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Physical Review A

Dissipatively driven non-Gaussian mechanical entanglement and remote preparation of motional Schrödinger cat states

Zunbo Yu, Miaomiao Wei, Huatang Tan

Published Aug 26, 2025• 1 citation
Publisher

Abstract

In this paper, we propose a driven-dissipative scheme for generating non-Gaussian entangled mechanical states and consider the remote preparation of motional Schr\"odinger cat states via mechanical entanglement. The system under our study consists of a cavity optomechanical setup with two frequency-mismatched mechanical oscillators simultaneously coupled to a bichromatically driven cavity field. We show that under appropriate conditions, an effective Hamiltonian for nondegenerate parametric down-conversion involving the two mechanical oscillators and the cavity field can be engineered. We demonstrate analytically and numerically that the cavity dissipation drives the mechanical oscillators into a steady-state non-Gaussian entangled state. The properties of the mechanical state, including non-Gaussianity, Wigner negativity, entanglement, and quantum steering, are investigated in detail. We further reveal that through the non-Gaussian mechanical entanglement, the remote preparation of the Schr\"odinger cat states of one mechanical oscillator can be achieved by coupling the other one to an auxiliary probe cavity and homodyning the output of the probe cavity. We also discuss the robustness of the mechanical states against thermal fluctuations. Our scheme provides a feasible approach for the dissipative and remote preparation of non-Gaussian mechanical nonclassical states.

DOI
10.1103/rm6d-49zs

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In this paper, we propose a driven-dissipative scheme for generating non-Gaussian entangled mechanical states and consider the remote preparation of motional Schr"odinger cat states via mechanical entanglement. The system under our study consists of a cavity optomechanical setup with two frequency-mismatched mechanical oscillators simultaneously coupled to a bichromatically driven cavity field. We show that under appropriate conditions, an effective Hamiltonian for nondegenerate parametric down-conversion involving the two mechanical oscillators and the cavity field can be engineered. We demonstrate analytically and numerically that the cavity dissipation drives the mechanical oscillators into a steady-state non-Gaussian entangled state. The properties of the mechanical state, including non-Gaussianity, Wigner negativity, entanglement, and quantum steering, are investigated in detail. We further reveal that through the non-Gaussian mechanical entanglement, the remote preparation of the Schr"odinger cat states of one mechanical oscillator can be achieved by coupling the other one to an auxiliary probe cavity and homodyning the output of the probe cavity. We also discuss the robustness of the mechanical states against thermal fluctuations. Our scheme provides a feasible approach for the dissipative and remote preparation of non-Gaussian mechanical nonclassical states.
In this paper, we propose a driven-dissipative scheme for generating non-Gaussian mechanical entangled states and remotely preparing mechanical Schrödinger cat states via the entanglement. The system under study consists of a cavity optomechanical setup with two frequency-mismatched mechanical oscillators coupled to a cavity field driven by a bichromatic pump. We show that under proper conditions, an effective Hamiltonian for nondegenerate parametric downconversion involving the two mechanical oscillators and the cavity field can be engineered. We demonstrate analytically and numerically that the cavity dissipation drives the mechanical oscillators into a steady-state pair-coherent state. The no-Gaussianity and nonclassical properties, including Winger negativity, entanglement and quantum steering, of the achieved non-Gaussian mechanical state are investigated in detail. We further show that homodyne detection on one mechanical oscillator enables the remote generation of Schrödinger cat states in the other oscillator through the non-Gaussian mechanical entanglement. As we show, this detection can be implemented by transferring the mechanical state to the output field of an auxiliary probe cavity coupled to the target oscillator, followed by homodyne detection on the output field. We also discuss the robustness of the mechanical entangled states and cat states against thermal fluctuations. Our findings establish a feasible approach for the dissipative and remote preparation of mechanical nonclassical states.
In this paper, we present a scheme for remotely generating large-size motional Schr\"odinger cat states in cavity optomechanical (OM) systems with non-Gaussian quantum steering of continuous variables. We consider that the output field from the OM cavity undergoes three typical kinds of multiphoton operations: multiphoton subtraction, multiphoton addition, or multiphoton catalysis, followed by homodyne detection. We first demonstrate that these multiphoton operations can lead to non-Gaussian OM quantum steerable correlations, which are unveiled by the subsequent homodyne detection with a Fisher-information-based steering criterion. It is found that the non-Gaussian steering is obviously enhanced with an increasing number nnn of photons in the multiphoton operations, which, as we show, fails to be revealed with the well-known Reid's steering criterion. It therefore suggests that the Fisher-information-based criterion is more effective for witnessing non-Gaussian quantum steering. We next show that the strong OM steering enables the remote preparation of large-size Schr\"odinger odd or even cat states of the mechanical oscillator by the homodyne detection. Accordingly, the amplitudes of the cat states also increase significantly with the photon number nnn, particularly in the cases of multiphoton subtraction and addition. Our results reveal the properties of non-Gaussian steering generated by multiphoton operations, and the large cat states of macroscopic mechanical resonators hold promise for fundamental tests in quantum mechanics and practical applications in quantum science.
We investigate a dissipation-engineering approach to produce a phase-dependent collective-mode Schrödinger cat state involving two modes. Our model features a single cavity mode that interacts with two spectrally identical mechanical oscillators. Both oscillators are coupled through a phase-dependent hopping interaction. We demonstrate that by adjusting the phase of the phonon-hopping interaction, one can control the bipartite entanglement of the phase-dependent two-mode cat state during its generation. Additionally, our study reveals that phonon interactions act as a tunable parameter, enabling the manipulation of steady-state entanglement between the bare mechanical modes, even in the presence of environmental effects and thermal excitations. Our scheme provides a feasible approach for the phase-dependent multi mode non-Gaussian states preparation.
In this paper we propose a scheme for the generation of a nonclassical non-Gaussian motional state of a mechanical resonator (MR) in the three-mode optomechanical system in which two linearly coupled single-mode cavities interact dispersively with the mechanical oscillator simultaneously. With one cavity driven by a weak laser field and by properly tuning the driving frequency, a desirable phononic Liouvillian superoperator can be obtained by engineering the selective interaction Hamiltonian confined to Fock subspaces. It is shown that the MR can be driven dissipatively into a steady non-Gaussian nonclassical state, which possesses sub-Poisson statistics, although its Wigner function is positive. The present scheme can be useful for obtaining single phonons.
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 present a method to implement two-phonon interactions between mechanical resonators and spin qubits in hybrid setups, and show that these systems can be applied for the dissipative generation of nonclassical mechanical states. In particular, we demonstrate that the implementation a two-phonon Jaynes-Cummings Hamiltonian under coherent driving of the qubit yields a dissipative phase transition with similarities to the one predicted in the model of the degenerate parametric oscillator: beyond a certain threshold in the driving amplitude, the driven-dissipative system sustains a steady state consisting of a jumping cat, i.e., a Schr\odinger cat undergoing random jumps between two phases. We consider realistic setups and show that, in samples within reach of current technology, the low rate at which jumps between Schr\odinger cat states occur allows these to survive with fidelities >0.99>0.99>0.99 for longer than one milisecond, without the need of any particular protocol or preparation.