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arXiv:cond-mat/0608585 · Physical Review Letters

Long Phase Coherence Time and Number Squeezing of Two Bose-Einstein Condensates on an Atom Chip

Gyu-Boong Jo, Yong-il Shin, Sebastian Will, Thomas A. Pasquini, Michele Saba, Wolfgang Ketterle, David E. Pritchard, Mukund Vengalattore, Mara Goff Prentiss

Published Jan 19, 2007• 354 citations
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Abstract

We measure the relative phase of two Bose-Einstein condensates confined in a radio frequency induced double-well potential on an atom chip. We observe phase coherence between the separated condensates for times up to approximately 200 ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrate a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.

DOI
10.1103/physrevlett.98.030407

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•1 citation
We measure the relative phase of two Bose-Einstein condensates confined in a radio frequency induced double-well potential on an atom chip. We observe phase coherence between the separated condensates for times up to approximately 200 ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrate a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.
A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by 13 microm for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.
Atom chips promise manipulation of matter waves with high precision. Our exceptionally smooth atom chips potentials allow to experiment with continuous 1 mm long 1d condensates at strong transversal confinement (>10kHz) and extreme aspect ratio up to 10000. In these atom chip traps we employ RF induced adiabatic potentials to split a 1d condensate along its long axis. Bringing the two split clouds together we observe interference between the two ensembles. The RF potentials allow unprecedented precise control enabling a coherent splitting process as demonstrated by the deterministic and stable phase of the interference. The interference pattern itself is sensitive probe of the order parameter in the 1d quantum gas:
Coherence properties of Bose-Einstein condensates offer the potential for improved interferometric phase contrast. However, decoherence effects due to the mean-field interaction shorten the coherence time, thus limiting potential sensitivity. In this work, we demonstrate increased coherence times with number squeezed states in an optical lattice using the decay of Bloch oscillations to probe the coherence time. We extend coherence times by a factor of 2 over those expected with coherent state Bose-Einstein condensate interferometry. We observe quantitative agreement with theory both for the degree of initial number squeezing as well as for prolonged coherence times.
We have used a microfabricated atom chip to split a single Bose-Einstein condensate of sodium atoms into two spatially separated condensates. Dynamical splitting was achieved by deforming the trap along the tightly confining direction into a purely magnetic double-well potential. We observed the matter wave interference pattern formed upon releasing the condensates from the microtraps. The intrinsic features of the quartic potential at the merge point, such as zero trap frequency and extremely high field-sensitivity, caused random variations of the relative phase between the two split condensates. Moreover, the perturbation from the abrupt change of the trapping potential during the splitting was observed to induce vortices.
We have used a microfabricated atom chip to split a single Bose-Einstein condensate of sodium atoms into two spatially separated condensates. Dynamical splitting was achieved by deforming the trap along the tightly confining direction into a purely magnetic double-well potential. We observed the matter wave interference pattern formed upon releasing the condensates from the microtraps. The intrinsic features of the quartic potential at the merge point, such as zero trap frequency and extremely high field-sensitivity, caused random variations of the relative phase between the two split condensates. Moreover, the perturbation from the abrupt change of the trapping potential during the splitting was observed to induce vortices.
Summary form only given. Atom chips [1] have shown to be very successful for trapping and manipulating cold atoms. Atom interferometry in the vicinity of an atom chip has been recently achieved by coherently splitting a Bose-Einstein condensate with radiofrequency [2] and microwave [3] dressing. However, some limitations on the precision of the phase measurement occur in this case due to the phase diffusion process resulting from mean field interactions in the Bose-Einstein condensate.In this communication, we will discuss the possibility of using a thermal (i.e. non-condensed) ensemble of ultra-cold atoms trapped on an atom chip in order to create a trapped-atom interferometer with much weaker atomic interactions. In such a scheme (which can be seen as the atomic equivalent of a white light interferometer in optics), the coherence time will strongly depend on the level of symmetry that can be achieved between the potentials forming the two arms of the interferometer. For example, in a simple model of two harmonic potentials, it can be shown that a slight relative frequency difference Δω/ω can be associated with a limitation on the coherence time T given by the following expression: T≈ 2π1ίω kΘ Δω where Θ is the temperature of the atomic ensemble and k the Boltzmann constant (the latter expression being valid only for kΘ >> ! ω). For example, a relative asymmetry of 10-3 will result, for a temperature of about 1μK, to a limitation on the coherence time of 40ms, which favourably compares to what has been achieved experimentally with Bose-Einstein condensates [2]. We will then discuss how we plan to achieve, with the on-going experiment at Thales TRT [4], a splitting of the atomic cloud with the highest possible level of symmetry. The basic idea is to use internal state labelling on the so-called “clock states” of the 87Rb atom and microwave dressing [3] with two independent coplanar waveguides, each waveguide being preferentially resonant with one of the two internal states involved in the process. This way, we expect to have quasi-independent control over the two arms of the interferometer and thus to be able to achieve a coherent splitting as much symmetrical as possible.We will finally discuss the potential applications of this technique in terms of acceleration and gravity measurement with cold atoms on a chip, which could be of great interest in the future if combined, for example, with high bandwidth microelectromechanical sensors.