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Journal of Physics B Atomic Molecular and Optical Physics

Establishment of phase between coupled Bose-Einstein condensates

Jacob Dunningham, Keith R. Burnett

Published Sep 14, 2000• 21 citations
Publisher

Abstract

We study how phase information is developed and transferred between Bose-Einstein condensates. First, we investigate how the phase of an output pulse of an idealized atom laser can be controlled. We then use quantum simulations to show how a relative phase between coupled systems is established by dissipation and atomic interactions. Our simulations show that each realization settles to the same relative phase between modes: for uncoupled systems the phase varies from realization to realization. We use this to demonstrate how condensates may `naturally' possess a relative phase, and to explain the phase-locking mechanism in a recent experimental demonstration of a mode-locked atom laser.

DOI
10.1088/0953-4075/33/19/301

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We study how phase information is developed and transferred between Bose-Einstein condensates. First, we investigate how the phase of an output pulse of an idealized atom laser can be controlled. We then use quantum simulations to show how a relative phase between coupled systems is established by dissipation and atomic interactions. Our simulations show that each realization settles to the same relative phase between modes: for uncoupled systems the phase varies from realization to realization. We use this to demonstrate how condensates may `naturally' possess a relative phase, and to explain the phase-locking mechanism in a recent experimental demonstration of a mode-locked atom laser.
We consider a possible technique for mode-locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to \hbar/2. It emerges naturally, when the condensate is stirred at the soliton velocity, and subsequently outcoupled with a periodic Raman pulse-train. The result is a replicating coherent field inside the atom laser. We give a numerical demonstration of the generation and stabilization of the soliton.
Motivated by a recent experiment [Chikkatur et al., Science, 296, 2193 (2002)] on the merging of atomic condensates, we investigate how two independent condensates with random initial phases can develop a unique relative phase when we move them together. In the adiabatic limit, the uniting of independent condensates can be understood from the eigenstate evolution of the governing Hamiltonian, which maps degenerate states (corresponding to fragmented condensates) to a single state (corresponding to a united condensate). In the nonadiabatic limit corresponding to the practical experimental configurations, we give an explanation on why we can still obtain a large condensate fraction with a unique relative phase. Detailed numerical simulations are then performed for the nonadiabatic merging of the condensates, which confirm our explanation and qualitative estimation. The results may have interesting implications for realizing a continuous atom laser based on the merging of condensates.
The introduction of a steady-state spatially periodic Raman coupling between two components of an ultracold atomic gas produces a dressed-state gas with an anisotropic and tunable dispersion relation. A Bose-Einstein condensate (BEC) formed in such a gas is consequently characterized by an anisotropic superfluid critical velocity. The anisotropic dissipation of superfluid flow is quantified by considering the scattering of impurities flowing through this superfluid. A gradual transition from the isotropic nature of an uncoupled BEC to the anisotropic periodically-dressed condensate is obtained as the strength of the Raman coupling is varied. These results present a clear signature for future experimental realizations of this novel superfluid.
We have measured the relative phase of two Bose-Einstein condensates using a time-domain, separated-oscillatory-field condensate interferometer. A single two-photon coupling pulse prepares the double-condensate system with a well-defined relative phase; at a later time, a second pulse reads out the phase difference accumulated between the two condensates. We find that the accumulated phase difference reproduces from realization to realization of the experiment, even after the individual components have separated spatially and their relative center-of-mass motion has damped.
The recent experimental advances in the field of quantum spin materials have led to well-controlled systems which can be used in order to simulate complex quantum models in a clean fashion. Here we discuss how fascinating effects normally known from bosonic systems such as the Bose-Einstein condensation can be investigated with the help of such materials. We discuss as an example how a crossover between an effectively one-dimensional geometry described by a Luttinger liquid to a three-dimensional Bose-Einstein condensation can be induced. Additionally, we point out how more complex phases as the Bose-glass phase could be realized in these quantum magnets. Introduction Although it can seem paradoxical, the quantum magnetic states found in insulators offer an interesting route to study Bose-Einstein condensation (BEC) and more generally phenomena related to itinerant, interacting bosonic systems. In many materials, the repulsion between the electrons causes the ground state to be a Mott insulator with one electron localized per site. In such a case, the charge degrees of freedom are completely locked by large charge gaps (usually of the order of tens of electron volts). However, one can study the fascinating physics of the spin degrees of freedom. As was shown a long time ago, the localized spins are coupled by a so-called superexchange which may be ferro- or antiferromagnetic. The properties of the exchange coupling between the spins depend mainly on the underlying atomic structure of the material. The resulting physics is extremely rich and such materials can have a host of phases ranging from ordered magnetic phases to so-called spin-liquid phases in which spin–spin correlations decay extremely fast with distance. The field of research concerning these materials, dubbed quantum magnetism, is thus an extremely active field in its own right [1]. Additionally, one can exploit the formal mapping that exists between spin operators and bosonic ones, as will be described in the next section, to connect the magnetic materials to itinerant bosonic systems with interactions between the bosons. This opens the way to use such quantum spin systems as quantum simulators. A quantum simulator means that the experimental system can be employed in order to “solve” in a controlled way a problem/Hamiltonian known from a different less controlled physical realization, e.g., inspired by fundamental many-body physics, quantum information or computational applications.