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Modern Physics Letters B

Breathing dynamics of a trapped impurity in a dipolar Bose gas

Fang-Qi Hu, Ju-Kui Xue

Published Aug 30, 2014• 1 citation
Publisher

Abstract

With the consideration of impurity-bosons coupling and dipole–dipole interactions (DDI), we study the breathing dynamics of a harmonically trapped impurity interacting with a separately trapped background of dipolar Bose gas. By using the variational approach, the breathing equations, the breathing frequencies and the effective potentials governing the breathing dynamics of the impurity in dipolar gas are obtained. The effects of DDI, impurity-bosons interaction and external trapping potentials on breathing dynamics of impurity are discussed. We find that, because of the anisotropic and long-range characters of DDI, the effects of DDI, impurity-bosons interaction and external trapping potentials on breathing dynamics of impurity are strongly coupled. DDI has significant modification on dynamics, which depends on the external trapping potentials. For spherically symmetric external trapping, DDI makes the impurity more cigar-shaped along axial direction and the breathing oscillation in radial direction is suppressed by DDI. However, the effect of DDI on the breathing dynamics is weakened for cigar-shaped external trapping. Interestingly, for strong external pancake-shaped trapping, the symmetries of the breathing dynamics with respect to attractive and repulsive impurity-bosons coupling recover. Especially, for some critical value of impurity-bosons coupling, the breathing dynamics undergo a sudden quench.

DOI
10.1142/s0217984914501851

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With the consideration of impurity-bosons coupling and dipole–dipole interactions (DDI), we study the breathing dynamics of a harmonically trapped impurity interacting with a separately trapped background of dipolar Bose gas. By using the variational approach, the breathing equations, the breathing frequencies and the effective potentials governing the breathing dynamics of the impurity in dipolar gas are obtained. The effects of DDI, impurity-bosons interaction and external trapping potentials on breathing dynamics of impurity are discussed. We find that, because of the anisotropic and long-range characters of DDI, the effects of DDI, impurity-bosons interaction and external trapping potentials on breathing dynamics of impurity are strongly coupled. DDI has significant modification on dynamics, which depends on the external trapping potentials. For spherically symmetric external trapping, DDI makes the impurity more cigar-shaped along axial direction and the breathing oscillation in radial direction is suppressed by DDI. However, the effect of DDI on the breathing dynamics is weakened for cigar-shaped external trapping. Interestingly, for strong external pancake-shaped trapping, the symmetries of the breathing dynamics with respect to attractive and repulsive impurity-bosons coupling recover. Especially, for some critical value of impurity-bosons coupling, the breathing dynamics undergo a sudden quench.
\n Motivated by a recent experiment (Catani J.\net al., Phys. Rev. A, 85 (2012) 023623) we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. The amplitudes of breathing oscillations are suppressed by self-trapping, due to interactions with the Bose gas. Further, exciting phonons in the Bose gas leads to damped oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results, supported by simulations, reproduce the main features of the dynamics observed by Catani et al. despite the temperature of that experiment. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.\n
Motivated by a recent experiment (Catani J. et al. , Phys. Rev. A , 85 (2012) 023623 ) we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. The amplitudes of breathing oscillations are suppressed by self-trapping, due to interactions with the Bose gas. Further, exciting phonons in the Bose gas leads to damped oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results, supported by simulations, reproduce the main features of the dynamics observed by Catani et al. despite the temperature of that experiment. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.
Abstract We study the dynamics of dipolar Bose polarons in the presence of normal and anomalous fluctuations using the time-dependent Hartree–Fock-Bogoliubov theory. The density profiles of the condensate, the anomalous component and the impurity are deeply analyzed. The time evolution of the width and the center-of-mass oscillation of such quantities are also highlighted. We calculate corrections due to quantum fluctuations and impurity to the chemical potential and the radius of the condensate, and of the anomalous component, in the weak coupling regime using the Thomas–Fermi approximation. Effects of the dipole–dipole interaction, impurity–host interaction and the anomalous fluctuation on the width and on the breathing frequencies of the impurity are discussed by variational and numerical means.
We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuring the anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contact interaction. Within the realm of the Bogoliubov--de Gennes theory, we consider static properties and low-lying excitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system, the condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed in detail. Making use of the local density approximation, we extend these results in order to study the properties of a dipolar Bose gas in a harmonic trap and in the regime of large particle numbers. After deriving the equations of motion for the general case of a triaxial trap, we analyze the influence of quantum fluctuations on important properties of the gas, such as the equilibrium configuration and the low-lying excitations in the case of a cylinder-symmetric trap. In addition to the monopole and quadrupole oscillation modes, we also discuss the radial quadrupole mode. We find that the latter acquires a quantum correction exclusively due to the dipole-dipole interaction. As a result, we identify the radial quadrupole as a reasonably accessible source for the signature of dipolar many-body effects and stress the enhancing character that dipolar interactions have for quantum fluctuations in the other oscillation modes.
The path-integral Monte Carlo method is used to simulate dilute trapped Bose gases and to investigate the equilibrium properties at finite temperatures. The quantum particles have a long-range dipole-dipole interaction and a short-range sss-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range sss-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand.
Two-dimensional (2D) dipolar atomic gases present unique opportunities for exploring novel quantum phases due to their anisotropic and long-range interactions. However, the behavior of strongly dipolar Bose gases in 2D remains unclear, especially when dipoles are tilted. Here, we demonstrate the creation and characterization of strongly dipolar 2D condensates in a quasi-2D harmonic trap with tunable dipole orientation. By investigating scale invariance properties through breathing collective mode measurements, we observe significant breaking of scale invariance when dipoles are tilted in-plane indicating the dominance of the nonlocal dipole-dipole interactions (DDIs) in this regime. Interestingly, the breaking of the scale invariant dynamics is accompanied by an increase in quantum fluctuations, as shown by comparison with mean-field and beyond mean-field theoretical studies. Our experiments also reveal that at critical tilt angles around 70°, stripe-type density modulations emerge, suggesting the presence of a roton spectrum in 2D, while the system still shows hydrodynamic nature with the phase-locking breathing behavior. This observation elucidates the many-body effect induced by DDIs in 2D, thus marking a crucial step toward realizing 2D supersolids and other exotic quantum phases.