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arXiv:2505.01942

Deterministic Mechanical Wigner Negativity via Nonlinear Cavity Quantum Optomechanics in the Unresolved-Sideband Regime

Clarke, Jack, Pascal Neveu, Ewold Verhagen, Michael Ross Vanner

Published May 3, 2025• 1 citation
arXivHTMLPDF

Abstract

Non-Gaussian quantum states of mechanical motion exhibiting Wigner negativity offer promising capabilities for quantum technologies and tests of fundamental physics. Within the field of cavity quantum optomechanics, it is commonly held that deterministic preparation of mechanical Wigner negativity in the unresolved-sideband regime is not possible, as the intracavity interaction Hamiltonian is linear in mechanical position. Here, we show that, despite this, by accounting for the nonlinearity of the cavity response with mechanical position, mechanical Wigner negativity can be prepared deterministically in the unresolved-sideband regime, without additional nonlinearities, nonclassical drives, or conditional measurements. In particular, we find that Wigner negativity can be prepared with an optical pulse, even without single-photon strong coupling, and the negativity persists in the steady state of a continuously driven system. Our results deepen our understanding of cavity-enhanced radiation pressure and establish a pathway for deterministic preparation of nonclassical mechanical states in the unresolved sideband regime.

DOI
10.48550/arxiv.2505.01942

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Non-Gaussian quantum states of mechanical motion exhibiting Wigner negativity offer promising capabilities for quantum technologies and tests of fundamental physics. Within the field of cavity quantum optomechanics, it is commonly held that deterministic preparation of mechanical Wigner negativity in the unresolved-sideband regime is not possible, as the intracavity interaction Hamiltonian is linear in mechanical position. Here, we show that, despite this, by accounting for the nonlinearity of the cavity response with mechanical position, mechanical Wigner negativity can be prepared deterministically in the unresolved-sideband regime, without additional nonlinearities, nonclassical drives, or conditional measurements. In particular, we find that Wigner negativity can be prepared with an optical pulse, even without single-photon strong coupling, and the negativity persists in the steady state of a continuously driven system. Our results deepen our understanding of cavity-enhanced radiation pressure and establish a pathway for deterministic preparation of nonclassical mechanical states in the unresolved sideband regime.
A growing number of unresolved-sideband optomechanics experiments are now observing nonlinearities, which cannot be described within the linearized approximation. However, a suitable theoretical framework for describing these nonlinearities is needed for optomechanics to advance beyond the current state-of-the-art. In this talk, I will introduce our framework of cavity quantum optomechanics, which captures the nonlinearities of both the radiation-pressure interaction and the cavity response. I will then describe how this framework can be used to perform position measurement well beyond the breakdown of the linearized approximation.
The ability to prepare a macroscopic mechanical resonator into a quantum superposition state is an outstanding goal of cavity optomechanics. Here, we propose a technique to generate cat states of motion using the intrinsic nonlinearity of a dispersive optomechanical interaction. By applying a bichromatic drive to an optomechanical cavity, our protocol enhances the inherent second-order processes of the system, inducing the requisite two-phonon dissipation. We show that this nonlinear sideband cooling technique can dissipatively engineer a mechanical resonator into a cat state, which we verify using the full Hamiltonian and an adiabatically reduced model. While the fidelity of the cat state is maximized in the single-photon, strong-coupling regime, we demonstrate that Wigner negativity persists even for weak coupling. Finally, we show that our cat state generation protocol is robust to significant thermal decoherence of the mechanical mode, indicating that such a procedure may be feasible for near-term experimental systems.
