We have found an expression for the full many-body Green's function of N pairwise finite-range interacting atoms, in a form of a chain fraction involving two-body T-matrices only, with no explicit presence of the interaction potentials themselves. We show that in the limit of infinitely small potential range, this expression reduces to the Green's function for N atoms interacting via a generalized pseudo-potential, function of a free parameter \Lambda. Using this \Lambda-freedom we resolve all inconsistensies of the Hartree-Fock-Bogoliubov formalism known so far, with no ad hoc modifications of the theory.

Maxim Olshanii Ludovic Pricoupenko

We derive exact closed form expressions for the first few terms of the short-distance Taylor expansion of the one-body correlation function of the Lieb-Liniger gas. As an intermediate result we obtain the high-p asymptotics of the momentum distribution of both free and harmonically trapped atoms and show that it obeys a universal 1/p^4 law for_all_ values of the interaction strength. We discuss the ways to observe the predicted momentum distributions experimentally, regarding them as a sensitive identifier for the Tonks-Girardeau regime of strong correlations.

Maxim Olshanii Vanja Dunjko

In this paper we update the existing schemes for computation of atom-interferometric signal in single-atom interferometers to interferometry with dense Bose-condensed atomic samples. Using the theory developed we explain the fringe contrast degradation observed, for longer duration of interferometric cycle, in the Michelson interferometer on a chip recently realized at JILA (Ying-Ju Wang, Dana Z. Anderson, Victor M. Bright, Eric A. Cornell, Quentin Diot, Tetsuo Kishimoto, Mara Prentiss, R. A. Saravanan, Stephen R. Segal, Saijun Wu, Phys. Rev. Lett. 94, 090405 (2005)). We further suggest several recipes for suppression of the interaction-related contrast degradation.

Maxim Olshanii Vanja Dunjko

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such state are. We confirm the relaxation hypothesis through a thorough ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which having already been observed in the recent experiment on the non-equilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita, T. Wenger, D. S. Weiss, Nature (London) 440, 900 (2006)].

Marcos Rigol Vanja Dunjko Vladimir Yurovsky Maxim Olshanii

Two zero-range-interacting atoms in a circular, transversely harmonic waveguide are used as a test-bench for a quantitative description of the crossover between integrability and chaos in a quantum system with no selection rules. For such systems we show that the expectation value after relaxation of a generic observable is given by a linear interpolation between its initial and thermal expectation values. The variable of this interpolation is universal; it governs this simple law to cover the whole spectrum of the chaotic behavior from integrable regime through the well- developed quantum chaos. The predictions are confirmed for the waveguide system, where the mode occupations and the trapping energy were used as the observables of interest; a variety of the initial states and a full range of the interaction strengths have been tested.

Maxim Olshanii Vladimir Yurovsky

This article is an attempt to provide a link between the quantum nonequilibrium dynamics of cold gases and fifty years of progress in the lowdimensional quantum chaos. We identify two atomic systems lying on the interface: two interacting atoms in a harmonic multimode waveguide and an interacting two-component Bose-Bose mixture in a double-well potential. In particular, we study the level spacing distribution, the wavefunction statistics, the eigenstate thermalization, and the ability to thermalize in a relaxation process as such.

Cavan Stone Yassine Ait El Aoud Vladimir A Yurovsky Maxim Olshanii

In this article, we propose an experimental scheme for observation of a quantum anomaly---quantum-mechanical symmetry breaking---in a two-dimensional harmonically trapped Bose gas. The anomaly manifests itself in a shift of the monopole excitation frequency away from the value dictated by the Pitaevskii-Rosch dynamical symmetry [L. P. Pitaevskii and A. Rosch, Phys. Rev. A, 55, R853 (1997)]. While the corresponding classical Gross-Pitaevskii equation and the derived from it hydrodynamic equations do exhibit this symmetry, it is---as we show in our paper---violated under quantization. The resulting frequency shift is of the order of 1% of the carrier, well in reach for modern experimental techniques. We propose using the dipole oscillations as a frequency gauge.

Maxim Olshanii Hélène Perrin Vincent Lorent

A central question of dynamics, largely open in the quantum case, is to what extent it erases a system's memory of its initial properties. Here we present a simple statistically solvable quantum model describing this memory loss across an integrability-chaos transition under a perturbation obeying no selection rules. From the perspective of quantum localization-delocalization on the lattice of quantum numbers, we are dealing with a situation where every lattice site is coupled to every other site with the same strength, on average. The model also rigorously justifies a similar set of relationships recently proposed in the context of two short-range-interacting ultracold atoms in a harmonic waveguide. Application of our model to an ensemble of uncorrelated impurities on a rectangular lattice gives good agreement with ab initio numerics.

Maxim Olshanii Kurt Jacobs Marcos Rigol Vanja Dunjko Harry Kennard Vladimir A. Yurovsky

The concept of ergodicity---the convergence of the temporal averages of observables to their ensemble averages---is the cornerstone of thermodynamics. The transition from a predictable, integrable behavior to ergodicity is one of the most difficult physical phenomena to treat; the celebrated KAM theorem is the prime example. This Letter is founded on the observation that for many classical and quantum observables, the sum of the ensemble variance of the temporal average and the ensemble average of temporal variance remains constant across the integrability-ergodicity transition. We show that this property induces a particular geometry of quantum observables---Frobenius (also known as Hilbert-Schmidt) one---that naturally encodes all the phenomena associated with the emergence of ergodicity: the Eigenstate Thermalization effect, the decrease in the inverse participation ratio, and the disappearance of the integrals of motion. As an application, we use this geometry to solve a known problem of optimization of the set of conserved quantities---regardless of whether it comes from symmetries or from finite-size effects---to be incorporated in an extended thermodynamical theory of integrable, near-integrable, or mesoscopic systems.

Maxim Olshanii

We analyze the atom field-effect transistor scheme [J. A. Stickney, D. Z. Anderson and A. A. Zozulya, Phys. Rev. A 75, 013608 (2007)] using the standard tools of nonequlilibrium dynamics. In particular, we study the deviations from the Eigenstate Thermalization Hypothesis, quantum fluctuations, and the density of states, both ab initio and using their mean-field analogues. Having fully established the quantum vs. mean-field correspondence for this system, we attempt, using a mean-field model, to interpret the off-on threshold in our transistor as the onset of ergodicity---a point where the system becomes able to visit the thermal values of the former integrals of motion in principle, albeit not being fully thermalized yet.

Zhedong Zhang Vanja Dunjko Maxim Olshanii