Abstract
We discuss the properties of bound states in finite-bandwidth waveguide QED beyond the Rotating Wave Approximation or excitation number conserving light-matter coupling models. Therefore, we extend the \emph{standard} calculations to a broader range of light-matter strengths, in particular, in the so-called ultrastrong coupling regime. We do this using the Polaron technique. Our main results are as follows. We compute the spontaneous emission rate, which is renormalized as compared to the Fermi Golden Rule formula. We generalise the existence criteria for bound states, their properties and their role in the qubits thermalization. We discuss effective spin-spin interactions through both vacuum fluctuations and bound states. Finally, we sketch a perfect state-transfer protocol among distant emitters.
Highlights
Photons are weakly coupled to matter, so they rarely interact, making them perfect information carriers
We can compare the difference between the results provided by the polaron transform to those obtained using the rotating wave approximation (RWA)
We have discussed the main properties of bound states in waveguide QED beyond the RWA paradigm
Summary
Photons are weakly coupled to matter, so they rarely interact, making them perfect information carriers. Trying to optimize the light-matter coupling, several experiments have reached the so-called ultrastrong coupling regime (USC) between light and a single quantum emitter, both in cavity [14,15] and waveguide QED [16,17,18]. On the other hand, dressed atom-field eigenstates localized around the quantum emitter, called bound states [40,41,42,43,44], generate nondissipative but exponentially bounded interactions [10,12,45,46,47,48,49,50,51,52,53,54]. The link to the python codes used in the numerical calculations is given in Appendix D
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