Sawtooth-wave adiabatic-passage slowing of dysprosium

We report on sawtooth-wave adiabatic-passage (SWAP) slowing of bosonic and fermionic dysprosium isotopes by using a 136-kHz-wide transition at 626 nm. A beam of precooled atoms is further decelerated in one dimension by the SWAP force and the amount of atoms at near zero velocity is measured. We demonstrate that the SWAP slowing can be twice as fast as in a conventional optical molasses operated on the same transition. In addition, we investigate the parameter range for which the SWAP force is efficiently usable in our setup and relate the results to the adiabaticity condition. Furthermore, we add losses to the hyperfine ground-state population of fermionic dysprosium during deceleration and observe more robust slowing with SWAP compared to slowing with the radiation pressure force.

Figure 1

(a) Excerpt of Dy energy levels for total angular momenta $J=8$, 9, and 10 [23]. Even (odd) parity levels are drawn in red (black). (b) Hyperfine structure of the ${}^{163}\mathrm{Dy}$ isotope [20, 24]. The arrows indicate the transitions used for the Zeeman slower at 421 nm, for the SWAP deceleration at 626 nm, and for the implementation of ground-state losses. (c) Schematic of the SWAP force mechanism. The black sawtooth function describes the time-dependent detuning of the counterpropagating laser beams with respect to an atom at rest. An atom moving with finite velocity $v$ experiences Doppler-shifted frequency ramps indicated by the blue and red dashed lines in the plot. Important parameters of the sawtooth ramps used for deceleration of dysprosium like the ramp amplitude ${\mathrm{\Delta }}_{\mathrm{ramp}}$ and ramp repetition rate $f_{\mathrm{ramp}}$ are indicated.

Figure 2

(a) Schematic of the vacuum chamber inside which the SWAP or RAD deceleration takes place. The gray arrow labeled “Dy” indicates the direction of atoms leaving the ZS after deceleration by the ZS beam labeled “ZS”. The direction of the magnetic field used as quantization axis is drawn in purple and the retro-reflected pump and probe beams are indicated by red arrows along with their polarizations. The photomultiplier tube used for the fluorescence measurements is placed below the vacuum chamber and is labeled “PMT”. (b) The part of the ${}^{163}\mathrm{Dy}$ hyperfine structure that is relevant for the described experimental scheme. The numbers next to the transition arrows indicate the relative transition strengths normalized to the $F=10.5\to F^{\prime }=11.5$ transition. (c) Sequence used to compare the RAD and SWAP force. When losses are added to the $F=10.5$ ground-state, the pump beam is switched on during the deceleration.

Figure 3

SWAP deceleration is applied for 1 ms for varying ramp repetition rates $f_{\mathrm{ramp}}$ (dark blue diamonds) and subsequently $I_{\mathrm{SWAP}}$ is measured. For comparison, RAD deceleration is applied for the same amount of time and the same saturation parameter with an optimized red detuning ${\mathrm{\Delta }}_{\mathrm{RAD}}=-15.5 {\mathrm{\Gamma }}_{626}$ (red circles). The measured intensities are normalized to the mean intensity after RAD deceleration $I_{\mathrm{RAD},\mathrm{mean}}$. When the slope of the sawtooth ramp is inverted, we measure negative background-subtracted fluorescence intensities (light blue squares). To estimate the error of the measured intensities we perform 270 measurements at $f_{\mathrm{ramp}}=400$ kHz and determine the standard deviation $\sigma$ of $I_{\mathrm{SWAP}}$ and $I_{\mathrm{RAD}}$. The error bars in this figure are the standard error $\sigma /\sqrt{N}$, with $N=15$ being the number of measurements done for each $f_{\mathrm{ramp}}$ setting.

Figure 4

(a) $I_{\mathrm{SWAP}}$ (dark blue diamonds) and $I_{\mathrm{RAD}}$ (red circles) are compared for increasing deceleration time. The SWAP and RAD beam settings and the error calculations are the same as for the data in Fig. 3. The dashed lines are the result of a linear fit to the first three data points. (b) A zoom into the data points of panel (a) up to 2 ms. In addition, results for SWAP deceleration with different ramp repetition rates but equal velocity-capture ranges are shown as black squares.

