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arXiv:1803.01867 · Physical review. D/Physical review. D.

Relativistic quantum optics: The relativistic invariance of the light-matter interaction models

Eduardo Martín-Martínez, Pablo Rodriguez-López

Published May 29, 2018• 70 citations
arXivHTMLPDF

Abstract

In this article we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.

DOI
10.1103/physrevd.97.105026

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In this article we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.
In this thesis, we study the interaction of a first-quantized atomic system with the quantum electromagnetic field within the context of relativistic quantum information (RQI). To that end, we examine common classes of Hamiltonians -- in particular, the dipolar coupling model as well as scalar field analogues (Unruh-DeWitt models) -- for their applicability in RQI setups. Firstly, we investigate how quantum randomness generation based on unbiased measurements on an atom can get compromised by an adversary that has access to the electromagnetic field. We show that preparing the atom in the ground state in the presence of no field excitations is, in general, not the best choice to generate randomness. Secondly, at the study of light-matter interactions inside optical cavities, we show that frequently employed approximations, such as the single-mode approximation and dimensional reduction, fail for relativistic regimes but can be already ill-behaved for non-relativistic scenarios. In particular, we show how approximating a very long and thin cavity by a one-dimensional system can be understood by recasting the D+1 dimensional quantum field inside the cavity as an infinite sum of massive 1+1 dimensional fields. The dimensional reduction approximation can subsequently be identified with ignoring all but one of these subfields or, equivalently, with a change of the atomic localization. Up to this point, we have treated the atomic center of mass classically -- a feature that is shared by usual Hamiltonians in RQI and quantum optics. We therefore revisit the interaction of atoms and light by considering all atomic degrees of freedom to be quantum. Further, we discuss subtleties with respect to the gauge nature of light and the effect that multipole approximations have. This allows us to connect the multipolar Hamiltonian with the common effective models of quantum optics and relativistic quantum information. In particular, we discuss the influence of atomic center-of-mass delocalization and the presence of the so-called Roentgen term. Significantly, Unruh-DeWitt models fail to account for the entangling interaction between all atomic and field degrees of freedom, and we present then a scalar analogue of the Roentgen term. Finally, we demonstrate how the usual dipole model preserves covariance when considering atoms on relativistic trajectories and how this model can be used as a qualitative means to study RQI scenarios.
We revisit the interaction of a first-quantized atomic system (consisting of two charged quantum particles) with the quantum electromagnetic field, pointing out the subtleties related to the gauge nature of electromagnetism and the effect of multipole approximations. We connect the full minimal-coupling model with the typical effective models used in quantum optics and relativistic quantum information such as the Unruh-DeWitt (UDW) model and the dipole coupling approximation. We point out in what regimes different degrees of approximation are reasonable and in what cases effective models need to be refined to capture the features of the light-matter interaction. This is particularly important when considering the center of mass (COM) of the atom as a quantum system that can be delocalized over multiple trajectories. For example, we show that the simplest UDW approximation with a quantum COM fails to capture crucial R\"ontgen terms coupling COM and internal atomic degrees of freedom with each other and the field. Finally we show how effective dipole interaction models can be covariantly prescribed for relativistically moving atoms.
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Does the measurement of a quantum system necessarily break Lorentz invariance? We present a simple model of a detector that measures the spacetime localization of a relativistic particle in a Lorentz invariant manner. The detector does not select a preferred Lorentz frame as a Newton-Wigner measurement would do. The result indicates that there exists a Lorentz invariant notion of quantum measurement and sheds light on the issue of the localization of a relativistic particle. The framework considered is that of single-particle mechanics as opposed to field theory. The result may be taken as support for the interpretation postulate of the spacetime-states formulation of single-particle quantum theory.
Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the multiparticle nature of quantum-delocalizable atoms in curved spacetime and generalize the special-relativistic center of mass (c.m.) and relative coordinates that have previously been studied for Minkowski spacetime to obtain the light-matter dynamics in curved spacetime. In particular, for a local Schwarzschild observer located at the surface of the Earth using Fermi-Walker coordinates, we find gravitational correction terms for the Poincaré symmetry generators and use them to derive general relativistic c.m. and relative coordinates. In these coordinates we obtain the Hamiltonian of a fully first-quantized two-particle atom interacting with the electromagnetic field in curved spacetime that naturally incorporates special and general relativistic effects.
We compare the predictions of the fundamentally motivated minimal coupling ($\stackrel{^}{\mathbit{p}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{\mathbit{A}}$) and the ubiquitous dipole coupling ($\stackrel{^}{\mathbit{x}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{\mathbit{E}}$) in the light-matter interaction. By studying the light-matter interaction for hydrogenlike atoms we find that the dipole approximation cannot be a priori justified to analyze the physics of vacuum excitations (a very important phenomenon in relativistic quantum information) since a dominant wavelength is absent in those problems, no matter how small (as compared to any frequency scale) the atom is. Remarkably, we show that the dipole approximation in those regimes can still be valid as long as the interaction time is longer than the light-crossing time of the atoms, which is a very reasonable assumption. We also highlight some of the subtleties that one has to be careful with when working with the explicitly gauge noninvariant nature of the minimal coupling, and we compare it with the explicitly gauge invariant dipole coupling.