Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Low-temperature ordering of the dimer phase of a two-dimensional model of core-softened particles

Purely pairwise interactions of the core-softened type, i.e., featuring a soft repulsion followed by a hard-core interaction at shorter distance, give rise to nontrivial equilibrium structures entirely different from the standard close packing of spheres. In particular, in a suitable low-temperature region of their phase diagram, such interactions are well known to favor a transition from a fluid to a cluster crystal. The residual mutual interaction between individual clusters can lead to the formation of patterns of their reciprocal orientations. In this work, we investigate two examples of such models in two dimensions, at the density most appropriate to the dimer phase, whereby clusters consist of just two particles, studying them with optimization techniques and Monte Carlo simulations. We focus on the dimer crystal, and unveil a second phase transition at extremely low temperature. This transition leads from a triangular dimer lattice with randomly disordered dimer orientations at high temperature to a reduced-symmetry ground state with nematic orientational order and a slightly distorted structure characterized by a centered-rectangular lattice at low temperature.

Emergence of an Ising critical regime in the clustering of one-dimensional soft matter revealed through string variables

Soft matter systems are renowned for being able to display complex emerging phenomena such as clustering phases. Recently, a surprising quantum phase transition has been revealed in a one-dimensional (1D) system composed of bosons interacting via a pairwise soft potential in the continuum. It was shown that the spatial coordinates undergoing two-particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model. In this work we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we study the low-temperature behavior of three different classical models of 1D soft matter, whose interparticle interactions allow for clustering. The same string variables highlight that, at the commensurate density for the two-particle cluster phase, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, namely the presence of an anomalous peak in the low-temperature specific heat, thus indicating the emergence of Schottky phenomenology in a nonmagnetic fluid.

Excitation Spectrum of a Trapped Dipolar Supersolid and Its Experimental Evidence

We study the spectrum of elementary excitations of a dipolar Bose gas in a three-dimensional anisotropic trap across the superfluid-supersolid phase transition. Theoretically, we show that, when entering the supersolid phase, two distinct excitation branches appear, respectively associated with dominantly crystal and superfluid excitations. These results confirm infinite-system predictions, showing that finite-size effects play only a small qualitative role, and connect the two branches to the simultaneous occurrence of crystal and superfluid orders. Experimentally, we probe compressional excitations in an Er quantum gas across the phase diagram. While in the Bose-Einstein condensate regime the system exhibits an ordinary quadrupole oscillation, in the supersolid regime we observe a striking two-frequency response of the system, related to the two spontaneously broken symmetries.