© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Chinese Physics Letters

Squeezing Effect of a Nanomechanical Resonator Coupled to a Two-Level System: an Equilibrium Approach

Jing Li, Zhide Chen

Published Feb 23, 2009• 0 citations

Abstract

The squeezing effect of a nanomechanical resonator coupled to a two-level system is studied by variational calculations based on both the displaced-squeezed-state (DSS) and the displaced-oscillator-state (DOS). The stable region of the DSS ground state at both T = 0 and T ≠ 0 and the corresponding squeezing factor are calculated. It is found that when the resonator frequency lies in (kBT, Δ), where Δ is the tunnelling splitting of the two-level-system in the presence of dissipation, tunnelling splitting of a DSS ground state decreases with the temperature, while tunnelling splitting of a DOS ground state increases with the temperature in low temperature region. This opposite temperature dependence can help to distinguish between the DSS and DOS ground state in the experiment.

DOI: 10.1088/0256-307x/26/3/038501

Related papers

Variational ground state of the model of a two-state system coupled with phonons

Hong Chen, Yumei Zhang, Xiang Xia Wu

The ground state of the model of a two-state system coupled with phonons is studied by a variational method. Two trial states, the displaced state, and the displaced-squeezed state, for the phonon subsystem are compared, and their dependence on tunneling parameter \ensuremath{\Delta}, phonon frequency \ensuremath{\omega}, and coupling strength g is analyzed. We find that for \ensuremath{\Delta}/\ensuremath{\omega}\ensuremath{\ll}1 the displaced state is more stable for g/\ensuremath{\omega}<1, while the displaced-squeezed state is preferable for g/\ensuremath{\omega}>1.

Physical review. B, Condensed matter•Dec 1, 1989•29 citations

VARIATIONAL STUDY FOR A COUPLED SYSTEM OF A QUANTUM TUNNELING STATE WITH PHONONS

Shi Yun-Long, Nie Yi-Hang, Chen Hong +2 more

The ground state energy of a coupled system of a quantum tunneling state with phonons is investegated by a variational approach. We find that the ground state of the system may be described by two variation states-displaced state and displaced-squeezed state, and the transition of the stable ground state from displaced state to displaced-squeezed state will occur as coupling strength increases. The phase diagram of the transition is also given.

Acta Physica Sinica•Jan 1, 1992•0 citations

Amplifying Two-Mode Squeezing in Nanomechanical Resonators

Muhdin Abdo Wodedo, Tesfay Gebremariam Tesfahannes, Tewodros Yirgashewa Darge +2 more

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.

arXiv:2508.18972•IEEE Transactions on Quantum Engineering•Jan 1, 2025•13 citations

Symmetry-breaking transition in a two-level system coupled to an Ohmic bath: A squeezed-state approach

Biswadeb Dutta, A. M. Jayannavar

Displaced squeezed states are proposed as variational ground states for phonons (Bose fields) coupled to two-level systems (spin systems). We have investigated the zero-temperature phase diagram for the localization-delocalization transition of a tunneling particle interacting with an Ohmic heat bath. Our results are compared with known existing approximate treatments. A modified phase diagram using the displaced squeezed state is presented.

Physical review. B, Condensed matter•Feb 1, 1994•9 citations

The localisation transition in a dissipative two-state system: a squeezed state approach

Yumei Zhang, Hong Chen, Xiang Xia Wu

A displaced squeezed state is used as the variational ground state of a spin-boson Hamiltonian describing the interaction of a two-state system with a phonon bath. The phase diagram for localisation in the ohmic dissipation is obtained by a method based on the self-consistent calculation of the effective tunnelling splitting. A comparison with the results of the usual displaced state approximation and the renormalisation group theory is also given.

Journal of Physics Condensed Matter•Apr 2, 1990•3 citations

Variational study of dissipative two-state systems

Yunlong Shi, Hong Chen, Xiang Xia Wu

Two variational states, the displaced state and the displaced-squeezed state, are compared for a two-state system with super-Ohmic dissipation, and their dependence on the form of the coupling strength ${\mathit{g}}_{\mathit{l}}$\ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}^{\ensuremath{\lambda}}$ (${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$ is the phonon frequency) is analyzed. We find that, in the strong-coupling region, the displaced-squeezed state is more stable and the ground-state properties depend not only on the spectral density but also on the index \ensuremath{\lambda}. Moreover, we find that the stable area of the displaced-squeezed state increases as \ensuremath{\lambda} decreases.

Physical review. B, Condensed matter•Jan 15, 1994•4 citations

The squeezing effect of a nanomechanical resonator coupled to a two-level system is studied by variational calculations based on both the displaced-squeezed-state (DSS) and the displaced-oscillator-state (DOS). The stable region of the DSS ground state at both T = 0 and T ≠ 0 and the corresponding squeezing factor are calculated. It is found that when the resonator frequency lies in (kBT, Δ), where Δ is the tunnelling splitting of the two-level-system in the presence of dissipation, tunnelling splitting of a DSS ground state decreases with the temperature, while tunnelling splitting of a DOS ground state increases with the temperature in low temperature region. This opposite temperature dependence can help to distinguish between the DSS and DOS ground state in the experiment.

The ground state of the model of a two-state system coupled with phonons is studied by a variational method. Two trial states, the displaced state, and the displaced-squeezed state, for the phonon subsystem are compared, and their dependence on tunneling parameter \ensuremath{\Delta}, phonon frequency \ensuremath{\omega}, and coupling strength g is analyzed. We find that for \ensuremath{\Delta}/\ensuremath{\omega}\ensuremath{\ll}1 the displaced state is more stable for g/\ensuremath{\omega}<1, while the displaced-squeezed state is preferable for g/\ensuremath{\omega}>1.

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.

Two variational states, the displaced state and the displaced-squeezed state, are compared for a two-state system with super-Ohmic dissipation, and their dependence on the form of the coupling strength

{\mathit{g}}_{\mathit{l}}

\ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}^{\ensuremath{\lambda}}$ (${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$ is the phonon frequency) is analyzed. We find that, in the strong-coupling region, the displaced-squeezed state is more stable and the ground-state properties depend not only on the spectral density but also on the index \ensuremath{\lambda}. Moreover, we find that the stable area of the displaced-squeezed state increases as \ensuremath{\lambda} decreases.