Effect of forcing on vacuum radiation

Abstract

Vacuum radiation has been the subject of theoretical study in both cosmology and condensed matter physics for many decades. Recently there has been impressive progress in experimental realizations as well. Here we study vacuum radiation when a field mode is driven both parametrically and by a classical source. We find that in the Heisenberg picture the field operators of the mode undergo a Bogolyubov transformation combined with a displacement; in the Schrödinger picture the oscillator evolves from the vacuum to a squeezed coherent state. Whereas the Bogolyubov transformation is the same as would be obtained if only the parametric drive were applied the displacement is determined by both the parametric drive and the force. If the force is applied well after the parametric drive then the displacement is the same as would be obtained by the action of the force alone and it is essentially independent of t f , the time lag between the application of the force and the parametric drive. If the force is applied well before the parametric drive the displacement is found to oscillate as a function of t f . This behavior can be understood in terms of quantum interference. A rich variety of behavior is observed for intermediate values of t f . The oscillations can turn off smoothly or grow dramatically and decrease depending on strength of the parametric drive and force and the durations for which they are applied. The displacement depends only on the Fourier component of the force at a single resonant fre-

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Classical-quantum correspondence and backreaction

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Vacuum radiation and frequency-mixing in linear light-matter systems

“…( 15), the last line of which is responsible for the time-nonlocal integral in Eq. (28). Instead this would act similarly to a driving force.…”

“…It is worth pointing out that had we instead chosen to temporally modulate the light-matter coupling strengths g i instead of the oscillator frequencies Ω i , it is easy to see that we would not get modifications to the oscillator propagator seen in equation (15), the last line of which is responsible for the time-nonlocal integral in equation (28). Instead this would act similarly to a driving force.…”

“…Calculations can however become complex within these frameworks, especially when introducing time-dependencies to the medium. Time-dependent optical media have been the subject of a range of studies, examples of which include acceleration radiation in a plasma [1], time-refraction [2,5], and more generically parametric oscillators [17][18][19][20][21][22][23][24][25][26] and vacuum radiation [6,7,27,28]. It is also closely linked to polariton physics, that is, the physics of collective excitations of light-matter systems.…”