Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1709.07111 · Physical Review A

Fidelity susceptibility in the quantum Rabi model

Bo-Bo Wei, Xiao-Chen Lv

Published Jan 26, 2018• 35 citations
arXivHTMLPDF

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 are 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.

DOI
10.1103/physreva.97.013845

Related papers

Quantum phase transitions in the Rabi-Stark model at finite frequency ratios

Xiang-You Chen, You-Fei Xie, Qing‐Hu Chen

In this work, we observe a continuous quantum phase transition in the Rabi-Stark model at finite ratios of the qubit and cavity frequencies if the nonlinear stark coupling strength is twice of the cavity frequency, in contrast to the quantum Rabi model where the quantum phase transition only emerges in the infinite frequency ratio. The quantum criticality of the Rabi-Stark model is then analyzed in terms of the energy gap, the order parameter, as well as the fidelity. The critical exponents are derived analytically. The finite size scaling analysis for the order parameter and the fidelity susceptibility is also performed. Several finite size exponents are then extracted from the universal scaling. The size independent energy gap exponent suggests the Rabi-Stark model and the quantum Rabi model are not in the same universality class, while the correlation length exponent could be the same with the specified definition of the effective system size.

•Jan 13, 2020•1 citation

Fidelity susceptibility in one-dimensional disordered lattice models

Bo-Bo Wei

We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr\'e model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generalized adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-Andr\'e model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-Andr\'e model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in the near future.

arXiv:1902.00200•Physical Review A•Apr 22, 2019•50 citations

Quantum criticality of the Rabi-Stark model at finite frequency ratios

Xiang-You Chen, You-Fei Xie, Qing‐Hu Chen

In this paper, we analyze the quantum criticality of the Rabi-Stark model at finite ratios of the qubit and cavity frequencies in terms of the energy gap and the order parameter, as well as the fidelity, if the Stark coupling strength is the same as the cavity frequency. The critical exponents are derived analytically. The energy gap and the length critical exponents are different from those in the quantum Rabi model and the Dicke model. A finite-size scaling analysis for the order parameter and the fidelity susceptibility is also performed. The universal scaling behaviors are demonstrated, and several finite-size exponents then can be extracted. Furthermore, universal critical behavior also can be established in terms of the bosonic Hilbert space truncation number, and the corresponding critical scaling exponents are found. Interestingly, the critical correlation length exponents in terms of the photonic truncation number as well as the equivalently effective length scales are different in the Rabi-Stark model and the quantum Rabi model, suggesting they belong to different universality classes. The second-order quantum phase transition is convincingly corroborated in the Rabi-Stark model at finite frequency ratios; by contrast, it emerges only at the infinite frequency ratio in the original quantum Rabi model without the Stark coupling.

arXiv:2001.04356•Physical Review A•Dec 29, 2020•20 citations

Quantum Phase Transition and Universal Dynamics in the Rabi Model

Myung-Joong Hwang, Ricardo Puebla, Martin Bodo Plenio

We consider the Rabi Hamiltonian, which exhibits a quantum phase transition (QPT) despite consisting only of a single-mode cavity field and a two-level atom. We prove QPT by deriving an exact solution in the limit where the atomic transition frequency in the unit of the cavity frequency tends to infinity. The effect of a finite transition frequency is studied by analytically calculating finite-frequency scaling exponents as well as performing a numerically exact diagonalization. Going beyond this equilibrium QPT setting, we prove that the dynamics under slow quenches in the vicinity of the critical point is universal; that is, the dynamics is completely characterized by critical exponents. Our analysis demonstrates that the Kibble-Zurek mechanism can precisely predict the universal scaling of residual energy for a model without spatial degrees of freedom. Moreover, we find that the onset of the universal dynamics can be observed even with a finite transition frequency.

arXiv:1503.03090•Physical Review Letters•Oct 29, 2015•446 citations

Quantum phase transitions and critical behaviors in the two-mode three-level quantum Rabi model

Yan Zhang, Bin-Bin Mao, Dazhi Xu +4 more

Abstract We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio η of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant phases are of second order relating to the spontaneous breaking of the discrete Z 2 symmetry. On the other hand, the quantum phase transition between the two different superradiant phases is discontinuous with a phase boundary line relating to the continuous U (1) symmetry. For a large enough but finite η , the scaling function and critical exponents are derived analytically and verified numerically, from which the universality class of the model is identified.

arXiv:1910.13043•Journal of Physics A Mathematical and Theoretical•May 13, 2020•9 citations

Quantum tricriticality and universal scaling in a tricritical quantum Rabi system

