Miguel A. Garcia-March

Quenching small quantum gases: Genesis of the orthogonality catastrophe

We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two distinct species is suddenly switched on (quenched). We examine the behavior of the densities, the entanglement, the Loschmidt echo and the spectral function for a large range of inter-species interactions and find that even in such small systems evidence of Andersons orthogonality catastrophe can be witnessed.

Sharp crossover from composite fermionization to phase separation in microscopic mixtures of ultracold bosons

We show that a two-component mixture of a few repulsively interacting ultracold atoms in a one-dimensional trap possesses very diverse quantum regimes and that the crossover between them can be induced by tuning the interactions in one of the species. Starting from the composite fermionization regime, in which the interactions between both components are large and neither gas is phase coherent, our results show that a phase-separated state can be reached by increasing the interaction in one of the species. In this regime, the weakly interacting component stays at the center of the trap and becomes almost fully phase coherent, while the strongly interacting one is expelled to the edges of the trap. The crossover is sharp, as can be witnessed in the systems energy and in the occupation of the lowest natural orbital of the weakly interacting species. We show that such a transition is a few-atom effect which disappears for a large population imbalance.

Tunneling, self-trapping, and manipulation of higher modes of a Bose-Einstein condensate in a double well

We consider an atomic Bose-Einstein condensate trapped in a symmetric one-dimensional double-well potential in the four-mode approximation and show that the semiclassical dynamics of the two ground-state modes can be strongly influenced by a macroscopic occupation of the two excited modes. In particular, the addition of the two excited modes already unveils features related to the effect of dissipation on the condensate. In general, we find a rich dynamics that includes Rabi oscillations, a mixed Josephson-Rabi regime, self-trapping, chaotic behavior, and the existence of fixed points. We investigate how the dynamics of the atoms in the excited modes can be manipulated by controlling the atomic populations of the ground states.

Non-equilibrium thermodynamics of harmonically trapped bosons

We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions after a quench and we find its occurrence analytically for an infinitely repulsive pair of atoms. We further show this phenomena is related to the fundamental excitations that dictate the dynamics from the spectral function. We establish a clear qualitative link between the amount of (irreversible) work performed on the system and the establishment of entanglement. We extend our analysis to multipartite systems by examining the case of three trapped atoms. We show the initial (pre-quench) interactions play a vital role in determining the dynamical features, while the qualitative features of the two particle case appear to remain valid. Finally, we propose the use of the atomic density profile as a readily accessible indicator of the non-equilibrium properties of the systems in question.

Quantum gas mixtures in different correlation regimes

Quantum Systems Unit, Okinawa Institute of Science and Technology, Okinawa, JapanWe present a many-body description for two-component ultracold bosonic gases when one of thespecies is in the weakly interacting regime and the other is either weakly or strongly interacting.In the one-dimensional limit the latter case system is a hybrid in which a Tonks-Girardeau gas isimmersed in a Bose-Einstein condensate, which is an example of a new class of quantum systeminvolving a tunable, superfluid environment. We describe the process of phase separation microscop-ically and semiclassically in both situations and show that the quantum correlations are maintainedin the separated phase.

Topological charge selection rule for phase singularities

We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.

Mesoscopic superpositions of Tonks-Girardeau states and the Bose-Fermi mapping

We study a one dimensional gas of repulsively interacting ultracold bosons trapped in a double-well potential as the atom-atom interactions are tuned from zero to infinity. We concentrate on the properties of the excited states which evolve from the so-called NOON states to the NOON Tonks-Girardeau states. The relation between the latter and the Bose-Fermi mapping limit is explored. We state under which conditions NOON Tonks-Girardeau states, which are not predicted by the Bose-Fermi mapping, will appear in the spectrum.

Macroscopic superposition states of ultracold bosons in a double-well potential

We present a thorough description of the physical regimes for ultracold bosons in double wells, with special attention paid to macroscopic superpositions (MSs). We use a generalization of the Lipkin-Meshkov-Glick Hamiltonian of up to eight single particle modes to study these MSs, solving the Hamiltonian with a combination of numerical exact diagonalization and high-order perturbation theory. The MS is between left and right potential wells; the extreme case with all atoms simultaneously located in both wells and in only two modes is the famous NOON state, but our approach encompasses much more general MSs. Use of more single particle modes brings dimensionality into the problem, allows us to set hard limits on the use of the original two-mode LMG model commonly treated in the literature, and also introduces a mixed Josephson-Fock regime. Higher modes introduce angular degrees of freedom and MS states with different angular properties.

Vortex macroscopic superpositions in ultracold bosons in a double-well potential

We study macroscopic superpositions in the orbital rather than the spatial degrees of freedom, in a three-dimensional double-well system. We show that the ensuing dynamics of N interacting excited ultracold bosons, which in general requires at least eight single-particle modes and N+7 N Fock vectors, is described by a surprisingly small set of many-body states. An initial state with half the atoms in each well, and purposely excited in one of them, gives rise to the tunneling of axisymmetric and transverse vortex structures. We show that transverse vortices tunnel orders of magnitude faster than axisymmetric ones and are therefore more experimentally accessible. The tunneling process generates macroscopic superpositions only distinguishable by their orbital properties and within experimentally realistic times.

The key role of off-axis singularities in free-space vortex transmutation

Abstract We experimentally demonstrate the generation of off-axis phase singularities in a vortex transmutation process induced by the breaking of rotational symmetry. The process takes place in free space by launching a highly charged vortex, owning full rotational symmetry, into a linear thin diffractive element presenting discrete rotational symmetry. It is shown that off-axis phase singularities follow straight dark rays bifurcating from the symmetry axis. This phenomenon may provide new routes toward the spatial control of multiple phase singularities for applications in atom trapping and particle manipulation.