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Full quantum distribution of contrast in interference experiments between interacting one-dimensional Bose liquids

Nature Physics volume 2, pages 705–709 (2006)Cite this article

Abstract

The existence of quantum noise is the most direct evidence for the probabilistic nature of quantum mechanics. In strongly interacting systems we expect quantum noise to reveal non-local correlations of the underlying many-body states. Here, we show that quantum noise in interference experiments with cold atoms can be used to investigate the unusual character of one-dimensional interacting systems. We analyse interference experiments for a pair of independent bosonic one-dimensional condensates and explicitly calculate the distribution function of fringe amplitudes using methods of conformal field theory. Moreover, we point out interesting relations between interference experiments with cold atoms, the problem of a quantum impurity in a one-dimensional Luttinger liquid and a variety of statistical models ranging from stochastic growth models to two-dimensional quantum gravity. Such connections can be exploited to design a quantum simulator of unusual two-dimensional models described by non-unitary conformal field theories with negative central charges.

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Figure 1: Typical experimental scheme.
Figure 2: Small K distribution function.
Figure 3: Large K distribution function.
Figure 4: Central charges.

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Acknowledgements

We are grateful to I. Affleck, C. Bender, P. Fendley, V. M. Galitski, M. Greiner, Z. Hadzibabic, H. Katzgraber, M. Lukin, S. L. Lukyanov, M. Oberthaller, M. Oshikawa, M. Pletyukhov, J. Schmiedmayer, V. Vuletic, D. Weiss, K. Yung and A. B. Zamolodchikov for useful discussions. V.G. is supported by the Swiss National Science Foundation, grant PBFR2-110423. E.A. is partially supported by the US–Israel BSF and the Alon fellowship. E.D. and A.P. are partially supported by the NSF grant DMR-0132874.

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Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA

    Vladimir Gritsev & Eugene Demler

  2. Department of Condensed Matter Physics, The Weizmann Institute of Science Rehovot, 76100, Israel

    Ehud Altman

  3. Department of Physics, Boston University, Boston, Massachusetts, 02215, USA

    Anatoli Polkovnikov

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  1. Vladimir Gritsev
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  2. Ehud Altman
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  4. Anatoli Polkovnikov
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Correspondence to Vladimir Gritsev.

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Gritsev, V., Altman, E., Demler, E. et al. Full quantum distribution of contrast in interference experiments between interacting one-dimensional Bose liquids. Nature Phys 2, 705–709 (2006). https://doi.org/10.1038/nphys410

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