Abstract
We present a theory for the emergence of a supersolid state in a cigar-shaped dipolar quantum Bose gas. Our approach is based on a reduced three-dimensional (3D) theory, where the condensate wavefunction is decomposed into an axial field and a transverse part described variationally. This provides an accurate fully 3D description that is specific to the regime of current experiments and efficient to compute. We apply this theory to understand the phase diagram for a gas in an infinite tube potential. We find that the supersolid transition has continuous and discontinuous regions as the averaged density varies. We develop two simplified analytic models to characterize the phase diagram and elucidate the roles of quantum droplets and of the roton excitation.
Highlights
A supersolid is a state of matter exhibiting both crystalline order and superfluidity [1,2,3,4,5]
Our results show that the latter case provides a good description of the continuous transition regime, which is initiated by the softening of a roton excitation
We have developed theory for a tube confined dipolar quantum gas to understand its phase diagram
Summary
A supersolid is a state of matter exhibiting both crystalline order and superfluidity [1,2,3,4,5]. Three experiments have reported the observation of a supersolid in a dipolar Bose-Einstein condensate (BEC) [20,21,22] and have studied its elementary excitations [23,24,25] These experiments have all used an elongated trap with the atomic magnetic dipoles polarized along a tightly confined direction [e.g., see Fig. 1(a)]. The supersolid transition was explored by reducing the s-wave scattering length below a critical value whereby crystalline order (spatial density modulation of the gas) develops along the weakly confined direction. 1(b) and 1(c) revealing the contrast of the density modulations (i.e., crystalline order) and the persistence of superfluidity, respectively These results show that the condensate to supersolid transition is continuous for a range of intermediate densities, but is otherwise discontinuous. Our results show that the latter case provides a good description of the continuous transition regime, which is initiated by the softening of a roton excitation
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