A Green’s function approach to the linear response of a driven dissipative optomechanical system

Abstract

In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation using the so-called generalized LRT. It is shown how the Green’s function equations of motion of a standard OMS as an open quantum system can be obtained from the quantum Langevin equations (QLEs) in the Heisenberg picture. The obtained results explain a wealth of phenomena, including the anti-resonance, normal mode splitting and the optomechanically induced transparency (OMIT). Furthermore, the reason why the Stokes or anti-Stokes sidebands are amplified or attenuated in the red or blue detuning regimes is clearly explained which is in exact coincidence, especially in the weak-coupling regime, with the Raman-scattering picture.

Dynamics of a hybrid optomechanical system in the framework of the generalized linear response theory

“…where ω pc = ω p − ω c is the detuning between the probe and coupling lasers frequencies In Ref. [33], the linear response of a standard OMS has been investigated in the framework of the GLRT. On the other hand, in Secs.II and III, it was shown that a hybrid OMS consisting of an atomic BEC behaves effectively as a standard OMS.…”

“…Recently, several researches have been conducted to generalize the SLRT to the theory of open quantum systems both in the Schrödinger picture through the master equation approach [29][30][31] and in the Heisenberg picture through the quantum Langevin equations (QLEs) [32,33]. In the so-called generalized linear response theory (GLRT) the linear response of * a dalafi@sbu.ac.ir an open quantum system to an external time-dependent perturbation is investigated while the effect of the environment is taken into account in the mathematical modeling as a multimode quantum field with an infinite number of degrees of freedom which interacts with the open quantum system.…”

“…Interestingly, the GLRT predicts a set of equations of motion for the open quantum system Green's functions which are derived in the Hisenberg picture through the QLEs [33]. The linear response of the open quantum system to the external source can be calculated through the solutions of Green's functions equations of motion.…”

“…As a practical application, in Ref. [33] the linear response of a standard bare OMS to an external time-dependent perturbation has been studied in the framework of GLRT.…”

Homodyne coherent quantum noise cancellation in a hybrid optomechanical force sensor

“…Optomechanical systems (OMSs) have been exploited in different areas of quantum technologies, such as quantum information processing and communication [1][2][3][4], quantum memories [5,6], reversible microwave-to-optics converters [7][8][9][10][11], microwave circulators [12,13], quantum correlations [14][15][16][17][18], quantum squeezing [19,20], as well as in fundamental physics [21][22][23][24][25][26][27][28][29][30]. Also, optomechanical-based sensors have been recognized as optimal candidate for the detection of minuscule forces at the quantum limit [31] such as observation of gravitational waves [32].…”