Feshbach resonances in an erbium-dysprosium dipolar mixture

We report on the observation of heteronuclear magnetic Feshbach resonances in several isotope mixtures of the highly magnetic elements erbium and dysprosium. Among many narrow features, we identify two resonances with a width greater than one Gauss. We characterize one of these resonances, in a mixture of ${}^{168}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$, in terms of loss rates and elastic cross section, and observe a temperature dependence of the on-resonance loss rate suggestive of a universal scaling associated with broad resonances. Our observations hold promise for the use of such a resonance for tuning the interspecies scattering properties in a dipolar mixture. We further compare the prevalence of narrow resonances in an ${}^{166}\mathrm{Er}-{}^{164}\mathrm{Dy}$ mixture to the single-species case, and observe an increased density of resonances in the mixture.

Figure 1

(a) Trap loss from the 13.5 G resonance in the Bose-Bose mixture ${}^{168}\mathrm{Er}-{}^{164}\mathrm{Dy}$ (red circles and blue squares points, respectively). Empty symbols correspond to narrow single-species resonances, which we exclude from fits. Each point is an average over four experimental repetitions. For each magnetic field, the atom number recorded after 200 ms of hold time is normalized to that at a short hold time of 10 ms. The lines are the Gaussian fits to the data. The inset shows erbium loss measured in a different dataset with 5-mG resolution, and highlights the structure present on the center of the feature. The same structure is visible also for the dysprosium atoms in the mixture. (b) Interspecies elastic cross section ${\sigma }_{\mathrm{ErDy}}$ measured across the Feshbach resonance using cross-species thermalization. Each value of ${\sigma }_{\mathrm{ErDy}}$ is extracted from thermalization data using a numerical model for thermalization that includes temporal variation in atom number and temperature; see main text and the Appendix.

Figure 2

Three-body loss coefficient $L_3$ extracted from on-resonance loss measurements at the resonance position for different temperatures (black circles), along with a fit to a $1/T^2$ scaling (black line), as expected for universal three-body loss. The inset shows the resonance width extracted as FWHM from Gaussian fits to the trap-loss spectra versus cloud temperature for a different dataset. Red circles and blue squares refer to erbium and dysprosium, respectively. The reported temperature comes from a TOF estimation.

Figure 3

High-resolution trap-loss spectroscopy for a balanced mixture of ${}^{166}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$ (red and blue curves respectively), with initial atom numbers of roughly ${10}^5$ per species at a temperature of 500 nK after 400 ms of interaction time. The magenta ticks indicate the heteronuclear resonance positions as extracted by our analysis (see main text). The measurement is composed of four datasets $[0,10]$ G, $[22,32]$ G, $[50,60]$ G, and $[60,70]$ G with a stepsize of 5 mG. Each point is an average over four experimental repetitions. Atom numbers are normalized to the maximum of each dataset for ease of reading. The broad loss feature in Dy near 68.8 G was not observed in previous work [45], and may result from a technical source of loss in our experiment.

Figure 4

(a)–(d) Staircase function describing the number of Feshbach resonances as a function of the four investigated magnetic-field ranges: $[0,10]$ G, $[22,32]$ G, $[50,60]$ G, and $[60,70]$ G respectively. The black line shows the number of heteronuclear resonances. The red and blue lines show the number of homonuclear resonances for ${}^{166}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$, respectively. The shaded areas represent our confidence intervals (see main text).

Figure 5

Trap loss spectra for fermionic ${}^{161}\mathrm{Dy}$ in combination with bosonic ${}^{166}\mathrm{Er}, {}^{168}\mathrm{Er}$, and ${}^{170}\mathrm{Er}$, and fermionic ${}^{167}\mathrm{Er}$ (a)–(d), respectively. Red circles represent erbium, blues squares represent dysprosium, and lines are Gaussian fits to the losses. The solid vertical gray lines highlight the peak centers from the fit over dysprosium losses. For the plots with bosonic erbium, the atom number after 100 ms of interaction time is normalized to a short hold time of 5 ms. In the plot with ${}^{167}\mathrm{Er}$, the normalization is performed using the maximum value in the dataset. For all panels, each point is an average over four experimental repetitions.

Figure 6

Sample temperature traces for erbium (filled circles) and dysprosium (hollow squares) after dysprosium is heated. Purple, green, and orange correspond to magnetic fields of 12, 13.5, and 17 G, respectively. Fit lines represent the results of the numerical integration of Eq. (A2), which fits the temperature profile of erbium based on its initial value and the dysprosium temperatures. Different evaporation conditions cause the curves to have slightly different initial and final conditions (see main text).