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arXiv:1412.4049

Interferometry with correlated matter-waves

Oksana Streltsova, Alexej I. Streltsov

Published Dec 12, 2014• 4 citations
arXivHTMLPDF

Abstract

Matter-wave interferometry of ultra-cold atoms with attractive interactions is studied at the full many-body level. First, we study how a coherent light-pulse applied to an initially-condensed solitonic system splits it into two matter-waves. The split system looses its coherence and develops correlations with time, and inevitably becomes fragmented due to inter-particle attractions. Next, we show that by re-colliding the sub-clouds constituting the split density together, along with a simultaneous application of the same laser-pulse, one creates three matter-waves propagating with different momenta. We demonstrate that the number of atoms in the sub-cloud with zero-momentum is directly proportional to the degree of fragmentation in the system. This interferometric-based protocol to discriminate, probe, and measure the fragmentation is general and can be applied to ultra-cold systems with attractive, repulsive, short- and long-range interactions.

DOI
10.48550/arxiv.1412.4049

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Matter-wave interferometry of ultra-cold atoms with attractive interactions is studied at the full many-body level. First, we study how a coherent light-pulse applied to an initially-condensed solitonic system splits it into two matter-waves. The split system looses its coherence and develops correlations with time, and inevitably becomes fragmented due to inter-particle attractions. Next, we show that by re-colliding the sub-clouds constituting the split density together, along with a simultaneous application of the same laser-pulse, one creates three matter-waves propagating with different momenta. We demonstrate that the number of atoms in the sub-cloud with zero-momentum is directly proportional to the degree of fragmentation in the system. This interferometric-based protocol to discriminate, probe, and measure the fragmentation is general and can be applied to ultra-cold systems with attractive, repulsive, short- and long-range interactions.
Experiments on ultracold attractive Bose-Einstein condensates (BECs) have demonstrated that at low dimensions atomic clouds can form localized objects, propagating for long times without significant changes in their shapes and attributed to bright matter-wave solitons, which are coherent objects. We consider the dynamics of bright soliton trains from the perspective of many-boson physics. The fate of matter-wave soliton trains is actually to quickly lose their coherence and become macroscopically fragmented BECs. The death of the coherent matter-wave soliton trains gives birth to fragmented objects, whose quantum properties and experimental signatures differ substantially from what is currently assumed.
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of many aspects of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. This field is a vast one, and in this chapter we shall touch briefly on selected topics. In Sec. 13.1 we describe the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap. Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. We shall analyse the reasons for this effect. The marked decrease in density fluctuations in a Bose gas when it undergoes Bose–Einstein condensation is demonstrated in Sec. 13.2. Gaseous Bose–Einstein condensates can be manipulated by lasers, and this has made possible the study of coherent matter wave optics. We describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves in Sec. 13.3. The atom laser and amplification of matter waves is taken up in Sec. 13.4. How to characterize Bose–Einstein condensation microscopically is the subject of Sec. 13.5, where we also consider fragmented condensates. Interference of two condensates One of the striking manifestations of the wave nature of Bose–Einstein condensates is the observation of an interference pattern when two condensed and initially separated clouds are allowed to overlap. An example is shown in Fig. 13.1.
The splitting and subsequent re-overlapping of a coherent light beam provides the basis for exquisitely sensitive detection of path-length differences; this technique of optical interferometry finds applications ranging from stellar observations to holographic imaging and characterization of optical components. Analogously, the cooling of a cloud of bosonic atoms into a Bose-Einstein condensate, a state in which all the atoms share the same quantum state, is described in terms of a coherent matter wave. Because atoms sense gravity, the interference of matter waves can then be used to provide a sensitive gravity detector, with a comparably diverse set of applications ranging from testing relativity to detecting underground bunkers. Unlike photons, however, which do not interact much with each other, the atoms in the trapped cloud do interact by way of collisions. These collisions then give rise to losses and induce shifts in the phase of the matter wave, thereby limiting the sensitivity of any atom interferometer. Gustavsson et al. and Fattori et al. present setups in which the interaction strength between the atoms in the condensate (cesium and potassium, respectively) is tuned via magnetic field so that the scattering between the atoms is significantly reduced. The resulting extension of the matter-wave coherence time leads to improved sensitivity of the atom interferometers. — ISO
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. In Sec. 13.1 we discuss Josephson tunnelling of a condensate between two wells and the role of fluctuations in particle number and phase. The number and phase variables play a key role in the description of the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap (Sec. 13.2). Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. Density fluctuations in a Bose gas are studied in Sec. 13.3, where we relate atomic clock shifts to the two-particle correlation function. The ability to manipulate gaseous Bose–Einstein condensates by lasers has made possible the study of coherent matter wave optics and in Sec. 13.4 we describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves. How to characterize Bose–Einstein condensation in terms of the density matrix is the subject of Sec. 13.5, where we also consider fragmented condensates.
The goal of this thesis is to study a novel approach towards all-optical continuous waveguide interferometers based on quasi-Bragg waveguide beam splitters. The Bragg beam splitter for matter waves is comprised of a periodic lattice produced by partial or full interference between two Gaussian laser beams and are used as waveguides for ultra-cold atoms. In the experimental conditions, where both waveguides have wide and deep potentials, atoms are unable to split from a single lattice. Instead, several spatially separated regions of the optical lattice are required, fulfilling the Bragg condition. This thesis will present clear evidence of the detection of discrete quantised momentum states of the atoms, created from a process of ultra-cold atoms undergoing interference in the single arms of a Michelson interferometer. A detailed investigation of the different regimes of the splitter has been completed by varying the initial atom velocity and the amplitude of the optical lattice. The findings from the study have produced optimal parameters where the splitting ratio of the atoms between the two waveguides can be finely controlled by the amplitude of the lattice within certain limits. A Michelson interferometer configuration is used to test the coherence of the atoms by decelerating them after splitting in the lattice. The return velocity of atoms is set to be equal to the initial velocity and the two clouds are recombined using the original lattice. A sinusoidal oscillation of the atomic momentum between the two output ports of the beam splitter is visible. However, only interference in single Michelson interferometer arms has been observed. The reasons are discussed in detail along with plans to move towards an all-optical design.
We present the first realization of a solitonic atom interferometer. A Bose-Einstein condensate of 1×10(4) atoms of rubidium-85 is loaded into a horizontal optical waveguide. Through the use of a Feshbach resonance, the s-wave scattering length of the 85Rb atoms is tuned to a small negative value. This attractive atomic interaction then balances the inherent matter-wave dispersion, creating a bright solitonic matter wave. A Mach-Zehnder interferometer is constructed by driving Bragg transitions with the use of an optical lattice colinear with the waveguide. Matter-wave propagation and interferometric fringe visibility are compared across a range of s-wave scattering values including repulsive, attractive and noninteracting values. The solitonic matter wave is found to significantly increase fringe visibility even compared with a noninteracting cloud.