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arXiv:2508.18972 · IEEE Transactions on Quantum Engineering

Amplifying Two-Mode Squeezing in Nanomechanical Resonators

Muhdin Abdo Wodedo, Tesfay Gebremariam Tesfahannes, Tewodros Yirgashewa Darge, Mauro Fernandes Pereira, Berihu Teklu

Published Jan 1, 2025• 13 citations
arXivHTMLPDF

Abstract

Quantum squeezing plays a crucial role in enhancing the precision of quantum metrology and improving the efficiency of quantum information processing protocols. We thus propose a scheme to amplify two-mode squeezing in nanomechanical resonators, harnessing parametric amplification and two-tone laser controls. The red-detuned laser drives facilitate the cooling of the nanomechanical resonators down to their ground state and allow optimal quantum state transfer in the weak-coupling, resolved sideband regime. In particular, the competing blue-detuned lasers in the driving pairs induce displacement squeezing in mechanical resonators. Thus, the quantum state transfer of the squeezing in nanomechanical resonators and the intracavity correlated photons of the parametric amplifier significantly enhance the two-mode mechanical squeezing. Notably, increasing the coupling strength of the red detuned laser and the ratio of blue-to-red detuned laser dramatically amplifies the two-mode mechanical squeezing under realistic experiment parameters of a typical optomechanical system. Our findings reveal that the proposed cooperative mechanism effectively enhances the level of two-mode mechanical squeezing with a considerable improvement and demonstrates exceptional resilience to thermal noise.

DOI
10.1109/tqe.2025.3603459

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Quantum squeezing plays a crucial role in enhancing the precision of quantum metrology and improving the efficiency of quantum information processing protocols. We thus propose a scheme to amplify two-mode squeezing in nanomechanical resonators, harnessing parametric amplification and two-tone laser controls. The red-detuned laser drives facilitate the cooling of the nanomechanical resonators down to their ground state and allow optimal quantum state transfer in the weak-coupling, resolved sideband regime. In particular, the competing blue-detuned lasers in the driving pairs induce displacement squeezing in mechanical resonators. Thus, the quantum state transfer of the squeezing in nanomechanical resonators and the intracavity correlated photons of the parametric amplifier significantly enhance the two-mode mechanical squeezing. Notably, increasing the coupling strength of the red detuned laser and the ratio of blue-to-red detuned laser dramatically amplifies the two-mode mechanical squeezing under realistic experiment parameters of a typical optomechanical system. Our findings reveal that the proposed cooperative mechanism effectively enhances the level of two-mode mechanical squeezing with a considerable improvement and demonstrates exceptional resilience to thermal noise.
A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.
We propose a scheme of an optomechanical system that optimizes entanglement in nanomechanical resonators through quantum state transfer of intracavity squeezing and squeezed reservoir field sources assisted by radiation pressure. The system is driven by red-detuned laser fields, which enable simultaneous cooling of the mechanical resonators and facilitate the quantum state transfer in a weak coupling and good cavity limit. Specifically, the mechanical entanglement is quantified using logarithmic negativity within the bipartite Gaussian states of the two mechanical modes. The results show that several key parameters, including the parametric phase and nonlinear gain of the non-degenerate optical parametric amplifier, the strength of the squeezing reservoir, optomechanical cooperativity, thermal excitation of phonons, and the temperature of mechanical baths, strongly influence the degree of mechanical entanglement. Hence, the findings indicate that careful tuning of the parameters can enable control over the enhancement of entanglement robustness, suggesting that this optomechanical scheme provides a viable pathway for applications in quantum sensing and information processing
We propose a novel scheme for generating mechanical squeezed states based on the combined mechanism of a two-tone driving and a squeezed vacuum field. This innovative approach achieves a remarkable improvement in mechanical squeezing performance across the entire range of red/blue detuning ratios. Our study reveals that the squeezed vacuum field not only induces position squeezing of the mechanical oscillator but also facilitates momentum squeezing through phase matching. Moreover, the total squeezing degree exhibits nonlinear enhancement with the increasing of squeezing parameter rrr. The mechanical squeezed state exhibits a 2π2π2π-periodic dependence in relation to the squeezing phase θθθ, offering experimental implementation with a high degree of operational flexibility. Notably, the scheme exhibits strong robustness against cavity dissipation and environmental thermal noise, substantially relaxing the strict parameter-matching requirements inherent in conventional approaches.
We propose an alternative experimentally feasible approach to achieve high-efficiency ground-state cooling of a mechanical oscillator in an optomechanical system under the deeply unresolved sideband condition with the assistance of both intracavity and extracavity squeezing. In the scheme, a degenerate optical parametric amplifier is placed inside the optical cavity, generating the intracavity squeezing; in addition, the optical cavity is driven by the extracavity squeezed light, namely the extracavity squeezing. The quantum interference effect generated by intracavity squeezing and extracavity squeezing can completely suppress the nonresonant Stokes heating process while greatly enhancing the anti-Stokes cooling process. Therefore, the joint-squeezing scheme is capable of cooling the mechanical oscillators to their quantum ground state in a regime far away from the resolved sideband condition. Compared with other traditional optomechanical cooling schemes, the single-photon cooling rate in this joint-squeezing scheme can be tremendously enlarged by nearly three orders of magnitude. At the same time, the coupling strength required to achieve ground-state cooling can be significantly reduced. This scheme is promising for cooling large-mass and low-frequency mechanical oscillators, which provides a prerequisite for preparing and manipulating nonclassical states in macroscopic quantum systems and lays a significant foundation for quantum manipulation.
The squeezing of a mechanical mode can break through the “standard quantum limit”, which has significant applications in high-precision measurement. In this paper, we employ a full quantum stochastic method to investigate the dynamics of an optomechanical system under multi-tone driving. Previous method usually sets the classical mean value as a constant. For the dynamic process, this mean value should be time dependent, especially under the multi-tone driving. Here, we use the full quantum stochastic method, and we find that the mechanical squeezing exhibits nonmonotonic behavior with the enhancement of blue-sideband driving, which declines after reaching its maximum value; meanwhile, this system requires a longer time to evolve into a steady state. Moreover, the nonmonotonic trend of squeezing can also be observed by enhancing the strengths of both red- and blue-sideband driving simultaneously, and a shorter time is required to reach the steady state. This work provides valuable insights into the dynamics of an optomechanical system under multi-tone driving for the first time, which is of significant importance for improving the sensitivity of quantum precision measurement.
Abstract We investigate the effect of a degenerate optical parametric amplifier (OPA) placed inside an optomechanical cavity on the steady-state entanglement of two cavity modes, which jointly interact with a mechanical resonator. Two cavity modes are, respectively, driven at the red and blue sideband associated with the mechanical resonator, which generates entanglement between them in the limit of resolved sideband. The OPA gives rise to single-mode squeezing of the cavity fields, which results in significant improvement of the two-mode entanglement. It is found that an optimal nonlinear gain of the OPA exists, depending on the system temperatures, which yields the maximum entanglement. The improvement is particularly remarkable for the system at cryogenic temperatures.