Abstract
Quantum radiated power emitted by an Unruh-DeWitt (UD) detector in linear oscillatory motion in (3+1)D Minkowski space, with the internal harmonic oscillator minimally coupled to a massless scalar field, is obtained non-perturbatively by numerical method. The signal of the Unruh-like effect experienced by the detector is found to be pronounced in quantum radiation in the highly non-equilibrium regime with high averaged acceleration and short oscillatory cycle, and the signal would be greatly suppressed by quantum interference when the averaged proper acceleration is sufficiently low. An observer at a fixed angle would see periods of negative radiated power in each cycle of motion, while the averaged radiated power over a cycle is always positive as guaranteed by the quantum inequalities. Coherent high harmonic generation and down conversion are identified in the detector’s quantum radiation. Due to the overwhelming largeness of the vacuum correlators of the free field, the asymptotic reduced state of the harmonics of the radiation field is approximately a direct product of the squeezed thermal states.
Highlights
To look at the quantum correction by the Unruh effect to the radiation emitted by a linearly accelerated charge or atom [8,9,10], which is called the “Unruh radiation”
Quantum radiated power emitted by an Unruh-DeWitt (UD) detector in linear oscillatory motion in (3+1)D Minkowski space, with the internal harmonic oscillator minimally coupled to a massless scalar field, is obtained non-perturbatively by numerical method
The physical reason for these results is that quantum interference between the vacuum fluctuations driving the detector and the radiation emitted by the driven detector is perfectly destructive in equilibrium conditions
Summary
Consider an Unruh-DeWitt detector with its internal degree of freedom acting as a harmonic oscillator and minimally coupled to a massless scalar field Φ in (3+1)D Minkowski space, described by the action. Due to the linearity, a mode function of the field has the form φκx = φ[0x]κ + φ[1x]κ (κ = a, {k}; φax and φkx are associated with aandbk, respectively), which is the superposition of the homogeneous solution φ[x0]κ corresponding to vacuum fluctuations of the free field and the inhomogeneous solution φ[1x]κ sourced from the point-like detector. We define the renormalized stress-energy tensor as Tμν(x) ren ≡ Tμν(x) − Tμ[0ν0](x) Doing this is nothing but setting the zero point of vacuum stress-energy. Suppose a set of the radiation-detecting apparatus are located at a large constant radius r at different angles from the spatial origin, namely, at xμ = (x0, x1, x2, x3) = (t, r sin θ cos φ, r sin θ sin φ, r cos θ) in the Minkowski coordinates. Let us look into more details of the correlators
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