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.

This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each Hamiltonian refers to physically different components as representing the "atom" and as representing the "field" and hence results in a different master equation, when assuming a photonabsorbing environment. It is shown that the master equations associated with the minimal coupling and the multipolar Hamiltonians predict enormous stationary state narrowband photon emission rates, even in the absence of external driving, for current experiments with single quantum dots and colour centers in diamond. These seem to confirm that the rotating wave Hamiltonian identifies the components of the atom-field system most accurately.

© 2016 American Physical Society. This is an author produced version of a paper published in Physical Review A. Uploaded in accordance with the publisher's self-archiving policy.eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.Quantum-enhanced metrology with the single-mode coherent states of an optical cavity inside a quantum feedback loop In this paper, we use the non-linear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until highly-entangled many-photon states become more readily available.

The formalism of quantum mechanical gauge fixing in quantum electrodynamics (QED) is extended using techniques from non-relativistic QED. This involves expressing the redundant gauge degrees of freedom through an arbitrary functional of the gauge invariant transverse degrees of freedom. Particular choices of functional can be made to yield the Coulomb or Poincaré gauge representation of the Hamiltonian. The Hamiltonian we derive therefore serves as a good starting point for the relativistic description of atoms and molecules. Important Implications of the gauge freedom present in the Hamiltonian with regards to the ontology of QED in general are discussed.

We consider a pair of dipoles such as Rydberg atoms 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 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.