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arXiv:2408.06251

Nonequilibrium entanglement between levitated masses under optimal control

Alexander N. Poddubny, Klemens Winkler, Benjamin A. Stickler, Uroš Delić, Markus Aspelmeyer, Anton V. Zasedatelev

Published Aug 12, 2024• 0 citations
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Abstract

We present a protocol that maximizes unconditional entanglement generation between two masses interacting directly through $1/r^{n}$ potential. The protocol combines optimal quantum control of continuously measured masses with their non-equilibrium dynamics, driven by a time-dependent interaction strength. Applied to a pair of optically trapped sub-micron particles coupled via electrostatic interaction, our protocol enables unconditional entanglement generation at the fundamental limit of the conditional state and with an order of magnitude smaller interaction between the masses compared to the existing steady-state approaches.

DOI
10.48550/arxiv.2408.06251

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We present a protocol that maximizes unconditional entanglement generation between two masses interacting directly through 1/rn1/r^{n}1/rn potential. The protocol combines optimal quantum control of continuously measured masses with their non-equilibrium dynamics, driven by a time-dependent interaction strength. Applied to a pair of optically trapped sub-micron particles coupled via electrostatic interaction, our protocol enables unconditional entanglement generation at the fundamental limit of the conditional state and with an order of magnitude smaller interaction between the masses compared to the existing steady-state approaches.
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We develop a feedback strategy based on optimal quantum feedback control for Gaussian systems to maximize the likelihood of steady-state entanglement detection between two directly interacting masses. We employ linear quadratic Gaussian control to engineer the phase-space dynamics of the two masses and propose Einstein-Podolsky-Rosen-type variance minimization constraints for the feedback to facilitate unconditional entanglement generation. This scheme allows for stationary entanglement in parameter regimes where strategies based on total energy minimization () would fail.
Levitated high-mass quantum systems provide access to unprecedented regimes in both fundamental science and technological applications. However, deterministic generation and manipulation of quantum non-Gaussian states, which are central to many continuous-variable quantum advantages, remain elusive in such platforms. In this work, we propose a theoretical protocol for preparing a continuous-variable degree of freedom of a levitated massive object in a variety of quantum states, including Fock and Schrödinger cat states, without coupling to auxiliary two-level systems. Our approach enhances otherwise weak nonharmonic effects by transient wave-function delocalization and combines this with optimal control of the potential. Specifically, time-dependent modulation of the linear component of the potential, in the presence of a static cubic nonharmonicity, provides a route to universal control of the mode. We analyze quantum state preparation under such control and estimate the required nonharmonicity, motional delocalization, and maximum tolerable decoherence for generating target non-Gaussian states. The proposed optimal-control scheme can also be readily extended beyond single-particle state preparation, for example, to unitary transformations and nonlinear measurements. As a concrete example, we demonstrate mechanical Bell-state preparation for two interacting particles using only local modulation of weakly nonharmonic potentials, while the interparticle interaction remains effectively linear. We emphasize that the protocols presented here apply to different mechanical degrees of freedom, such as center-of-mass motion and libration, and can also be implemented in other weakly nonharmonic systems with a leading cubic nonharmonicity.
We propose to optimally control the harmonic potential of a levitated nanoparticle to quantum delocalize its center-of-mass motional state to a length scale orders of magnitude larger than the quantum zero-point motion. Using a bang-bang control of the harmonic potential, including the possibility of inverting it, the initial ground-state-cooled levitated nanoparticle coherently expands to large scales and then contracts to the initial state in a time-optimal way. We show that this fast loop protocol can be used to enhance force sensing as well as to dramatically boost the entangling rate of two weakly interacting nanoparticles. We parameterize the performance of the protocol, and therefore the macroscopic quantum regime that could be explored, as a function of displacement and frequency noise in the nanoparticle's center-of-mass motion. This noise analysis accounts for the sources of decoherence relevant to current experiments.
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The generation of entanglement between disparate physical objects is a key ingredient in the field of quantum technologies, since they can have different functionalities in a quantum network. Here we propose and analyze a generic approach to steady-state entanglement generation between two oscillators with different temperatures and decoherence properties coupled in cascade to a common unidirectional light field. The scheme is based on a combination of coherent noise cancellation and dynamical cooling techniques for two oscillators with effective masses of opposite signs, such as quasispin and motional degrees of freedom, respectively. The interference effect provided by the cascaded setup can be tuned to implement additional noise cancellation leading to improved entanglement even in the presence of a hot thermal environment. The unconditional entanglement generation is advantageous since it provides a ready-to-use quantum resource. Remarkably, by comparing to the conditional entanglement achievable in the dynamically stable regime, we find our unconditional scheme to deliver a virtually identical performance when operated optimally.