Can angular oscillations probe superfluidity in dipolar supersolids?

Abstract

Angular oscillations can provide a useful probe of the superfluid properties of a system. Such measurements have recently been applied to dipolar supersolids, which exhibit both density modulation and phase coherence, and for which robust probes of superfluidity are particularly interesting. So far, these investigations have been confined to linear droplet arrays. Here, we explore angular oscillations in systems with 2D structure, which in principle have greater sensitivity to superfluidity. Surprisingly, in both experiment and simulation, we find that the frequency of angular oscillations remains nearly unchanged even when the superfluidity of the system is altered dramatically. This indicates that angular oscillation measurements do not always provide a robust experimental probe of superfluidity with typical experimental protocols.

Moment of Inertia and Dynamical Rotational Response of a Supersolid Dipolar Gas

“…Let us consider the supersolid "zig-zag" configuration shown in Fig. 1 (d) corresponfing to dd = 1.466, which is close to the value considered in the recent experiment of [25]. In the inset of Fig.…”

“…This was actually the procedure followed in [15]. As explicitly pointed out in [25] the situation is different in more two-dimensional configurations, characterized by a smaller deformation of the density profile. In [25] it was actually found that the frequency of the dominant oscillation, following the sudden release of the trap, is close to the irrotational value (3) even for configurations where the moment of inertia deviates from the irrotational value in a significant way, therefore raising the question whether the experimental measurement of the scissors mode can in general provide a measure of the moment of inertia and of the superfluid nature of the system.…”

“…1 we show f N CRI as a function of the relevant dimensionless dd = a dd /a interaction parameter across the superfluid/supersolid transition. Results are shown for the geometry considered in [13], corresponding to N = 4 × 10 4 atoms of 164 Dy in a harmonic trap of frequencies ω x,y,z = 2π(20, 40, 80)Hz (black squares), and for a geometry similar to the one considered in [25], i.e., N = 6 × 10 4 and ω x,y,z = 2π(40, 80, 160)Hz (red circles), in which the density peaks in the supersolid phase arrange in a "zig-zag" 467 respectively. e) Fraction of non-classical rotational inertia, fNCRI Eq.…”

“…e) Fraction of non-classical rotational inertia, fNCRI Eq. 5 (symbols and solid lines) and the ratio β 2 = Θirr/Θrig as function of dd (symobols and dotted lines) for the "zig-zag" (red circles) configuration [25] and for the small linear configuration (black squares) considered in [13,15]. * dd is the value of dd at which the superfluidsupersolid phase transition occurs.…”

“…[13,15] it was shown that the dominant frequency, resulting from the sudden rotation of the trap, is directly related to the value of the moment of inertia. In a very recent experiment carried out in Innsbruck [25], characterized by more two-dimensional configurations, it was shown that such a simple relationship is not longer applicable.…”