Weak force detection using a double Bose-Einstein condensate

A Bose-Einstein condensate may be used to make precise measurements of weak forces, utilizing the macroscopic occupation of a single quantum state. We present a scheme which uses a condensate in a double well potential to do this. The required initial state of the condensate is discussed, and the limitations on the sensitivity due to atom collisions and external coupling are analyzed.Comment: 12 pages, 2 figures, Eq.(41) has been correcte

Interference between the halves of a double-well trap containing a Bose-Einstein condensate

Interference between the halves of a double-well trap containing a Bose-Einstein condensate is studied. It is found that when the atoms in the two wells are initially in the coherent state, the intensity exhibits collapses and revivals, but it does not for the initial Fock states. Whether the initial states are in the coherent states or in a Fock states, the fidelity time has nothing to do with collision. We point out that interference and its fidelity can be adjusted experimentally by properly preparing the number and initial states of the system.Comment: 10 pages, 3 figures, accepted by Phy. rev.

Dissipative Dynamics of a Josephson Junction In the Bose-Gases

The dissipative dynamics of a Josephson junction in the Bose-gases is considered within the framework of the model of a tunneling Hamiltonian. The effective action which describes the dynamics of the phase difference across the junction is derived using functional integration method. The dynamic equation obtained for the phase difference across the junction is analyzed for the finite temperatures in the low frequency limit involving the radiation terms. The asymmetric case of the Bose-gases with the different order parameters is calculated as well

Testing Broken U(1) Symmetry in a Two-Component Atomic Bose-Einstein Condensate

We present a scheme for determining if the quantum state of a small trapped Bose-Einstein condensate is a state with well defined number of atoms, a Fock state, or a state with a broken U(1) gauge symmetry, a coherent state. The proposal is based on the observation of Ramsey fringes. The population difference observed in a Ramsey fringe experiment will exhibit collapse and revivals due to the mean-field interactions. The collapse and revival times depend on the relative strength of the mean-field interactions for the two components and the initial quantum state of the condensate.Comment: 20 Pages RevTex, 3 Figure

Persistent currents in a circular array of Bose-Einstein condensates

A ring-shaped array of Bose-Einstein condensed atomic gases can display circular currents if the relative phase of neighboring condensates becomes locked to certain values. It is shown that, irrespective of the mechanism responsible for generating these states, only a restricted set of currents are stable, depending on the number of condensates, on the interaction and tunneling energies, and on the total number of particles. Different instabilities due to quasiparticle excitations are characterized and possible experimental setups for testing the stability prediction are also discussed.Comment: 7 pages, REVTex

Barrier effects on the collective excitations of split Bose-Einstein condensates

We investigate the collective excitations of a single-species Bose gas at T=0 in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider onedimensional potentials consisting of two harmonic wells separated a distance 2 z_0, since they essentially contain all the barrier effects that one may visualize in the 3D situation. We find, within a hydrodynamic approximation, that regardless the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighbouring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results of exactly solving the time-dependent Gross-Pitaevskii equation. We analyze as well the characteristics of the spatial pattern of excitations of threedimensional boson systems according to the amount of splitting of the condensate.Comment: RevTeX, 12 pages, 13 ps figure

Macroscopic Quantum Fluctuations in the Josephson Dynamics of Two Weakly Linked Bose-Einstein Condensates

We study the quantum corrections to the Gross-Pitaevskii equation for two weakly linked Bose-Einstein condensates. The goals are: 1) to investigate dynamical regimes at the borderline between the classical and quantum behaviour of the bosonic field; 2) to search for new macroscopic quantum coherence phenomena not observable with other superfluid/superconducting systems. Quantum fluctuations renormalize the classical Josephson oscillation frequencies. Large amplitude phase oscillations are modulated, exhibiting collapses and revivals. We describe a new inter-well oscillation mode, with a vanishing (ensemble averaged) mean value of the observables, but with oscillating mean square fluctuations. Increasing the number of condensate atoms, we recover the classical Gross-Pitaevskii (Josephson) dynamics, without invoking the symmetry-breaking of the Gauge invariance.Comment: Submitte

Quantum Cryptography Using Single Particle Entanglement

A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.Comment: 4 pages, 3figures, revte

Robustness of nonclassical superpositions states against decoherence

We make a comparative study of quadrature squeezing, photon-number distribution and Wigner function in a decayed quantum system. Specifically, for a field mode prepared initially in cat states interacting with a zero-temperature environment, we show that the rate of reduction of the nonclassical effects in this system is proportional to the occurrence of the decoherence process.Comment: 11 pages, 4 figure

Bose-Einstein condensates in a one-dimensional double square well: Analytical solutions of the Nonlinear Schr\"odinger equation and tunneling splittings

We present a representative set of analytic stationary state solutions of the Nonlinear Schr\"odinger equation for a symmetric double square well potential for both attractive and repulsive nonlinearity. In addition to the usual symmetry preserving even and odd states, nonlinearity introduces quite exotic symmetry breaking solutions - among them are trains of solitons with different number and sizes of density lumps in the two wells. We use the symmetry breaking localized solutions to form macroscopic quantum superpositions states and explore a simple model for the exponentially small tunneling splitting.Comment: 11 pages, 11 figures, revised version, typos and references correcte