Excitations and Stripe Phase Formation in a Two-Dimensional Dipolar Bose Gas with Tilted Polarization

Abstract

We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a non-perpendicular polarization with respect to the system plane. For sufficiently high density an increase of the polarization angle leads to a density instability of the gas phase in the direction where the anisotropic interaction is strongest. Using a dynamic many-body theory, we calculate the dynamic structure function in the gas phase which shows the anisotropic dispersion of the excitations. We find that the energy of roton excitations in the strongly interacting direction decreases with increasing polarization angle and almost vanishes close to the instability. Exact path integral ground state Monte Carlo simulations show that this instability is indeed a quantum phase transition to a stripe phase, characterized by long-range order in the strongly interacting direction.Strongly correlated dipolar Bose gases in two dimensions (2D) polarized along the direction normal to the system plane have been extensively investigated in recent years [1][2][3][4]. The ratio between the dipolar length r 0 = mC dd /(4πh 2 ) and the average interparticle distance provides a measure of the strength of the interaction. C dd is the coupling constant proportional to the square of the (magnetic µ or electric d) dipole moment, resulting in a dipolar length that can range from a fewÅ for magnetic dipolar systems like 52 Cr (µ = 6µ B , with µ B the Bohr magneton), to thousands ofÅ for heteronuclear polar molecules like KRb, LiCs [5], or RbCs [6]. However, chemical reactions and three-body losses impose limitations on what can be measured in experiments with polar molecules. Therefore, recent efforts focus also on exotic lanthanide magnetic systems like 164 Dy or 168 Er, [7] where the combined effect of a large magnetic moment (µ = 10µ B for 164 Dy and µ = 7µ B for 168 Er) and a large mass, lead to dipolar length scales that, although still significantly lower than the corresponding value for polar molecules, is several times larger than that of 52 Cr. Er 2 with µ = 14µ B and twice the mass of Er would reach even higher values of r 0 [8].A 2D dipolar Bose gas polarized along the normal direction to the confining plane develops a roton excitation at high density due to the strong repulsion between dipoles at short distances [3]. Other works have revealed competing effects in a quasi-2D geometry due to the head-to-tail attraction of the dipole-dipole interaction when the third spatial dimension is added, to the point that the system becomes unstable against density fluctuation below a critical trapping frequency in that direction [9][10][11]. This leads to the question of whether a similar situation can hold in a purely 2D geometry when a head-to-tail component to the dipole-dipole interaction is added by tilting the polarization with respect to the direction normal to the system plane. The interaction becomes anisotropic, V (r) = V (x, y) = C dd 4πr 3 1 − 3 x 2 r 2 sin 2 α , with particles moving in the x, y...

Droplets of Trapped Quantum Dipolar Bosons

“…The particular form of this interaction leads to surprising new features not present in other systems, like stripe phases in two-dimensional (2D) Bose systems [10]. Similar phases in Fermi systems have also been predicted [11,12], although these are more controversial [13].…”

Vortices and vortex lattices in quantum ferrofluids

“…The relatively recent realization of dipolar cold atoms and molecules now provides an alternative venue for investigating supersolid phases. Apart from the strongly correlated dipolar systems [70,[72][73][74][75][76] cited in section 2, extended Bose-Hubbard lattice models are also thought to support supersolidity [287][288][289][290][291][292][293][294][295][296][297]. The common ingredient in both sets of investigations is the presence of long-range interactions.…”

Multicomponent correlated-basis-function method and its application to multilayered dipolar Bose gases

“…The ground state can be obtained, for example, from quantum Monte Carlo simulations. This provides exact ground state properties of dipolar quantum gases [22][23][24][38][39][40][41] , but it would be computationally very demanding for the large number of layers that we study in this work. For the fairly low partial denstities ρ α that we consider here, it is sufficient to use approximate methods.…”