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Acta Sinica Quantum Optica

The Dissipative Properties of Josephson Charge Qubit

Ji Ying

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Beginning with two different initial states for the bath modes(equilibrium states and number states),time evolution of Josephson charge quantum bit linearly coupled to a heat bath is investigated thoroughly.The couclusion shows: if the bath modes are initially in number states,then decay time of turnable operator is longer and asymptotical value of population operator is smaller than that if the equilibrium states are at high temperature.The dynamic properties of the charge quantum bit are not related to initial states if the bath mode are at low temperature.

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Beginning with two different initial states for the bath modes(equilibrium states and number states),time evolution of Josephson charge quantum bit linearly coupled to a heat bath is investigated thoroughly.The couclusion shows: if the bath modes are initially in number states,then decay time of turnable operator is longer and asymptotical value of population operator is smaller than that if the equilibrium states are at high temperature.The dynamic properties of the charge quantum bit are not related to initial states if the bath mode are at low temperature.
Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.
We investigate the effect of dissipation in a Bose Josephson junction (BJJ) coupled to bath of bosons at two sites as an application of the generalized spin-boson model. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within Holstein-Primakoff approximation, which exhibits vanishing of energy gap and enhanced quantum fluctuations at the critical coupling. We study the dynamics of BJJ using time-dependent variational method and analyze stability of different types of steady states. As a special case, we study in details the phase space dynamics of BJJ coupled to a single-mode, which reveals diffusive and incoherent behaviour with increasing coupling to the bath mode. The dynamical steady states corresponding to the Pi-oscillation and self-trapped state become unstable in the region where their oscillation frequencies are in resonance with the bath modes. We investigate the time evolution of number imbalance and relative phase in presence of Ohmic bath with Gaussian noise to incorporate thermal fluctuations. Apart from the damping of Josephson oscillations and transition to symmetry broken state for strong coupling, we observe the decay of Pi-oscillation and self-trapped state to the ground state as a result of dissipation. Variation of phase fluctuation with temperature of the bath shows similar behaviour as observed in the experiments.
We investigate the dynamics of a quantum particle coupled to a boson heat bath. Using a real-time path-integral formalism, we obtain the Wigner distribution of the particle in the form of a power series in the strength of the anharmonicity V0{V}_{0}V0​. This series is shown to converge for all V0{V}_{0}V0​ when t is fixed and for small V0{V}_{0}V0​ uniformly in t. The latter proves the convergence to equilibrium for small anharmonicities. The effects of initial conditions on the evolution are studied by explicitly considering two types of initial states: product states and mixed Gibbs states. We show that in certain cases the evolution of the mixed states which avoid many pathologies of the product states, arising from the removal of the cutoff on the frequency distribution of the bath, can be related to that of product states when the latter are started at t=-\ensuremath{\infty}. We also solve exactly a simple stationary nonequilibrium model, a harmonic system in contact with two thermal baths, and derive an alternative criterion for a practically useful quasiclassical approximation. Finally, some connections to the Josephson junction are discussed. These include (a) the Green-Kubo-Einstein relation between the mobility and the diffusion constant of the washboard potential and (b) the time evolution of a rf superconducting quantum interference device.
We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to baths of bosons at its two sites. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within a Holstein-Primakoff approximation, which exhibits vanishing of the energy gap and enhanced quantum fluctuations at the critical point. We study the dynamics of BJJ using a time-dependent variational method and analyze stability of different types of steady states. As a special case we study in detail the phase space dynamics of BJJ coupled to a single mode, which reveals diffusive and incoherent behavior with increasing coupling to the bath mode. The dynamical steady states corresponding to the π oscillation and self-trapped state become unstable when their oscillation frequencies are in resonance with the bath modes. We study the Josephson dynamics in the presence of an Ohmic bath with Gaussian noise to incorporate the thermal fluctuations and obtain the Josephson oscillation frequency and damping analytically. We also observe the transition to the symmetry-broken state for strong coupling as well as decay of π oscillation and a self-trapped state to the ground state due to dissipation. Variation of the phase fluctuation with temperature of the bath shows similar behavior as observed in experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ.
We consider a model which consists of two coupled superconducting charge qubits by sharing a large Josephson junction. The time evolution of entanglement between two Josephson charge qubits is investigated by employing the concurrence. We examine the influence of the initial mean photon number, the relative phase and the amplitude of the two qubits on the time evolution of entanglement. The results show that the initial mean photon number, the relative phase and the amplitude of the two qubits play an important role in the evolution of entanglement.