We consider the ground state properties of a trapped dipolar condensate under the influence of quantum fluctuations. We show that this system can undergo a phase transition from a low density condensate state to a high density droplet state, which is stabilized by quantum fluctuations. The energetically favored state depends on the geometry of the confining potential, the number of atoms and the two-body interactions. We develop a simple variational ansatz and validate it against full numerical solutions. We produce a phase diagram for the system and present results relevant to current experiments with dysprosium and erbium condensates.

We study the superfluid character of a dipolar Bose-Einstein condensate (DBEC) in a quasi-two dimensional (q2D) geometry. In particular, we allow for the dipole polarization to have some nonzero projection into the plane of the condensate so that the effective interaction is anisotropic in this plane, yielding an anisotropic dispersion for propagation of quasiparticles. By performing direct numerical simulations of a probe moving through the DBEC, we observe the sudden onset of drag or creation of vortex-antivortex pairs at critical velocities that depend strongly on the direction of the probe's motion. This anisotropy emerges because of the anisotropic manifestation of a roton-like mode in the system.A quintessential feature of a superfluid is its ability to support dissipationless flow, for example, when an object moves through a superfluid and experiences no drag force. This, however, only occurs when the object is moving below a certain critical velocity; when it exceeds this critical velocity it dissipates energy into excitations of the superfluid, resulting in a net drag force on the object and the breakdown of superfluid flow.In many superfluids, such as dilute Bose-Einstein condensates (BECs) of atoms, this critical velocity is simply the speed of sound in the system, which is set by the density and the s-wave scattering length of the atoms. However, for a dense superfluid such as liquid 4 He, this is not the case. In 4 He, the critical velocity is set by a roton mode, corresponding to a peak in the static structure factor of the system at some finite, non-zero momentum, with a characteristic velocity that is considerably less than the speed of sound in the liquid. This feature has been verified experimentally via measurements of ion-drift velocity in the fluid [1], thereby providing insight into the detailed structure of the system. Interestingly, a BEC of dipolar constituents (DBEC) is also expected to possess a roton-like dispersion, in spite of existing in a dilute gaseous state [2]. Unlike the dispersion of 4 He, the dispersion of a DBEC is highly tunable as a function of the condensate density and dipole-dipole interaction (ddi) strength. Additionally, the DBEC is set apart from liquid 4 He in that its interactions depend on how the dipoles are oriented in space. Thus, the DBEC provides an ideal system to study the effects that anisotropies have on the bulk properties of a superfluid, such as its critical velocity. Anisotropic dispersions have been predicted for a 1D lattice system of q2D DBECs [3], periodically dressed BECs [4] and for dipolar gases in a 2D lattice [5]. Additionally, anisotropic solitons have been predicted for dipolar gases [6].In this Letter we consider a DBEC in a quasi-twodimensional (q2D) geometry and allow for the dipoles to be polarized at a nonzero angle into this plane so that the in-plane interaction is anisotropic. We perform numerical simulations of a probe moving through the DBEC. This probe experiences a sudden onset of drag at a certain velocity, the critical veloci...

We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing perturbation theory, we relate these oscillations to a previously identified "rotonlike" mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously.

We demonstrate that a dipolar condensate can be prepared into a three-dimensional wavepacket that remains localized when released in free-space. Such self-bound states arise from the interplay of the two-body interactions and quantum fluctuations. We develop a phase diagram for the parameter regimes where these self-bound states are stable, examine their properties, and demonstrate how they can be produced in current experiments.