnau-Llobet, Thermodynamic length in open quantum systems, Quantum 3, 197 (2019).
- W. Ma, X. L. Huang, and S. L. Wu, Dynamics of a driven open double two-level system and its entanglement generation, Phys. Rev. A 107, 032409 (2023).
- M. Girardeau, Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension, J. Math. Phys. 1, 516 (1960).
- J. Jaramillo, M. Beau, and A. del Campo, Quantum supremacy of many-particle thermal machines, New J. Phys. 18, 075019 (2016).
- T. Fogarty and T. Busch, A many-body heat engine at criticality, Quantum Science and Technology 6, 015003 (2020).
- M. Boubakour, T. Fogarty, and T. Busch, Interaction-enhanced quantum heat engine, Phys. Rev. Res. 5, 013088 (2023).