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.
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.
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 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.
Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an 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.
The loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize. In structured photonic environments, necessary in practice to achieve strong light-matter coupling, a rigorous model of field quantization within the medium is also needed. Here we use the framework of macroscopic QED by quantizing the fields in an arbitrary material system, with a spatially dependent dispersive and absorptive dielectric, starting from a fundamental light-matter action. We truncate the material and mode degrees of freedom while respecting the gauge principle by imposing a partial gauge-fixing constraint during canonical quantization, which admits a large number of gauges including the Coulomb and multipolar gauges commonly used in quantum optics. We also consider gauge conditions with explicit time dependence, enabling us to unambiguously introduce additional phenomenologically time-dependent light-matter interactions in any gauge. Our results allow one to derive rigorous nonrelativistic models of ultrastrong light-matter interactions in structured photonic environments with no gauge ambiguity. Results for two-level systems and the dipole approximation are discussed, as well as how to go beyond the dipole approximation for effective single-particle models. By comparing with the limiting case of an inhomogeneous dielectric, where dispersion and absorption can be neglected and the fields can be expanded in terms of the generalized transverse eigenfunctions of the dielectric, we show how lossy systems can introduce an additional gauge ambiguity, which we resolve and predict to have fundamental implications for open quantum system models. Finally, we show how observables in mode-truncated systems can be calculated without ambiguity by using a simple gauge-invariant model of photodetection.
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.
Devoting some thought to the interactions between light and matter quickly conjure a myriad of different possibilities; different models for light and matter, different possible interaction Hamiltonians, different simplifying approximations and different initial conditions. This of course means that light-matter interactions has just as many uses and surprises yet to be explored. In this thesis we will approach light-matter interactions from three different perspectives: 1) How can light-matter interactions be used to manipulate quantum fields into exotic energy distributions, 2) How well does a classical light-matter approximation carry through to quantum light-matter interactions and 3) In a relativistic theory, what are the causal consequences of approximations commonly used to reduce the analytical and numerical complexity of quantum fields. \n \nMy first aim in this thesis is to develop an operationally feasible procedure for generating exotic energy distributions. Current proposals for generating negative energy densities include using the dynamical Casimir effects or by squeezed vacua, which require relativistically accelerating mirrors or non-linear crystals. Instead we seek an optimal protocol that does not require relativistically accelerating elements and exploits the coherent control of a detector. The quantum energy teleportation (QET) protocol is ideal for this task, and we present a QET protocol acting on a relativistic scalar field optimised for the generation of negative energy densities. We show that QET can be used to generate local negative energy densities using stationary qubits. In addition we discuss the consequences of detector smearings on the (QET generated) energy distribution, providing simple and intuitive guidelines for sculpting negative energy distributions. We also show that this protocol is capable of generating regions with an arbitrary amount of negative energy, with the total amount of negative energy ∆E increasing as the negative energy well’s width ∆r is decreased by ∆E ∼ ∆r⁻³ . However, this is accompanied by increasingly large (∼ ∆r⁻³ ) positive energy peaks on either side of the well. We further find this energy-distance scaling saturates the quantum interest conjecture, suggesting the near optimality of QET for generating negative energy densities. \n \nMy second aim is to determine the validity of the dipole model of light-matter interaction with a quantum EM field. This model, classically derived from the more fundamental minimal model, is dependent on the existence of a dominant mode, whose wavelength is required to be much larger than the size of the atom it is interacting with (dipole approximation criterion). Quantisation of the EM field result in vacuum fluctuations without a dominant wavelength. Past works have attempted to overcome this by using point-like atoms, however this introduces UV divergences in the response of the atoms and is inadequate for describing light-matter interactions. The full influence of gauge considerations and quantum behaviour in light matter interaction is quite involved and complex, particularly when the atomic nucleus’ mass is considered finite and the centre of mass degrees of freedom become relevant. We consider effective models (infinite nucleus mass), which neglect the centre of mass degrees of freedom and their additional complexity, whilst allowing accurate investigations of the electronic orbital behaviour. Here we will attempt to determine under what circumstances the dipole and minimal models agree; and hope to clarify and extend the dipole approximation validity criteria for general use in quantum fields. \n \nUsing the 'dressed state' formalism to remove gauge issues, we compare the transition probabilities of Hydrogen-like atoms under both models to determine the validity of the dipole model. We show that for atomic transitions with an initial EM vacuum state, both models noticeably disagree for short interaction times (i.e. shorter than the light-crossing time of the atom). We find the transition rates predicted by both models begin to converge for longer interaction times, particularly when considering vacuum excitations. Vacuum emissions have the additional requirement that the atomic energy gap must satisfy the dipole approximation criterion due to single mode approximation effects. In addition, we find that shrinking the atom (by increasing the atom’s proton number) does not improve the accuracy of the dipole model, a result of the infinite number of UV modes in the vacuum fluctuations. We determine that the dipole model can be used with a quantum EM field, provided any intrinsically dominant modes, e.g. atomic energy gap (for vacuum emissions) or excited EM modes, satisfy the dipole approximation criterion and the interaction time is longer than the light crossing time of the atom. \n \nOur final aim is to determine the causal consequences of the commonly used rotating wave approximation (RWA) and determine in what regimes it may be accurately used. The RWA removes terms from the (detector-field) interaction Hamiltonian that do not conserve excitation number, e.g. field creation operators tensored with SU(2) raising operators. This is justified by noting that these terms oscillate quickly in time and therefore, for long interaction times (T), will integrate to zero, where long interaction time is defined by the RWA criterion ΩT≫1, where Ω is the detector’s energy gap. We wish to determine the extent of the non-locality and causality violation introduced into this originally local and causal theory; as well as determine in what regime the RWA model can be used as a faithful substitute for the unapproximated UDW model. We quantify these violations by studying the non-locality of the RWA interaction Hamiltonian, inspecting the acausal expectation values of field amplitude squared (ϕ²) and the local energy density (T₀₀); and quantifying the superluminal communication in a 2 qubit communication protocol. \n \nWe verify and extend the previous results by showing the RWA interaction Hamiltonian has a 1/r² polynomial non-locality, proportional to the vacuum Wightman function of the field. We also show that this non-locality translates into causality violations of 1/d⁴ and 1/d⁶ for the expectation values ϕ² and T₀₀ respectively; where d is measured from the surface of the detector’s lightcone and this polynomial causality violation is independent of time. We also find similar 1/d² non-localities in the channel capacity of the 2 qubit communication protocol, with non-local influence in the space-like and time-like regions of the first detector’s interaction. We show that in setups that are not causally sensitive, e.g. measuring field observables within the bulk of a source detector’s light-cone, then the RWA criterion ΩT≫1 is sufficient for the RWA model with interaction strength λ to converge to the unapproximated UDW model with interaction strength λ/2. We establish that this factor of 1/2 comes from a mathematically unsound commutation of limits and integrals. \n \nIn the case of cavity fields, we introduced a numerical trick to make infinite mode sums computationally possible without requiring single or few mode approximations. Using this trick we found the RWA non-local behaviour to be generally similar to the free space case. We find the RWA model introduces some severe polynomial non-localities and causality violations, but if used to model light-matter interactions well within the bulk of the detector’s light-cone and ΩT≫1 then it is a good approximation for the half strength UDW model.