Phase Transitions, Two-Level Atoms, and theA2Term

Abstract

Phys. Rev. 165, 1579. 12 The quoted ranges include values of A T and A LS from Refs. 8, 10, and 11 and R. A. Arndt, R. H. Hackman, and L. D. Roper, Phys. Rev. C 9, 555 (1974). From the latter reference we include the phase shifts from the 1-500-MeV analysis and two sets of phase shifts obtained from the analysis of the 1-27.6-MeV data.13 Arndt, Hackman, and Roper, Ref. 12. The caption of Fig. 3 is incorrect. The floated curves are the upper one for Fig. 3(a) and the lower ones for Figs. 3(b) and 3(c). The numbers on the vertical scale in Figs. 2(b) and 3(b) should be negative and the values in Fig. 3(b) should be integer multiples of 0.2 [R. A. Arndt, private communication].14

Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime

“…This can indeed be the case with atomic qubits, and it leads to the no-go theorem in those systems 15 .…”

“…Using our experimental results, we can make a statement regarding the A 2 term and the superradiance no-go theorem 15 in our set-up. A direct consequence of the no-go theorem is that, provided that the condition of the theorem (C A2 > g /∆) is satisfied, the system parameters will be renormalized such that the experimentally measured parameters will satisfy the inequality 2g / √ ∆ω o < 1 (see Methods).…”

“…If the coupling strength g becomes as large as the atomic and cavity frequencies (∆ and ω o , respectively), the energy eigenstates including the ground state are predicted to be highly entangled 14 . There has been an ongoing debate 15 We begin by describing the Hamiltonian of each component in the qubit-oscillator circuit, which comprises a superconducting flux qubit and an LC oscillator inductively coupled to each other by sharing a tunable inductance L c , as shown in the circuit diagram in Fig. 1a.…”

Instabilities of the Dicke model with field interactions

“…It is interesting to find that the excitation number L is added It is interesting to discuss the effect of the interacting bosonic field in the atom-field system. As the interactions vector potential A, caused by the longitudinal part of the bosonic field, are taken into account, the Hamiltonian in the RWA DM can be evaluated with an additional term A 2 [16,17].The additional term A 2 has been discussed classically about thermodynamic properties by Rzażewski et al [17,18]. To extensively quantify the contributions of the A 2 term, we employ the quantum information tools such as the BP and the ground state fidelity to detect the quantum-phase-like transitions.…”

“…[15], the absence of field A 2 term from the minimal coupling Hamiltonian in the approximation of the DM leads to the possibility of the instability. In the presence of A 2 term, the classical thermodynamic properties have been studied previously [16,17,18]. Whether the instabilities disappear when the interaction of the bosonic field A 2 term is taken into account is a long-standing issue and remains very controversial to date [12,15,16].…”