Localized nonrelativistic quantum systems in curved spacetimes: A general characterization of particle detector models

Abstract

In this manuscript we provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a background curved spacetime. Namely, using Fermi normal coordinates, we identify an inner product and canonically conjugate position and momentum operators defined in the rest space of the trajectory for each value of its proper time. This framework then naturally provides a recipe for mapping a quantum theory defined in a non-relativistic background to a theory around a timelike trajectory in curved spacetimes. This is done by reinterpreting the position and momentum operators and by introducing a local redshift factor to the Hamiltonian, which gives rise to new dynamics due to the curvature of spacetime and the acceleration of the trajectory. We then apply our formalism to particle detector models, that is, to the case where the non-relativistic quantum system is coupled to a quantum field in a curved background. This allows one to write a general definition for particle detector models which is able to recover the previous models in the literature. Our framework also allows one to estimate the regime of validity of these models, characterizing the situations where particle detectors can be used to accurately probe quantum fields.

Finite pulse-time effects in long-baseline quantum clock interferometry

“…Specifically, we refer to the works of Sonnleitner et al 74 and Schwartz et al 75,76 for systems with quantized COM motion, respectively, without and with gravity. A field theoretical derivation has recently been performed by Aßmann et al 77 Moreover, Perche et al 78,79 contain a discussion under which conditions and by which guiding principles, effective models for composite systems can be constructed in curved spacetime. Extensions examining the coupling of Dirac particles to gravitational backgrounds have recently also been discussed, 78,80,81 yielding overall sensible but in the details slightly differing results in the weak-field limit.…”

Quantum teleportation with relativistic communication from first principles

“…Since the communication part (which requires maximum channel capacity) only involves A 2 and B 1 , the dynamics of detectors A and B can be evaluated perturbatively so we do not need to make any restrictions to the type of interactions or detectors, beyond the assumption that the coupling with the field is weak (to justify perturbative calculation). If we wish to study nonperturbatively how non-trivial states of motion can impact the teleportation protocol, then we can consider the moving detectors A and B to be gapless (as done in [64]) since delta-coupled detector cannot really capture the impact of the states of motion beyond the fact that the spatial profile gets distorted asymmetrically, e.g., when one considers detector B's centre of mass to be uniformly accelerated (see, for instance, [68] for how to capture accelerated motion of a finite-sized detector in Fermi normal coordinates).…”

“…For much more comprehensive discussions on Fermi normal coordinates, its applications and limitations, see[68] 9. Note that this can be really difficult in general unless the trajectories have some symmetries, since there is a lot of arbitrariness in how to embed Cauchy slices in M.…”

Fermi two-atom problem: non-perturbative approach via relativistic quantum information and algebraic quantum field theory

“…Mathematically, each detector interacts at some fixed τ j = τ j,0 in its own centre-of-mass rest frame. In terms of the detector's proper frame (e.g., using Fermi normal coordinates [22,23,55]) the spacetime smearing can be factorized into products of switching functions and its spatial profile:…”

“…Since FNC is an adapted coordinate system along a timelike curve, two timelike curves associated to Alice and Bob's centre of mass will not share the same FNC. This makes concrete computations involving two disjoint regions of spacetime quite awkward (however, for single detector this is an excellent choice, as can be seen in [55]), and in some cases it is simply impossible to use a single FNC for both detectors, such as two accelerating detectors on two separate Rindler wedges because of the so-called Fermi bound [55]. There are two ways to avoid this.…”