Nonorthogonal-qubit-state expansion for the asymmetric quantum Rabi model

Abstract

We present a physically motivated variational wave function for the ground state of the asymmetric quantum Rabi model (AQRM). The wave function is a weighted superposition of squeezed coherent states entangled with non-orthogonal qubit states, and relies only on three variational parameters. The variational expansion describes the ground state remarkably well in almost all parameter regimes, especially with arbitrary bias. We use the variational result to calculate various relevant physical observables of the ground state, and make a comparison with existing approximations and the exact solution. The results show that the variational expansion is a significant improvement over the existing approximations for the AQRM.

Generalized adiabatic approximation to the quantum Rabi model

“…Therefore, the GAA brings no improvement to the ground state and the first excited state. For completeness, we note that these states can be well described by the non-orthogonal qubit states in all parameter regimes [27,38]. More generally, the description of the lowest k pairs of energy levels cannot be well improved by the GAA for ∆ in the range 2k < ∆/ω < 2(k + 1).…”

“…1. This interpretation is known as the displaced oscillator picture and has been extensively used in lightmatter interaction models [24][25][26][27].…”

“…The two oscillators are displaced by a distance of ±g/ω, which becomes exact when ∆ = 0. However, if ∆ is nonzero, the tunnelling leads to an effective displacement on the oscillators [27]. This effect due to ∆ is neglected in the AA.…”

General symmetry operators of the asymmetric quantum Rabi model

“…Theoretically, the AQRM does not possess any obvious symmetry. So the observed double degeneracy in the asymmetric model is certainly due to unknown hidden symmetries, which have attracted a lot of attentions in the past decade [11][12][13][14][15][16][17][18][19][20][21]. On the other hand, since the AQRM is ubiquitous in the modern solid devices, many celebrated properties described in conventional quantum optics, where the static bias is usually lacking, would appear in the artificial superconducting qubit setups if the hidden symmetry is generated by manipulating the static bias.…”

“…Very interestingly, the symmetry operators at small integer biases 1, 2 are rigorously derived in [16] by the expansion in original Fock space.. The extensions to the various QRMs have been performed within the same framework [17,18]. Some interesting remarks on the hidden symmetry are also given in [20].…”