Session Q34: Bose Gases

Damping of excitations in a dipolar Bose gas

In a Bose-condensed gas, quasiparticle excitations can undergo damping via effective condensate-mediated interactions in the collisionless regime. Motivated by recent experimental advances with condensates of highly magnetic atoms, we consider quasiparticle damping in Bose gases with dipolar interactions, where the dispersion exhibits a roton-maxon character in the appropriate trapping geometry. Following standard perturbative arguments, we derive the rates for quasiparticle damping in a collisionless Bose gas interacting with long range interactions. We find that in the experimentally relevant temperature regime, phonons and rotons are effectively undamped in a dipolar gas owing to the nature of the low energy dispersion. Furthermore, by tuning the external magnetic field, the dipolar interaction can be made strongly anisotropic, which leads to a non-trivial dependence of the damping processes on the direction of the applied magnetic field. We discuss the implications of this work for recent experiments with highly magnetic atoms.   

Breakdown of the scale invariance in a near-Tonks-Girardeau gas: some exact results and beyond

In this presentation, we consider {\it elementary} monopole excitations of harmonically trapped one-dimensional Bose gas in the vicinity of a Tonks-Girardeau limit. Using the Girardeau Fermi-Bose mapping we obtain the first dominant correction to the excitation frequency, beyond the scale-invariance-protected value of $2\omega$. In limit of a large number of atoms, our result coincides with the upper bound predicted by Menotti and Stringari [Phys. Rev. A \textbf{66}, 043610 (2002)]. We find further that, surprisingly, the frequency of the {\it collective} excitations, obtained using the perturbation theory [Phys. Rev. Lett. \textbf{81}, 4541 (1998)], is found to be substantially below the Menotti-Stringari bound. In the latter case, the value of the frequency correction is $9/4$ times higher than in the former. Finally, an ab initio numerical calculation of the collective excitation frequency returns to the value predicted for the elementary excitation. We conjecture that the sharp boundary of the TG cloud, characterized by an infinite density gradient, renders the perturbation theory for the collective excitation frequencies unapplicable. We also discuss an extension of our results to the case of spin-polarized $p$-wave-interacting fermions in a cold waveguide.   

Cavity-mediated near-critical dissipative dynamics of a driven condensate

We [1] investigate the near-critical dynamics of atomic density fluctuations in the non-equilibrium self-organization transition of an optically driven quantum gas coupled to a single mode of a cavity. In this system cavity-mediated long-range interactions between atoms, tunable by the drive strength, lead to softening of an excitation mode recently observed in experiments. This phenomenon has previously been studied within a two-mode approximation for the collective motional degrees of freedom of the atomic condensate which results in an effective open-system Dicke model. Here, including the full spectrum of atomic modes we find a finite lifetime for a roton-like mode in the Bogoliubov excitation spectrum that is strongly pump-dependent. The corresponding decay rate and critical exponents for the phase-transition are calculated explaining the non-monotonic pump-dependent atomic damping rate observed in recent experiments. We compute the near-critical behavior of the intra-cavity field fluctuations. We highlight the role of the finite size of the system in the suppression of it below the expectations of the open Dicke model.\\[4pt] [1] M. Kulkarni, B. Oztop, H. E. Tureci, arXiv:1306.3889 (PRL 2013, in press)   

Nonlinear novel oscillation of polaritons in the optical microcavity

As a kind of new state of matter, Bose-Einstein condensation (BEC) in a dilute gas of trapped atoms is able to exhibit quantum phenomena on macroscopic scales. Recently, BEC of microcavity polaritons had been experimentally demonstrated. As a kind of bosonic quasi-particle which generates from the strong light-matter coupling, the polariton can be manipulated by the external laser field, and it provides a platform to simulate strongly correlated many-body models in the photon-coupled microcavity array. In this talk we present a scheme for simulating the nonlinear tunneling between two bosonic condensations in the microcavity system. Due to the controllability of the polariton, the effective nonlinear tunneling between two condensates of polaritons can be easily induced by the external controlling fields. In our work, a kind of two modes polariton model is derived, in which nonlinear tunneling strength depends on the difference of the particles in such two kinds of modes. We investigate the mean-field behaviors for such kind of double-mode polariton model, and we find that it is analogous to the model of the pendulum with variable pendulum length. Furthermore, some novel oscillation modes are revealed.   

Transport Theory for Dilute Bose-Einstein Condensates

We obtain microscopic expressions for the six hydrodynamic modes of a dilute Bose-Einstein condensate: two transverse (shear) modes and four longitudinal modes corresponding to first and second sound [1]. Our microscopic expressions include both the speed of the two types of sound and the rate of relaxation of the sound waves. We obtain numerical values for the shear viscosity of a dilute BEC composed of bosons that interact via a contact potential. Our values for the shear viscosity are obtained using the eigenvalues and eigenvectors of the three types of collision operators that govern the relaxation of the condensate [2]. 1. L.E. Reichl and Erich D. Gust, Phys. Rev. A 88 053603 (2013). 2. E. D. Gust and L.E. Reichl, J. Low Temp. Phys. 170 43 (2013).   

