Back-action from inertial and non-inertial Unruh-DeWitt detectors revisited in covariant perturbation theory

Abstract

We investigate the back-action from a spatially pointlike particle detector on a quantum scalar field, as characterised by the expectation value of the field's stress-energy tensor, without conditioning on a measurement of the detector. First, assuming the field to be initially in a zero-mean Gaussian Hadamard state in a globally hyperbolic spacetime, we evaluate the field's two-point function in second-order perturbation theory by techniques of covariant curved spacetime quantum field theory, which allow a full control of the time and space localisation of the interaction, and do not rely on field mode decompositions or non-local particle countings. The detector's two-point function splits into a deterministic and a fluctuating part, and we show that this split is maintained in the back-action. We then specialise to a two-level Unruh-DeWitt detector, prepared in an energy eigenstate, for which the back-action is fully fluctuating. We compute the renormalised stress-energy tensor for a massless scalar field in $(3+1)$-dimensional Minkowski spacetime for a general detector trajectory, using the manifestly causal two-point function. We present explicit analytic and numerical results for an inertial detector and a uniformly linearly accelerated detector, switched on in the asymptotic past. The energy flux into and out of the accelerated detector accounts exactly for the energy gained and lost by the detector in its transitions due to the Unruh effect. The same holds for the outward flux associated with de-excitations of the inertial detector, which has a vanishing excitation rate and no inward flux. A novelty with the accelerated detector is two regions of negative energy density when the detector is initially prepared in its ground state, one near the Rindler horizon that bounds the causal future of the trajectory, the other in the far future of the trajectory.

34 pages, 11 figures. v2: typos corrected; a comment added on renormalisation in curved spacetime generalisations

References in corpus (25)

• The Unruh effect and its applications
• Wavepacket detection with the Unruh-DeWitt model
• Relativistic Quantum Information in Detectors-Field Interactions
• Backreaction and Unruh effect: New insights from exact solutions of uniformly accelerated detectors
• Information transmission without energy exchange
• A detector-based measurement theory for quantum field theory
• Broken covariance of particle detector models in relativistic quantum information
• Unruh-deWitt detectors in quantum superpositions of trajectories
• Unruh and analogue Unruh temperatures for circular motion in 3+1 and 2+1 dimensions
• Quantum signatures of black hole mass superpositions
• Open quantum system approach to Gibbons-Hawking effect of de Sitter space-time
• Quantum superpositions of Minkowski spacetime
• Unruh effect for detectors in superposition of accelerations
• Unruh-like effects: Effective temperatures along stationary worldlines
• Second-quantized Unruh-DeWitt detectors and their quantum reference frame transformations
• Classical and quantum reconciliation of electromagnetic radiation: vector Unruh modes and zero-Rindler-energy photons
• Classical Larmor formula through the Unruh effect for uniformly accelerated electrons
• Detecting the massive bosonic zero-mode in expanding cosmological spacetimes
• Quantum Radiation and Dissipation in Relation to Classical Radiation and Radiation Reaction
• Connecting the circular and drifted Rindler Unruh effects
• Accelerated detector in a superposed spacetime
• Acceleration-induced radiation from a qudit particle detector model
• What happens once an accelerating observer has detected a Rindler particle?
• Waiting around for Unruh
• Vacua in locally de Sitter cosmologies, and how to distinguish them