On the gauge of the natural lineshape

We use a general formulation of nonrelativistic quantum electrodynamics in which the gauge freedom is carried by the arbitrary transverse component of the the Green's function for the divergence operator to calculate the natural lineshape of spontaneous emission, thus discerning the full dependence of the result on the choice of gauge. We also use a representation of the Hamiltonian in which the virtual field associated with the atomic ground state is explicitly absent. We consider two processes by which the atom is excited; the first is resonant absorption of incident radiation with a sharp line. This treatment is then adapted to derive a resonance fluorescence rate associated with the Lamb line in atomic hydrogen. Second we consider the atom's excitation due to irradiation with a laser pulse treated semi-classically. An experiment could be used to reveal which of the calculated lineshape distributions is closest to the measured one. This would provide an answer to a question of fundamental importance; how does one best describe atom-radiation interactions with the canonical formalism?Comment: 17 pages, 2 figures, 3 table

Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED

Ultrastrong-coupling between two-level systems and radiation is important for both fundamental and applied quantum electrodynamics (QED). Such regimes are identified by the breakdown of the rotating-wave approximation, which applied to the quantum Rabi model (QRM) yields the apparently less fundamental Jaynes-Cummings model (JCM). We show that when truncating the material system to two levels, each gauge gives a different description whose predictions vary significantly for ultrastrong-coupling. QRMs are obtained through specific gauge choices, but so too is a JCM without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this JCM provides more accurate predictions than the QRM for the ground state, and often for the first excited state as well. Thus, Jaynes-Cummings physics is not restricted to light-matter coupling below the ultrastrong limit. Among the many implications is that the system's ground state is not necessarily highly entangled, which is usually considered a hallmark of ultrastrong-coupling.Comment: 9 pages, plus 20 page Supplementary Information. See also related independent work arXiv:1805.05339

A master equation for strongly interacting dipoles

We consider a pair of dipoles for which direct electrostatic dipole-dipole interactions may be significantly larger than the coupling to transverse radiation. We derive a master equation using the Coulomb gauge, which naturally enables us to include the inter-dipole Coulomb energy within the system Hamiltonian rather than the interaction. In contrast, the standard master equation for a two- dipole system, which depends entirely on well-known gauge-invariant S-matrix elements, is usually derived using the multipolar gauge, wherein there is no explicit inter-dipole Coulomb interaction. We show using a generalised arbitrary-gauge light-matter Hamiltonian that this master equation is obtained in other gauges only if the inter-dipole Coulomb interaction is kept within the interaction Hamiltonian rather than the unperturbed part as in our derivation. Thus, our master equation, while still gauge-invariant, depends on different S-matrix elements, which give separation-dependent corrections to the standard matrix elements describing resonant energy transfer and collective decay. The two master equations coincide in the large separation limit where static couplings are negligible. We provide an application of our master equation by finding separation-dependent corrections to the natural emission spectrum of the two-dipole system.Comment: 18 pages including appendix, 8 figure

Composite quantum systems and environment-induced heating

In recent years, much attention has been paid to the development of techniques which transfer trapped particles to very low temperatures. Here we focus our attention on a heating mechanism which contributes to the finite temperature limit in laser sideband cooling experiments with trapped ions. It is emphasized that similar heating processes might be present in a variety of composite quantum systems whose components couple individually to different environments. For example, quantum optical heating effects might contribute significantly to the very high temperatures which occur during the collapse phase in sonoluminescence experiments. It might even be possible to design composite quantum systems, like atom-cavity systems, such that they continuously emit photons even in the absence of external driving.Comment: 4 pages, 1 figur

Non-conjugate quantum subsystems

We introduce the notion of non-conjugate quantum subsystems as an alternative way to understand the decomposition of a quantum system into interacting parts. The definition is shown to be natural in situations where a conventional decomposition is incompatible with fundamental and operationally motivated identifications of physical subsystem observables, such as in non-relativistic quantum electrodynamics. We apply the concept to quantum thermodynamics, obtaining a reduced state of the working system that unlike the usual reduced state is compatible with the definition of the working system's energy often used within the literature. This yields non-trivial and purely quantum corrections to previous results.Comment: 11 pages + Supplementary Note, 2 figure