Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge studying such non-equilibrium dynamics the scarcity experimental tools for characterizing their complex transient states. We employ measurements full quantum mechanical probability distributions matter-wave interference to study a coherently split one-dimensional Bose gas and obtain unprecedented information about dynamical states system. Following initial rapid evolution, reveal...

Detecting multiple temperatures Most people have an intuitive understanding of temperature. In the context statistical mechanics, higher temperature, more a system is removed from its lowest energy state. Things become complicated in nonequilibrium governed by quantum mechanics and constrained several conserved quantities. Langen et al. showed that as many 10 temperature-like parameters are necessary to describe steady state one-dimensional gas Rb atoms was split into two particular way (see...

Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning interatomic interactions lead to emergence two new states matter: liquid-like self-bound droplets supersolid crystals formed from these droplets. We review properties exotic matter summarize experimental progress made using gases mixtures. conclude with an outline important...

We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals ground state phase diagram with three distinct regimes - regular condensate, incoherent coherent arrays quantum droplets. In latter droplets are connected by finite superfluid density, which leads addition to periodic density modulation robust coherence throughout whole system. further demonstrate that we able dynamically approach our experiment its...

We demonstrate single-site addressability in a two-dimensional optical lattice with 600 nm spacing. After loading Bose-Einstein condensate the potential, we use focused electron beam to remove atoms from selected sites. The patterned structure is subsequently imaged by means of scanning microscopy. This technique allows one create arbitrary patterns mesoscopic atomic ensembles. find that are remarkably stable against tunneling diffusion. Such microengineered quantum gases versatile resource...

The relaxation of isolated quantum many-body systems is a major unsolved problem connecting statistical and physics. Studying such processes remains challenge despite considerable efforts. Experimentally, it requires the creation manipulation well-controlled truly systems. In this context, ultracold neutral atoms provide unique opportunities to understand nonequilibrium phenomena because large set available methods isolate, manipulate, probe these Here, we give an overview rapid experimental...

We study the lifetime of a Bose gas at and around unitarity using Feshbach resonance in lithium 7. At unitarity, we measure temperature dependence three-body decay coefficient ${L}_{3}$. Our data follow ${L}_{3}={\ensuremath{\lambda}}_{3}/{T}^{2}$ law with ${\ensuremath{\lambda}}_{3}=2.5(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }(\ensuremath{\mu}\mathrm{K}{)}^{2}\text{ }{\mathrm{cm}}^{6}\text{...

We review the recent progress in understanding of relaxation isolated near-integrable quantum many-body systems. Focusing on prethermalization and universal dynamics following a quench, we describe experiments with ultracold atomic gases that illustrate these phenomena summarize essential theoretical concepts employed to interpret them. Our discussion highlights key topics link different approaches this interdisciplinary field, including generalized Gibbs ensemble, non-thermal fixed points,...

We study theoretically and experimentally the behavior of a strongly confined dipolar Bose-Einstein condensate in regime quantum-mechanical stabilization by beyond-mean-field effects. Theoretically, we demonstrate that self-organized ``striped'' ground states are predicted framework extended Gross-Pitaevskii theory. Experimentally, tilting magnetic dipoles show striped can be generated, likely their metastable state. Matter-wave interference experiments with multiple stripes there is no...

The authors use a model based on the Gross-Pitaevskii equation and quantum Monte-Carlo simulations, combined with experimental results, to show that correlations in dipolar droplets are not negligible play role onset of an observable shift critical atom number self-bound state.

We report on the observation of scissors mode a single dipolar quantum droplet. The existence this is due to breaking rotational symmetry by dipole-dipole interaction, which fixed along an external homogeneous magnetic field. By modulating orientation field, we introduce new spectroscopic technique for studying droplets. This provides precise probe interactions in system, allowing us extract background scattering length $^{164}\mathrm{Dy}$ $69(4){a}_{0}$. Our results establish analogy...

Pattern formation is a ubiquitous phenomenon observed in nonlinear and out-of-equilibrium systems. In equilibrium, quantum ferrofluids formed from ultracold atoms were recently shown to spontaneously develop coherent density patterns, manifesting supersolid. We theoretically investigate the phase diagram of such oblate trap geometries find an even wider range exotic states matter. Two-dimensional supersolid crystals individual ferrofluid droplets dominate at low densities. For higher...

We observe signatures of radial and angular roton excitations around a droplet crystallization transition in dipolar Bose-Einstein condensates. In situ measurements are used to characterize the density fluctuations near this transition. The static structure factor is extracted identify by their characteristic symmetries. These peak as function interaction strength indicating system. compare our observations theoretically calculated excitation spectrum allowing us connect mechanism with...

We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. observe formation self-bound droplets, and explore phase diagrams that feature a variety exotic supersolid states. In all these cases, large tunable dipole moments enable unexplored regimes phenomena, including liquidlike density saturation universal stability scaling laws for as well pattern limits droplet supersolidity. discuss realistic experimental approach to realize...

The combination of topology and quantum criticality can give rise to an exotic mix counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly correlated Hamiltonian: the 1D extended Bose-Hubbard model. In particular, reveal presence two distinct critical points with localized edge states gapless bulk excitations. Our results separate phases, one topologically protected other trivial, both characterized by long-range ordered string...

We detail the experimental observation of non-equilibrium many-body phenomenon prethermalization. study dynamics a rapidly and coherently split one-dimensional Bose gas. An analysis based on use full quantum mechanical probability distributions matter wave interference contrast reveals that system evolves toward quasi-steady state. This state, which can be characterized by an effective temperature, is not final thermal equilibrium compare evolution to integrable Tomonaga–Luttinger liquid...

We describe the relaxation dynamics of a coherently split one-dimensional (1D) Bose gas in harmonic approximation. A dephased, prethermalized state emerges light-cone-like evolution which is connected to spreading correlations with characteristic velocity. In our description we put special emphasis on influence longitudinal trapping potential and finite size system, both are highly relevant experiments. particular, quantify their phase correlation properties velocity established. Finally,...

We experimentally study the dynamics of a degenerate one-dimensional Bose gas that is subject to continuous outcoupling atoms. Although standard evaporative cooling rendered ineffective by absence thermalizing collisions in this system, we observe substantial cooling. This proceeds through homogeneous particle dissipation and many-body dephasing, enabling preparation otherwise unexpectedly low temperatures. Our observations establish scaling relation between temperature number, provide...

We theoretically investigate the spectrum of elementary excitations a trapped dipolar quantum gas across BEC-supersolid phase transition. Our calculations reveal existence distinct Higgs and Nambu-Goldstone modes that emerge from softening roton BEC at transition point. On supersolid side transition, energy mode increases rapidly, leading to strong coupling higher-lying modes. study highlights how symmetry-breaking nature state translates finite-size systems.