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The externally-driven nonequilibrium dicke model

V. M. Bastidas

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

In this thesis, we study the nonequilibrium dynamics of the time dependent single mode Dicke model in the thermodynamic limit in the context of the Liouville-von Neumann canonical method. We report an exact solution for this model under a non-equilibrium situation, generated by time dependent control parameters. We compute the correlations: in the atom-field ground state by means of the density operator for the pure state of the universe, and the corresponding reduced density operator for the atoms when the field is in resonance with the atomic ensemble. We obtain a closed relationship between the correlations in the ground state, the localisation of the atom¿s Wigner function in phase space, and the localisation of the wave function of the universe. As a measure of bipartite entanglement, we calculate the linear entropy from which we study the atom-field entanglement dynamics. In particular, we find a strong relationship between the stability of the auxiliary dynamical parameters, the reported entanglement, and the dynamics of certain physical observables. Furthermore, we use the Liouville-von Neumann technique to study the influence of quantum and thermal fluctuations on the dynamics of the normal and the superradiant phase. In addition, we calculate the density matrix for the quantum mechanical evolution of an initial thermal equilibrium state in the case of an instantaneous atom-field coupling and time independent ω and ω0.

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We study the entanglement dynamics in the externally-driven single-mode Dicke model in the thermodynamic limit, when the field is in resonance with the atoms. We compute the correlations in the atoms-field ground state by means of the density operator that represents the pure state of the universe and the reduced density operator for the atoms, which results from taking the partial trace over the field coordinates. As a measure of bipartite entanglement, we calculate the linear entropy, from which we analyze the entanglement dynamics. In particular, we found a strong relation between the stability of the dynamical parameters and the reported entanglement.

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Abstract. We study the entanglement dynamics in the externally-driven single-mode Dicke model in the thermodynamic limit, when the field is in resonance with the atoms. We compute the correlations in the atoms-field ground state by means of the density operator that represents the pure state of the universe and the reduced density operator for the atoms, which results from taking the partial trace over the field coordinates. As a measure of bipartite entanglement, we calculate the linear entropy, from which we analyze the entanglement dynamics. In particular, we found a strong relation between the stability of the dynamical parameters and the reported entanglement. 1.

