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


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

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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.

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

[2] 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).

[3] 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).

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

[5] 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.

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

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[8] 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).

[9] J. G. Muga, S. Martínez-Garaot, M. Pons, M. Palmero, and A. Tobalina, “Time-dependent harmonic potentials for momentum or position scaling”, arXiv:2007.09949.

[10] Andreas Hartmann, Victor Mukherjee, Glen Bigan Mbeng, Wolfgang Niedenzu, and Wolfgang Lechner, “Multi-spin counter-diabatic driving in many-body quantum Otto refrigerators”, arXiv:2008.09327.

[11] Esteban Calzetta, “The importance of being measurement”, arXiv:1909.13178.

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

[13] Léonce Dupays and Aurélia Chenu, “Dynamical engineering of squeezed thermal states”, arXiv:2008.03307.

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