Wigner Analysis of Particle Dynamics and Decoherence in Wide Nonharmonic Potentials

Andreu Riera-Campeny; Marc Roda-Llordes; Piotr T. Grochowski; Oriol Romero-Isart

doi:10.22331/q-2024-07-02-1393

Wigner Analysis of Particle Dynamics and Decoherence in Wide Nonharmonic Potentials

Andreu Riera-Campeny^1,2, Marc Roda-Llordes^1,2, Piotr T. Grochowski^1,2,3, and Oriol Romero-Isart^1,2,4,5

¹Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
²Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
³Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
⁴ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
⁵ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain

Published:	2024-07-02, volume 8, page 1393
Eprint:	arXiv:2307.14106v5
Doi:	https://doi.org/10.22331/q-2024-07-02-1393
Citation:	Quantum 8, 1393 (2024).

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Abstract

We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting for both the classical dynamics of the centroid of the initial state and the rotation and squeezing about that trajectory. Subsequently, we employ two crucial approximations, namely the constant-angle and linearized-decoherence approximations, upon which our results rely. These approximations are effective in the regime of wide potentials and small fluctuations, namely potentials that enable spatial expansions orders of magnitude larger than the one of the initial state but that remain smaller compared to the relevant dynamical length scale (e.g., the distance between turning points). Our analytical result elucidates the interplay between classical and quantum physics and the impact of decoherence during nonlinear dynamics. This analytical result is instrumental to designing, optimizing, and understanding proposals using nonlinear dynamics to generate macroscopic quantum states of massive particles.

Popular summary

The one-dimensional motion of a quantum particle is one of the simplest dynamical systems. Its study in the early days of quantum mechanics significantly contributed to our current understanding of quantum theory. A convenient way to represent the quantum state of such a system is through the Wigner function, a quantum analog of the phase space probability distribution in classical mechanics. However, due to inherent interference effects in quantum mechanics, the Wigner function can take negative values in the quantum phase space, a genuine quantum property. Both classical and quantum descriptions coincide for Gaussian dynamics, where the potential is at most quadratic. For wide nonharmonic potentials, classical and quantum dynamics start to diverge as the system delocalizes over large distances, leading to negativities in the Wigner function. Interestingly, the quantum nonlinear dynamics of such a system can result in very rich and complex phase-space structures, with potentially very small areas of alternating signs, making them highly sensitive to decoherence. In this paper, we propose an approximate method to analytically evaluate the nonlinear evolution of the Wigner function in the presence of decoherence. This method is key for the design, understanding, and optimization of protocols for preparing and certifying quantum states of mechanical systems.

► BibTeX data

@article{RieraCampeny2024wigneranalysisof,
  doi = {10.22331/q-2024-07-02-1393},
  url = {https://doi.org/10.22331/q-2024-07-02-1393},
  title = {Wigner {A}nalysis of {P}article {D}ynamics and {D}ecoherence in {W}ide {N}onharmonic {P}otentials},
  author = {Riera-Campeny, Andreu and Roda-Llordes, Marc and Grochowski, Piotr T. and Romero-Isart, Oriol},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1393},
  month = jul,
  year = {2024}
}

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Cited by

[1] M. Roda-Llordes, A. Riera-Campeny, D. Candoli, P. T. Grochowski, and O. Romero-Isart, "Macroscopic Quantum Superpositions via Dynamics in a Wide Double-Well Potential", Physical Review Letters 132 2, 023601 (2024).

[2] Silvia Casulleras, Piotr T. Grochowski, and Oriol Romero-Isart, "Optimization of Static Potentials for Large Delocalization and Non-Gaussian Quantum Dynamics of Levitated Nanoparticles Under Decoherence", arXiv:2406.19932, (2024).

[3] Andrey A. Rakhubovsky, Darren W. Moore, and Radim Filip, "Quantum non-Gaussian optomechanics and electromechanics", Progress in Quantum Electronics 93, 100495 (2024).

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