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arXiv:2111.08285

Experimental Demonstration of Topological Charge Protection in Wigner Current

Yi-Ru Chen, Hsien-Yi Hsieh, Jingyu Ning, Hsun-Chung Wu, Hua Li Chen, You-Lin Chuang, Popo Yang, Ole Steuernagel, Chien-Ming Wu, Ray‐Kuang Lee

Published Nov 16, 2021• 0 citations
arXivHTMLPDF

Abstract

We experimentally reconstruct Wigner's current of quantum phase space dynamics for the first time. We reveal the ``push-and-pull" associated with damping and diffusion due to the coupling of a squeezed vacuum state to its environment. In contrast to classical dynamics, where (at zero temperature) dissipation only ``pulls" the system toward the origin of phase space, we also observe an outward ``push" because our system has to obey Heisenberg's uncertainty relations. With squeezed vacuum states generated by an optical parametric oscillator at variable pumping levels, we identify the pure squeezing dynamics and its central stagnation point with a topological charge of `$-1$'. We experimentally verify that this charge is protected for weakly as well as strongly decohering conditions. This work demonstrates high resolving power and establishes an experimental paradigm for measuring quantumness and non-classicality of the dynamics of open quantum systems.

DOI
10.48550/arxiv.2111.08285

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We experimentally reconstruct Wigner's current of quantum phase space dynamics for the first time. We reveal the push-and-pull" associated with damping and diffusion due to the coupling of a squeezed vacuum state to its environment. In contrast to classical dynamics, where (at zero temperature) dissipation only pulls" the system toward the origin of phase space, we also observe an outward ``push" because our system has to obey Heisenberg's uncertainty relations. With squeezed vacuum states generated by an optical parametric oscillator at variable pumping levels, we identify the pure squeezing dynamics and its central stagnation point with a topological charge of `−1-1−1'. We experimentally verify that this charge is protected for weakly as well as strongly decohering conditions. This work demonstrates high resolving power and establishes an experimental paradigm for measuring quantumness and non-classicality of the dynamics of open quantum systems.
We experimentally reconstruct Wigner's current of quantum phase-space dynamics. We reveal the ``push-and-pull'' associated with damping and diffusion due to the coupling of a squeezed vacuum state to its environment. In contrast to classical dynamics, where (at zero temperature) dissipation only ``pulls'' the system toward the origin of phase space, we also observe an outward ``push'' because our system has to obey Heisenberg's uncertainty relations. With squeezed vacuum states generated by an optical parametric oscillator at variable pumping levels, we identify the pure squeezing dynamics and its central stagnation point with a topological charge of ``$\ensuremath{-}1$''. This work demonstrates high resolving power and establishes an experimental paradigm for measuring the quantumness and nonclassicality of the dynamics of open quantum systems.
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The behaviour of classical systems is characterised by their phase portraits; the collections of their trajectories. In quantum mechanics phase portraits are still considered impossible to compute due to the complexity of quantum trajectories arising from the introduction of the quantum correction terms. Instead, in this thesis, we identify the Wigner current (the rate of flow per unit area of the Wigner distribution), as the quantum analogue of the classical phase-space current, and through Wigner current's fieldline portraits we show that it reveals hidden features of quantum dynamics and extra complexity. In our analysis, we focus on the simplest, most intuitive, and analytically accessible aspects of the Wigner current. We investigate its features for weakly-anharmonic weakly-excited bound-states of time-reversible one-dimensional quantum-mechanical systems. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline portraits can be characterised by the Wigner current's discrete stagnation points, how these arise and how a quantum system's dynamics is constrained by the stagnation points' topological charge conservation. We additionally demonstrate the conceptual power of the Wigner current by addressing some confusion found in the literature. We also stress the usefulness of the integral form of Wigner's representation as an alternative to the popular Moyal bracket. The integral form brings out the symmetries between momentum and position representations of quantum mechanics, is numerically stable, and allows us to perform some calculations using elementary integrals instead of Groenewold starproducts. The associated integral form of the Wigner current is used here in an elementary proof which shows that only systems up to quadratic in their potential fulfil Liouville's theorem of volume preservation in quantum mechanics.
Non-Gaussian states, and specifically the paradigmatic cat state, are well known to be very sensitive to losses. When propagating through damping channels, these states quickly lose their nonclassical features and the associated negative oscillations of their Wigner function. However, by squeezing the superposition states, the decoherence process can be qualitatively changed and substantially slowed down. Here, as a first example, we experimentally observe the reduced decoherence of squeezed optical coherent-state superpositions through a lossy channel. To quantify the robustness of states, we introduce a combination of a decaying value and a rate of decay of the Wigner function negativity. This work, which uses squeezing as an ancillary Gaussian resource, opens new possibilities to protect and manipulate quantum superpositions in phase space.
Motivated by quantum experiments with nanomechanical systems, the evolution of a Kerr oscillator with focus on creation of states with a negative Wigner function is investigated. Using the phase space formalism, results are presented that demonstrate an asymptotic behavior in the large squeezing regime for the negativity of a squeezed vacuum state under unitary evolution. The analysis and model are extended to squeezed vacuum states of open systems, adding the decoherence effects of damping and dephasing. To increase experimental relevance, the regime of strong damping is considered. These effects are investigated, yielding similar asymptotic results for the behavior of these effects in the large squeezing regime. Combining these results, it is shown that a weak nonlinearity as compared to damping may be improved by increasing the squeezing of the initial state. It is also shown that this may be done without exacerbating the effects of dephasing.