Chen Qing-Hu

Variational Path-Integral Study on Bound Polarons in Parabolic Quantum Dots and Wires

The expression of the ground-state energy of an electron coupled simultaneously with a Coulomb potential and a longitudinal-optical phonon field in parabolic quantum dots and wires is derived within the framework of Feynman variational path-integral theory. We obtain a general result with arbitrary electron-phonon coupling constant, Coulomb binding parameters, and confining potential strength, which could be used for further numerical calculation of polaron properties. Moreover, it is shown that all the previous path-integral formulae for free polarons, bound polarons, and polarons confined in parabolic quantum dots and wires can be recovered in the present formalism.

Second-order perturbative treatment for confined polarons in low-dimensional polar semiconductors

Within the framework of second-order Rayleigh-Schrodinger perturbation theory, the effects of the interaction of the electrons and longitudinal optical phonons in low-dimensional semiconducting heterostructures can be investigated in a unified way. As a result, the ground-state energy for polarons confined in a general potential can be explicitly expressed as a one-dimensional integral. Moreover, some interesting problems, such as those of polarons in quantum wells, quantum wires, and quantum dots, can be readily addressed just by taking different limits. Finally, in a general sense, it is shown on the basis of numerical calculations that the polaronic effect is enhanced with lowering dimensionality and increasing asymmetry.

Vacuum Rabi Splitting and Dynamics of the Jaynes—Cummings Model for Arbitrary Coupling

The effects of counter-rotating terms (CRTs) on Rabi splitting and the dynamic evolution of atomic population in the Jaynes—Cummings model are studied with a coherent-state approach. When the coupling strength increases, the Rabi splitting becomes of multi-Rabi frequencies for the initial state of an excited atom in a vacuum field, and the collapses and revivals gradually disappear, and then reappear with quite good periodicity. Without the rotating-wave approximation (RWA), the initial excited state contains many eigenstates rather than two eigenstates under the RWA, which results in the multi-peak emission spectrum. An analytical approximate solution for the strong coupling regime is obtained, which gives a new oscillation frequency and explains the recovery of collapses and revivals due to the equal energy spacing.

The Spectrum in Qubit-Oscillator Systems in the Ultrastrong Coupling Regime

Recent measurement on an LC resonator magnetically coupled to a superconducting qubit [Phys. Rev. Lett. 105 (2010) 237001] shows that the system operates in the ultra-strong coupling regime and crosses the limit of validity for the rotating-wave approximation of the Jaynes-Cummings model. By using extended bosonic coherent states, we solve the Jaynes—Cummings model exactly without using the rotating-wave approximation. Our numerically exact results for the spectrum of the flux qubit coupled to the LC resonator are fully consistent with the experimental observations. The smallest Bloch—Siegert shift obtained is consistent with that observed in this experiment. In addition, the Bloch—Siegert shifts in arbitrary level transitions and for arbitrary coupling constants are predicted.

Second-Order Phase Transition in the Two-Dimensional Classical Lattice Coulomb Gas of Half-Integer Charges

The second-order phase transition in the two-dimensional (2D) classical Coulomb gas of half-integer charges on a square lattice is investigated by using Monte Carlo simulations. Based on the finite-size scaling analysis, we estimate the second-order phase transition temperature Tc and the static critical exponents β and ν with a new numerical analysis method. More precise critical temperature Tc = 0.1311(2) and critical exponents β/ν = 0.1152(12) and ν = 0.857(15) are obtained. The estimated value of ν indicates that the charge lattice melting transition is different from the pure 2D Ising transition.

Ground-state description for polarons in parabolic quantum wells

Within the framework of Feynman-Haken variational path integral theory, for the first time, we calculate the ground-state energy of the electron and longitudinal-optical phonon system in parabolic quantum wells with respect to a general potential. We propose a simple expression for the Feynman energy, and compare it with those obtained by the second-order Rayleigh-Schrodinger perturbation theory and Landau-Pekar strong-coupling theory. It is shown both analytically and numerically that the results obtained from Feynman-Haken variational path integral theory can be better than those from the other two theories. We also find in numerical calculations that the binding energy of polarons becomes monotonically stronger as the effective well depth decreases in the whole coupling regime. More interestingly, the localization, which is caused by the effective potential, also can be perceived in the strong-coupling regime.

