We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of ato...We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.展开更多
Out-of-time-ordered correlation(OTOC)functions have been used as an indicator of quantum chaos in a lot of physical systems.In this work,we numerically demonstrate that zero temperature OTOC can detect quantum phase t...Out-of-time-ordered correlation(OTOC)functions have been used as an indicator of quantum chaos in a lot of physical systems.In this work,we numerically demonstrate that zero temperature OTOC can detect quantum phase transition in the anisotropic Dicke model.The phase diagram is given with OTOC.The finite-size effect is studied.Finally,the temperature effect is discussed.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12135003)。
文摘We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.
文摘Out-of-time-ordered correlation(OTOC)functions have been used as an indicator of quantum chaos in a lot of physical systems.In this work,we numerically demonstrate that zero temperature OTOC can detect quantum phase transition in the anisotropic Dicke model.The phase diagram is given with OTOC.The finite-size effect is studied.Finally,the temperature effect is discussed.
