Atom Interferometry with Bose-Einstein Condensates in a Double-Well Potential

Abstract

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 µm for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.PACS numbers: 03.75. Dg, 39.20.+q, 03.75.Lm Demonstrating atom interferometry with particles confined by magnetic [1,2,3,4] and optical [5] microtraps and waveguides would realize the matter wave analog of optical interferometry using fiber-optic devices. Current proposals for confined-atom interferometers rely on the merger and separation of two potential wells to coherently divide atomic wavepackets [6,7,8]. This type of division differs from previously demonstrated atomic beam splitters. To date, atomic beams and vapors have been coherently diffracted into different momentum states by mechanical [9,10] and optical [11] gratings, and Bose-Einstein condensates have been coherently delocalized over multiple sites in optical lattices [12,13,14,15,16,17]. Atom interferometers utilizing these beam splitting elements have been used to sense accelerations [12,18] and rotations [19,20], monitor quantum decoherence [21], characterize atomic and molecular properties [22], and measure fundamental constants [18,23].In this Letter, we demonstrate a trapped-atom interferometer with gaseous Bose-Einstein condensates confined in an optical double-well potential. Condensates were coherently split by deforming an initially single-well potential into two wells separated by 13 µm. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the atoms from the separated potential wells [17,24]. This recombination method avoids deleterious mean field effects [25,26] and detects applied phase shifts on a single realization of the experiment, unlike in-trap recombination schemes [6,7,8].The large separation between the split potential wells allowed the phase of each condensate to evolve independently and either condensate to be addressed individually. An ac Stark phase shift was applied to either condensate by temporarily turning off the optical fields generating its potential well. The spatial phase of the resulting matter wave interference pattern shifted linearly with the applied phase shift and was independent of the time of its application. This verified the phase sensitivity of the interferometer and the independent phase evolution of the separated condensates. The measured coherence time of the separated condensates was 5 ms.The present work demonstrates a trapped-atom interferometer with two interfering paths. This geometry has the flexibility to measure either highly localized...

Transmission and reflection of Bose-Einstein condensates incident on a Gaussian tunnel barrier

“…Consequently, the dynamics reduce to two-dimensional motion in the x − y plane. At time t = 0, we create an additional Gaussian potential barrier [14] …”

“…To our knowledge, however, there has been no consideration of the effect of vortices on BECs approaching a potential barrier of finite width and height, where quantum-mechanical tunneling is possible as well as reflection. Quantum tunneling of BECs can be studied experimentally by using sheets of laser light to create the potential barrier [14] and plays a crucial role in the dynamics and macroscopic coherence of cold atoms in optical lattices [15].…”

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

“…Finally, a rich toolbox of atomic physics makes it possible to provide a detailed characterization of many-body systems, which is crucial for describing complicated transient states resulting from nonequilibrium dynamics. Recent experimental studies addressed such questions as the relaxation of high-energy metastable states [4][5][6], hydrodynamic expansion of strongly interacting fermions in optical lattices [7], decoherence of split condensates [8,9], coherent superexchange-mediated spin dynamics [10], spinor dynamics [11,12], relaxation and thermalization in 1D systems [13,14], as well as interaction quenches in fermionic systems [15].…”

“…However, it may be more illuminating to measure SðtÞ in the time domain using Ramsey-type interference, which is a well-established experimental technique in atomic physics. While it was originally designed for metrology applications, it has been realized recently that it can also be used as a probe of many-body dynamics [8,[61][62][63][64][65].…”

“…Performing a second =2 pulse after time t and measuring hÉðtÞjŜ x jÉðtÞi gives hŜ x ðtÞi ¼ Rehc 0 je iĤ i t=@ e ÀiĤ f t=@ jc 0 i ¼ ReSðtÞ: (8) In the equation above, we neglected the trivial phase factor arising from the energy difference of states j "i and j #i. Thus, the Ramsey interferometry provides a direct measurement of the OC overlap [67].…”