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Physical Review A

Gravitational and collective effects in an output coupler for a Bose-Einstein condensate in an atomic trap

Weiping Zhang, Daniel F. Walls

Published Feb 1, 1998• 37 citations
Publisher

Abstract

A three-component vector quantum field theory is developed to describe the electronic-spin-resonance interaction of a magnetically trapped Bose-Einstein condensate with a radio frequency field. The theory is directly applied to simulate the recent experiment of Mewes et al. for an output coupler for a Bose-Einstein condensate in a magnetic trap [Phys. Rev. Lett. 78, 582 (1997)]. By employing the mean-field approach, we study the collective dynamics of the multicomponent matter field via the nonlinear Schr\"odinger equation. Including the effect of gravity, we study the spin-resonance Rabi oscillations for the three-component Bose-Einstein condensate in three ground-state hyperfine levels and simulate the dynamic expansion of the condensate components coupled out of the magnetic trap.

DOI
10.1103/physreva.57.1248

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A three-component vector quantum field theory is developed to describe the electronic-spin-resonance interaction of a magnetically trapped Bose-Einstein condensate with a radio frequency field. The theory is directly applied to simulate the recent experiment of Mewes et al. for an output coupler for a Bose-Einstein condensate in a magnetic trap [Phys. Rev. Lett. 78, 582 (1997)]. By employing the mean-field approach, we study the collective dynamics of the multicomponent matter field via the nonlinear Schr"odinger equation. Including the effect of gravity, we study the spin-resonance Rabi oscillations for the three-component Bose-Einstein condensate in three ground-state hyperfine levels and simulate the dynamic expansion of the condensate components coupled out of the magnetic trap.
Bose-Einstein condensates present to us the opportunity to probe into the atomic interac- tions that govern a macroscopic quantum mechanical system. The degenerate hyperfine manifold in the bosonic atoms splits in the presence of an external B-field; radio-frequency induced coupling releases experimentally-attainable knowledge about the Zeeman mani- fold in 87Rb. The purpose of this study is to investigate quantum dynamics in two and three-component Bose-Einstein condensate (BEC) systems. We start with a theoretical analysis of Josephson tunneling dynamics between identical BECs trapped in a double potential well, paying particular attention to the non-linear self-trapping effect observed as a consequence of the intra-well interaction. We present a model for the non-equilibrium dynamics in a two-level system and introduce the Rabi oscillations. This is followed by a numerical and experimental investigation of Rabi oscillations in a three-level 87Rb BEC between the F = 1 hyperfine level spin states mF = {1, 0, 1}. The relation between the observed total Rabi frequency and the detuning, along with its effect on the BEC population dynamics is explored. Finally, we explore the possible suspects for the shift of the resonance at strong Rabi frequencies .
Bose-Einstein condensate(BEC) provides a nice stage when the nonlinear Schrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom. The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass. Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance rij on short scale and logarithmic in rij on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore “the chaos in the three-body problem” in the context of vortices with inertia.
A linear quantum dynamic theory for output coupler of Bose–Einstein condensed atoms in a trap is considered with the Bogoliubov approximation in the thermodynamical limit based on the recent MIT experiment ( Phys. Rev. Lett. 78 (1997) 582) for atomic laser. In evolution of total system, the solution of the many-body problem shows a factorization of dynamic process, i.e., the wave function initially prepared in a direct product of a vacuum state and a coherent state remains in a direct product of coherent states at any instance. Physically, this factorizable structure predicts that an ideal condensate in the trap will remain in such a condensate state after the radiation frequency interaction while the output-coupler pulse of atoms forms a macroscopic quantum state in a propagating mode, i.e., the atomic laser.
Two internal hyperfine states of a Bose-Einstein condensate in a dilute magnetically trapped gas of 87Rb{}^{87}\mathrm{Rb}87Rb atoms are strongly coupled by an external field that drives Rabi oscillations between the internal states. Due to their different magnetic moments and the force of gravity, the trapping potentials for the two states are offset along the vertical axis, so that the dynamics of the internal and external degrees of freedom are inseparable. The rapid cycling between internal atomic states in the displaced traps results in an adiabatic transfer of population from the condensate ground state to its first antisymmetric topological state. This has a pronounced effect on the internal Rabi oscillations, modulating the fringe visibility in a manner reminiscent of collapses and revivals. We present a detailed theoretical description based on zero-temperature mean-field theory.
The evolution of a two component Bose-Einstein condensate, consisting of atoms in two distinct hyperfine states, is modeled using a generalization of the Gross-Pitaevskii equation. Coherent coupling of the components by a microwave or RF field gives rise to a range of spatiotemporal behaviors, controlled by the strength and detuning of the applied field. From an initial trapped single component state, a second component can be generated which may escape from the trapping region or remain trapped within the first component. The initiating mechanism is identified and characterized.
Study of the physical properties of Bose condensed gases has recently become a very active topic due to the experimental realizations of Bose-Einstein condensation in magnetically trapped gases of alkali atoms. In this paper we theoretically study the microwave electronic spin resonance of a weakly interacting Bose gas. For a Bose gas above the critical temperature for Bose-Einstein condensation, the microwave radiation induced by the driving microwave field in the electronic spin resonance exhibits the ordinary Rabi oscillation damped by the inhomogeneous Doppler dephasing. For a Bose gas with a condensate, the induced radiation is composed of two components. One is the strong coherent Rabi oscillation from the condensate. The other is a modulated Rabi oscillation due to the noncondensed part of the gas. We show that the modulation of Rabi oscillation of the noncondensed gas is directly related to the elementary collective excitation of atoms in the gas.