We demonstrate that two coupled Bose-Einstein condensates (BECs) at zero temperature can be used to realize a qubit which is the counterpart of Josephson charge qubits. The two BECs are weakly coupled and confined in an asymmetric double-well trap. When the ``charging energy'' of the system is much larger than the Josephson energy and the system is biased near a degeneracy point, the two BECs represent a qubit with two states differing only by one atom. The realization of the BEC qubits in realistic BEC experiments is briefly discussed.
We demonstrate that two coupled Bose-Einstein condensates (BECs) at zero temperature can be used to realize a qubit which is the counterpart of Josephson charge qubits. The two BECs are weakly coupled and confined in an asymmetric double-well trap. When the ``charging energy'' of the system is much larger than the Josephson energy and the system is biased near a degeneracy point, the two BECs represent a qubit with two states differing only by one atom. The realization of the BEC qubits in realistic BEC experiments is briefly discussed.
We study the coherence fluctuations in a Josephson junction created by two weakly coupled Bose-Einstein condensates. We apply the two-mode approximation in the full quantum theory analysis, and so that the system is described by a two-site Bose-Hubbard Hamiltonian. The coherence fluctuations are determined by the total number of particles N, charging energy EC, junction energy EJ, asymmetry δ and temperature T. For zero-temperature symmetric systems, the coherence fluctuations increase with EC/EJ, however, the number squeezing increases with N2EC/EJ. For zero-temperature asymmetric systems, the coherence fluctuations are suppressed by the balance effects between asymmetry and interparticle interaction and the single-atom resonance effects. The coherence fluctuations grow with temperature, and the formation of a self-trapping state will cause abnormal behaviors at high temperatures.
The subject of this work is the experimental implementation of a single bosonic Josephson junction and the discussion of the performed investigations. To generate this new kind of Josephson junction a 87-Rubidium Bose-Einstein condensate is split in a double well potential into two matter wave packets, which are coupled coherently to each other via quantum mechanical tunneling of atoms through the barrier. The state of the system can be described by two dynamical variables, the population imbalance of the two wells and their phase difference. The investigation of the dynamical response of the Josephson junction shows, that two dynamical regimes can be identified, the plasma oscillation regime, where atoms tunnel back and forth between the wells, and the self trapping regime, where no tunneling is found. Furthermore, the investigation at finite temperature reveals, that the relative phase in steady state is not locked to zero but fluctuates according to its temperature and the tunneling coupling. By measuring the fluctuations and calculating the tunneling coupling it is possible to deduce the temperature of the atomic cloud. With this a new method for thermometry is realized, which also works in a regime, where the standard methods can not be applied.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.
We discuss a laser-trapped cold-atom superfluid qubit system. Each qubit is proposed as a macroscopic two-state system based on a set of Bose-Einstein condensate (BEC) currents circulating in a ring, cut with a Josephson barrier. We review the effective low energy description of a single BEC ring. In particular, it is demonstrated that such system has a set of metastable current states which, for certain range of parameters, form an effective two-state system, or a qubit. We show how this qubit can be initialized and manipulated with currently available laser-trapping techniques. We also discuss mechanisms of coupling several such ring qubits as well as measuring individual qubit-ring systems.
We study the coherent atomic tunneling between two zero-temperature Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by a transfer matrix element, describe the dynamics in terms of the interwell phase difference and population imbalance. In addition to the anharmonic generalization of the familiar ac Josephson effect and plasma oscillations occurring in superconductor junctions, the nonlinear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel ``macroscopic quantum self-trapping'' effect.
Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.