You-Qi Lu, Yuyu Zhang

Quantum tricriticality, a unique form of high-order criticality, is expected to exhibit fascinating features including unconventional critical exponents and universal scaling laws. However, a quantum tricritical point (QTCP) is much harder to access, and the corresponding phenomena at tricriticality have rarely been investigated. In this study, we explore a tricritical quantum Rabi model, which incorporates a nontrivial parameter for adjusting the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of a first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analyses for quantum fluctuations and the mean photon number, universal critical exponents differentiate the QTCP from the second-order critical point. We find that the phase transition at the tricritical point goes beyond the conventional second-order phase transition. Our work explores an interesting direction in the generalization of the well-known Rabi model for the study of higher-order critical points due to its high control and tunability.

arXiv:2402.12827•Feb 20, 2024•0 citations
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 4/34/34/3 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 3/23/23/2 and 1/31/31/3, respectively. Since the fidelity susceptibility and the generalized adiabatic susceptibility are the moments of the quantum noise spectrum which are 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.
In this work, we observe a continuous quantum phase transition in the Rabi-Stark model at finite ratios of the qubit and cavity frequencies if the nonlinear stark coupling strength is twice of the cavity frequency, in contrast to the quantum Rabi model where the quantum phase transition only emerges in the infinite frequency ratio. The quantum criticality of the Rabi-Stark model is then analyzed in terms of the energy gap, the order parameter, as well as the fidelity. The critical exponents are derived analytically. The finite size scaling analysis for the order parameter and the fidelity susceptibility is also performed. Several finite size exponents are then extracted from the universal scaling. The size independent energy gap exponent suggests the Rabi-Stark model and the quantum Rabi model are not in the same universality class, while the correlation length exponent could be the same with the specified definition of the effective system size.
We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr\'e model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generalized adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-Andr\'e model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-Andr\'e model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in the near future.
In this paper, we analyze the quantum criticality of the Rabi-Stark model at finite ratios of the qubit and cavity frequencies in terms of the energy gap and the order parameter, as well as the fidelity, if the Stark coupling strength is the same as the cavity frequency. The critical exponents are derived analytically. The energy gap and the length critical exponents are different from those in the quantum Rabi model and the Dicke model. A finite-size scaling analysis for the order parameter and the fidelity susceptibility is also performed. The universal scaling behaviors are demonstrated, and several finite-size exponents then can be extracted. Furthermore, universal critical behavior also can be established in terms of the bosonic Hilbert space truncation number, and the corresponding critical scaling exponents are found. Interestingly, the critical correlation length exponents in terms of the photonic truncation number as well as the equivalently effective length scales are different in the Rabi-Stark model and the quantum Rabi model, suggesting they belong to different universality classes. The second-order quantum phase transition is convincingly corroborated in the Rabi-Stark model at finite frequency ratios; by contrast, it emerges only at the infinite frequency ratio in the original quantum Rabi model without the Stark coupling.
We consider the Rabi Hamiltonian, which exhibits a quantum phase transition (QPT) despite consisting only of a single-mode cavity field and a two-level atom. We prove QPT by deriving an exact solution in the limit where the atomic transition frequency in the unit of the cavity frequency tends to infinity. The effect of a finite transition frequency is studied by analytically calculating finite-frequency scaling exponents as well as performing a numerically exact diagonalization. Going beyond this equilibrium QPT setting, we prove that the dynamics under slow quenches in the vicinity of the critical point is universal; that is, the dynamics is completely characterized by critical exponents. Our analysis demonstrates that the Kibble-Zurek mechanism can precisely predict the universal scaling of residual energy for a model without spatial degrees of freedom. Moreover, we find that the onset of the universal dynamics can be observed even with a finite transition frequency.
Abstract We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio η of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant phases are of second order relating to the spontaneous breaking of the discrete Z 2 symmetry. On the other hand, the quantum phase transition between the two different superradiant phases is discontinuous with a phase boundary line relating to the continuous U (1) symmetry. For a large enough but finite η , the scaling function and critical exponents are derived analytically and verified numerically, from which the universality class of the model is identified.
Quantum tricriticality, a unique form of high-order criticality, is expected to exhibit fascinating features including unconventional critical exponents and universal scaling laws. However, a quantum tricritical point (QTCP) is much harder to access, and the corresponding phenomena at tricriticality have rarely been investigated. In this study, we explore a tricritical quantum Rabi model, which incorporates a nontrivial parameter for adjusting the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of a first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analyses for quantum fluctuations and the mean photon number, universal critical exponents differentiate the QTCP from the second-order critical point. We find that the phase transition at the tricritical point goes beyond the conventional second-order phase transition. Our work explores an interesting direction in the generalization of the well-known Rabi model for the study of higher-order critical points due to its high control and tunability.