Three-body loss rate of unitary Bose gas

Quantum gases at unitarity can exhibit interesting features, for instance their universal thermodynamics. In the past, unitary Fermi gases in degenerate limit have been studied extensively. As recent experiments [1, 2] show unitary Bose gases can be stabilized at relatively high temperatures, we would like to ask an important question whether a Bose gas can persist in a well defined thermodynamic state at lower temperatures, even to the degenerate limit [3] where the medium affects the three-body loss rate crucially. By calculating the three-body recombination rate while taking into account the scattering with the medium, we have an estimate of the temperature (scale) above which thermodynamic quantities of a metastable branch can be studied in a unitary Bose gas. [1] Rem, B. S., et al. ``Lifetime of the Bose Gas with Resonant Interactions." Physical review letters 110.16 (2013): 163202. [2] Fletcher, Richard J., et al. ``Stability of a unitary Bose gas." Physical review letters 111.12 (2013): 125303. [3] Makotyn, Philip, et al. ``Universal dynamics of a degenerate unitary Bose gas." arXiv preprint arXiv:1308.3696 (2013).   

Many-body Physics of Rydberg Polaritons

Electromagnetically induced transparency (EIT) in cold dense atomic gasses with Rydberg states in has attracted considerable interest as a means of realizing strong nonlinear photon-photon interactions. The coherent light-matter coupling provided by the EIT medium combined with interactions between Rydberg states whose strength and shape can be engineered provide a parameter space with rich phenomenology including photon bound states and spatially ordered structures. Past theoretical treatments of these systems have relied on equations of motion to predict dynamics in particular limits. Here we present progress towards a full many-body path integral description that considers interaction effects beyond the Dicke model as well as the intrinsically non-equilibrium nature of the system, and explore a tentative phase diagram.   

Excitation of ultra-long-range nd Rydberg molecules

A recently discovered class of ultra-long-range Rydberg molecules has generated a significant amount of theoretical and experimental interest [1,2]. The binding mechanism of these molecules arises from a scattering-induced, attractive interaction between the low-energy electron of a highly-excited Rydberg atom and a nearby neutral perturber [3]. The bond formed between a Rydberg atom and a ground-state atom via this interaction, and the nature of the resulting molecule, is largely dependent on the Rydberg electron wave function. We present here the experimental observation of ultra-long-range $^{87}Rb_2$ Rydberg molecules formed by a $Rb(nd_j)$ Rydberg atom and a $Rb(5s_{1/2})$ ground-state atom, for principal quantum numbers 34$\le n \le$40. The molecular ground states are isolated spectroscopically and their measured binding energies scale as $\sim n^{-6}$, in good agreement with theory [1]. The molecular binding energies are found to be the same for angular momentum $j=5/2$ and $3/2$ of the $nd_{j}$ Rydberg state over a selected $n$ range, within the measurement precision. [1] C. H. Greene, A. S. Dickinson, and H. R. Sadeghpour, PRL, 85, 2458-2461 (2000). [2] V. Bendkowsky et al., Nature, 458, 1005-1008 (2009). [3] E. Fermi, Il Nuovo Cimento, 11, 1934.   

Field-theoretical Study of the Bose Polaron - Challenges for Quantum Simulation with ultracold Atoms

We study the properties of the Bose polaron, an impurity strongly interacting with a Bose-Einstein condensate, using a field-theoretic approach and make predictions for the spectral function and various quasiparticle properties that can be tested in experiment. We find that most of the spectral weight is contained in a coherent attractive and a metastable repulsive polaron branch. We show that the qualitative behavior of the Bose polaron is well described by a non-selfconsistent T-matrix approximation by comparing analytical results to numerical data obtained from a fully selfconsistent T-matrix approach. The latter takes into account an infinite number of bosons excited from the condensate. Finally we discuss the implications of our results for the attempted quantum simulation of the Froehlich Hamiltonian using ultracold atoms.   

Fermionized photons in one-dimensional coupled cavities

We consider the properties of a one-dimensional array of evanescently coupled high-finesse cavities each containing a single neutral atom, in the limit of low photon densities. The ground state of the corresponding Jaynes-Cummings-Hubbard (JCH) model is obtained numerically using the Density Matrix Renormalization Group algorithm. We find strong evidence for the existence of a Tonks-Girardeau phase, in which the photons are strongly fermionized, between the Mott-insulating and superfluid phases as a function of the inter-cavity coupling. Results for photon and spin excitation densities, one- and two-body correlation functions, and superfluid and condensate fractions are all found to be consistent with this conclusion.   

