Doppler spectroscopy of an ytterbium Bose-Einstein condensate on the clock transition

We describe Doppler spectroscopy of Bose-Einstein condensates of ytterbium atoms using a narrow optical transition. We address the optical clock transition around 578 nm between the ${}^1{S}_0$ and the ${}^3{P}_0$ states with a laser system locked on a high-finesse cavity. We show how the absolute frequency of the cavity modes can be determined within a few tens of kilohertz using high-resolution spectroscopy on molecular iodine. We show that optical spectra reflect the velocity distribution of expanding condensates in free fall or after release inside an optical waveguide. We demonstrate subkilohertz spectral linewidths, with long-term drifts of the resonance frequency well below 1 kHz/h. These results open the way to high-resolution spectroscopy of many-body systems.

Figure 1

Layout of the optical setup. A laser source at 578.4 nm is sent to three paths: one leading to an ultrastable cavity to which the laser frequency is locked, one leading to the trapped atomic sample, and one used for iodine spectroscopy. Inset: Spacing between the various frequencies involved, with ${\omega }_{\mathrm{cav}}^{\left(n\right)}$ the cavity mode to which the laser frequency is locked and ${\omega }_{eg}$ the clock transition frequency. AOM, acousto-optical modulator; EOM, electro-optical modulator; ULE, ultralow-expansion glass; SA, saturated absorption.

Figure 2

(a) Frequency ruler showing the relative positions of several cavity resonances, labeled with mode indexes $n$ to $n+3$; the clock transition frequency, labeled ${\omega }_{eg}$; and the iodine resonance, labeled ${\omega }_{I_2}$. (b) Closeup near the iodine resonance, showing the relative positions of the laser frequencies used for spectroscopy when the iodine spectroscopy laser is resonant. (c) Experimental iodine absorption spectrum (top) and cavity transmission (bottom) as a function of the laser frequency. Inset: Zoom-in on the narrow cavity resonance.

Figure 3

Cavity resonance frequency (mode $n+3)$ versus cavity temperature. The frequency is measured using iodine spectroscopy and reported in terms of the difference from an arbitrarily chosen reference point at $T_{\mathrm{cav}}=5{}^{\circ }\mathrm{C}$. The maximum corresponds to the minimized sensitivity to environmental drifts.

Figure 4

(a) Optical spectrum of a ${}^{174}\mathrm{Yb}$ condensate probed in time of flight. (b) Drift of the line center versus time, for a cavity far from the zero crossing $(T_{\mathrm{cav}}\approx 5.0{}^{\circ }\mathrm{C};$ green circles) or close to it $(T_{\mathrm{cav}}\approx 4.3{}^{\circ }\mathrm{C}$; blue squares). (c) Drift-corrected optical spectra for $T_{\mathrm{cav}}\approx 5.0{}^{\circ }\mathrm{C}.$ Points shown correspond to all spectra in (b) with $T_{\mathrm{cav}}\approx 5.0{}^{\circ }\mathrm{C}$ recentered to correct for the drift.

Figure 5

Doppler velocimetry of an expanding BEC. (a) Experimental pictures versus probe laser frequency. (b) Position of the resonant slice (blue squares) and of the cloud center (red circles) versus frequency of the probe laser. The slice position is linear with the laser frequency, as expected when probing the velocity distribution (see text). The lower panels (p1, p2) show two profiles (integrated along the horizontal direction) together with the fit used to extract the cloud and “hole” centers and widths.

Figure 6

(a) Measured change in the resonance frequency ${\omega }_{\mathrm{res}}$ from TOF spectroscopy (green diamonds) and from the slice positions before (gray square) and after (black square) correction for the measured acceleration of the cloud. The shaded (light-green) area corresponds to the full width at half-maximum of the TOF spectrum. (b) Position of the cloud center (red circles) versus expansion time. (c) Width of the cloud center (blue triangles) versus expansion time. Solid lines in (b) and (c) are fits to the data using the scaling model, leaving the waveguide trap frequencies as free parameters.