Mesoscopic Bose-Einstein condensates as quantum simulators

Physical Review A, 2013

A two-body correlated basis set is used to develop a many-body theory which is valid for any number of bosons in the trap. The formalism incorporates the van der Waals interaction and two-body correlations in an exact way. The theory has successfully been applied to Bose-Einstein condensates-dilute weakly interacting and also dilute but having a large scattering length. Even in the extreme dilute condition, we observe the breakdown of the shape-independent approximation and the interatomic correlation plays an important role in the large particle-number limit. This correlated many-body calculation can handle, within the two-body correlation approximation, the entire range of atom number of experimentally achieved condensates. Next we successfully push the basis function for large scattering lengths where the mean-field results are manifestly bad. The sharp increase in correlation energy clearly shows the beyond-mean-field effect. We also calculate one-particle densities for various scattering lengths and particle numbers. Our many-body calculation exhibits the finite-size effect in the one-body density.

We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactly soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives quite accurate description of the system in the limit of weak interactions.

We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactly soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives quite accurate description of the system in the limit of weak interactions.

Physical Review Letters, 2012

We investigate theoretically the phase diagram of a spin-orbit coupled Bose gas in two-dimensional harmonic traps. We show that discrete Landau levels develop at strong spin-orbit coupling. For a weakly interacting gas, quantum states with skyrmion lattice patterns emerge spontaneously and preserve either parity symmetry or combined parity-time-reversal symmetry. These phases can be readily observed by experimentally engineering spin-orbit coupling and interatomic interactions for a cloud of 87 Rb atoms in a highly oblate trap. PACS numbers: 05.30.Jp, 03.75.Mn, 67.85.Fg, 67.85.Jk Spin-orbit (SO) coupling leads to many fundamental phenomena in a wide range of quantum systems from nuclear physics, condensed matter physics to atomic physics. For instance, in electronic condensed matter systems spin-orbit coupling can lead to quantum spin Hall states or topological insulators [1], which have potential applications in quantum devices. Recently, SO coupling has been induced in ultracold spinor Bose gases of 87 Rb atoms [2] by the so-called "synthetic non-Abelian gauge fields". Combined with unprecedented controllability of interactions and geometry in ultracold atoms, this manipulation of SO coupling opens an entirely new paradigm for studying strong correlations of quantum many-body systems under non-Abelian gauge fields.

The analytical theory of Bose–Einstein condensation of an ideal gas in mesoscopic systems has been briefly reviewed in application to traps with arbitrary shapes and dimension. This theory describes the phases of the classical gas and the formed Bose–Einstein condensate, as well as the entire vicinity of the phase transition point. The statistics and thermodynamics of Bose–Einstein condensation have been studied in detail, including their self-similar structure in the critical region, transition to the thermodynamic limit, effect of boundary conditions on the properties of a system, and nonequivalence of the description of Bose–Einstein condensation in different statistical ensembles. The complete classification of universality classes of Bose–Einstein condensation has been given.

Physical Review A, 2012

Ultracold atoms provide an ideal system for the realization of quantum technologies, but also for the study of fundamental physical questions such as the emergence of decoherence and classicality in quantum many-body systems. Here, we study the global structure of the quantum dynamics of bosonic atoms in a double-well trap and analyze the conditions for the generation of many-particle entanglement and spin squeezing which have important applications in quantum metrology. We show how the quantum dynamics is determined by the phase space structure of the associated mean-field system and where true quantum features arise beyond this 'classical' approximation.

2014

We study the properties of Bose-Einstein Condensates in a harmonic trap. We consider a mean-field description in terms of the Gross-Pitaevskii equation. We study properties of its solutions, especially the ground state of the system, paying a special attention to the effects of interaction. To obtain numerically the exact stationary states we use the Crank-Nicholson Scheme.

Physical Review A, 2003

Motivated by the recent development of the Feshbach technique, we studied the ground and lowlying excited states of attractive Bose-Einstein condensates on a one-dimensional ring as a function of the strength of interactions. The Gross-Pitaevskii mean-field theory predicts a quantum phase transition between a uniform condensate and a bright soliton, and a gapless singular cusp in the Bogoliubov excitation spectrum at the critical point. However, the exact diagonalization reveals the presence of an energy gap at the critical point, where the singularity is smeared by quantum fluctuations.

Journal of Optics B-quantum and Semiclassical Optics, 2004

In this tutorial we present an introduction to some theoretical methods of quantum field theory applied to the description of a trapped Bose-Einstein condensate. First of all, we give a brief account of the main characteristics of the phenomenon of condensation and present the many-body Hamiltonian of the system. We outline some of the most important approaches used in the characterization of a condensed Bose gas, including the mean-field theory and the Hartree-Fock-Bogoliubov method. Finally we illustrate the use of these techniques addressing some important issues in quantum atom optics. We characterize the quantum state of a Bose-Einstein condensate (BEC) at zero temperature. We also describe a process of Beliaev coupling between quasiparticles using a method that includes terms beyond the usual Bogoliubov approach.