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Electronics

The Evolution of Squeezing in Coupled Macroscopic Mechanical Oscillator Systems

Xin-Chang Liu, Xiao-Dong Shi, Xiao-Lei Zhang, Lingxiao Chen, Yi Zhang

Published Jul 13, 2025• 0 citations
Publisher

Abstract

Quantum squeezing in macroscopic oscillator systems plays a critical role in bridging quantum mechanics with classical-scale phenomena, enabling high-precision measurements and fundamental tests of quantum physics. In this work, we investigate the effect of squeezing on the phonon state in a hybrid macroscopic mechanical system consisting of an ensemble of Rydberg atoms coupled to two macroscopic mechanical oscillators. We notice that the dipole–dipole coupling between atoms and mechanical oscillators can be transferred to the indirectly coupled mechanical interaction, and the nonlinear effective Hamiltonian can be solved to generate a squeezed effect on the mechanical mode. We also discuss the noise effects induced by amplitude and phase fluctuations on the squeezed quadratures of the system.

DOI
10.3390/electronics14142817

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Quantum squeezing in macroscopic oscillator systems plays a critical role in bridging quantum mechanics with classical-scale phenomena, enabling high-precision measurements and fundamental tests of quantum physics. In this work, we investigate the effect of squeezing on the phonon state in a hybrid macroscopic mechanical system consisting of an ensemble of Rydberg atoms coupled to two macroscopic mechanical oscillators. We notice that the dipole–dipole coupling between atoms and mechanical oscillators can be transferred to the indirectly coupled mechanical interaction, and the nonlinear effective Hamiltonian can be solved to generate a squeezed effect on the mechanical mode. We also discuss the noise effects induced by amplitude and phase fluctuations on the squeezed quadratures of the system.
We investigate the interplay between mechanical forces and the internal-state dynamics of Rydberg excitations in atom-tweezer arrays. Dipole interactions between Rydberg atoms facilitate excitation spreading, but at the same time couple electronic (spin) degrees of freedom with motional (phonon) states. With increasing spin-phonon coupling, the growth dynamics of a cluster of excited Rydberg atoms changes from ballistic spreading to Bloch-like oscillations and eventually to Anderson-like localization. We show that these effects are caused by quantum fluctuations in the phonon field: The dynamics of a Rydberg cluster can be mapped to a single particle in a semi-infinite lattice subject to phonon-induced energy shifts. The mean-field contribution of this energy shift leads to a linear potential gradient, resulting into Bloch-like oscillations. In addition, quantum fluctuations of phonons create a random local potential causing a transition from a regime of Bloch oscillations to localization. The spin-phonon coupling leads furthermore to highly correlated and non-classical phonon states in the form of squeezed states of the position of the Rydberg atoms. Depending on the form of the dipolar interaction potential, either in- or out-of-phase correlated oscillations of atoms emerge.
This thesis concentrates on generating and measuring non-classical states of mechanical oscillators by coupling them to atomic and molecular quantum systems. We start with a discussion of what novel physics can be explored by mechanical systems operating in the quantum regime. We then discuss one technique making it a possibility- cavity optomechanics, particularly optomechanical cooling. We investigate the limits of optomechanical cooling and review how the coupling of mechanical oscillators to external heat baths limits the minimum attainable phonon occupation number. As a possible alternative for circumventing clamping losses, we consider an all-optical approach where the mechanical element (in this case, a Bragg mirror) is suspended via optical forces, and discuss some limitations of this approach. We explore several schemes aimed at the generation of quantum states in mechanical oscillators. We consider specifically two examples: one in which the mechanical oscillator is coupled to polar molecules via dipole-dipole interaction, and another where it is magnetically coupled to a Bose condensate. The first example emphasizes that such an interaction can generate parametric squeezing and entanglement. The second scheme demonstrates that the back action of BEC spin measurements can be used to generate quantum states of motion of a mechanical oscillator. We then discuss possible methods for measuring the entire density matrix of a mechanical oscillator. The first method achieves the tomographic reconstruction of the mechanical Wigner function by coupling it simultaneously to a classical optical oscillator and a qubit. The second approach involves a state transfer scheme between momentum excitations of a bose-condensate in a cavity and a moving mirror of the cavity that is entirely mediated by the light field. We conclude with a discussion of the broader implications of this work, and some future research directions.
We investigate a hybrid electromechanical system consisting of a pair of charged macroscopic mechanical oscillators coupled to a small ensemble of Rydberg atoms. The resonant dipole-dipole coupling between an internal atomic Rydberg transition and the mechanics allows cooling to its motional ground state with a single atom despite the considerable mass imbalance between the two subsystems. We show that the rich electronic spectrum of Rydberg atoms, combined with their high degree of optical control, paves the way towards implementing various quantum-control protocols for the mechanical oscillators.
We study the quantum properties of a nano-mechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force 0 F close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nano-mechanical oscillator are to be obtained from the Hamiltonian of the form H = a+a + β(a+ + a) / 4 . This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms a+2 a2, (a2a)2 and a+4 + a4 - (a+2 a2 + a2 a+2 ) previously employed in quantum optics to study squeezing. Here we solve the Schrodinger equation numerically and show that in-phase quadrature gets squeezed for both vacuum and coherent states. The squeezing can be controlled by bringing F0 close to or far from the critical value Fc. We further study the effect of the transverse driving force on the squeezing in nano-mechanical oscillator.
In this paper, we investigate theoretically the quantum state transfer in a laser-driven hybrid optomechanical cavity with two Duffing-like anharmonic movable end mirrors containing an ensemble of identical two-level trapped atoms. The quantum state transfer from the Bogoliubov modes of the two anharmonic oscillators to the atomic mode results in the atomic quadrature squeezing beyond the standard quantum limit of 3 dB, which can be controlled by both the optomechanical and atom-field coupling strengths. Interestingly, the generated atomic squeezing can be made robust against the noise sources by means of the Duffing anharmonicity. Moreover, the results reveal that the presence of the Duffing anharmonicity provides the possibility of transferring strongly squeezed states between the two mechanical oscillators in a short operating time and with high fidelity.
We theoretically investigate the macroscopic quantum coherence and the mechanical squeezing of a mechanical oscillator in a hybrid optomechanical system consisting of a suspended graphene sheet and an ultracold atomic ensemble trapped inside a Fabry-P\'erot cavity. In the study the vacuum is used to mediate an effective optomechanical coupling between the graphene oscillator and the cavity field driven by an external laser beam. We find that in the presence of this coupling, the macroscopic quantum coherence and the mechanical squeezing of the graphene sheet can be attained in a certain range of driving power. In particular, the quantum coherence in the optomechanical system can be transferred from the optical field to the mechanical oscillator. We also investigate in detail the spectrum and the squeezing of the output field and the attained results may be used to study the mechanical squeezing of a graphene sheet.