Figure 5

All three graphs show the ratio $I_{\mathrm{SWAP}}/I_{\mathrm{RAD}}$ as a measure of the SWAP deceleration efficiency. In panels (a) and (b) the dashed lines indicate lines of a constant adiabaticity parameter $\kappa$. (a) For a fixed SWAP ramp amplitude ${\mathrm{\Delta }}_{\mathrm{ramp}}=190 {\mathrm{\Gamma }}_{626}$ the squared Rabi frequency ${\mathrm{\Omega }}_0^2$ and the ramp repetition rate $f_{\mathrm{ramp}}$ are varied. For this data set, ${}^{162}\mathrm{Dy}$ is used. The velocities below the squared Rabi frequencies denote the lower limits to the high-velocity regime. (b) For a fixed ${\mathrm{\Omega }}_0^2=860\times {10}^{12} {\mathrm{s}}^{-2}$ the ramp amplitude ${\mathrm{\Delta }}_{\mathrm{ramp}}$ and the ramp repetition rate $f_{\mathrm{ramp}}$ are varied. (c) The intensity of the pump beam, $I_{\mathrm{pump}}$, which induces losses to the $F=10.5$ ground state is increased stepwise and plotted versus $f_{\mathrm{ramp}}$. The deceleration time is 1 ms for the data presented in panels (a) and (c) and 0.75 ms for the data plotted in panel (b).

Figure 6

(a) Sketch of the setup used for measuring the velocity distribution of atoms leaving the ZS. The velocity measurement is done in ${45}^{\circ }$ to the $x$ axis while all velocities given in this figure are transformed to be along the $x$ axis, which is the atomic beam direction. (b) Fluorescence spectrum obtained by scanning two counterpropagating laser beams as shown in panel (a) with $\mathrm{\Delta }f=0$. The Doppler-free fluorescence signal is visible at 0 m/s and its FWHM is about 0.45 m/s. (c) Decaying fluorescence signals of atoms with 0, 14.9, and 34.3 m/s velocity in the $x$ direction plotted in blue, red, and black, respectively, after suddenly switching off the ZS. The initial intensity is measured by averaging the signals over a time span of 0.6 ms after switching on the probe beams at time $t=0$. (d) For two different current settings of the ZS two continuous velocity spectra in blue and green are measured by using and scanning only beam 2 marked in panel (a). The red and black data points are results for the same ZS settings but are measured by VSSFS. The normalization of these intensities is described in the main text. (e) Typical fluorescence signals measured with the sequence outlined in Fig. 2 to obtain $I_{\mathrm{SWAP}}$ and $I_{\mathrm{RAD}}$.

Figure 7

(a) Schematic of the RF electronics used to generate the sawtooth frequency ramps at around 95 MHz to drive the SWAP double-pass AOM. All components except the function generator, the AOM, and the direct digital synthesizer (DDS) are manufactured by Mini-Circuits. (b) Results of an optical beat measurement between a constant-frequency laser beam and a laser beam that is modulated with ${\mathrm{\Delta }}_{\mathrm{ramp}}=190 {\mathrm{\Gamma }}_{626}$ and $f_{\mathrm{ramp}}=500$ kHz (left) and $f_{\mathrm{ramp}}=1900$ kHz (right) sawtooth waves by using the setup outlined in panel (a).

Figure 8

The relative intensity change $I_{\mathrm{pump}\mathrm{on}}/I_{\mathrm{pump}\mathrm{off}}$ for SWAP (blue circles) and RAD deceleration (white circles) versus the pump-beam detuning. The parameters of the SWAP force are set to $f_{\mathrm{ramp}}=500$ kHz, ${\mathrm{\Delta }}_{\mathrm{ramp}}=190 {\mathrm{\Gamma }}_{626}$, and ${\mathrm{\Omega }}_0=29\times {10}^6 {\mathrm{s}}^{-1}$, while the parameters of the RAD force are set to ${\mathrm{\Omega }}_0=29\times {10}^6 {\mathrm{s}}^{-1}$ and ${\mathrm{\Delta }}_{\mathrm{RAD}}=-15.5 {\mathrm{\Gamma }}_{626}$ (green line labeled “a”). The green line labeled “b” indicates the resonance position of the $F=10.5\to F^{\prime }=10.5$ transition found by an independent spectroscopic measurement and it marks the pump-beam detuning used to obtain the data presented in Fig. 5. The pump-beam intensity is $I_{\mathrm{pump}}=5.7{\mathrm{I}}_{\mathrm{sat}}$ and corresponds to a Rabi frequency of $2\pi \times 35$ kHz.