Quantum discord dynamics of two qubits in single-mode cavities

The dynamics of quantum discord for two identical qubits in two independent single-mode cavities and a common single-mode cavity are discussed. For the initial Bell state with correlated spins, while the entanglement sudden death can occur, the quantum discord vanishes only at discrete moments in the independent cavities and never vanishes in the common cavity. Interestingly, quantum discord and entanglement show opposite behavior in the common cavity, unlike in the independent cavities. For the initial Bell state with anti-correlated spins, quantum discord and entanglement behave in the same way for both independent cavities and a common cavity. It is found that the detunings always stabilize the quantum discord.

An effective approach for two-dimensional polarons in an asymmetric quantum dot

Within the framework of Feynman-Haken path integral theory, we calculate the ground-state energy of two-dimensional polarons in asymmetric quantum dots for arbitrary electron-phonon coupling constants. From a general three-dimensional Hamiltonian, some interesting problems, such as polarons in quasi-one-dimensional quantum wires and quasi-zero-dimensional asymmetric or symmetric quantum dots can be easily discussed only by taking different limit in the whole coupling regime. After the numerical calculation, we find that the relative polaronic correction increases monotonically with the decrease of effective dot size, and it becomes more pronounced with increasing dimension and asymmetry. Moreover, despite the insensitivity of relative polaronic enhancement to the variation of coupling constant at weak coupling, the correction is related to the coupling constant as the latter becomes larger.

A new variational calculation for N-dimensional polarons in the strong-coupling limit.

A novel variational approach is presented for the calculation of the ground-state energy of the polaron in arbitrary N dimensions in the strong-coupling limit. By using the phonon coherent state to represent the wavefunction of phonons, a self-consistent integro-differential equation for the electron wavefunction is derived. The calculated results of the ground-state energy for N = 1, 2 and 3 agree well with the best results in the literature. It is also found that, for arbitrary N, the present results are less than the Feynman path integral ones by small percentages. It is proposed that this approach should be universal for systems involving polarons in the strong-coupling regime.

Unified analytical treatments of qubit—oscillator systems

An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study qubit—oscillator systems analytically in a unified way. Many previous analytical treatments, such as generalized rotating-wave approximation (GRWA) [Phys. Rev. Lett. 99, 173601 (2007)] and an expansion in the qubit tunneling matrix element in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 (2010)] can be recovered straightforwardly within the present scheme. Moreover, further improving GRWA and the extension to the finite-bias case are implemented easily. The algebraic formulae for the eigensolutions are then derived explicitly and uniquely, which work well in a wide range of the coupling strengths, detunings, and static bias including the recent experimentally accessible parameters. The dynamics of the qubit for an oscillator in the ground state is also studied. At the experimentally accessible coupling regime, GRWA can always work well. When the coupling is enhanced to the intermediate regime, only the improving GRWA can give the correct description, while the result of GRWA shows strong deviations. The previous Van Vleck perturbation theory is not valid to describe the dynamics in the present-day experimentally accessible regime, except for the strongly biased cases.An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study qubit-oscillator systems analytically in an unified way. Many previous analytical treatments, such as generalized rotating-wave approximation (GRWA) [Phys. Rev. Lett. 99, 173601 (2007)] and an expansion in the qubit tunneling matrix element in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 (2010)] can be recovered straightforwardly in the present scheme. Moreover, further improving GRWA and extension to the finite-bias case are implemented easily. The analytical expressions are then derived explicitly and uniquely, which work well in a wide range of the coupling strengthes, detunings, and static bias including the recent experimentally accessible parameters.