A mathematical analysis of dressed photon in ground state of generalized quantum Rabi model using pair theory

Abstract

We consider the generalized quantum Rabi model with the so-called A 2 -term in the light of the Hepp-Lieb-Preparata quantum phase transition. We investigate the dressed photon in its ground state when the atom-light coupling strength is in the deep-strong coupling regime. We show how the dressed photon appears in the ground state. We dedicate this paper to Pavel Exner and Herbert Spohn on the occasion of their 70th birthdays, and Klaus Hepp on the occasion of his 80th birthday.

Schrodinger-Cat-Likeness in Adiabatic Approximation for Generalized Quantum Rabi Model without and with A^2-Term

“…is obtained in the same way as in Appendix B of Ref. [37]. The mathematical establishment of the adiabatic approximation also says that (∆Φ) 2 ∼ (1 + 4g 2 /ω c )/2ω c as g → ∞ for ε = 0; (∆Φ) 2 ∼ 1/2ω c as g → ∞ for ε = 0.…”

“…As shown in Ref. [37,41], the adiabatic approximation given by Eq. (3.9) is mathematically justified in the following: We define the unitary operator U (g/ω c ) by U (g/ω c ) := σ + σ − D(g/ω c )+ σ − σ + D(−g/ω c ).…”

“…Thus, the energy g 2 /ω c plays a role of a counter term for mass renormalization (i.e., for the bare-photon divergence) in the strong coupling limit. The displacement operators D (±g/ω c ) decay to the zero operator in a mathematically proper sense [37,41] in the strong-coupling limit. Developing this fact and using Theorem VIII.19(a) of Ref.…”

“…In Ref. [37], we show a mathematical theory so that the adiabatic approximation is actually obtained under the strong-coupling limit in the norm resolvent sense.…”

Advances in synthetic gauge fields for light through dynamic modulation

“…Finally, we note that most previous works have focused solely on the regime where the modulation strength is far less than the modulation frequency [42,45,49,50], allowing for the application of the rotating-wave approximation. On the other hand, there has been recent interest in light-matter interactions in the ultra-strong coupling regime [51][52][53][54][55][56][57], where the RWA is no longer valid. In such ultra-strong coupling systems, it has been shown that topologically protected one-way edge states in dynamic modulation are less susceptible to intrinsic losses [19].…”