Double-slit interferometry with a Bose-Einstein condensate

Abstract

A Bose-Einstein "double-slit" interferometer has been recently realized experimentally by Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevski equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong dephasing observed experimentally. The role of quantum fluctuations is discussed. PACS numbers:Introduction. Several current efforts in the field of dilute Bose-Einstein condensates (BEC) are focusing on the creation of new technological devices, including quantum computers [1] and ultrasensitive interferometers [2] to detect and measure weak forces. Atom wave interferometry already provides unprecedented sensitivities to detect rotations, accelerations, and gravity gradients [3]. Performances can be further improved with interferometers based on BEC, which are the highest brilliant coherent sources of matter waves and which allow for larger separations between different interferometric paths.Interference between two spatially separated condensates was first demonstrated in [5], and theoretically analyzed in [7]. A BEC trapped in a harmonic magnetic trap was split in two symmetric halves by a laser knife. After releasing the external fields, the interference pattern of the overlapping condensates was observed with destructive imaging. The measured relative phase, however, was not reproducible from shot to shot but was randomly distributed due to the presence of a large noise in the relative positions of the laser and the magnetic trap and of parasite currents when switching off the magnetic fields. Reproducible interference patterns were eventually observed by trapping a condensate in deep optical periodic potentials [6]. Neighboring wells of optical lattices, however, are separated only by a fraction of a micron and cannot be individually addressed, limiting their applications in technological devices.Recently, a stable double-well trap has been created in [4]. A single collimated laser beam was split with an acoustic-optical modulator, and finally focused by a lens. A single, cigar-shaped condensate was trapped in a double-well having a barrier much smaller than the BEC chemical potential, see Fig. (1a). The condensate was then split along the axial direction by linearly increasing, in a ramping time t ramp , both the distance between the two wells and the height of the interwell barrier, see Fig. (1b). The final distance between the two condensates was ∼ 12 µm, allowing for individual addressing and manipulation. After holding the two condensates in the respective traps for a time t hold , the confining field was turned off. The interference pattern of the two overlapping condensates was measured by destructive tech-

A Survey of Atom Interferometer Beam-Combination Configurations and Beam Splitter Designs

“…As is well known, the effective long coherent length of the BEC (similar to the long coherent length of an optical laser) dictates that two BEC clumps will show interfering fringes even if they are generated independently of each other and are of arbitrary relative phase. This point has been corroborated in an earlier MIT ``atom laser'' experiment 21 : In fact, the Shin et al experiment is nothing more than a repeat of the Andrews et al BEC interfering experiment in a double-well splitting potential, the only difference being the presence of the chip environment. Without a deterministic, knowable, relative phase between the two interfering paths, the application which will imprint onto one of the two paths an additional phase shift would have difficulty disentangling the application-imprinted phase from the double-well splitting imprinted relative phase.…”

Dephasing and breakdown of adiabaticity in the splitting of Bose–Einstein condensates

“…The Gaussian ansatz will fail when the wavefunction touches the borders φ = ±π, namely when σ φ (t) 1. With the variational ansatz (11), the equation of motion for the width of the phase amplitude becomes 3 :…”

“…We expect that there will be a time at which the solution ε(t) becomes a significant correction to 3 The differential equations for the parameters σ φ and δ of the variational wave function (11) are [12]:…”

“…The recent experimental realizations of a stable double-well trap [1,2] is renewing the interest in these topics. Even though residual sources of noise might still be limiting the coherence lifetime of the two coupled systems [1,3], the experimental progress is quite promising for future developments and possible technological applications.…”

Limits to phase resolution in matter-wave interferometry

“…One key element in any practical device is a coherent beam splitter, and much effort has been devoted to the realization and the understanding of these devices, both experimentally [3][4][5] and theoretically [6][7][8][9][10][11][12][13].…”