Unruh-DeWitt detectors as mirrors: Dynamical reflectivity and Casimir effect

Abstract

We demonstrate that the Unruh-DeWitt harmonic-oscillator detectors in (1+1) dimensions derivative-coupled with a massless scalar field can mimic the atom mirrors in free space. Without introducing the Dirichlet boundary condition to the field, the reflectivity of our detector/atom mirror is dynamically determined by the interaction of the detector's internal oscillator and the field. When the oscillator-field coupling is strong, a broad frequency range of the quantum field can be mostly reflected by the detector mirror at late times. Constructing a cavity model with two such detector mirrors, we can see how the quantum field inside the cavity evolves from a continuous to a quasi-discrete spectrum which gives a negative Casimir energy density at late times. In our numerical calculations, the Casimir energy density in the cavity does not converge until the UV cutoff is sufficiently large, with which the two internal oscillators are always separable.

23 pages, 9 figures; v2: minor changes, published version

References in corpus (4)

• Large Bragg Reflection from One-Dimensional Chains of Trapped Atoms Near a Nanoscale Waveguide
• The dynamical Casimir effect in superconducting microwave circuits
• Quantum super-cavity with atomic mirrors
• Backreaction and Unruh effect: New insights from exact solutions of uniformly accelerated detectors

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• Fluctuation-Dissipation and Correlation-Propagation Relations from the Nonequilibrium Dynamics of Detector-Quantum Field Systems
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• Atom-Field-Medium Interactions I: Graded Influence Actions for $N$ Harmonic Atoms in a Dielectric-Altered Quantum Field
• Canonical Quantization of the U(1) Gauge Field in the right Rindler-wedge in the Rindler Coordinates