Quantised mass-energy effects in a particle detector - RQI2022

Abstract

The Unruh-DeWitt (UDW) detector is a simple but powerful model of a quantum particle interacting with an external environment, e.g. a field. The particle’s internal state can change in response to the field—e.g., internal energy can increase at the expense of decreasing field energy. Research with UDW models has mostly used a classical description of the detector’s external degrees of freedom (DOFs), i.e. assigning it a classical trajectory, and treating only the internal state as a quantum DOF. On the other hand, formal field-theoretic versions describe the detector itself as a quantum field. Neither model captures the natural scenario of a low-energy quantum particle, e.g. an atom, interacting with a quantum field, e.g. light. Hence much recent interest has arisen in more realistic quantum descriptions of the detector’s centre of mass, where it has been described either as moving in superposition along classical trajectories, or dynamically evolving under a non-relativistic Hamiltonian.

Yet results in atomic physics show mass-energy equivalence plays a crucial role in energy and momentum conservation for atom-light interactions. Neither of the above UDW models can capture this effect, as absorption or emission of field quanta must also change the detector’s rest mass by an equivalent energy.

Here we address this problem and incorporate quantisation of the detector’s mass-energy into the UDW model. We show that changes in internal energy due to emission/absorption persist even at low energies. Specifically, corrections to transition rates due to mass changes cannot be ignored unless the entirety of the center of mass dynamics is also ignored. Our results imply that one cannot model a massive particle interacting with a relativistic quantum field consistently without at the least including relativistic mass-energy equivalence in the particle’s dynamics.

Carolyn Wood

Postdoctoral Scientist

Carolyn Wood is a postdoctoral researcher at the University of Queensland, in Brisbane, Australia focusing on quantum machine learning and physics at the interface between quantum mechanics and general relativity.