Shortcuts to adiabaticity in quantum many-body systems: a quantum dynamical microscope

The evolution of a quantum system induced by a shortcut to adiabaticity mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need of auxiliary non-local interactions for matter-waves [1,2]. Here experimentally realizable driving protocols are found for a large class of single-particle, many-body, and non-linear systems without demanding the spectral properties as an input. The method is applied to the expansion of a trapped ultracold gas which spatially scales up the size of the cloud while conserving the quantum correlations of the initial many-body state. This shortcut to adiabatic expansions acts as a quantum dynamical microscope [3]. [1] Adolfo del Campo, Shortcuts to adiabaticity by counter-diabatic driving, Phys. Rev. Lett. 111, 100502 (2013). [2] Adolfo del Campo, Marek M. Rams, Wojciech H. Zurek, Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model, Phys. Rev. Lett. 109, 115703 (2012) [3] Adolfo del Campo, Frictionless quantum quenches in ultracold gases: a quantum dynamical microscope, Phys. Rev. A 84, 031606(R) (2011).   

Quantum Shock waves and Population Inversion in Collisions of Ultracold Atomic Clouds

Using Time-Dependent Density Matrix Renormalization Group (TDMRG) we study the collision of one-dimensional atomic clouds confined in a harmonic trap and evolving with the Lieb-Liniger Hamiltonian [1]. It is observed that the motion is essentially periodic with the clouds bouncing elastically in agreement with the results of the ``quantum Newton cradle'' experiment of Kinoshita et al. [Nature 440, 900 (2006)]. We compare the results for the density profile against a hydrodynamic description with the pressure term taken from the Bethe Ansatz solution of the Lieb-Liniger model. We find that hydrodynamics can describe the breathing mode of a harmonically trapped cloud for arbitrary long times while it breaks down almost immediately for the collision of two clouds due to the formation of shock waves (gradient catastrophe). Concomitantly with the shock waves formation we observe a local energy distribution typical of population inversion, i.e., an effective negative temperature. Our results are an important step towards understanding the hydrodynamics of quantum many-body systems out of equilibrium and the role of integrability in their dynamics. \\[4pt] [1] S.. Peotta and M. Di Ventra, arXiv:1303.6916   

Thermometry of ultracold atoms based on momentum-distribution noise

Ultracold atoms have the puzzling feature of representing, within a good approximation, a microcanonical system, whose temperature cannot be controlled in a direct manner. Yet thermometry is essential for the use of cold atoms as quantum simulators reconstructing, e.g., equilibrium phase diagrams of strongly correlated models. Here I propose a very general thermometry scheme based on the fluctuations of the momentum distribution - a primary observable of cold-atom experiments. Relying on model-independent fluctuation-dissipation relations, the temperature can be estimated from a combined measurement of 1) the gradient of the momentum distribution, or its response to the application of a gauge field; 2) the fluctuations of the momentum distribution. This estimator provides the exact temperature in a translationally invariant system, or in a lattice system without interactions and further confining potentials - in these cases the fluctuations of the (quasi-)momentum distribution are purely thermal. When quantum fluctuations are also present, their effect does not jeopardize the thermometry down to temperatures well below the onset of quantum degeneracy; in the case of bosons, the proposed thermometry becomes exact in the thermodynamic limit in the presence of Bose condensation.   

Probing the optical conductivity of harmonically-confined charge neutral quantum gases

Using a linear response formulation, we study the centre-of-mass response of a harmonically trapped gas to a small amplitude, time-dependent displacement of the trap. We show that the response to this kind of excitation is directly related to the bulk optical conductivity. Thus, a measurement of the time-dependent centre-of-mass dynamics of the cloud provides information about the complex bulk conductivity tensor of the many-body system. For systems with pure harmonic confinement, the response is prescribed by the generalized Kohn theorem and is independent of interactions and quantum statistics. However, non-trivial responses and optical conductivities arise when the harmonicity of the system is compromised by the presence of an additional external potential, such as an optical lattice or impurity. We demonstrate the usefulness of this scheme by calculating the optical conductivity of a one-dimensional Mott insulator of Bose or Fermi atoms confined in a harmonic trap, as well as the optical Hall conductivity of an ideal rotating trapped gas interacting with a Gaussian impurity. Our calculations provide a proof-of-principle demonstration that our proposal should be able to give considerable information about the optical conductivity of strongly-correlated quantum gases.   

Rapid coherent control of population transfer in lattice systems

During the last three decades there have been dramatic advances in understanding of the requirements for control of quantum dynamics. Lattice models are widely used to describe quantum systems, examples of which are a BEC in an optical lattice, a network of nonlinear waveguides and optical fibers, etc. The existing studies clearly reveal the value of the ability to manipulate BECs in optical lattices for the purpose of preparing well-defined quantum states. We have been stimulated by this observation to extend the theory of accelerated adiabatic transfer to lattice systems so as to determine the potential that drives specified state-to-state population transfer without excitation of unwanted quantum states. In this talk we provide a derivation of that driving potential, and we apply the theory to site-to-site population transfer of a BEC in a quasi-one-dimensional optical lattice. We show that modulation of the lattice potential can transfer the population of the BEC between sites of the lattice without unwanted excitations. The theory is applicable to any lattice in which the on-site potential is tunable. We also demonstrate the robustness of the accelerated population transfer to approximation of the driving potential.