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Physical Review A

Atom interferometry using Kapitza-Dirac scattering in a magnetic trap

Rachel Sapiro, R. Zhang, Georg A. Raithel

Published Apr 28, 2009• 44 citations
Publisher

Abstract

We demonstrate two atom interferometric schemes based on Kapitza-Dirac scattering in a magnetic trap. In the first method, two Kapitza-Dirac scattering pulses are applied with a small time delay between them. High contrast interference is observed both using a thermal cloud and a Bose-Einstein condensate (BEC). In the second method, two Kapitza-Dirac scattering pulses are applied to a BEC with a time separation sufficiently large that the interfering orders complete half an oscillation in the magnetic trap; this enables interferometry between spatially separated paths.

DOI
10.1103/physreva.79.043630

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We demonstrate two atom interferometric schemes based on Kapitza-Dirac scattering in a magnetic trap. In the first method, two Kapitza-Dirac scattering pulses are applied with a small time delay between them. High contrast interference is observed both using a thermal cloud and a Bose-Einstein condensate (BEC). In the second method, two Kapitza-Dirac scattering pulses are applied to a BEC with a time separation sufficiently large that the interfering orders complete half an oscillation in the magnetic trap; this enables interferometry between spatially separated paths.
Atom interferometers detect inertial effects with considerably larger sensitivity than that of traditional light wave interferometers. They uti- lize the relative small group velocity of coherent matter waves for more precise measurements, which is crucial for possible next-generation in- ertial navigation systems. In a hybrid optical dipole and magnetic trap system we generate Bose-Einstein condensates to be used as the source of matter waves for atom interferometry. We use tailored light pulse sequences to induce Kapitza-Dirac diffraction in the condensates, splitting them into multiple parts at discrete momentum orders. Nu- merical simulation and experimental realization is given for novel pulse sequences that splits ±4hk momentum orders.
We have demonstrated a novel atom interferometer which uses a free oscillation of 87Rb BEC atoms in a magnetic harmonic potential on an atom chip. This interferometer can effectively suppress the dephasing due to the trap potential by applying two Bragg laser pulses with an time interval T equal to the oscillation period of the axial mode of the magnetic trap. We observed a high contrast (~30 %) interference fringe signal for T = 58 ms. When we increased the time interval T to 97 ms, an interference fringe was washed out by the random phase fluctuation. We attributed this phase fluctuation to the external vibrational noise from the floor.
This chapter describes the Bose--Einstein condensate (BEC) interferometry. We first introduce the optical interferometer, briefly discussing the role of fringe contrast in observing interference patterns. Next, we examine a BEC interferometer in a Michelson geometry that consists of a BEC in a trapping potential well. The BEC cloud in the potential well is put into a linear superposition of two clouds that travel along different paths in the trap and are recombined using the same light beams. By studying the population of atoms in the different motional states of the BEC clouds that emerge after recombination, we obtain information about the relative phase shift accumulated by the two traveling superposed condensates during the interferometry. We then characterize the atom distribution that is found in the output of the interferometer by finding the probability density distribution and calculating the features of the probability density such as the mean, the variance, and the interference fringe contrast. Finally, we parameterize the effect of two-body collisional interactions on the observed interference fringes in a way that can be directly controlled in an experiment.
A Bose-Einstein condensation (BEC) production machine has been assembled and operated, using two vacuum chambers isolated from each other by a thin tube. A magnetooptical trap (MOT) is operated in the first chamber, where atoms are captured out of a thermal vapor and cooled to about 200 µK. The atoms are then transferred to a magnetic trap which is mounted on to a movable stage. A programmable motor moves the stage about half a meter, carrying the atoms to the second vacuum chamber where they are evaporatively cooled in a time-orbiting potential trap. We successfully used this apparatus to observe the first BEC's at the University of Virginia. We have also implemented a novel atom trap for BEC's of 87 Rb to be used in atom interferometry experiments. The trap is based on a time-orbiting potential waveguide. It supports the atoms against gravity while providing weak confinement to minimize interaction effects. We have loaded a condensate into the waveguide, and removed all other confinement fields. Up to 2 ×10 4 condensate atoms have been loaded into the trap, at estimated temperatures as low as 850 pK. We expect this novel type of trap will be useful for a variety of applications in condensate interferometry. Finally, we have characterized our trap by perturbing the atomic cloud with a sudden change in the confinement field. We subsequently obtain harmonic oscillation frequencies vi (ω x ,ω y ,ω z ) as low as 2π×(6.0, 1.2, 3.3) Hz. We have developed a mathematical description of the waveguide fields to account for the residual fields from the trap leads, obtaining good agreement between the measured and predicted trap behavior. The weak confinement of our guide should greatly reduce the limiting effects of atomic interactions. We anticipate that interferometer measurement times of 1 s or more should be achievable in this device. With suitable modifications, our waveguide could be used to precisely measure electric polarizability, gravitational forces, rotations, and other phenomena. We expect that the trap design presented here will play an essential role in allowing condensate interferometry to realize its potential. Note: Abstract extracted from PDF text
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 interferometry with high visibility is of high demand for precision measurements. Here, a parallel multicomponent interferometer is achieved by preparing a spin-2 Bose-Einstein condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms confined in a hybrid magneto-optical trap. After the preparation of a spinor Bose-Einstein condensate with spin degrees of freedom entangled, we observe four spatial interference patterns in each run of measurements corresponding to four hyperfine states we mainly populate in the experiment. The atomic populations in different Zeeman sublevels are made controllably using magnetic-field-pulse induced Majorana transitions. The spatial separation of atom cloud in different hyperfine states is reached by Stern-Gerlach momentum splitting. The high visibility of the interference fringes is reached by designing a proper overlap of the interfering wave packets. Due to uncontrollable phase accumulation in Majorana transitions, the phase of each individual spin is found to be subjected to unreproducible shift in multiple experimental runs. However, the relative phase across different spins is stable, paving a way towards noise-resilient multicomponent parallel interferometers.