Photon-mediated qubit interactions in one-dimensional discrete and continuous models

Abstract

(2015) Photon-mediated qubit interactions in one-dimensional discrete and continuous models. Physical Review A (PRA), 91 (6).This version is available from Sussex Research Online: http://sro.sussex.ac.uk/57191/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and reuse:Sussex Research Online is a digital repository of the research output of the University.Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available.Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. In this work we study numerically and analytically the interaction of two qubits in a one-dimensional waveguide, as mediated by the photons that propagate through the guide. We develop strategies to assert the Markovianity of the problem, the effective qubit-qubit interactions, and their individual and collective spontaneous emission. We prove the existence of collective Lamb shifts that affect the qubit-qubit interactions and the dependency of coherent and incoherent interactions on the qubit separation. We also develop the scattering theory associated with these models and prove single-photon spectroscopy does probe the renormalized resonances of the singleand multiqubit models, in sharp contrast to earlier toy models in which individual and collective Lamb shifts cancel. PHYSICAL REVIEW A 91, 063828 (2015) Photon-mediated qubit interactions in one-dimensional discrete and continuous models

Dynamical polaronAnsatz: A theoretical tool for the ultrastrong-coupling regime of circuit QED

“…It is interesting to note that, in analogy to the original calculation of the Lamb shift of the EM field where the selfenergy is subtracted, the variational polaron formalism includes this self-energy directly in the groundstate energy instead of the Lamb shift. This contrasts the calculations within the RWA [55], where the self-energy is not subtracted, and the Lamb shifts diverge with the cutoff frequency δ RWA i = −α(ω c − 1 2 ∆ log(∆/ω c )) + α 2 γ∆. If we take the Lamb shift (44) together with the polaron renormalisation, the frequency of the quantum emitter becomes ∆ cp r (1 − α), which predicts that the evolution of coherences will stop at α = 1, instead of the prediction α = 1/2 of the coherent-incoherent transition by other methods [20].…”

Dynamics of multiple atoms in one-dimensional fields

“…However, as discussed previously, the system energy is slightly corrected by the dressing of the environment, and therefore the resonance to the band-gap edge is shifted to values of ∆ slightly below zero. The energy corrections are very similar to the ones found in [59] for atoms in free space while the single atom correction is also analyzed in the similar model of Ref. 20.…”

Atom-field dressed states in slow-light waveguide QED

“…For previous work on bare atom-atom interactions near band-structures see, for example, Refs. [60][61][62][63].…”