We consider two two-level atoms interacting collectively with all the modes of the quantum electromagnetic field. The center-of-mass motion of each atom is quantized in three dimensions and each atom is placed in a harmonic oscillator potential. We describe a method that factorizes an approximate density operator of the two atoms in parts which evolve under different portions of the Hamiltonian. We apply this method to the system under consideration to study the effect of the uncertainty in the position of the atoms on the dissipation rates and on the entanglement between the internal degrees of freedom of the two atoms. We find that the uncertainty in position can give rise to smaller dissipation rates. This in turn affects the entanglement which may decay exponentially with smaller decay rates or may even decay asymptotically by a power law.
We consider two two-level atoms interacting collectively with all the modes of the quantum electromagnetic field. The center-of-mass motion of each atom is quantized in three dimensions and each atom is placed in a harmonic oscillator potential. We describe a method that factorizes an approximate density operator of the two atoms in parts which evolve under different portions of the Hamiltonian. We apply this method to the system under consideration to study the effect of the uncertainty in the position of the atoms on the dissipation rates and on the entanglement between the internal degrees of freedom of the two atoms. We find that the uncertainty in position can give rise to smaller dissipation rates. This in turn affects the entanglement which may decay exponentially with smaller decay rates or may even decay asymptotically by a power law.
An approximate solution is given for the interaction of a set of A two-level atoms with a single mode of a quantized radiation field when the field is damped by a reservoir at zero temperature. Assuming that the average photon number is much larger than the number of atoms, we study the influence of dissipation on the approximate factorization of the density matrix. For realistic values of the parameters, the factorization survives under the presence of field damping. The main effect of dissipation is an exponential decay of the average photon number and a loss of coherence among the different factorized states. The influence of field dissipation on the atomic inversion, purity, and field squeezing are studied.
Throughout this project, the case of a composite system formed by a harmonic oscillator and a two-state atom will be studied; considering both affect each other as \na consequence of a Jaynes-Cummings interaction, and being both coupled to different reservoirs that are assumed to be independent from each other. The effects \nof the decoherence in the evolution of the populations and coherences will be analyzed; specifically the energy dissipation and the coherence loss, as well as the stationary states and the relevance of the Jaynes-Cummings interaction. Finally, the \nsolution of stochastic equations will be analyzed, particularly the evolution of the \nexpectation value of the position operator for the harmonic oscilator; for the case of \nsimultaneous measurements in both subsystems, as well as for a measurement in \nthe harmonic oscillator when the two-state atom undergoes a decoherence process.
In this paper, we analyzed squeezing in the information entropy, quantum state fidelity, and qubit-qubit entanglement in a time-dependent system. The proposed model consists of two qubits that interact with a two-mode electromagnetic field under the dissipation effect. An analytical solution is calculated by considering the constants for the equations of motion. The effect of the general form of the time-dependent for qubit-field coupling and the dissipation term on the temporal behavior of the qubit-qubit entanglement, quantum state fidelity, entropy, and variance squeezing are examined. It is shown that the intervals of entanglement caused more squeezing for the case of considering the time-dependent parameters. Additionally, the entanglement between the qubits became more substantial for the case of time dependence. Fidelity and negativity rapidly reached the minimum values by increasing the effect of the dissipation parameter. Moreover, the amount of variance squeezing and the amplitude of the oscillations decreased considerably when the time dependence increased, but the fluctuations increased substantially. We show the relation between entropy and variance squeezing in the presence and absence of the dissipation parameter during the interaction period. This result enables new parameters to control the degree of entanglement and squeezing, especially in quantum communication.
The link of two concepts, indistinguishability and entanglement, with the energy-time uncertainty principle is demonstrated in a system composed of two strongly coupled bosonic modes. Working in the limit of a short interaction time, we find that the inclusion of the antiresonant terms to the coupling Hamiltonian leads the system to relax to a state which is not the ground state of the system. This effect occurs passively by just presence of the antiresonant terms and is explained in terms of the time-energy uncertainty principle for the simple reason that at a very short interaction time, the uncertainty in the energy is of order of the energy of a single excitation, thereby leading to a distribution of the population among the zero, singly and doubly excited states. The population distribution, correlations, and entanglement are shown to substantially dependent on whether the modes decay independently or collectively to an exterior reservoir. In particular, when the modes decay independently with equal rates, entanglement with the complete distinguishability of the modes is observed. The modes can be made mutually coherent if they decay with unequal rates. However, the visibility in the single-photon interference cannot exceed 50. When the modes experience collective damping, they are indistinguishable even if decay with equal rates and the visibility can, in principle, be as large as unity. We find that this feature derives from the decay of the system to a pure entangled state rather than the expected mixed state. When the modes decay with equal rates, the steady-state values of the density matrix elements are found dependent on their initial values.
We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance x21. We obtain collective decaying states, belonging to a complex spectral representation of the Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and the real parts give the average energy of the collective states. In one dimension there is strong interference between the fields emitted by the atoms, producing cooperative effects even when the atoms are far apart. The decay rates and the energy oscillate with the distance x21. Depending on x21, the decay rates will either decrease, vanish, or increase as compared with the one-atom decay rate. We have sub- and superradiance at periodic intervals. Our model may be used to study two-cavity electron waveguides. The vanishing of the collective decay rates then suggests the possibility of obtaining stable configurations, where an electron is trapped inside the two cavities.
The entanglement between two Λ-type three-level atoms interacting with coherent field in a dissipative cavity is investigated by means of the entanglement degree of quantum conditional entropy.A solution of the master equation is obtained by super operator method.The authors discuss the entanglement between the two atoms based on two kinds of different initial states(|ψa(0),|Φa(0)) and analyze the influence of decay coefficient of the cavity and mean photon number of the field on entanglement degree.In conclusion,when the atoms are initially in entangled state |ψa(0),the evolution of the entanglement degree depends on decay coefficient of the cavity and intensity of the field.If there is absence of dissipation,the entanglement degree evolves periodically;otherwise,the entanglement degree decays sharply and approaches a stable value.The weaker the intensity of the field is,the greater the stable value becomes.The greater the decay coefficient is,the faster it reaches the stable value.But for the other initial entangled state |Φa(0),the entanglement between the two atoms doesn't evolve with the time.It implies that the entangled state |Φa(0) can be preserved in such a dissipative system.