A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Nonclassical rotational effects have also been considered in the context of the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here, we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. Using a dipolar gas of dysprosium atoms, we studied a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, previously investigated in ordinary superfluids. From the measured moment of inertia, we deduced a superfluid fraction that is different from zero and of order of unity, providing direct evidence of the superfluid nature of the dipolar supersolid.
A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Nonclassical rotational effects have also been considered in the context of the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here, we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. Using a dipolar gas of dysprosium atoms, we studied a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, previously investigated in ordinary superfluids. From the measured moment of inertia, we deduced a superfluid fraction that is different from zero and of order of unity, providing direct evidence of the superfluid nature of the dipolar supersolid.
Distinctive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment of inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation, we show that the moment of inertia determines the value of the frequency of the scissors mode, which is significantly affected by the reduction of superfluidity in the supersolid phase. The case of an in-plane isotropic trapping is instead well suited to study the formation of quantized vortices, which are shown to be characterized, in the supersolid phase, by a sizeable deformed core, caused by the presence of the surrounding density peaks.
The elusive supersolid, an exotic quantum phase that combines the properties of a crystalline solid and those of a superfluid, has been recently discovered in a system of Bose-condensed strongly magnetic atoms. In this paper, I report on an experiment that directly demonstrates the superfluid behavior of the dipolar supersolid measuring its anomalous response to a rotational excitation. I complement the illustration of the experimental results with a review and an original interpretation of a seminal model due to Leggett.
Abstract Supersolid states simultaneously feature properties typically associated with a solid and with a superfluid. Like a solid, they possess crystalline order, manifesting as a periodic modulation of the particle density; but unlike a typical solid, they also have superfluid properties, resulting from coherent particle delocalization across the system. Such states were initially envisioned in the context of bulk solid helium, as a possible answer to the question of whether a solid could have superfluid properties1–5. Although supersolidity has not been observed in solid helium (despite much effort)6, ultracold atomic gases provide an alternative approach, recently enabling the observation and study of supersolids with dipolar atoms7–16. However, unlike the proposed phenomena in helium, these gaseous systems have so far only shown supersolidity along a single direction. Here we demonstrate the extension of supersolid properties into two dimensions by preparing a supersolid quantum gas of dysprosium atoms on both sides of a structural phase transition similar to those occurring in ionic chains17–20, quantum wires21, 22 and theoretically in chains of individual dipolar particles23, 24. This opens the possibility of studying rich excitation properties25–28, including vortex formation29–31, and ground-state phases with varied geometrical structure7, 32 in a highly flexible and controllable system.
We show that knowledge of the time-dependent response of a trapped gas, subject to a sudden rotation of a confining harmonic potential, allows for the determination of the moment of inertia of dipolar supersolid configurations. While in the presence of one-dimensional arrays of droplets the frequency of the resulting scissors oscillation provides accurate access to the value of the moment of inertia, two-dimensional-like configurations are characterized by low-frequency resonances in the rotating signal, reflecting the presence of significant rigid-body components in the rotational motion. Using the formalism of response-function theory and simulations based on the so-called extended time-dependent Gross-Pitaevskii equation, we point out the crucial role played by the low-frequency components in the determination of the moment of inertia and of its deviations from the irrotational value. We also propose a protocol based on the stationary rotation of the trap, followed by its sudden stop, which might provide a promising alternative to the experimental evaluation of the moment of inertia.
This thesis discusses the experiments on 2D dipolar Bose gas of ultracold erbium atoms. Long-range and anisotropic dipole-dipole interaction induces complex orders in quantum many-body systems. Highly magnetic lanthanide atoms such as dysprosium and erbium have the largest magnetic moment in the periodic table, which has attracted significant attention in the past decades. Starting from quantum degenerate dysprosium and erbium atoms, exotic phases like quantum droplets, supersolid, dipolar quantum solid in the Hubbard regime have been studied. However, the 2D dipolar superfluid still remains understudied, despite being theoretically discussed for over two decades. Although tremendous theoretical proposals predict different phenomena in 2D dipolar superfluids, our first interest is to know how the superfluidity emerges in the 2D dipolar gases at finite temperatures. Our observations suggest that the superfluid transition can be well described by the Berezinskii-Kosterlitz-Thouless transition with an effective contact interaction as a function of dipolar orientation. With the 2D dipolar superfluid with strong DDI, we characterized the elementary excitation of the matter: the collective breathing mode. Our measurements establish how the competition between local and nonlocal interaction in strongly dipolar 2D superfluid retains quasi-scale invariance or strongly breaks scale invariance. By further searching the interaction parameters, we created stripes with global coherence, which are the first supersolid stripes in 2D. Experiments including measuring density fluctuation, coherence, and collective mode have been performed to understand the 2D supersolid. At last, we also observe unconventional light scattering from round-disk dipolar BECs, which provides new possibilities for atom optics.
We show that a sudden change in the polarization direction of the magnetic dipole moments of the atoms in a dipolar Bose-Einstein condensate (BEC) can serve as a useful dynamical probe to sense its superfluid and solid-like properties. We find that for small angular deviation of the polarization direction, actuated for instance by modifying an external magnetic field, the superfluid state undergoes an undamped scissors mode oscillation, a characteristic signature of superfluidity. In contrast, both the droplet and supersolid states exhibit a scissors-mode oscillation, which is effectively damped due to multiple closely spaced frequency components. Notably, we find that this damping rate provides a qualitative measure for the rigidity of different phases of a dipolar BEC. Furthermore, there exists a maximum angular deviation of the polarization direction, beyond which the droplet and the supersolid states undergo a permanent deformation i.e., we find an analog of the usual elastic to plastic phase transition of solids. We characterize this transition numerically using the fidelity of the condensate wavefunction with the ground state as well as the droplet width and periodicity of the supersolid density of the condensate which are experimentally accessible. Thus, the dynamical protocol introduced here can be an important experimental benchmark to identify and characterize the superfluid and solid properties of different phases of dipolar BECs.