High-order interactions in quantum optomechanics: fluctuations, dynamics and thermodynamics

Abstract

Quantum optomechanics describes the interaction between a confined field and a fluctuating wall due to radiation pressure. The dynamics of this system is typically understood using perturbation theory up to second order in the small coupling. Improving beyond this regime can shed light onto new phenomena. In this work we study high-order resonant wall-field interactions characterized by two- and three-phonon scattering processes. We obtain the Hamiltonian, compute the perturbed energy spectrum and explicitly calculate corrections to the ground state. Finally, we study the dynamics of the system when second- and third-order resonance conditions are activated, showing that the presence of high-order terms in the Hamiltonian drastically affects the populations of all particles, as well as the entropy production rate.

Figures (7)

• Figure 1: Eigenenergies of the system as a function of the mechanical frequency (a). The blue lines represent the eigenvalues of the whole Hamiltonian in Eq. (\ref{['wholeH']}), whereas the gray lines indicate the eigenvalues calculated from Eq. (\ref{['firstord']}). Zoom around the first-order resonance $\Omega=2\omega_1$ (b), the second-order resonance $2\Omega=2\omega_1$ (c), and the third-order resonance $3\Omega=2\omega_1$ (d), respectively. Graphs are realized by setting $\epsilon=0.07$.
• Figure 2: Time evolution of the populations of the mirror (red line), of cavity mode 1 (blue line), and of cavity mode 2 (green line), fixing the resonant condition $\Omega=2\omega_1$. The solid lines represent the dynamics of the populations evolving via the whole Hamiltonian in Eq. (\ref{['wholeH']}), whereas the dashed lines indicate the evolution due to the only contribution in Eq. (\ref{['firstord']}). The two graphs are realized by setting $\epsilon=0.03$ (a), and $\epsilon=0.07$ (b).
• Figure 3: Time evolution of $\mathcal{J}_{\text{w}}(t)$ (red line) and $\mathcal{J}_{\text{c}}(t)$ (blue line) after enforcing the resonant condition $\Omega=2\omega_1$. The solid lines represent the dynamics of the heat flows evolving via the whole Hamiltonian in Eq. (\ref{['wholeH']}), whereas the dashed lines indicate the evolution due to the only contribution in Eq. (\ref{['firstord']}). The graphs are realized by setting $\epsilon=0.03$ (a), and $\epsilon=0.07$ (b).
• Figure 4: Time evolution of the entropy production rate fixing the resonant condition $\Omega=2\Omega_1$. The solid lines represent the dynamics of the entropy production rate evolving via the whole Hamiltonian in Eq. (\ref{['wholeH']}), whereas the dashed lines indicate the evolution due to the only contribution in Eq. (\ref{['firstord']}). Plots have been realized by setting $\epsilon=0.03$ (red lines), and $\epsilon=0.07$ (blue lines).
• Figure 5: Time evolution of the populations of the mirror (red line), of the cavity mode 1 (blue line), and of cavity mode 2 (green line), fixing the resonant conditions $\Omega=\omega_{1}$ (a) and $3\Omega=2\omega_{1}$ (b). The solid lines represent the dynamics of the populations evolving via the whole Hamiltonian in Eq. (\ref{['wholeH']}), whereas the dashed lines indicate the evolution due to the only contribution in Eq. (\ref{['firstord']}).