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 Bogoliubov transformation combined with a displacement; in the Schrödinger picture the oscillator evolves from the vacuum to a squeezed coherent state. Whereas the Bogoliubov 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 essentially the same as would be obtained by the action of the force alone. If the force is applied well before, then the displacement is found to oscillate as a function of the time lag between the forcing and the parametric driving; the oscillations can be understood in terms of quantum interference. A rich variety of behavior is found when the force and parametric drive act simultaneously. The displacement depends only on the Fourier component of the force at a single resonant frequency when the forcing and parametric drive are well separated in time. However, for a weak parametric drive that is applied concurrently with the force we show that the displacement responds to a broad range of frequencies of the force spectrum. We apply our results to a superconducting circuit consisting of a Josephson junction-terminated transmission line. Implications for other experimental systems are also briefly discussed.
- Received 23 January 2018
- Revised 8 November 2018
DOI:https://doi.org/10.1103/PhysRevA.99.022504
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