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arXiv:0812.4836 · New Journal of Physics

Interference of interacting matter waves

Mattias Karl Gustavsson, Elmar Haller, Manfred J. Mark, Johann Georg Danzl, Russell Hart, Andrew J. Daley, Hanns‐Christoph Nägerl

Published Jun 28, 2010• 37 citations
arXivHTMLPDF

Abstract

The phenomenon of matter-wave interference lies at the heart of quantum physics. It has been observed in various contexts in the limit of non-interacting particles as a single-particle effect. Here we observe and control matter-wave interference whose evolution is driven by interparticle interactions. In a multi-path matter-wave interferometer, the macroscopic many-body wave function of an interacting atomic Bose–Einstein condensate develops a regular interference pattern, allowing us to detect and directly visualize the effect of interaction-induced phase shifts. We demonstrate control over the phase evolution by inhibiting interaction-induced dephasing and by refocusing a dephased macroscopic matter wave in a spin-echo-type experiment. Our results show that interactions in a many-body system lead to a surprisingly coherent evolution, possibly enabling narrow-band and high-brightness matter-wave interferometers based on atom lasers.

DOI
10.1088/1367-2630/12/6/065029

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The phenomenon of matter-wave interference lies at the heart of quantum physics. It has been observed in various contexts in the limit of non-interacting particles as a single-particle effect. Here we observe and control matter-wave interference whose evolution is driven by interparticle interactions. In a multi-path matter-wave interferometer, the macroscopic many-body wave function of an interacting atomic Bose–Einstein condensate develops a regular interference pattern, allowing us to detect and directly visualize the effect of interaction-induced phase shifts. We demonstrate control over the phase evolution by inhibiting interaction-induced dephasing and by refocusing a dephased macroscopic matter wave in a spin-echo-type experiment. Our results show that interactions in a many-body system lead to a surprisingly coherent evolution, possibly enabling narrow-band and high-brightness matter-wave interferometers based on atom lasers.
We implement two types of matter-wave interferometers using trapped Bose-condensed Feshbach molecules, from weak to strong interactions. In each case, we focus on investigating interaction effects and their implications for the performance. In the Ramsey-type interferometer where interference between the two motional quantum states in an optical lattice is observed, interparticle interactions are found to induce energy shifts in the states. Consequently, this results in a reduction of the interferometer frequency and introduces a phase shift during the lattice pulses used for state manipulation. Furthermore, nonuniformity leads to dephasing and collisional effects contribute to the degradation of contrast. In the Michelson-type interferometer, where matter waves are spatially split and recombined in a waveguide, interference is observed in the presence of significant interaction, however coherence degrades with increasing interaction strength. Notably, coherence is also observed in thermal clouds, indicating the white-light nature of the implemented Michelson-type interferometer. Published by the American Physical Society 2024
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.
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.
Understanding the effect of interactions in the phase evolution of expanding atomic Bose-Einstein condensates is fundamental to describing the basic phenomenon of matter wave interference. Many theoretical and experimental works tackled this problem, always with the implicit assumption that the mutual interaction between two expanding condensates rigidly modifies the phase evolution through an effective force. In this paper, we present a combined experimental and theoretical investigation of the interference profile of expanding 87Rb^{87}\mathrm{Rb}87Rb condensates, with a specific focus on the effect of interactions. We come to the different conclusion that the mutual interaction produces local modifications of the condensate phase only in the region where the wave packets overlap.
We observe the build-up of a matter wave interference pattern from single atom detection events in a double-slit experiment. The interference arises from two overlapping atom laser beams extracted from a rubidium Bose-Einstein condensate. Our detector is a high-finesse optical cavity which realizes a quantum measurement of the presence of an atom and thereby projects delocalized atoms into a state with zero or one atom in the resonator. The experiment reveals simultaneously the granular and the wave nature of matter. We present a setup which is suited for applications in atom interferometry and cavity QED.
Matter-wave optics is often viewed as a linear analogue of photonics, where noninteracting particles are coherently split, diffracted, and recombined, and interference arises from single-particle coherence. In ultracold quantum gases, however, interactions are intrinsic and can rival or exceed kinetic and optical energy scales. This drives matter-wave optics into a nonlinear regime: diffraction and momentum distributions become interaction-dependent, interference contrast degrades or collapses, and revival dynamics appear. In the mean time, interactions can generate squeezing and entanglement, enabling sensitivities beyond the standard quantum limit. We showcase representative examples - covering diffraction, splitting, and interferometry - that illustrate how interactions reshape the basic elements of matter-wave optics and open new opportunities for nonlinear quantum technologies.