Dipolar Bose Supersolid Stripes

Abstract

We study the superfluid properties of a system of fully polarized dipolar bosons moving in the XY plane. We focus on the general case where the polarization field forms an arbitrary angle α with respect to the Z axis, while the system is still stable. We use the diffusion Monte Carlo and the path integral ground state methods to evaluate the one-body density matrix and the superfluid fractions in the region of the phase diagram where the system forms stripes. Despite its oscillatory behavior, the presence of a finite largedistance asymptotic value in the s-wave component of the one-body density matrix indicates the existence of a Bose condensate. The superfluid fraction along the stripes direction is always close to 1, while in the Y direction decreases to a small value that is nevertheless different from zero. These two facts confirm that the stripe phase of the dipolar Bose system is a clear candidate for an intrinsic supersolid without the presence of defects as described by the Andreev-Lifshitz mechanism. DOI: 10.1103/PhysRevLett.119.250402 Supersolid many-body systems appear in nature when two continuous U(1) symmetries are broken. The first one is associated with the translational invariance of the crystalline structure, while the second one corresponds to the appearance of a nontrivial global phase of the superfluid state [1]. Supersolid phases were predicted to exist in helium already in the late 1960s [2], though their experimental observation has been elusive. In fact, the claims for detection made at the beginning of this century have been refuted, as the observed behavior is not caused by finite nonconventional rotational inertia but rather to elastic effects [3]. In this way, a neat observation of supersolidity in 4 He is still lacking. In fact, it is not clear yet whether a pure, defect-free supersolid structure like the one that would be expected in 4 He really exists. Recently, the issue of supersolidity has emerged again, but now in the field of ultracold atoms. Two different experimental teams have claimed that spatial local order and superfluidity have been simultaneously observed in lattice setups [4] and in stripe phases [5]. In this way, the definition of what a supersolid really is seems to still be under discussion [6].Superfluid properties of solidlike phases are also of fundamental interest in quantum condensed matter. One of these is the stripe phase, where the system presents spatial order in one direction but not in the others. For instance, stripe phases have been of major interest since 1990, when nonhomogeneous metallic structures with broken spatial symmetry were found to favor superconductivity [7,8]. More recently, stripe phases have been observed in Bose-Einstein condensates with synthetically created spin-orbit coupling [5], where the momentum dependence of the interaction induces spatial ordering along a single direction in some regions of the phase diagram [9]. Stripe phases have also been discussed in the context of quantum dipolar physics, including very recent theoret...

Finite-range effects in ultradilute quantum drops

“…The drops originate from a delicate balance between the collapsed state, predicted by mean-field (MF) theory, and the repulsive character of the first beyond mean-field term (Lee-Huang-Yang -LHY-). The same perturbative theoretical scheme predicts self-binding in low-dimensional mixtures [2,3] and dipolar systems [4,5]. Recently, these predicted quantum drops have been observed in several experiments [6][7][8][9] and they resemble the well-known liquid Helium drops [10,11].…”

“…as it can be seen in Fig. 2 experiments, are then used in the functional form (5) with E int = ρ E/N . With the new functional, based on our DMC results, we can study the quantum drops with the proper number of particles which is too large for a direct DMC simulation.…”

Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipolar stripes

“…The system is stable towards collapse as long as the tilting angle α is smaller than the critical value α c 0.61. Our simulations are carried out in a rectangular box, with periodic boundary conditions (PBC), to correctly commensurate the stripes [12], similarly to what is made in the simulation of crystals.…”

“…In Fig. 3, we show PIMC results for the superfluid fraction at a density nr 2 0 = 256 and tilting angle α = 0.6 where the stripe phase is stable [12]. In the left panel, we show the behavior of the superfluid fraction as a function of temperature and for different number of particles in the simulation box.…”

“…In a previous work [12], the superfluid properties of the different phases of a dipolar system in two dimensions were studied at zero temperature. The stripe phase, that appears for certain densities and tilting angles, was shown to exhibit the characteristics which define a supersolid state.…”