Sawtooth wave adiabatic passage in a grating magneto-optical trap

TL;DR

The paper investigates SWAP cooling in a grating MOT for Sr atoms, addressing polarization- and geometry-induced cooling challenges in compact platforms. It combines 3D optical Bloch equation simulations with an experimental demonstration, showing that SWAP delivers stronger cooling and doubles the transfer efficiency from a broad-line MOT to a narrow-line MOT, achieving up to $3\times10^6$ atoms at about $5\ \mu$K with a $0.7$ s lifetime. This work demonstrates that SWAP can significantly enhance duty cycle and atom numbers for miniaturized, high-precision sensors, even in non-orthogonal tetrahedral beam geometries. It also highlights the role of shelving and spontaneous emission in these systems and points to avenues for optimizing SWAP in similar compact architectures.

Abstract

We demonstrate sawtooth wave adiabatic passage (SWAP) in a grating magneto-optical trap (MOT) operating on the $^1$S$_0$ $\rightarrow$ $^3$P$_1$ transition of neutral $^{88}$Sr. From numerical simulations of SWAP using our laser beam geometry, we find that SWAP provides greater cooling than triangle wave frequency modulation despite the complex polarization environment of a grating MOT. The simulation is confirmed by our experimental results, where we demonstrate a factor of two improvement in transfer efficiency between our $^1$S$_0$ $\rightarrow$ $^1$P$_1$ grating MOT and our $^1$S$_0$ $\rightarrow$ $^3$P$_1$ grating MOT. We trap up to $3\times10^6$ $^{88}$Sr atoms in the $^1$S$_0$ $\rightarrow$ $^3$P$_1$ grating MOT, at an average temperature of 4.9 $μ$K with a lifetime of approximately 0.7 s. Our results show that SWAP is effective in non-orthogonal laser beam geometries, allowing greater duty cycles or higher atom number in sensors based on narrow-line grating MOTs.

Figures (7)

• Figure 1: Possible transitions that can be made in a single laser frequency sweep. Subfigures (a) and (b) show the resonant laser detuning $\Delta$ of transitions excited by the input and diffracted laser beams as a function of the axial magnetic field $B_z$ normalized by the axial atomic speed $|v_z|$ for positive and negative velocity $v_z$, respectively. The dashed line indicates the transition due to the input beam and the solid lines indicate the transitions due to the diffracted beams. The arrows are labeled corresponding to the subfigures below, where the direction of the arrow indicates the direction of the frequency sweep across the transitions. (c)-(j) show the populations of the atomic energy levels as a function of time and laser detuning for a single increasing sawtooth frequency sweep for an atom at the particular value of $B_z/|v_z|$ indicated by the corresponding arrow in subfigure (a) or (b). Subfigures (c)-(f) have positive $v_z$ and (g)-(j) have negative $v_z$.
• Figure 2: Examples of the atomic velocity over time for a variety of parameters. Subplots (a), (c), and (e) show axial velocities (along $\hat{z}$). Subplots (b), (d), and (f) show transverse velocities (along $\hat{x}$). Subplots (a) and (b) use zero magnetic field, while (c), (d), (e) and (f) use a non-zero field along $\hat{z}$ or $\hat{x}$ (as indicated near the subplot label). The red traces show the atomic velocities for a triangular frequency sweep, while the blue traces show the atomic velocities for a sawtooth frequency sweep (SWAP). The gray dashed lines represent a change in velocity of $\hbar k / m$ per sweep, which is the maximum cooling expected from SWAP in a six-beam MOT.
• Figure 3: Schematic of experimental apparatus. The atomic beam (light blue line) propagates in the $-\hat{z}$ direction (against gravity) and enters the broad-line MOT beam overlap through a triangular hole in the diffraction grating chip. The broad-line MOT and narrow-line MOT beam overlap volumes indicate the region where all four MOT laser beams have non-zero intensity for each MOT. Two sets of electromagnets create the broad-line MOT magnetic field gradient (orange) and narrow-line MOT magnetic field gradient (brown). The input laser beams for both MOTs enter the vacuum chamber from the top and propagate in the $+\hat{z}$ direction.
• Figure 4: Transferred atom number $N$ as a function of $1/t_s$ for SWAP. The vertical lines show the sweep time where adiabaticity breaks down (given by $\Omega^2 t_s/|\delta_f(0)-\delta_i(0)| = 1$) for each polarization component in a single diffracted beam at the start of the transfer.
• Figure 5: Transferred atom number $N$ as a function of final detuning at the end of the ramp sequence $\delta_f(t_{\rm ramp})$ for different sweep times and shapes. The blue, orange, green, and red circles show data for SWAP sweep at $t_s=50$$\mu$s, triangle sweep at $t_s=25$$\mu$s, anti-SWAP sweep at $t_s=50$$\mu$s, and triangle sweep at $t_s=50$$\mu$s, respectively.