In a nutshell, a cavity optomechanical system consists of a mechanical oscillator inside an optical cavity. Cavity optomechanics studies the interplay between the light-matter radiation-pressure interaction and the change in the cavity frequency induced by mechanical motion. By leveraging the tools of quantum optics and quantum measurement, cavity quantum optomechanics enables the engineering of nonclassical quantum states of bulk matter. In this thesis, I present protocols for engineering such nonclassical quantum states in Part II. First, I introduce a scheme to ‘grow’ a quantum kitten state of a mechanical oscillator into a macroscopic Schrödinger cat state using a series of nonlinear pulsed optomechanical interactions. Next, I detail our proposed schemes to generate and verify entanglement between two mechanical oscillators. Moving on from pulsed optomechanics, I describe the theory behind an experiment that achieved multi-phonon subtraction from a mechanical oscillator in a continuously driven Brillouin optomechanical system. In the final chapter of Part II, I provide a theoretical preview of an experiment that investigates the behaviour of the mechanical oscillator when no light is detected at the output. In Part III, I introduce a new framework for nonlinear cavity quantum optomechanics that incorporates the intrinsic nonlinearity of the radiation-pressure interaction, the nonlinearity from the cavity enhancement, and higher-order mechanical position terms in the expansion of the cavity frequency. I then propose a scheme for measuring mechanical position using general-dyne detection, applicable to pulsed and continuous measurements. This predicts a new regime of operation, the “stochastic Gaussian” regime. Finally, I discuss a protocol for deterministic mechanical squeezing that utilizes the cavity response.
Entanglement had played a crucial role in developing frontier technologies as a critical resource, for instance, in quantum teleportation and quantum sensing schemes. Notably, thanks to the ability to cool down the vibrational modes of mechanical oscillators to its quantum regime, entanglement between mechanical modes and the production of nonclassical mechanical states have emerged as central resources for quantum technological applications. Thus, proposing deterministic schemes to achieve those tasks is of paramount importance. While the dominant scheme for bipartite mechanical entanglement involves Gaussian optomechanical interactions (linearized regime) to generate two-mode squeezed vacuum states, entangling two-modes exploiting the bare non-Gaussian optomechanical interaction (nonlinear strong single-photon regime) remains less covered. This work proposes an on-demand scheme to engineer phononic non-Gaussian bipartite entanglement in the nonlinear regime by exploiting cavity dissipation. Interestingly, our protocol (operating in the resolved sideband and photon blockade regime) renders the possibility of achieving a high degree of steady-state entanglement. We further show that our deterministic scheme is robust in the presence of decoherence and temperature within state-of-the-art optomechanics, along with the required conditions to obtain non-Gaussianity of the achieved bipartite mechanical steady-state.
We put forward a deterministic dissipative protocol to prepare phonon Fock states in nonlinear quantum optomechanical devices. The system is composed of a mechanical mode interacting with an optical field via radiation pressure, whereas the light mode is laser driven in the resolved blue-sideband regime. To keep our results tractable, we switch to an interaction picture in a displaced basis, where the effective Hamiltonian exhibits the selective photon-phonon interaction explicitly. After proper parameter adjustment and similarly to cavity-cooling schemes, the quantum evolution allows steering of the mechanical degree of freedom to the desired Fock state by directing the optical excitations dynamically towards the target phonon state. The numerical results, including decoherence on both the mechanical and the optical degrees of freedom, prove to be quite robust in the good- and bad-cavity regimes, with fidelities exceeding 95%. Finally, characterization of the achieved nonclassicality, as well as the limitations and feasibility of our protocol under experimental parameters, is also discussed.
We show that a Kerr-nonlinear cavity coupled to an incoherently pumped two-level qubit can stabilize a nonclassical steady state with pronounced Wigner negativity. Without the qubit, two-photon drive and dissipation preserve photon-number parity and confine vacuum-initiated dynamics to the even-parity Fock subspace, preventing the emergence of odd-parity-induced central Wigner negativity. The qubit opens a frequency-selective injection channel into the odd-parity Fock subspace, while Kerr nonlinearity suppresses unwanted higher-order transitions, driving the system toward a steady state dominated by the single-photon Fock state that can approach a nearly pure state in the optimal regime. The resulting Wigner negativity remains robust over broad experimentally relevant loss and dephasing regimes, providing a route to the dissipative stabilization of nonclassical light in cavity quantum electrodynamics platforms.