K.L. Liu

Exact eigenstates of the intensity-dependent Jaynes–Cummings model with the counter-rotating term

We have investigated the eigenenergy spectrum of the intensity-dependent Jaynes–Cummings (JC) model with and without the rotating-wave approximation (RWA). Our analysis has indicated that the counter-rotating term dramatically changes the nature of the RWA energy spectrum and that the non-RWA spectrum can be approximated by the RWA spectrum only in the range of a sufficiently small coupling constant. Furthermore, the intensity-dependent JC model without the RWA is well defined only if the coupling parameter is below a certain critical value. As a result, the dynamics of the intensity-dependent JC model without the RWA is significantly different from its RWA counterpart. For instance, the counter-rotating term can dramatically enhance the field squeezing effect. Furthermore, we believe that our results are of immediate relevance to the system of a trapped and laser-irradiated ion, which has been shown to exhibit an intensity-dependent JC dynamics recently.

A study of the Fokker–Planck equation of bistable systems by the method of state-dependent diagonalization

We study the Fokker–Planck equation of one-dimensional bistable systems with symmetric as well as asymmetric potentials. In this work, the method of state-dependent diagonalization (SDD) is proposed for solving the eigenvalue problem of the associated Schrodinger equation. The example of a quartic bistable potential is used to illustrate its validity. Unlike the conventional exact diagonalization, the SDD method is found to be quite efficient for the high eigenstates. We use the eigenfunctions and eigenvalues obtained by this method to calculate the propagator, the spectral density of the autocorrelation function, and the response of the system to a weak periodic driving force for various noise intensities. The asymmetry of the potential is found to play an important role, and it strongly influences the signal-to-noise ratio.

The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms

In this paper we have investigated the eigen energy spectrum of the k-photon intensity-dependent Jaynes–Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis shows that for k⩾2 the k-photon intensity-dependent JC model without the RWA does not have eigenstates in the Hilbert space spanned by the photon number states, i.e. the model becomes ill-defined. Hence, the k-photon intensity-dependent JC model without the RWA is qualitatively different from the RWA counterpart which is valid for all values of k and the coupling parameter. As a consequence, previous studies of the effects of the counterrotating terms in the k-photon intensity-dependent JC model for k⩾2 are all invalid.

Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term

Abstract:We have investigated the eigenenergy spectrum of the two-photon Jaynes-Cummings (JC) model with and without the rotating-wave approximation (RWA). Our analysis has indicated that the counter-rotating term dramatically changes the nature of the RWA energy spectrum and that the non-RWA spectrum can be approximated by the RWA spectrum only in the range of a sufficiently small coupling constant. Furthermore, unlike the one-photon counterpart, the two-photon JC model without the RWA is well defined only if the coupling parameter is below a certain critical value. As a result, the dynamics of the two-photon JC model without the RWA is significantly different from its RWA counterpart. For instance, the counter-rotating term can dramatically enhance the field squeezing effect. Besides, we would expect that the quantum dynamics of the two-photon JC model without the RWA is qualitatively different from that of the usual one-photon case.

Coherent stochastic resonance in a sextic double-well potential

We study the response of a stochastic system described by the one-dimensional Fokker–Planck equation with a sextic double-well potential U6(x)=(−c4x4+c6x6) to a weak sinusoidal periodic signal. Two types of boundary conditions have been investigated: (i) absorbing boundary conditions, and (ii) natural boundary conditions. The unperturbed propagators are calculated by the eigenfunction-expansion method. We find that for case (i), the mean survival time shows the coherent stochastic resonance, and for case (ii), the signal-to-noise ratio exhibits the stochastic resonance. The results are compared with those of the bistable quartic double-well potential U4(x)=(−12x2+14x4).

Statistical mechanics of nonlinear Klein–Gordon chains: the φ8-chain and the Gaussian double-well model

We study the statistical mechanics of two models of nonlinear Klein–Gordon chain: the ‘φ8-chain’ with the single-site potential v(y)=a(y2−1)4, and the Gaussian double-well model with v(y)=12ky2+bexp(−12cy2) where a,b,c and k are positive constants. The thermodynamics of the classical chains is investigated by the transfer-integral equation technique and the pseudo-Schrodinger equation approximation. The results for the heat capacity, the displacement correlation function, and the wave-vector-dependent susceptibility are compared with those of the familiar φ4-chain. The partition functions of the quantum chains are calculated by the low-coupling effective potential method. The effects of quantum fluctuations on the low-temperature heat capacity are examined.

The multiquantum q-deformed Jaynes–Cummings model with the counter-rotating terms

In this paper we have investigated the eigenenergy spectrum of the k-quantum q-deformed Jaynes–Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis has shown that the k-quantum q-deformed JC model without the RWA does not have eigenstates in the Hilbert space spanned by the photon number states, i.e. the model becomes ill-defined. Hence, the k-quantum q-deformed JC model without the RWA is qualitatively different from the RWA counterpart which is valid for all values of k and the coupling parameter. In other words, the counter-rotating terms do drastically alter the nature of the system.

Is there a spontaneous breaking of the parity symmetry of the Jaynes - Cummings model without the rotating-wave approximation?

Recently, Bishop and co-workers (1996 Phys. Rev. A 54 R4657) applied the coupled-cluster method to study the ground state of the Jaynes - Cummings model without the rotating-wave approximation and reported strong evidence for a second-order quantum phase transition which was believed to be caused by spontaneous breaking of the parity symmetry of the system. In the present work we have re-investigated this conjecture via examining the nature of the exact (numerical) ground state of the system. Our analysis has indicated that the ground state has definite positive parity and there is no spontaneous breaking of the parity symmetry of the system.