In the short time since the first observation of supersolid states of ultracold dipolar atoms, substantial progress has been made in understanding the zero-temperature phase diagram and low-energy excitations of these systems. Less is known, however, about their finite-temperature properties, particularly relevant for supersolids formed by cooling through direct evaporation. Here, we explore this realm by characterizing the evaporative formation and subsequent decay of a dipolar supersolid by combining high-resolution in-trap imaging with time-of-flight observables. As our atomic system cools toward quantum degeneracy, it first undergoes a transition from thermal gas to a crystalline state with the appearance of periodic density modulation. This is followed by a transition to a supersolid state with the emergence of long-range phase coherence. Further, we explore the role of temperature in the development of the modulated state.
In the short time since the first observation of supersolid states of ultracold dipolar atoms, substantial progress has been made in understanding the zero-temperature phase diagram and low-energy excitations of these systems. Less is known, however, about their finite-temperature properties, particularly relevant for supersolids formed by cooling through direct evaporation. Here, we explore this realm by characterizing the evaporative formation and subsequent decay of a dipolar supersolid by combining high-resolution in-trap imaging with time-of-flight observables. As our atomic system cools toward quantum degeneracy, it first undergoes a transition from thermal gas to a crystalline state with the appearance of periodic density modulation. This is followed by a transition to a supersolid state with the emergence of long-range phase coherence. Further, we explore the role of temperature in the development of the modulated state.
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.
Dipolar condensates have recently been coaxed to form the long-sought supersolid phase. While one-dimensional supersolids may be prepared by triggering a roton instability, we find that such a procedure in two dimensions (2D) leads to a loss of both global phase coherence and crystalline order. Unlike in 1D, the 2D roton modes have little in common with the supersolid configuration. We develop a finite-temperature stochastic Gross-Pitaevskii theory that includes beyond-mean-field effects to explore the formation process in 2D and find that evaporative cooling directly into the supersolid phase-hence bypassing the first-order roton instability-can produce a robust supersolid in a circular trap. Importantly, the resulting supersolid is stable at the final nonzero temperature. We then experimentally produce a 2D supersolid in a near-circular trap through such an evaporative procedure. Our work provides insight into the process of supersolid formation in 2D and defines a realistic path to the formation of large two-dimensional supersolid arrays.
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.
Fluctuations typically destroy long-range order in two-dimensional (2D) systems, posing a fundamental challenge to the existence of exotic states like supersolids, which paradoxically combine solid-like structure with frictionless superfluid flow. While long-predicted, the definitive observation of a 2D supersolid has remained an outstanding experimental goal. Here, we report the observation of a supersolid stripe phase in a strongly dipolar quantum gas of erbium atoms confined to 2D. We directly image the periodic density modulation, confirming its global phase coherence through matter-wave interference and demonstrating its phase rigidity relevant to the low-energy Goldstone mode, consistent with numerical calculations. Through collective excitation measurements, we demonstrate the hydrodynamic behavior of the supersolid. This work highlights a novel mechanism for supersolid formation in low dimensions, and opens the door for future research on the intricate interplay between temperature, supersolidity, and dimensionality.
High-energy scattering spectroscopy is a widely established technique for probing the characteristic properties of complex physical systems. Motivated by the recent observation of long-sought supersolid states in dipolar quantum Bose gases, I investigate the general relationships existing between the density contrast, the superfluid fraction, and the response to a high-energy scattering probe of density-modulated states within a classical-field approach. I focus on the two extreme regimes of shallow and deep supersolids, which are of particular interest in describing the phase transitions of the supersolid to a uniform superfluid and an incoherent crystal state, respectively. Using relevant Ans\"atze for the fields of dipolar supersolid states in these regimes, I specify and illustrate the scaling laws relating the three observables. This work was first prompted to develop an intuitive understanding of a concomitant study based on experiments and mean-field numerical simulations. Beyond this specific application, this works provides a simple and general framework to describe density-modulated states and in particular the intriguing case of supersolids. It describes key properties characterizing the supersolid order and highlights possibilities for probing such properties based on high-energy scattering response.
We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate.The theory reveals a ground state phase diagram with three distinct regimes-a regular Bose-Einstein condensate and incoherent and coherent arrays of quantum droplets.The coherent droplets are connected by a background condensate, which leads-in addition to the periodic density modulation-to a robust phase coherence throughout the whole system.We further theoretically demonstrate that we are able to dynamically approach the ground state in our experiment and that its lifetime is limited only by three-body losses.Experimentally we probe and confirm the signatures of the phase diagram by observing the in situ density modulation as well as the phase coherence using matter wave interference.