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Quantum Electronics

Spatial order in interference of a chain of Bose condensates with random phases

Vasiliy Makhalov, Andrei V. Turlapov

Published Sep 1, 2017• 1 citation
Publisher

Abstract

We have observed the interference of a long chain of Bose condensates prepared at the initial time moment in antinodes of a standing electromagnetic wave. The initial distribution of the condensate density in the system under consideration is periodic while the condensate phases can be different. Then the standing wave is quickly turned off, and the condensates start to expand and interfere. A spatial order of the interference fringes is observed with a period being substantially different from the period arising in the case of the Talbot effect.

DOI
10.1070/qel16466

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We have observed the interference of a long chain of Bose condensates prepared at the initial time moment in antinodes of a standing electromagnetic wave. The initial distribution of the condensate density in the system under consideration is periodic while the condensate phases can be different. Then the standing wave is quickly turned off, and the condensates start to expand and interfere. A spatial order of the interference fringes is observed with a period being substantially different from the period arising in the case of the Talbot effect.
For a long periodic chain of Bose condensates prepared in the free space, the subsequent evolution and interference dramatically depend on the difference between the phases of the adjacent and more distant condensates. If the phases are equal, the initial periodic density distribution reappears at later times, which is known as the Talbot effect. For randomly-related phases, we have found that a spatial order also appears in the interference, while the evolution of the fringes differs with the Talbot effect qualitatively. Even a small phase disorder is sufficient for qualitatively altering the interference, though maybe at long evolution times. This effect may be used for measuring the amount of coherence between adjacent condensates and the correlation length along the chain.
Bose-Einstein condensates initially arranged in a long chain freely expand and interfere. If the initial phases of the condensates are identical, the initial density distribution is restored periodically during the expansion, giving rise to the Talbot effect. Even a slight disorder in the initial phases leads to a transformation of the interference pattern. In response to the phase disorder, the spectrum of the spatial density distribution acquires peaks that are absent in the case of identical phases. We derive an analytical expression for the spectrum of the spatial density distribution for an arbitrary phase disorder. We show that the new peaks emerging due to the phase disorder originate from pairwise interferences of the condensates. The positions of these peaks coincide with the wave vectors of the density modulations (wavelets) generated by such pairwise interferences. The absence of these peaks, when the initial phases are identical, is explained by the mutual destruction of the overlapping wavelets during their summation.
A long chain of Bose condensates freely expands and interferes after being released from an optical lattice. The interference fringes are well resolved both in the case of equal phases of the condensates and in the case of fluctuating phases. In the second case the positions of the fringes also fluctuate. The spectrum of the spatial density distribution, however, is reproducible despite the fluctuations. Moreover two types of peaks are distinguishable in the spectrum. The first type arises due to the phase fluctuations, the second type is associated with the coherence between the condensates. In the framework of the Pitaevskii-Gross equation we calculate the interference of the condensates and compare the calculation with experiment [Phys. Rev. Lett. 122, 090403 (2019)]. The calculation reproduces the positions of the spectrum peaks, including the dependence on the interparticle interaction. The calculated heights of the peaks, however, in some cases differ with the experimental ones.
The matter-wave interference picture, which appears within the quantum Talbot effect, changes qualitatively in response to even a small randomness in the phases of the sources. The spatial spectrum acquires peaks which are absent in the case of equal phases. The mathematic model of the effect is presented. The manifestations of the phase randomness in experiments with atomic and molecular Bose-Einstein condensates are discussed. Thermometry based on observable consequences of phase randomness is proposed.