Abstract
We study the impact of the zero-mode of a quantum field on the evolution of a particle detector. For a massless scalar field in a periodic cavity, we show that the impact of the zero mode on the Unruh-DeWitt detector and its derivative-coupling generalisation is necessarily nonvanishing but can be made negligible in some limits, including those commonly occurring in non-relativistic quantum optics. For the derivative-coupling detector this can be accomplished by just tuning the zero mode's initial state, but the standard Unruh-DeWitt detector requires a more subtle and careful tuning. Applications include an inertial detector with arbitrary velocity, where we demonstrate the regularity of the ultrarelativistic limit, and a detector with uniform acceleration.
Highlights
The response of a particle detector coupled to a quantum field has been subject of extensive research since the 70s to the present
A spatially pointlike detector has a particular advantage in that it can be identified with an ‘observer’ who is moving through the spacetime: such detectors have been used to quantify the particle content in a given state of a quantum field as seen by a local observer [1,2,3,4,5], to analyze the entanglement contained in the vacuum state of a quantum field [6], to study metrology settings [7], to analyze the decoherence effects of relativistic trajectories [8, 9], to propose schemes of universal quantum computing via relativistic motion [10] and to set up scenarios of quantum communication in the relativistic limit [11, 12]
The question ‘How many times does a particle detector click for a given field state and a given trajectory in spacetime?’ is relevant from quantum optics [13] to the study of very fundamental problems as the quantum effects associated with the presence of horizons [14], or to serve as a witness of primordial quantum fluctuations which may give information about the nature of the gravitational interaction [15]
Summary
The response of a particle detector coupled to a quantum field has been subject of extensive research since the 70s to the present. Dropping the zero mode by hand from the coupling between the detector and the field would give a detector model that is as such mathematically consistent; as seen in [17], the full linear coupling is necessary to model the p·A term by which an atomic electron couples to the quantized electromagnetic field In quantum optics, these zero-mode issues arise with the common UDW and Jaynes-Cummings models with periodic and Neumann boundary conditions, and there it is usual to assume at the outset that any zero modes will have negligible effect and to drop them by hand. We find that, by suitably choosing the initial state of the quantum field, it is possible to minimize zero-mode effects on the detector dynamics under the UDW interaction.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
