Abstract
We study the non-Gaussian character of quantum optomechanical systems evolving under the fully nonlinear optomechanical Hamiltonian. By using a measure of non-Gaussianity based on the relative entropy of an initially Gaussian state, we quantify the amount of non-Gaussianity induced by both a constant and time-dependent cubic light–matter coupling and study its general and asymptotic behaviour. We find analytical approximate expressions for the measure of non-Gaussianity and show that initial thermal phonon occupation of the mechanical element does not significantly impact the non-Gaussianity. More importantly, we also show that it is possible to continuously increase the amount of non-Gassuianity of the state by driving the light–matter coupling at the frequency of mechanical resonance, suggesting a viable mechanism for increasing the non-Gaussianity of optomechanical systems even in the presence of noise.
Highlights
Understanding nonlinear, interacting physical systems is paramount across many areas in physics
We proceed to examine the behaviour of the non-Gaussianity in optomechanical systems for two cases: a constant light–matter coupling in section 5; and a time-dependent coupling in section 6, where we show that driving the coupling results in continuously generated non-Gaussianity
We have quantified the non-Gaussianity of initially Gaussian coherent states evolving under the standard, timedependent optomechanical Hamiltonian
Summary
Understanding nonlinear, interacting physical systems is paramount across many areas in physics. ‘nonlinear’ (or ‘anharmonic’) dynamical systems include all those whose Hamiltonian cannot be expressed as a second-order polynomial in the quadrature operators. These systems allow us to generate nonGaussian states, which cannot be done, given only quadratic couplings. It has been shown that nonlinearities in the form of non-Gaussian states constitute an important resource for quantum teleportation protocols [1], universal quantum computation [2, 3], quantum error correction [4], and entanglement distillation [5,6,7]. It has been found that non-Gaussianity provides a certain degree of robustness in the presence of noise [11, 12]
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