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Register a new userSupersolid behaviour of a dipolar Bose-Einstein condensate confined in a tube
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Added by
Francesco Ancilotto
Publication date
2018
fields
Physics
and research's language is
English
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Motivated by a recent experiment [L.Chomaz et al., Nature Physics 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein Condensate (BEC) in a tubular confinement at T=0 within Density Functional Theory, where the beyond-mean-field correction to the ground state energy is included in the Local Density Approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov-de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops in its ground-state a periodic, linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e. (i) a finite non-classical translational inertia along the tube axis and (ii) the appearance, besides the phonon mode, of the Nambu-Goldstone gapless mode corresponding to phase fluctuations, and related to the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.
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We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a gaussian ansatz.
We consider the quasi-particle excitations of a trapped dipolar Bose-Einstein condensate. By mapping these excitations onto radial and angular momentum we show that the roton modes are clearly revealed as discrete fingers in parameter space, whereas the other modes form a smooth surface. We examine the properties of the roton modes and characterize how they change with the dipole interaction strength. We demonstrate how the application of a perturbing potential can be used to engineer angular rotons, i.e. allowing us to controllably select modes of non-zero angular momentum to become the lowest energy rotons.
We report on the observation of the confinement-induced collapse dynamics of a dipolar Bose-Einstein condensate (dBEC) in a one-dimensional optical lattice. We show that for a fixed interaction strength the collapse can be initiated in-trap by lowering the lattice depth below a critical value. Moreover, a stable dBEC in the lattice may become unstable during the time-of-flight dynamics upon release, due to the combined effect of the anisotropy of the dipolar interactions and inter-site coherence in the lattice.
We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalised Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction and approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $hbar$, reflecting the reduction of the global superfluidity. The real-time vortex nucleation in a rotating trap is shown to be triggered, as for a standard condensate, by the softening of the quadrupole mode. For large angular velocities, when the distance between vortices becomes comparable to the interdroplet distance, the vortices are arranged into a honeycomb structure, which coexists with the triangular geometry of the supersolid lattice and persists during the free expansion of the atomic cloud.
Vortices are expected to exist in a supersolid but experimentally their detection can be difficult because the vortex cores are localized at positions where the local density is very low. We address here this problem by performing numerical simulations of a dipolar Bose-Einstein Condensate (BEC) in a pancake confinement at $T=0$ K and study the effect of quantized vorticity on the phases that can be realized depending upon the ratio between dipolar and short-range interaction. By increasing this ratio the system undergoes a spontaneous density modulation in the form of an ordered arrangement of multi-atom droplets. This modulated phase can be either a supersolid (SS) or a normal solid (NS). In the SS state droplets are immersed in a background of low-density superfluid and the system has a finite global superfluid fraction resulting in non-classical rotational inertia. In the NS state no such superfluid background is present and the global superfluid fraction vanishes. We propose here a protocol to create vortices in modulated phases of dipolar BEC by freezing into such phases a vortex-hosting superfluid (SF) state. The resulting system, depending upon the interactions strengths, can be either a SS or a NS To discriminate between these two possible outcome of a freezing experiment, we show that upon releasing of the radial harmonic confinement, the expanding vortex-hosting SS shows tell-tale quantum interference effects which display the symmetry of the vortex lattice of the originating SF, as opposed to the behavior of the NS which shows instead a ballistic radial expansion of the individual droplets. Such markedly different behavior might be used to prove the supersolid character of rotating dipolar condensates.
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