[Paper Review] Radiation by an Unruh-DeWitt Detector in Oscillatory Motion

Shih-Yuin Lin|arXiv (Cornell University)|Jan 26, 2016

Quantum Electrodynamics and Casimir Effect1 references3 citations

TL;DR

This paper investigates quantum radiation from an Unruh-DeWitt detector in linear oscillatory motion using numerical methods in (3+1)D Minkowski spacetime. It shows that quantum interference suppresses radiation at low averaged acceleration, while high acceleration and short cycles enhance Unruh-like signals; negative energy flux periods reveal squeezed state characteristics, consistent with quantum inequalities and analogies to moving-mirror models.

ABSTRACT

Quantum radiated energy flux emitted by an Unruh-DeWitt (UD) detector, with the internal harmonic oscillator coupled to a massless scalar field, in linear oscillatory motion in (3+1) dimensional Minkowski space is studied by numerical methods. Our results show that quantum interference can indeed suppress the signal of the Unruh effect if the averaged proper acceleration is sufficiently low, but not in the regime with high averaged acceleration and short oscillatory cycle. While the averaged radiated energy flux over a cycle is always positive as guaranteed by the quantum inequalities, an observer at a fixed angle may see short periods of negative radiated energy flux in each cycle of motion, which indicates that the radiation is squeezed. This reveals another resemblance between the detector theory and the moving-mirror model.

Motivation & Objective

• To investigate quantum radiation from a detector in oscillatory motion, a non-uniform acceleration scenario, to probe the detectability of the Unruh effect beyond uniform acceleration.
• To analyze how quantum interference between vacuum fluctuations and emitted radiation affects the radiated energy flux in non-equilibrium conditions.
• To determine whether the Unruh effect can be observed via radiation signals in oscillatory motion, especially in regimes with high averaged acceleration and short cycles.
• To explore the connection between detector radiation and squeezed states of the field, as indicated by negative energy flux periods.
• To compare numerical results with naive estimates based on uniformly accelerated detectors and assess the validity of effective temperature approximations.

Proposed method

• Numerical simulation of the Unruh-DeWitt detector model with a harmonic oscillator coupled to a massless scalar field in (3+1)D Minkowski spacetime.
• Use of linear response theory to compute the radiated energy flux via time-ordered correlators of the field operator after detector-field coupling is switched on.
• Decomposition of the field operator into homogeneous and inhomogeneous mode functions, each associated with creation/annihilation operators of the free field and detector.
• Computation of the renormalized stress-energy tensor expectation values using the full correlator $ G(x,x') $, including interference terms between vacuum fluctuations and radiation.
• Application of quantum inequalities to ensure the averaged energy flux over a cycle remains positive, even when instantaneous flux is negative.
• Comparison of full numerical results with naive estimates based on uniformly accelerated detectors, using effective acceleration $ a_{\text{eff}} = 2\pi T_{\text{eff}} $ to refine predictions.

Experimental results

Research questions

• RQ1 Can the Unruh effect be detected in a detector undergoing oscillatory motion, where acceleration is non-uniform and time-dependent?
• RQ2 How does quantum interference between vacuum fluctuations and emitted radiation suppress or enhance the radiated energy flux in oscillatory motion?
• RQ3 Under what conditions—specifically, low vs. high averaged acceleration and long vs. short oscillation periods—does the Unruh-like signal become pronounced?
• RQ4 Why does the radiated energy flux exhibit negative values at fixed angles during certain phases of oscillation, and what does this imply about the quantum state of the field?
• RQ5 To what extent can the effective temperature derived from averaged acceleration accurately predict the radiation spectrum, and how do deviations from the naive Unruh temperature affect the results?

Key findings

• Quantum interference suppresses the radiated energy flux at low averaged proper acceleration ($ \bar{a} = 2.5 $), indicating that the Unruh effect signal is not easily detectable in such regimes.
• At high averaged proper acceleration ($ \bar{a} = 20 $), the full radiated energy flux closely matches the naive estimate for a uniformly accelerated detector, suggesting a pronounced Unruh-like signal.
• Negative energy flux periods occur at fixed observation angles during each oscillation cycle, indicating that the Unruh radiation corresponds to a multi-mode squeezed state of the field.
• The effective temperature $ T_{\text{eff}} \approx 1.6754 $ to $ 1.6767 $ at low $ \bar{a} $ is slightly higher than the naive Unruh temperature $ \bar{a}/(2\pi) \approx 1.5916 $, while at high $ \bar{a} $, $ T_{\text{eff}} \approx 3.156 $ is slightly lower than $ \bar{a}/(2\pi) \approx 3.183 $, showing small but non-negligible deviations due to non-uniform acceleration.
• The averaged energy flux over a cycle remains positive at all angles, as required by quantum inequalities, despite transient negative fluxes, confirming energy conservation in the quantum regime.