Scissors Mode of Dipolar Quantum Droplets of Dysprosium Atoms

Abstract

We report on the observation of the scissors mode of a single dipolar quantum droplet. The existence of this mode is due to the breaking of the rotational symmetry by the dipole-dipole interaction, which is fixed along an external homogeneous magnetic field. By modulating the orientation of this magnetic field, we introduce a new spectroscopic technique for studying dipolar quantum droplets. This provides a precise probe for interactions in the system, allowing us to extract a background scattering length for ^{164}Dy of 69(4)a_{0}. Our results establish an analogy between quantum droplets and atomic nuclei, where the existence of the scissors mode is also only due to internal interactions. They further open the possibility to explore physics beyond the available theoretical models for strongly dipolar quantum gases.

Dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equation

“…Taking the average of these two procedures we end up with a bg,162 = 140(4) a 0 , in good agreement with the quoted literature value [25][26][27]. Note, however, that the systematic uncertainties for the measurement of the background scattering length of 164 Dy [6] apply here as well, leading to a final value with the respective uncertainty of a bg,162 = 140(7) a 0 .…”

“…Free from the systematic shift of the measurement, we can extract the ratio of the respective background scattering lengths of the two isotopes, 162 Dy and 164 Dy. With this we find a ratio of a bg,162 /a bg,164 = 2.03 (6).…”

“…This effect is smaller than our uncertainty in this quantity, and we can thus safely neglect it. For the comparison with the 164 Dy measurements we use the Feshbach resonances discussed in [2,5] together with the latest measurement of the background scattering length in the droplet state a bg,164 = 69(4) a 0 [6]. With this we observe systematically lower critical atom numbers compared to the eGPE simulations, that could be accounted for by the uncertainty of the scattering length calibration.…”

“…Naturally, the same procedure can be done using any quantum many-body theory able to predict critical atom numbers for a self-bound droplet. Starting from the latest measurement of the background scattering length of 164 Dy [6] we first shift the eGPE critical number curve [33] in order to minimize the difference to the experimental data for 164 Dy [24]. From this point on we optimize the background scattering length a bg,162 to minimize the residual of our new measurements with respect to this shifted theory curve [24].…”

“…Using the latest measurement of the background scattering length of 164 Dy [6] as a starting point, we use the sensitive scaling of the critical atom number to extract the background scattering length of 162 Dy. This procedure, that is described in detail below, assumes that the critical atom number does not depend on other parameters, e.g.…”