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arXiv:2202.02285

Enhancing the Formation of Wigner Negativity in a Kerr Oscillator via Quadrature Squeezing

Christian Anker Rosiek

Published Feb 4, 2022• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2202.02285

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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.
Generating macroscopic nonclassical quantum states is a long-standing challenge in physics. Anharmonic dynamics is an essential ingredient to generate these states, but for large mechanical systems, the effect of the anharmonicity tends to become negligible compared with the effect of decoherence. As a possible solution to this challenge, we propose using a motional squeezed state as a resource to effectively increase the anharmonicity. We analyze the production of negativity in the Wigner distribution of a quantum anharmonic resonator initially in a squeezed state. We find that initial squeezing increases the rate at which negativity is generated. We also analyze the effect of two common sources of decoherence—namely, energy damping and dephasing—and find that the detrimental effects of energy damping are suppressed by strong squeezing. In the limit of large squeezing, which is needed for state-of-the-art systems, we find good approximations for the Wigner function. Our analysis is significant for current experiments attempting to prepare macroscopic mechanical systems in genuine quantum states. We provide an overview of several experimental platforms featuring nonlinear behaviors and low levels of decoherence. In particular, we discuss the feasibility of our proposal with carbon nanotubes and levitated nanoparticles. Published by the American Physical Society 2024
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.
We discuss nonclassical properties of single-photon subtracted squeezed vacuum states in terms of the sub-Poissonian statistics and the negativity of the Wigner function. We derive a compact expression for the Wigner function from which we find the region of phase space where Wigner function is negative. We find an upper bound on the squeezing parameter for the state to exhibit sub-Poissonian statistics. We then study the effect of decoherence on the single-photon subtracted squeezed states. We present results for two different models of decoherence, viz. amplitude decay model and the phase diffusion model. In each case we give analytical results for the time evolution of the state. We discuss the loss of nonclassicality as a result of decoherence. We show through the study of their phase-space properties how these states decay to vacuum due to the decay of photons. We show that phase damping leads to very slow decoherence, slower than the photon-number decay.
We study the squeezing dynamics in a Kerr-nonlinear oscillator, and quantify the metrological usefulness of the resulting states. Even if the nonlinearity limits the attainable squeezing by making the evolution non-Gaussian, the states obtained still have a high quantum Fisher information for sensing displacements. However, contrary to the Gaussian case, the amplitude of the displacement cannot be estimated by simple quadrature measurements. Therefore, we propose the use of a measurement-after-interaction protocol where a linear quadrature measurement is preceded by an additional nonlinear evolution, and show the significant sensitivity enhancement that can be obtained. Our results are robust when considering realistic imperfections such as energy relaxation, and can be implemented in state-of-the-art experimental setups.
Abstract We theoretically investigate the nonclassicality of the squeezed Hermite polynomial state (SHPS) by examining the squeezing feature, the oscillation of photon-number distribution (PND) and the negativity of the Wigner function (WF). Our results indicate that the squeezing operation leads to a large squeezing degree and negative volume of the WF, but the Hermite polynomial creation operation has less impact on them, and the two operations have opposite modulations of the PND. In addition, we study the evolution law of the SHPS in the amplitude decay channel (ADC). It is found that the density-operator evolution is related to two conjugated operator Hermite polynomials within normal ordering, which brings about a new two-variable special function and its generating function. We also find that the analytical WF evolution is represented as the compact form of this new special function, and that the large squeezing is more robust against the decoherence of the SHPS in the ADC.
Non-Gaussian states of light are a critical resource for fault-tolerant quantum computing and enhanced metrology, but are typically faint and often obtained via post-selection. Here, we demonstrate the deterministic generation of a bright non-Gaussian state by introducing a Kerr nonlinearity to a macroscopic state of light called bright squeezed vacuum (BSV). To characterize the resulting state, we use a single-shot f-2f interferometer to sample its Husimi function. We observe a clear transformation from a 2D Gaussian distribution to an 'S'-shaped non-Gaussian profile, which is the direct statistical evidence of the intensity-dependent nonlinear phase. The negativity of the Wigner function, which is an intrinsic property of any pure non-Gaussian state, cannot be observed because BSV is a mixed state even under minute optical loss. However, we show that BSV can be considered as a mixture of pure squeezed coherent states, for some of which Kerr-induced Wigner-function negativity is quite tolerant to loss. This work bridges the gap between quantum optics and ultrafast nonlinear optics, opening a path to quantum applications that require high photon flux.