Abstract
We compare two approaches for deriving corrections to the “linear model” of cavity optomechanics, in order to describe effects that are beyond first order in the radiation pressure coupling. In the regime where the mechanical frequency is much lower than the cavity one, we compare: (I) a widely used phenomenological Hamiltonian conserving the photon number; (II) a two-mode truncation of C. K. Law’s microscopic model, which we take as the “true” system Hamiltonian. While these approaches agree at first order, the latter model does not conserve the photon number, resulting in challenging computations. We find that approach (I) allows for several analytical predictions, and significantly outperforms the linear model in our numerical examples. Yet, we also find that the phenomenological Hamiltonian cannot fully capture all high-order corrections arising from the C. K. Law model.
Highlights
Cavity quantum optomechanics is a rapidly developing research field exploring the interaction of quantised light with macroscopic mirrors, membranes and levitated nano-objects through radiation pressure[1,2,3,4]
A further appealing feature of strong coupling optomechanics is that the Hamiltonian can be diagonalized analytically upon linearising the cavity frequency around the origin, as per ω(x) ω(0) + x ω′(0)
In this paper we explore and compare two different starting points that may be used to go beyond the linear model: (I) a widely used phenomenological Hamiltonian, which conserves the cavity photon number; (II) a two-mode truncation of C
Summary
We compare two approaches for deriving corrections to the “linear model” of cavity optomechanics, in order to describe effects that are beyond first order in the radiation pressure coupling. Even in systems that are far from the SC, the quest for ultra-precise measurements (e.g. those pertaining Planck scale physics)[14], or for the detection of dynamical Casimir effects[24], demand a more accurate Hamiltonian description of quantum optomechanics Armed with these motivations, in this paper we explore and compare two different starting points that may be used to go beyond the linear model: (I) a widely used phenomenological Hamiltonian, which conserves the cavity photon number (phenomenological approach); (II) a two-mode truncation of C. The numerical examples we explored suggest that the phenomenological approach does a good job in improving the linear model in the typical parameter regimes of optomechanics experiments, yet it does not fully capture the second-order corrections arising from the microscopic treatment.
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