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Physical Review A

Contrast oscillations of the Bose-Einstein-condensation-based atomic interferometer

Shinichi Watanabe, Shinnosuke Aizawa, Tomotake Yamakoshi

Published Apr 24, 2012• 4 citations
Publisher

Abstract

We analyze how the contrast of a quasi-one-dimensional Bose-Einstein-condensation (BEC)-based atomic interferometer is affected by the number density of atoms. In our numerical contrast of a Mach-Zehnder-type BEC-based interferometer a regularly spaced oscillatory structure emerges as a function of both the number density and the recombination time. We attribute this effect to the phase singularities in Husimi representation of the overlapping BEC wave packets caused by the residual nonuniform velocity distribution.

DOI
10.1103/physreva.85.043621

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We analyze how the contrast of a quasi-one-dimensional Bose-Einstein-condensation (BEC)-based atomic interferometer is affected by the number density of atoms. In our numerical contrast of a Mach-Zehnder-type BEC-based interferometer a regularly spaced oscillatory structure emerges as a function of both the number density and the recombination time. We attribute this effect to the phase singularities in Husimi representation of the overlapping BEC wave packets caused by the residual nonuniform velocity distribution.
We numerically implement a Mach-Zehnder interferometer, where the coherence and oscillatory properties of Bose-Einstein condensates are explored and the system is modeled by the Gross-Pitaevskii equation. Several time-dependent external trapping potentials were engineered seeking the adiabatic regime which is quantified using fidelity measurements with respect to the actual ground-state of the trap. The dynamics of both conjugate variables, namely density and phase of the matter-wave function, are shown. Moreover, the density and fidelity profiles of the system are presented when the phase-shifter is switching-on and -off, being found in the presented profiles that the system exhibits three different regimes during the recombination stage among them even an orthogonal BEC to the original one is obtained. We achieve the numerical solution through an adequate implementation of the finite-difference method for the spatial discretization and a Runge-Kutta method for the time evolution.
We use the mean-field approximation to numerically study the dynamics of a split condensate in Mach-Zehnder-type atom interferometers that employ Bragg diffraction. The Husimi representation is used as a direct tool for diagnosing the dynamics in phase space, thus providing information on the interference fringe contrast. We analyze how optimization of the contrast of interference signals can result by means of compensating for the nonlinear interaction and the trapping potential for three alternative experimental schemes. The phase-space overlap in Husimi distribution as well as dynamics in phase space is shown to be important in determining the interference fringe contrast.
We analyze a Bose-Einstein condensate (BEC)-based free oscillation atom Michelson interferometer in a weakly confining harmonic magnetic trap. A BEC at the center of the trap is split into two harmonics by a laser standing wave. The harmonics move in opposite directions with equal speeds and turn back under the influence of the trapping potential at their classical turning points. The harmonics are allowed to pass through each other and a recombination pulse is applied when they overlap at the end of a cycle after they return for the second time. We derive an expression for the contrast of the interferometric fringes and obtain the fundamental limit of performance of the interferometer in the parameter space.
An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.
Atom interferometers and gyroscopes are highly sensitive atom-optical devices which are capable to measure inertial, gravitational, electric, and magnetic fields and to sense rotations. Theoretically, the signal-to-noise ratio of atomic gyroscopes is about a hundred billion times more than that of their optical counterparts for the same particle flux and the enclosed area. Ultra cold atoms from a Bose-Einstein condensate (BEC) can easily be controlled and coherently manipulated on small chips by laser pulses. Atom-optical devices will therefore play a significant role in fundamental research, precision measurements, and navigation systems. In BEC-based atom interferometers, a BEC in a trap is split by using laser pulses, the split clouds are allowed to evolve, they are reflected, and then recombined by laser pulses to observe interference. The split clouds accumulate spatial phase because of the trap and the nonlinearity caused by atom-atom interactions. A velocity mismatch due to reflection laser pulses also introduces a phase gradient across each cloud. These factors contribute to spatial relative phase between the clouds at recombination, causing the loss of contrast of the interference fringes. The main objective of this dissertation is to study the dynamics of a split condensate in atom Michelson interferometers, investigate the effect of trap frequencies, nonlinearity, and the velocity mismatch on the contrast, and to obtain the best theoretical limit of performance in terms of the experimental parameters: trap frequencies, number of atoms, and the velocity imparted to the clouds by the splitting laser pulses.