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

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 (k_BT,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.