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.
Highlights
A moving mirror can produce quantum radiation from a vacuum [1,2,3,4]; two mirrors at rest can form a cavity with a negative Casimir energy density inside [3,4,5,6,7], and one or two such cavity mirrors moving in specific ways can create particles in the cavity [8,9,10,11]
We employed the derivative-coupling Unruh-DeWitt (UD0) HO detector theory in (1 þ 1) dimensions to model the atom mirror interacting with a massless quantum field (OF coupling) and an environment of mechanical degrees of freedom (OE coupling)
In the strong OF coupling regime, the effect of the mechanical environment is negligible and the detector acts like a perfect mirror at late times, when the energy density of the field outside the detector vanishes while the field spectrum is nontrivial
Summary
A moving mirror can produce quantum radiation from a vacuum [1,2,3,4]; two mirrors at rest can form a cavity with a negative Casimir energy density inside [3,4,5,6,7], and one or two such cavity mirrors moving in specific ways can create particles in the cavity [8,9,10,11]. [22] Sinha, Hu and the author of the present paper realized that the mirrors in the MOF models with the minimal and the derivative couplings behave like metal and dielectric mirrors, respectively They introduced a new coupling to a harmonic-oscillator bath to describe the interaction between the mirror’s internal degree of freedom and the mechanical degrees of freedom such as the vibration of the mirror substrate and the environment connected. The late-time reflectivity of our “detector mirror” in the weak oscillator-field (OF) coupling regime is similar to the atom mirrors in the cavity and waveguide QED [11,31,32,33,34,35,36,37], whose reflectivity are peaked in a narrow band around a single frequency of resonance The cavity of those atom mirrors can only generate few cavity modes inside since the detector and atom mirrors are almost transparent for other harmonics [32].
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