Fidelity susceptibility in the quantum Rabi model

Abstract

Quantum criticality usually occurs in many-body systems. Recently it was shown that the quantum Rabi model, which describes a two-level atom coupled to a single model cavity field, presents quantum phase transitions from a normal phase to a superradiate phase when the ratio between the frequency of the two level atom and the frequency of the cavity field extends to infinity. In this work, we study quantum phase transitions in the quantum Rabi model from the fidelity susceptibility perspective. We found that the fidelity susceptibility and the generalized adiabatic susceptibility present universal finite size scaling behaviors near the quantum critical point of the Rabi model if the ratio between frequency of the two level atom and frequency of the cavity field is finite. From the finite size scaling analysis of the fidelity susceptibility, we found that the adiabatic dimension of the fidelity susceptibility and the generalized adiabatic susceptibility of fourth order in the Rabi model are 4/3 and 2, respectively. Meanwhile the correlation length critical exponent and the dynamical critical exponent in the quantum critical point of the Rabi model are found to be 3/2 and 1/3 respectively. Since the fidelity susceptibility and the generalized adiabatic susceptibility are the moments of the quantum noise spectrum which is directly measurable by experiments in linear response regime, the scaling behavior of the fidelity susceptibility in the Rabi model could be tested experimentally. The simple structure of the quantum Rabi model paves the way for experimentally observing the universal scaling behavior of the fidelity susceptibility at a quantum phase transition. the quantum information theory and condensed matter physics and shall deepen our understanding on the various condensed matter phenomena.

Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules

“…The QFS has been used in the characterization of ground state quantum phase transitions and their universality in relevant many-body quantum systems, e.g. the 1D Hubbard model [103,106], the Kitaev honeycomb model [107], the 1D asymmetric Hubbard model [104], the Lipkin-Meshkov-Glick model [108][109][110], the two-dimensional transverse-field Ising and XXZ models [111], the Rabi model [112], Gaussian random ensambles [113], or 1D lattice models [114][115][116][117].…”

Quantum criticality and state engineering in the simulated anisotropic quantum Rabi model

“…QPT in systems with few degrees of freedom has recently been a topic of major interest recently [10,25,31,32,45]. Although the quantum criticality is commonly believed to take place in a many-body system in the thermodynamic limit, it is newly realized that a few-body system may undergo QPTs provided the energy barrier between two local-minima states is infinite.…”

“…The fidelity susceptibility is of fundamental interest in QPTs because it provides direct manifestation of their universal properties without prior knowledge of order parameters. More importantly, the fidelity susceptibility can be in general reconstructed from the power spectral density of driving field [45,50], which is accessible experimentally for example via Rabi oscillation measurements, spin-echo measurements, and energy relaxation measurements [51]. Last but not the least, there is a refreshing proposed duality, which connects the fidelity susceptibility and the max volume of a codimension-one time slice in antide Sitter (AdS) space [52,53].…”

“…This implies T≈7 μs, which approximately satisfies the adiabatic condition. In combination with the dedicated microwave manipulation techniques, the simulation protocol by principle is suited for exploring novel QPTs in the AQRM [10,25,31,45]. For practice experimental implementations, it is worthy of mentioning that since the state preparation time T is inverse proportional to the effective resonator frequency, longer T is required for larger η, which certainly leads to more errors accumulated from the imperfect operations and the decay processes.…”

Quantum criticality driven by the cavity coupling in Rabi-dimer model

“…Regarding the SPT, it is clear that the superradiance appears when the ratio of the atomic frequency and the photonic frequency approaching the thermodynamic limit, by which the universal dynamics of the Rabi model is well studied [45]. Recently, this finding has stimulated the researches on SPT in other photonic systems [46][47][48][49][50][51].…”