A Lorentz-invariant look at quantum clock synchronization protocols based on distributed entanglement

Recent work has raised the possibility that quantum information theory techniques can be used to synchronize atomic clocks nonlocally. One of the proposed algorithms for quantum clock synchronization (QCS) requires distribution of entangled pure singlets to the synchronizing parties. Such remote entanglement distribution normally creates a relative phase error in the distributed singlet state which then needs to be purified asynchronously. We present a fully relativistic analysis of the QCS protocol which shows that asynchronous entanglement purification is not possible, and, therefore, that the proposed QCS scheme remains incomplete. We discuss possible directions of research in quantum information theory which may lead to a complete, working QCS protocol.Comment: 5 pages; typeset in RevTe

Measuring the temporal coherence of an atom laser beam

We report on the measurement of the temporal coherence of an atom laser beam extracted from a $^{87}$Rb Bose-Einstein condensate. Reflecting the beam from a potential barrier creates a standing matter wave structure. From the contrast of this interference pattern, observed by magnetic resonance imaging, we have deduced an energy width of the atom laser beam which is Fourier limited by the duration of output coupling. This gives an upper limit for temporal phase fluctuations in the Bose-Einstein condensate.Comment: 4 pages, 3 figure

Coherent Evolution of Bouncing Bose-Einstein Condensates

We investigate the evolution of Bose-Einstein condensates falling under gravity and bouncing off a mirror formed by a far-detuned sheet of light. After reflection, the atomic density profile develops splitting and interference structures which depend on the drop height, on the strength of the light sheet, as well as on the initial mean field energy and size of the condensate. We compare experimental results with simulations of the Gross-Pitaevski equation. A comparison with the behaviour of bouncing thermal clouds allows to identify quantum features specific for condensates.Comment: 4 page

On Multiparticle Entanglement via Resonant Interaction between Light and atomic Ensembles

Multiparticle entangled states generated via interaction between narrow-band light and an ensemble of identical two-level atoms are considered. Depending on the initial photon statistics, correlation between atoms and photons can give rise to entangled states of these systems. It is found that the state of any pair of atoms interacting with weak single-mode squeezed light is inseparable and robust against decay. Optical schemes for preparing entangled states of atomic ensembles by projective measurement are described.Comment: 11 pages, 1 figure, revtex

Cooling the Collective Motion of Trapped Ions to Initialize a Quantum Register

We report preparation in the ground state of collective modes of motion of two trapped 9Be+ ions. This is a crucial step towards realizing quantum logic gates which can entangle the ions' internal electronic states. We find that heating of the modes of relative ion motion is substantially suppressed relative to that of the center-of-mass modes, suggesting the importance of these modes in future experiments.Comment: 5 pages, including 3 figures. RevTeX. PDF and PostScript available at http://www.bldrdoc.gov/timefreq/ion/qucomp/papers.htm . final (published) version. Eq. 1 and Table 1 slightly different from original submissio

Experimental observation of the Bogoliubov transformation for a Bose-Einstein condensed gas

Phonons with wavevector $q/\hbar$ were optically imprinted into a Bose-Einstein condensate. Their momentum distribution was analyzed using Bragg spectroscopy with a high momentum transfer. The wavefunction of the phonons was shown to be a superposition of +q and -q free particle momentum states, in agreement with the Bogoliubov quasiparticle picture.Comment: 4 pages, 3 figures, please take postscript version for the best version of Fig

Purifying two-bit quantum gates and joint measurements in cavity QED

Using a cavity QED setup we show how to implement a particular joint measurement on two atoms in a fault tolerant way. Based on this scheme, we illustrate how to realize quantum communication over a noisy channel when local operations are subject to errors. We also present a scheme to perform and purify a universal two-bit gate.Comment: 4 pages RevTeX, 2 figures include

Theory of four-wave mixing of matter waves from a Bose-Einstein condensate

A recent experiment [Deng et al., Nature 398, 218(1999)] demonstrated four-wave mixing of matter wavepackets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this description to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.Comment: 18 pages Revtex preprint form, 13 eps figure

Scheme for the preparation of the multi-particle entanglement in cavity QED

Here we present a quantum electrodynamics (QED) model involving a large-detuned single-mode cavity field and $n$ identical two-level atoms. One of its applications for the preparation of the multi-particle states is analyzed. In addition to the Greenberger-Horne-Zeilinger (GHZ) state, the W class states can also be generated in this scheme. The further analysis for the experiment of the model of $n=2$ case is also presented by considering the possible three-atom collision.Comment: 5 Pages, 1 Figure. Minor change

Generic entanglement generation, quantum statistics and complementarity

A general and an arbitrarily efficient scheme for entangling the spins (or any spin-like degree of freedom) of two independent uncorrelated identical particles by a combination of two particle interferometry and which way detection is formulated. It is shown that the same setup could be used to identify the quantum statistics of the incident particles from either the sign or the magnitude of measured spin correlations. Our setup also exhibits a curious complementarity between particle distinguishability and the amount of generated entanglement.Comment: To appear in Phys. Rev. Let