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Physical Review A•Apr 23, 2004•66 citations
In this thesis, we study the nonequilibrium dynamics of the time dependent single mode Dicke model in the thermodynamic limit in the context of the Liouville-von Neumann canonical method. We report an exact solution for this model under a non-equilibrium situation, generated by time dependent control parameters. We compute the correlations: in the atom-field ground state by means of the density operator for the pure state of the universe, and the corresponding reduced density operator for the atoms when the field is in resonance with the atomic ensemble. We obtain a closed relationship between the correlations in the ground state, the localisation of the atom¿s Wigner function in phase space, and the localisation of the wave function of the universe. As a measure of bipartite entanglement, we calculate the linear entropy from which we study the atom-field entanglement dynamics. In particular, we find a strong relationship between the stability of the auxiliary dynamical parameters, the reported entanglement, and the dynamics of certain physical observables. Furthermore, we use the Liouville-von Neumann technique to study the influence of quantum and thermal fluctuations on the dynamics of the normal and the superradiant phase. In addition, we calculate the density matrix for the quantum mechanical evolution of an initial thermal equilibrium state in the case of an instantaneous atom-field coupling and time independent ω and ω0.
We study the entanglement dynamics in the externally-driven single-mode Dicke model in the thermodynamic limit, when the field is in resonance with the atoms. We compute the correlations in the atoms-field ground state by means of the density operator that represents the pure state of the universe and the reduced density operator for the atoms, which results from taking the partial trace over the field coordinates. As a measure of bipartite entanglement, we calculate the linear entropy, from which we analyze the entanglement dynamics. In particular, we found a strong relation between the stability of the dynamical parameters and the reported entanglement.
Abstract. We study the entanglement dynamics in the externally-driven single-mode Dicke model in the thermodynamic limit, when the field is in resonance with the atoms. We compute the correlations in the atoms-field ground state by means of the density operator that represents the pure state of the universe and the reduced density operator for the atoms, which results from taking the partial trace over the field coordinates. As a measure of bipartite entanglement, we calculate the linear entropy, from which we analyze the entanglement dynamics. In particular, we found a strong relation between the stability of the dynamical parameters and the reported entanglement. 1.
The exact steady-state solution for the reduced atomic density operator for a model system of N identical two-level atoms confined to a single site (the Dicke model) and driven by a totally incoherent broad-band (chaotic) field is derived through the equivalent Fokker-Planck equation of the system. Steady-state values of the atomic observables, higher moments and atomic fluctuations are calculated for an arbitrary N and an arbitrary field strength. It is shown that when the chaotic field is a thermal (black-body) field the atomic system is driven into a steady relative occupation number that obeys the Boltzmann distribution law only for N=1. (The same result for N>1 atoms can be reached only if the cooperative interactions between the atoms are ignored.) In the thermodynamic limit N to infinity there is no critical behaviour in contrast to the resonant coherently driven case. It is also shown that semiclassical (direct) factorisation of the equations of motion does not lead to the correct results for the N to infinity limit of the exact quantum case. Within the exact theory numerical results for finite N (<or=100) are presented for the time-dependent expectation values of the atomic operators, the intensity and the intensity autocorrelation function. Superradiant pulses are emitted by N initially inverted atoms but as the incident intensity is increased this superradiant behaviour is obscured. The steady-state fluorescence spectrum is a single Lorentzian of width proportional to N in the weak-field case. In the strong-field case the spectrum is insensitive to the number of atoms and the result is similar to the one-atom situation. Photon bunching and antibunching effects are investigated for the weak- and strong-field limits. When the chaotic driving field is simply a single-mode thermal field the approach to atomic saturation is delayed in comparison with the case of the broad-band chaotic field.
We use the so-called Liouville--von Neumann (LvN) approach to study the nonequilibrium quantum dynamics of time-dependent second order phase transitions. The LvN approach is a canonical method that unifies the functional Schr\"odinger equation for the quantum evolution of pure states and the LvN equation for the quantum description of mixed states of either equilibrium or nonequilibrium. As nonequilibrium quantum mechanical systems we study a time-dependent harmonic and an anharmonic oscillator and find the exact Fock space and density operator for the harmonic oscillator and the nonperturbative Gaussian Fock space and density operator for the anharmonic oscillator. The density matrix and the coherent, thermal, and coherent-thermal states are found in terms of their classical solutions, for which the effective Hamiltonians and equations of motion are derived. The LvN approach is further extended to quantum fields undergoing time-dependent second order phase transitions. We study an exactly solvable model with a finite smooth quench and find the two-point correlation functions. Because of the spinodal instability of long wavelength modes, the two-point correlation functions lead to the t1/4{t}^{1/4}t1/4-scaling relation during the quench and the Cahn-Allen scaling relation t1/2{t}^{1/2}t1/2 after completion of the quench. Further, after the finite quench the domain formation shows a time-lag behavior at the cubic power of the quench period. Finally we study the time-dependent phase transition of a self-interacting scalar field.
Ground state properties and level statistics of the Dicke model for a finite number of atoms are investigated based on a progressive diagonalization scheme (PDS). Particle number statistics, the entanglement measure and the Shannon information entropy at the resonance point in cases with a finite number of atoms as functions of the coupling parameter are calculated. It is shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the quantum phase transition where the system is most chaotic. Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed. In addition, the quantum phase transition may be observed not only in the ground state mean photon number and the ground state atomic inversion as shown previously, but also in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.
The dynamical properties of quantum entanglement in the Dicke model without rotating-wave approximation are investigated in terms of the reduced-density linear entropy. The characteristic time of decoherence process in the early-time evolution is numerically obtained and it is shown that the characteristic time decreases as the coupling parameter increases. The mean entanglement, which is defined to be averaged over time, is employed to describe the influences of both quantum phase transition and corresponding classical chaos on the behavior of entanglement. For a given energy, initial conditions are taken to be minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. It is shown that the entanglement has a distinct change at the quantum phase transition, and that the entanglement for regular initial conditions is smaller than that for chaotic ones in the case of weak coupling, while it fluctuates with small amplitude in strong coupling and for chaotic initial conditions.