Quantised mass–energy effects in an Unruh–DeWitt detector

—by Carolyn Wood

Carolyn Wood and Magdalena Zych have shown that mass–energy equivalence must be incorporated into the traditional model of a quantum particle interacting with an external environment to represent realistic scenarios in which particles such as atoms interact with, for example, light.

The traditional model of a particle interacting with, for example, light is known as the Unruh–DeWitt model, and is widely used in theoretical physics.  This simple model consists of a point-like particle with internal energy levels, which interacts with a quantum field but travels on a classical trajectory (that is, there is no quantum uncertainty in its position or momentum).  If the particle ‘detects’ energy from the field, then it absorbs that energy and is excited to a higher internal energy level (like when an atom absorbs a photon and its electrons move to higher energy levels).  Alternately, the particle may emit energy to the field and drop to a lower energy level.  However, researchers have recently begun to include a quantum centre of mass for the detector in an effort to create a model that, while still simple, more closely resembles a real quantum particle.

We incorporated Einstein’s mass–energy equivalence (which also gives us E = mc²) into the traditional model.  In our new model, the internal energy levels of the particle have an associated mass, and exchanging energy with the field alters not only the energy but also the mass of the detector—as required by relativity.  To understand the implications of this, we investigated the role mass has in our model and in previous models that assume a fixed mass.

Although effects of mass–energy equivalence would usually be considered negligible in the low-energy limit, we found that, surprisingly, not only are they present in that regime, but they are of the same order of magnitude as the energy of the centre of mass of the detector.  This means that anyone wishing to adapt the Unruh–DeWitt model to realistic quantum particles (such as atoms) must include the mass–energy equivalence.

Our approach strengthens the connection between the research areas of quantum field theory, relativistic quantum information and atomic physics. Besides showing that mass–energy equivalence cannot be neglected even in the regime previously assumed to be fully non-relativistic, the incorporation of mass–energy equivalence into the model opens new possibilities for testing the interplay between quantum physics and gravity.

This project is only just beginning, and we will continue to explore the consequences of including mass–energy equivalence in this model.  The research began at the height of the COVID-19 pandemic, when we and any overseas colleagues we were in contact with went into lockdown, and I was completely new to the topic and the mathematical formalism, so it was a steep (but rewarding) learning curve.  We’re always happy to hear from any EQUS members with ideas, particularly from the atomic physics side or for possible laboratory tests.

Read the full paper here: https://doi.org/10.1103/PhysRevD.106.025012.  This work fits into EQUS’ Quantum Clocks Flagship research program.  Carolyn submitted her PhD thesis in May this year and is now actively looking for postdoc opportunities!  In addition to the work described here, she conducts research in quantum information and quantum thermodynamics.