No Arabic abstract
The concept of a roton, a special kind of elementary excitation, forming a minimum of energy at finite momentum, has been essential to understand the properties of superfluid $^4$He. In quantum liquids, rotons arise from the strong interparticle interactions, whose microscopic description remains debated. In the realm of highly-controllable quantum gases, a roton mode has been predicted to emerge due to magnetic dipole-dipole interactions despite of their weakly-interacting character. This prospect has raised considerable interest; yet roton modes in dipolar quantum gases have remained elusive to observations. Here we report experimental and theoretical studies of the momentum distribution in Bose-Einstein condensates of highly-magnetic erbium atoms, revealing the existence of the long-sought roton mode. By quenching the interactions, we observe the roton appearance of peaks at well-defined momentum. The roton momentum follows the predicted geometrical scaling with the inverse of the confinement length along the magnetisation axis. From the growth of the roton population, we probe the roton softening of the excitation spectrum in time and extract the corresponding imaginary roton gap. Our results provide a further step in the quest towards supersolidity in dipolar quantum gases.
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 and used to identify the radial and angular roton excitations by their characteristic symmetries. These fluctuations peak as a function of interaction strength indicating the crystallization transition of the system. We compare our observations to a theoretically calculated excitation spectrum allowing us to connect the crystallization mechanism with the softening of the angular roton modes.
We characterize the immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a roton-like IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled non-local Gross-Pitaevskii equations.
The deformation of a Fermi surface is a fundamental phenomenon leading to a plethora of exotic quantum phases. Understanding these phases, which play crucial roles in a wealth of systems, is a major challenge in atomic and condensed-matter physics. Here, we report on the observation of a Fermi surface deformation in a degenerate dipolar Fermi gas of erbium atoms. The deformation is caused by the interplay between strong magnetic dipole-dipole interaction and the Pauli exclusion principle. We demonstrate the many-body nature of the effect and its tunability with the Fermi energy. Our observation provides basis for future studies on anisotropic many-body phenomena in normal and superfluid phases.
Quantum fluctuations are the origin of genuine quantum many-body effects, and can be neglected in classical mean-field phenomena. Here we report on the observation of stable quantum droplets containing $sim$ 800 atoms which are expected to collapse at the mean-field level due to the essentially attractive interaction. By systematic measurements on individual droplets we demonstrate quantitatively that quantum fluctuations stabilize them against the mean-field collapse. We observe in addition interference of several droplets indicating that this stable many-body state is phase coherent.
We measure the excitation spectrum of a stable dipolar Bose--Einstein condensate over a wide momentum-range via Bragg spectroscopy. We precisely control the relative strength, $epsilon_{rm dd}$, of the dipolar to the contact interactions and observe that the spectrum increasingly deviates from the linear phononic behavior for increasing $epsilon_{rm dd}$. Reaching the dipolar dominated regime $epsilon_{rm dd}>1$, we observe the emergence of a roton minimum in the spectrum and its softening towards instability. We characterize how the excitation energy and the strength of the density-density correlations at the roton momentum vary with $epsilon_{rm dd}$. Our findings are in excellent agreement with numerical calculations based on mean-field Bogoliubov theory. When including beyond-mean-field corrections, in the form of a Lee-Huang-Yang potential, we observe a quantitative deviation from the experiment, questioning the validity of such a description in the roton regime.