Abstract
We propose an approach for generating steady-state mechanical entanglement in a coupled optomechanical system. By applying four-tone driving lasers with weighted amplitudes and specific frequencies, we obtain an effective Hamiltonian that couples the delocalized Bogoliubov modes of the two mechanical oscillators to the cavity modes via beam-splitter-like interactions. When the mechanical decay rate is small, the Bogoliubov modes can be effectively cooled by the dissipative dynamics of the cavity modes, generating steady-state entanglement of the mechanical modes. The mechanical entanglement obtained in the stationary regime is strongly dependent on the values of the ratio of the effective optomechanical coupling strengths. Numerical simulation with the full linearized Hamiltonian shows that significant amount of mechanical entanglement can indeed be obtained by balancing the opposing effects of varying the ratio and by carefully avoiding the system parameters that may lead to amplified oscillations of the mechanical mean values detrimental to the entanglement generation.
Highlights
Entanglement, especially the entanglement of macroscopic objects, is of great interest both for fundamental physics and for possible applications in quantum information processing
We note that the generation of distant mechanical entanglement in coupled optomechanical systems can be achieved via optical-fiber mediated coupling[36] and by periodically modulating the pumping amplitudes[37,38]
Greatly enhancing the entanglement is to drive the coupled cavity modes with four-tone lasers of weighted amplitudes and specific frequencies so that we obtain an effective system Hamiltonian where two nonlocal Bogoliubov modes of the mechanical oscillators are coupled to the cavity modes via beam-splitter-like interactions
Summary
We consider a coupled microtoroidal optomechanical system[39,40,41,42,43] where two phonon modes B1 and B2 respectively interact with two photon modes A1 and A2 which in turn are coupled via the photon tunneling. Κ is the cavity decay rate; ajin(t) and bjin(t) stand for independent input vacuum noise operators with zero mean value and the following nonzero auto-correlation functions: ajin(t)ajin†(t′) = δ(t − t′),. Bj = βj(t) + bj where aj and bj are quantum fluctuation operators with zero mean value around classical c-number amplitudes αj(t) and βj(t) linearization techniques[4] of the system operators, respectively. One can get the following linearized QLEs for the quantum fluctuations by neglecting the terms containing classical mean values only and all nonlinear terms such as a1b1 and a2b2†.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
