Shortcuts to Squeezed Thermal States

Léonce Dupays1,2 and Aurélia Chenu1,2,3

1Donostia International Physics Center, E-20018 San Sebastián, Spain
2Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
3Ikerbasque, Basque Foundation for Science, E-48013 Bilbao, Spain

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Squeezed state in harmonic systems can be generated through a variety of techniques, including varying the oscillator frequency or using nonlinear two-photon Raman interaction. We focus on these two techniques to drive an initial thermal state into a final squeezed thermal state with controlled squeezing parameters – amplitude and phase – in arbitrary time. The protocols are designed through reverse engineering for both unitary and open dynamics. Control of the dissipation is achieved using stochastic processes, readily implementable via, e.g., continuous quantum measurements. Importantly, this allows controlling the state entropy and can be used for fast thermalization. The developed protocols are thus suited to generate squeezed thermal states at controlled temperature in arbitrary time.

The Heisenberg uncertainty principle prevents measuring position and momentum simultaneously with arbitrary accuracy. However, one can gain precision on position at the expense of uncertainty in momentum, or vice versa. This is known as squeezing and allows reducing the uncertainty on a chosen conjugate variable.
Squeezing is having a plethora of applications: it enhances the precision of measurement and thus helped the detection of gravitational waves and the development of atomic clocks. Knowing how to generate squeezed states in a fast way is relevant to quantum technologies, for instance in order to increase the rate of computation in information processing. In the context of quantum thermodynamics, squeezed thermal states can be used as a resource to enhance the performance of quantum engines.
Here, we design control protocols to dynamically generate squeezed thermal states in controled time at arbitrary temperature. The control of temperature is made possible thanks to engineered dissipation, that we propose, can be implemented using stochastic fields. We present control protocols for experimental implementation in a stochastically shaken harmonic trap or via two-photon Raman interaction.

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Cited by

[1] R. T. Sutherland, S. C. Burd, D. H. Slichter, S. B. Libby, and D. Leibfried, "Motional Squeezing for Trapped Ion Transport and Separation", Physical Review Letters 127 8, 083201 (2021).

[2] Christiane P. Koch, Ugo Boscain, Tommaso Calarco, Gunther Dirr, Stefan Filipp, Steffen J. Glaser, Ronnie Kosloff, Simone Montangero, Thomas Schulte-Herbrüggen, Dominique Sugny, and Frank K. Wilhelm, "Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe", EPJ Quantum Technology 9 1, 19 (2022).

[3] Manash Jyoti Sarmah, Akanksha Bansal, and Himangshu Prabal Goswami, "Nonequilibrium fluctuations in boson transport through squeezed reservoirs", Physica A: Statistical Mechanics and its Applications 615, 128620 (2023).

[4] Daniel Martínez-Tibaduiza, Luis Pires, and Carlos Farina, "Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes", Journal of Physics B: Atomic, Molecular and Optical Physics 54 20, 205401 (2021).

[5] Javed Akhtar, Jimli Goswami, and Himangshu Prabal Goswami, "Geometric phaselike effects of driven transport in presence of reservoir squeezing", Physical Review E 109 5, 054122 (2024).

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[7] Koushik Mandal and M. V. Satyanarayana, "Atomic Inversion and Entanglement Dynamics for Squeezed Coherent Thermal States in the Jaynes-Cummings Model", International Journal of Theoretical Physics 62 7, 140 (2023).

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