We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states. Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence is analysed.
We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states. Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence is analysed.
We analyse the effects of intrinsic decoherence on the probability of generating a tripartite GHZ state using a cool trapped ion coupled to a single mode of the cavity field and interacting with a resonant laser field. Milburn equation is solved for this tripartite system to obtain the time evolution of density matrix as a function of cavity-ion coupling, laser-ion coupling, and the size of unitary time step relative to the time scale determined by system parameters. Starting with the system prepared initially in a separable state, density matrix is used to calculate the probability of tripartite GHZ state generation using coupling strengths reported in a recent experiment.
Maximally entangled states are of utmost importance to quantum communication, dense coding, and quantum teleportation. With a trapped ion placed inside a high finesse optical cavity, interacting with field of an external laser and quantized cavity field, a scheme to generate a maximally entangled three qubit GHZ state, is proposed. The dynamics of tripartite entanglement is investigated, using negativity as an entanglement measure and linear entropy as a measure of mixedness of a state. It is found that (a) the number of modes available to the subsystem determines the maximum entanglement of a subsystem, (b) at entanglement maxima and minima, linear entropy and negativity uniquely determine the nature of state, but the two measures do not induce the same ordering of states, and (c) for a special choice of system parameters maximally entangled tripartite two mode GHZ state is generated. The scheme presented for GHZ state generation is a single step process and is reduction-free.
We analyse the effects of intrinsic decoherence on the probability of generating a tripartite GHZ state using a cool trapped ion coupled to a single mode of the cavity field and interacting with a resonant laser field. Milburn equation is solved for this tripartite system to obtain the time evolution of density matrix as a function of cavity-ion coupling, laser-ion coupling, and the size of unitary time step relative to the time scale determined by system parameters. Starting with the system prepared initially in a separable state, density matrix is used to calculate the probability of tripartite GHZ state generation using coupling strengths reported in a recent experiment.
It is not always justified to model the environment of a realistic quantum system as a collection of harmonic oscillators or two-level systems. To explore interesting physics associated with a composite environment, here we study the dynamics of a qubit coupled to a second two-level system, which is in turn coupled to a harmonic-oscillator bath. That is, the qubit of interest is in the presence of a composite environment consisting of the second two-level system and a conventional harmonic-oscillator bath. We investigate the issue of pointer states of decoherence for the qubit for different coupling strengths between the qubit and such a composite environment. It is shown that for weak-, intermediate-, or strong-coupling strengths, the qubit's reduced density matrix has a coupling-strength-dependent diagonal representation, thus yielding coupling-strength-dependent computational pointer states. Interestingly, the associated decoherence rate can decrease as the coupling strength increases.
Quantum entanglement is one of most remarkable features of quantum mechanics,and in recent years it has played a more and more important role in quantum information.However,real quantum system inevitably interacts with the environment,resulting in the entanglement decay or even entanglement sudden death,so it is necessary to study the entanglement dynamical properties of an open system under different environments.In this paper,we investigate the entanglement dynamic behaviors of three interacting two-level atoms in an optical cavity which is coupled to a structured zero-temperature bosonic reservoir.Laplace transform,LBC and other methods are utilized,through numerical method we analyze the entanglement dynamic behavios of tripartite of three atoms and bipartite of cavity and reservoir.We also discuss how the coupling parameters affect the entanglement dynamics.Results show that in a short time,the entanglement of tripartite increases with coupling strength of three atoms increasing,and a periodic oscillation appears, but entanglement of bipartite decreases.The entanglement of tripartite decreases with the coupling strength between atoms and cavity increasing and damping oscillation appears,but the entanglement of bipartite increases.In a long-time limit,the entanglement approaches to a steady value.The non-Markovian dynamics of the qubits is determined by both the coupling strength and the spectral width.The strong system-reservoir coupling regime results in the non-Markovian dynamics of system.As the spectral width increases,the system of three atoms transforms from non-Markovian regime to Markovian regime.The increasing of spectral width results in the Markovian dynamic behavior of system,but the system of the atoms falls into the non-Markovian regime once more.When the coupling between the cavity and reservoir is weak,the entanglement of three atoms increases as the detuning of the cavity and reservoir increases,but it is not obvious.When the coupling between the cavity and reservoir is strong,the entanglement of three atoms increases and a periodic oscillation appears with increasing the detuning between the cavity and reservoir,so we can effectively restrain the effects of dissipation of reservoir on entanglement decay by adjusting the detuning between the cavity and reservoir.
A scheme to generate three qubit maximally entangled W-states, using three trapped ions interacting with the red sideband tuned single-mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating the three-ion W-state is calculated. By using the ion-cavity coupling strengths achieved in experimental realizations, the interaction time needed for W-state generation is found to be of the order of 10 µs. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by an appropriate choice of the initial-state phonon number. The ionic qubits in the W-like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial K -way negativities ( K = 2 to 4) are obtained to study the evolution of entanglement distribution as a function of the interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of the interaction parameter, the three ions and photon–phonon system are found to have 4-partite entanglement, generated by 2-way and 3-way correlations.