## Theory

Theoretical studies at the Quantum Optics Group are carried out by Dr. Igor Mazets. At the focus of these studies are the properties of one-dimensional Bose gases on atom chips, especially their thermalization and dephasing. The main results are the following:

1) The mechanism of violation of integrability in quasi-1D bosonic gases. Even if the collision energy of two atoms in a tight waveguide is insufficient to really excite the radial degrees of freedom, the latter ones can be excited virtually, and the system is brought back to the energy shell by collision with the third atom. Such effective three-body elastic collisions are always present in the system and violate the symmetry underlying the integrable Lieb-Liniger model. As the result, the system becomes slightly non-integrable and can thermalize, in agreement with the experimental observations. On the other hand, if the interatomic repulsion is strong enough (so that the system tends to the Tonks-Girardeau limit), the three-particle correlation function decreases, and so does the elastic three-body collision rate. In other words, correlations induced by atomic repulsion restore the integrability (as seen in David Weiss’ experiments). In the strong interaction limit this result is rigorously proven by analyzing the problem in “hyperlinear” (1D analog of hyperspherical) coordinates. See: I.E. Mazets and J. Schmiedmayer, New J. Phys. **12**, 055023 (2010). .

2) The experimentally observed dephasing of two coherently-split quasicondensates has been a puzzle for a while. Burkov, Lukin and Demler [Phys. Rev. Lett. **98**, 200404 (2007)] attempted to describe it by a certain field-theoretical model. However, it was shown that their model is unsatisfactory since it predicts an unphysical overdamping of elementary excitations with an energy of the order of the chemical potential. We put forward an alternative theory (supported by numerical simulations) that explains the experimentally observed sub-exponential dephasing behavior, but with a characteristic time by an order of magnitude longer than previously expected. This controversy calls for more thorough experimental investigation of the subject.

3) We develop a unified theory that predicts a steady-state integrated-contrast distribution of the interference pattern formed by two quasi-condensates released from the trap (free expansion regime). Our method [H.-P. Stimming, N. J. Mauser, J. Schmiedmayer, and I. E. Mazets, Phys. Rev. Lett. **105**, 015301 (2010)] is not only in excellent agreement with the results obtained by Demler, Altman and Polkovnikov by means of the Luttinger liquid approach for fully separated quasi-condensates, but also is applicable for quasi-condensates with a finite tunnel coupling. We also rigorously prove now that quantum fluctuations play much less of a role in the integrated-contrast pattern formation under typical experimental conditions than expected before.

4) We investigated theoretically the evolution of the two-point density correlation function of a low-dimensional ultracold Bose gas after release from a tight transverse confinement. In the course of expansion, thermal and quantum fluctuations present in the trapped systems transform into density fluctuations. For the case of free ballistic expansion relevant to current experiments, we present simple analytical relations between the spectrum of “density ripples” and the correlation functions of the original confined systems. We analyze several physical regimes, including weakly and strongly interacting one-dimensional (1D) Bose gases and two-dimensional (2D) Bose gases below the Berezinskii-Kosterlitz-Thouless (BKT) transition. For weakly interacting 1D Bose gases, we obtain an explicit analytical expression for the spectrum of density ripples which can be used for thermometry. Our theory [A. Imambekov, I. E. Mazets, D. S. Petrov, V. Gritsev, S. Manz, S. Hofferberth, T. Schumm, E. Demler, and J. Schmiedmayer, Phys. Rev. A **80**, 033604 (2009)] allowed us to eexplain the experimental observations [S. Manz, R. Bücker, T. Betz, Ch. Koller, S. Hofferberth, I. E. Mazets, A. Imambekov, E. Demler, A. Perrin, J. Schmiedmayer, and T. Schumm, Phys. Rev. A **81**, 031610 (2010)], thus providing a new method to look deeper into the properties of low-dimensional ultracold atomic systems.

5) We examined theoretically [David Petrosyan, Guy Bensky, Gershon Kurizki, Igor Mazets, Johannes Majer, and Jörg Schmiedmayer, Reversible state transfer between superconducting qubits and atomic ensembles, Phys. Rev. A **79**, 040304 (2009)] the possibility of coherent reversible information transfer between solid-state superconducting qubits and ensembles of ultracold atoms. Strong coupling between these systems is mediated by a microwave transmission line resonator that interacts near resonantly with the atoms via their optically excited Rydberg states. We showed that the solid-state qubits can then be used to implement rapid quantum logic gates, while collective metastable states of the atoms can be employed for long-term storage and optical readout of quantum information.