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arXiv:2312.12986 · PRX Quantum

Quadrature Squeezing Enhances Wigner Negativity in a Mechanical Duffing Oscillator

Christian Anker Rosiek, Massimiliano Rossi, Albert Schließer, Anders Søndberg Sørensen

Published Jul 19, 2024• 20 citations
arXivHTMLPDF

Abstract

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

DOI
10.1103/prxquantum.5.030312

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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
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.
Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macroscopic quantum coherence. Considering various exactly solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the entropic nonlinearity of the considered potentials and their ground-state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing, which is not captured by the negativity of the Wigner function, we focus on the Glauber-Sudarshan PPP function and address the nonclassicality-nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators.
The generation of entangled states that display negative values of the Wigner function in the quantum phase space is a challenging task, particularly elusive for massive, and possibly macroscopic, systems such as mechanical resonators. In this work, we propose two schemes based on reservoir engineering for generating Wigner-negative entangled states unconditionally. We consider two noninteracting mechanical resonators that are radiation-pressure coupled to either one or two common cavity fields; the optomechanical coupling with the field(s) features both a linear and quadratic part in the mechanical displacement and the cavity is driven at multiple frequencies. We show analytically that both schemes stabilize a Wigner-negative entangled state that combines the entanglement of a two-mode squeezed vacuum with a cubic nonlinearity, which we dub cubic-phase entangled (CPE) state. We then perform extensive numerical simulations to test the robustness of Wigner-negative entanglement attained by approximate CPE states stabilized in the presence of thermal decoherence. Published by the American Physical Society 2024
Nonclassical states of nano- and micro-mechanical motion enable measurements beyond the standard quantum limit and constitute a key resource for quantum sensing and metrology. The most strongly squeezed mechanical states to date have been generated with electromechanical platforms under cryogenic refrigeration and using reservoir engineering. To push mechanical systems deeper into the quantum-squeezed regime requires protocols that increase the rate at which squeezing is generated to more strongly overcome the decoherence rate at which state purity is lost. Here, we squeeze the 800 kHz libration mode of a silica nanoparticle optically levitated in vacuum at room temperature. We expose our mechanical oscillator to an optically generated inverted potential, where the squeezing operation proceeds at an exponentially accelerated rate. We reach a squeezed quadrature variance 11 dB below the vacuum fluctuations within 250 ns. Our protocol establishes a new paradigm for generating quantum squeezing of mechanical motion and offers a platform for quantum-enhanced sensing with massive oscillators.
Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators below threshold for all possible up-to-quadratic Hamiltonians, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often more vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. Therefore, a stability of nonlinear squeezing is essential. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters which can be optimized and adjusted to achieve the maximal robustness for the potential applications.
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.