Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

http://absimage.aps.org/image/DAMOP06/MWS_DAMOP06-2006-000603.pdf

A quantum Newton's cradle

From Superfluid to Mott Insulator One of the most attractive characteristics of cold atomic gases in optical lattices is their ability to simulate condensed-matter systems. The results of these quantum simulations are usually averaged over the atomic ensemble, or course-grained over several lattice sites. Now, Bakr et al. (p. 547, published online 17 June; see the Perspective by DeMarco) provide a single lattice site view onto the transition of a Bose gas of Rb-87 from the superfluid to the Mott-insulating state. Characteristic concentric shells of uniform number density were observed deep in the Mott insulator regime, and probing the local quantum dynamics revealed unexpectedly short time scales. The low-defect Mott structures identified may provide a starting point for quantum magnetism experiments. Imaging of atoms that were optically trapped in lattice sites reveals local dynamics of a quantum phase transition. Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We used single atom–single lattice site imaging to investigate the Bose-Hubbard model on a microscopic level. Our technique enables space- and time-resolved characterization of the number statistics across the superfluid–Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low-entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition time scales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low-entropy phases in a lattice.

Probing the Superfluid to Mott Insulator Transition at the Single Atom Level

Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles.

In 1970, Vitaly Efimov predicted that three interacting particles can form an infinite series of bound trimer states, even when none of the two-particle subsystems is stable. Experimental evidence for such an exotic state was obtained in 2006, but now an Efimov spectrum, containing two such states with the predicted scaling between them, has been observed.

Observation of an Efimov spectrum in an atomic system

Impact of the range of the interaction on the quantum dynamics of a bosonic Josephson junction

We analyze the effect of spin degree of freedom on fidelity decay and entropy production of a many-particle fermionic(bosonic) system in a mean-field, quenched by a random two-body interaction preserving many-particle spin $S$. The system Hamiltonian is represented by embedded Gaussian orthogonal ensemble (EGOE) of random matrices (for time-reversal and rotationally invariant systems) with one plus two-body interactions preserving $S$ for fermions/bosons. EGOE are paradigmatic models to study the dynamical transition from integrability to chaos in interacting many-body quantum systems. A simple general picture, in which the variances of the eigenvalue density play a central role, is obtained for describing the short-time dynamics of fidelity decay and entropy production. Using some approximations, an EGOE formula for the time ($t_{sat}$) for the onset of saturation of entropy, is also derived. These analytical EGOE results are in good agreement with numerical calculations. Moreover, both fermion and boson systems show significant spin dependence on the relaxation dynamics of the fidelity and entropy.

https://iopscience.iop.org/article/10.1088/1742-5468/2016/04/043101/pdf

Fidelity decay and entropy production in many-particle systems after random interaction quench

A correlated quantum many-body method is applied to describe resonance states of atomic Bose-Einstein condensates (BEC) in a realistic shallow trap (as opposed to the infinite traps commonly used). The realistic van der Waals interaction is adopted as the interatomic interaction. We calculate experimentally measurable decay rates of the lowest quasibound state in the shallow trap. The most striking result is the observation of a metastable branch besides the usual one for attractive BEC in a pure harmonic trap. As the particle number increases the metastable branch appears and then gradually disappears, and finally the usual metastable branch (associated with the attractive BEC in a harmonic trap) appears, eventually leading to the collapse of the condensate.

Resonance states and quantum tunneling of Bose-Einstein condensates in a three-dimensional shallow trap

By using a correlated many body method and using the realistic van der Waals potential we study several statistical measures like the specific heat, transition temperature and the condensate fraction of the interacting Bose gas trapped in an anharmonic potential As the quadratic plus a quartic confinement makes the trap more tight, the transition temperature increases which makes more favourable condition to achieve Bose-Einstein condensation (BEC) experimentally BEC in 3D isotropic harmonic potential is also critically studied, the correction to the critical temperature due to finite number of atoms and also the correction due to inter-atomic interaction are calculated by the correlated many-body method Comparison and discussion with the mean-field results are presented

Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap

A correlated many-body calculation is presented to characterize the Shannon information entropy of trapped interacting bosons We reformulate the one-body Shannon information entropy in terms of the one-body probability density The minimum limit of the entropy uncertainty relation (EUR) is approached by making $N$ very small in our numerical work We examine the effect of correlations in the calculation of information entropy Comparison with the mean-field result shows that the correlated basis function is indeed required to characterize the important features of the information entropies We also accurately calculate the point of critical instability of an attractive BEC, which is in close agreement with the experimental value Next we calculate two-body entropies in position and momentum spaces and study quantum correlations in the attractive BEC

Sudip Kumar Haldar

Papers

Impact of the range of the interaction on the quantum dynamics of a bosonic Josephson junction

Fidelity decay and entropy production in many-particle systems after random interaction quench

Resonance states and quantum tunneling of Bose-Einstein condensates in a three-dimensional shallow trap

Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap

Correlated many-body calculation to study characteristics of Shannon information entropy for ultracold trapped interacting bosons