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arXiv:1209.4127 · Physical Review A

Effect of trap anharmonicity on a free-oscillation atom interferometer

Robert H. Leonard, Charles A. Sackett

Published Oct 11, 2012• 12 citations
arXivHTMLPDF

Abstract

A free-oscillation interferometer uses atoms confined in a harmonic trap. Bragg scattering from an off-resonant laser is used to split an atomic wave function into two separated packets. After one or more oscillations in the trap, the wave packets are recombined by a second application of the Bragg laser to close the interferometer. Anharmonicity in the trap potential can lead to a phase shift in the interferometer output. In this paper, analytical expressions for the anharmonic phase are derived at leading order for perturbations of arbitrary power in the position coordinate. The phase generally depends on the initial position and velocity of the atom, which are themselves typically uncertain. This leads to degradation in the interferometer performance, and can be expected to limit the use of a centimeter-scale device to interaction times of about 0.1 s. Methods to improve performance are discussed.

DOI
10.1103/physreva.86.043613

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A free-oscillation interferometer uses atoms confined in a harmonic trap. Bragg scattering from an off-resonant laser is used to split an atomic wave function into two separated packets. After one or more oscillations in the trap, the wave packets are recombined by a second application of the Bragg laser to close the interferometer. Anharmonicity in the trap potential can lead to a phase shift in the interferometer output. In this paper, analytical expressions for the anharmonic phase are derived at leading order for perturbations of arbitrary power in the position coordinate. The phase generally depends on the initial position and velocity of the atom, which are themselves typically uncertain. This leads to degradation in the interferometer performance, and can be expected to limit the use of a centimeter-scale device to interaction times of about 0.1 s. Methods to improve performance are discussed.
A Sagnac atom interferometer can be constructed using a Bose–Einstein condensate trapped in a cylindrically symmetric harmonic potential. Using the Bragg interaction with a set of laser beams, the atoms can be launched into circular orbits, with two counterpropagating interferometers allowing many sources of common-mode noise to be excluded. In a perfectly symmetric and harmonic potential, the interferometer output would depend only on the rotation rate of the apparatus. However, deviations from the ideal case can lead to spurious phase shifts. These phase shifts have been theoretically analyzed for anharmonic perturbations up to quartic in the confining potential, as well as angular deviations of the laser beams, timing deviations of the laser pulses, and motional excitations of the initial condensate. Analytical and numerical results show the leading effects of the perturbations to be second order. The scaling of the phase shifts with the number of orbits and the trap axial frequency ratio are determined. The results indicate that sensitive parameters should be controlled at the 10−5 level to accommodate a rotation sensing accuracy of 10−9 rad/s. The leading-order perturbations are suppressed in the case of perfect cylindrical symmetry, even in the presence of anharmonicity and other errors. An experimental measurement of one of the perturbation terms is presented.
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.
We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semiclassical approximation. The calculation benefits from the use of generalized coherent states for a basis. We find that the form of the semiclassical approximation remains valid to first order in the anharmonic perturbation, but that phase differences arise because the trajectory of a quantum wave packet will generally deviate from that of a classical particle. The quantum correction to the phase is a factor ${\ensuremath{\ell}}^{2}/{A}^{2}$ smaller than the semiclassical perturbation itself, where $\ensuremath{\ell}$ is the quantum harmonic-oscillator lengthscale, and AAA is the classical amplitude of the motion. We provide analytical results for one-dimensional perturbations of power 3 through 6 in the position coordinate.
We investigate interference properties of a trapped atom interferometer where two symmetric optical dipole traps (ODTs) act as the atomic wave-packets splitter and combiner with internal state labelling. After the preparation of initial superposition states, the atomic wave-packet is adiabatically split and moves into two spatially separate asymmetric ODTs. The atomic wave-packets in two ODTs are then adiabatically recombined after a duration of free evolving in traps, completing the interference cycle of this atom interferometer. We show that the interferogram exhibits a series of periodic revivals in interference visibility. Furthermore, the revival period decreases as the asymmetry of two dipole potentials increases. By introducing an echo sequence to the interferometer, we show that while the echo effect is not influenced by the asymmetry of the two ODTs, the onset of periodic revivals changes by the echo sequence. Our study provides an effective method to cancel or compensate the phase shift caused by position and time correlated force.
Guided-wave atom interferometers measure interference effects using atoms held in a confining potential. In one common implementation, the confinement is primarily two dimensional, and the atoms move along the nearly free dimension after being manipulated by an off-resonant standing wave laser beam. In this configuration, residual confinement along the nominally free axis can introduce a phase gradient to the atoms that limits the arm separation of the interferometer. We experimentally investigate this effect in detail, and show that it can be alleviated by having the atoms undergo a more symmetric motion in the guide. This can be achieved by either using additional laser pulses or by allowing the atoms to freely oscillate in the potential. With these techniques, we demonstrate interferometer measurement times up to 72ms72\phantom{\rule{0.3em}{0ex}}\mathrm{ms}72ms and arm separations up to 0.42mm0.42\phantom{\rule{0.3em}{0ex}}\mathrm{mm}0.42mm with a well controlled phase, or times of 0.91s0.91\phantom{\rule{0.3em}{0ex}}\mathrm{s}0.91s and separations of 1.7mm1.7\phantom{\rule{0.3em}{0ex}}\mathrm{mm}1.7mm with an uncontrolled phase.
We study the dynamics of Bose-Einstein condensates in time-dependent microtraps in view of applications in atom interferometry. The scheme is based on the slow splitting and recombination of an elongated harmonic trap. It is shown that the nonlinearity due to the mean field atom-atom interaction increases the sensitivity of the interferometers to an applied phase shift. This feature is connected with the adiabatic generation of a dark soliton. The soliton typically oscillates in the recombined trap, and its amplitude provides an alternative readout of the interferometer phase. We analyse the robustness of this phenomenon with respect to thermal fluctuations, due to (i) initially excited Bogoliubov modes and (ii) magnetic near fields in an electromagnetic surface trap.