Master-equation treatment of nonlinear optomechanical systems with optical loss

Abstract

Open-system dynamics play a key role in the experimental and theoretical study of cavity optomechanical systems. In many cases, the quantum Langevin equations have enabled excellent models for optical decoherence, yet a master-equation approach to the fully nonlinear optomechanical Hamiltonian has thus far proven more elusive. To address this outstanding question and broaden the mathematical tool set available, we derive a solution to the Lindblad master equation that models optical decoherence for a system evolving with the nonlinear optomechanical Hamiltonian. The method combines a Lie-algebra solution to the unitary dynamics with a vectorization of the Lindblad equation, and we demonstrate its applicability by considering the preparation of optical cat states via the optomechanical nonlinearity in the presence of optical loss. Our results provide a direct way of analytically assessing the impact of optical decoherence on the optomechanical intracavity state.

Interplay between optomechanics and the dynamical Casimir effect

“…While single-and twomode gates have already been discussed in the context of resonances for field modes of cavity fields [37,38,63], our current work moves beyond the ideal scenario where abstract boundary conditions are varied as functions of time and allows to concretely study the gate-induced operations in relation to the additional interplay between the different degrees of freedom. While our work does not include decoherence or dissipation, which are are significant and unavoidable in cavity systems [21,25], we believe that the current study provides the first steps towards more concrete realizations. However, we expect that the dynamic effects, as show in Fig.…”

“…The most common approach to the analysis of optomechanical interactions treats the mirror and the electromagnetic field as two independent quantum harmonic oscillators [18][19][20]. In this approach, modelling the electromagnetic field as a single harmonic oscillator turns out to be extremely helpful for the description of the effects of cavity losses [21]. Moreover, it can be employed in order to investigate phenomena of vacuum squeezing acting on either the mechanical mode [22,23] or the cavity field.…”

Exploiting non-linear effects in optomechanical sensors with continuous photon-counting

“…In contrast, considering the novel optomechanical setups that exhibit strong single-photon coupling, e.g. ones involving ultracold atoms [13,14] or hybrid devices achieving non-linearity by employing an auxiliary system [35][36][37][38], but also anticipating their advent within other platforms [39], one must return to the exact solutions of system dynamics [7,8] that, however, are analytically tractable only if particular limited forms of decoherence and optical driving are accounted for [40] -unless one resorts to numerical methods [41,42]. Importantly, it is the non-linear effects that allow a single photon to be converted into multiple phonons and vice versa, so that phenomena such as blockades [43,44] or cascades [45] of photons become then possible, with the light leaving the cavity exhibiting a clear non-classical character [46].…”

Atom-Mechanical Hong-Ou-Mandel Interference

“…A. Rakhubovsky: rakhubovsky@optics.upol.cz R. Filip: filip@optics.upol.cz able for quantum sensing [17][18][19][20] and fundamental physics tests [21][22][23]. Importantly, mechanical systems offer an access to quantum nonlinearities in continuous-variable regime [16,24,25] not easily accessible in atomic systems. Recently, coupling between mechanical oscillators and atoms reached a new phase of experimental development.…”