Dartmouth Events

Abstract: We consider a system consisting of a qubit and a microwave transmission line that are coupled by a capacitor which, in turn, is driven sinusoidally. The Unruh effect is the simultaneous production from vacuum of a pair of photons, one in the qubit and the other in the cavity. The dynamical Casimir effect is the production from vacuum of a pair of photons in the cavity. We analyze this qubit--cavity system and show that the system can be viewed as a pair of coupled quantum-mechanical oscillators and that both the Unruh effect and the dynamical Casimir effect are resonances of this coupled oscillator system. Without making the single-mode assumption, we derive the allowed modes in the cavity as well as the quantum Hamiltonian for the qubit-cavity system. Then, for the case of a single-mode cavity, we analytically approximate the driving frequency for the Unruh and dynamical Casimir effects, and numerically confirm the accuracy of our approximation. Finally, for the case where the cavity supports multiple propagating modes, in addition to the Unruh and dynamical Casimir effect at each of the supported modes, we predict what we call a ``paired Casimir effect,'' where one photon is emitted in the cavity in each of two allowed modes, at the appropriate driving frequency. We further calculate analytical approximations to the driving frequencies for all three effects.