Rapid multi-mode trapped-ion laser cooling in a phase-stable standing wave

Abstract

Laser cooling is fundamental to precise control and interrogation of atomic quantum systems. In the context of quantum computing and metrology with trapped ions, the integrated optical control of interest for scaling may additionally enable increased performance of coherent and incoherent operations. Here we utilize multi-channel integrated delivery of ultraviolet to infrared wavelengths required for calcium ion control including in passively phase-stable ultraviolet standing waves to demonstrate rapid, broadband laser cooling. We experimentally verify a long-standing prediction, realizing Doppler cooling to below the conventional Doppler limit at a standing-wave (SW) node. Utilizing electromagnetically induced transparency (EIT), we experimentally cool motional modes spanning an approximately 5 MHz bandwidth from the Doppler temperature to near the ground state within 150 $μ$s, reaching $\bar n \approx 0.05$ phonon number occupancies for the target mode. Direct evaluation against the comparable running-wave (RW) scheme shows the SW implementation's simultaneous advantage in cooling rate, motional mode bandwidth, and final phonon number as previously theoretically predicted. Our results demonstrate structured light's capability for robust ground-state laser cooling, and a clear advantage in a fundamental functionality enabled by scalable approaches to optical control.

Figures (12)

• Figure 1: (a) Relevant energy levels of $^{40}\mathrm{Ca}^+$ and Zeeman sub-levels of $S_{1/2}$ and $P_{1/2}$ energy levels for EIT cooling. The $\lambda=397$ nm transition is used for Doppler cooling and state readout; light at 729 nm drives an electric quadrupole transition for spectroscopy and motional diagnostics; and 854 and 866 nm serve as repumpers. $\Delta_p$ and $\Delta_c$ denote the detuning of the EIT pump ($\hat{\bm\sigma}_+$) and the probe beam ($\hat{\bm \pi}$) from the $\ket{4S_{1/2},m_j={-1/2}} \leftrightarrow \ket{4P_{1/2},m_j={+1/2}}$ and the $\ket{4S_{1/2},m_j={+1/2}} \leftrightarrow \ket{4P_{1/2},m_j={+1/2}}$ transitions respectively. (b) Layer stack-up schematic, incorporating $\mathrm{Al}_2\mathrm{O}_3$ and multi-layered $\mathrm{Si}_3\mathrm{N}_4$ waveguide features for routing and emission on a silicon substrate. A 500-nm-thick Au layer (using Ti for adhesion) forms both the ground plane and the top RF and DC electrodes. A 20-nm-thick conductive ITO film is used to mitigate potential surface charging at top electrode openings. (c) Layout of the trap zone used along with the free-space and integrated optical waveguide and grating elements at the indicated wavelengths, $B$-field orientation, top metal, and ITO features. (d) Bright-field microscope image of the same zone.
• Figure 2: Scanning electron microscope (SEM) images of (a) fabricated $\mathrm{Al}_2\mathrm{O}_3$ and $\mathrm{Si}_3\mathrm{N}_4$ waveguides features near the trap zone employed in this work and (b) the $1 \times 2$$\mathrm{Al}_2\mathrm{O}_3$ MMI splitter, overlaid with the simulated intensity profile for $\lambda=397$ nm, feeding the 'SW1' and 'SW2' grating couplers. (c) Measured grating emission profiles at the labeled wavelengths along the "longitudinal" direction $x'$ for each grating (e.g., dashed line in (a) for the SW couplers), obtained from images of the radiated fields of the integrated grating couplers at different heights above the trap electrode; line crossings indicate the target ion position, demonstrating realized targeting accuracy of $\lesssim 2$$\mu$m for all wavelengths.
• Figure 3: SW profiling via AC Stark shift measurements on the optical quadrupole transition. (a) AC stark shift on $|4S_{1/2}, m_j = +1/2\rangle$ vs. axial displacement with (black) and without (purple) RW EIT cooling the axial mode, and fits to SW profile with Gaussian amplitude envelope. (b) The AC Stark shift near the center after RW EIT cooling, yielding an extinction ratio $\gamma \equiv \delta_{\text{an}}/\delta_{\text{n}} = 10.83(3)$. 1$\sigma$ error bars in both plots are smaller than data points.
• Figure 4: (a) Final $R_1$ mode phonon number after SW Doppler cooling (black points) as a function of axial position. Dashed line and uncertainty indicates the $\bar{n}$ measured after RW cooling. Zero displacement corresponds to the central SW node, where the ion was positioned for the measurements reported in Table. \ref{['tab:Dopplercooling']}. Error bars indicate 1$\sigma$ uncertainty. (b) Carrier flopping of $|4S_{1/2}, m_j = +1/2\rangle \leftrightarrow |3D_{5/2}, m_j = +1/2\rangle$ at the SW node and anti-node after SW Doppler cooling. Error bars indicate 1$\sigma$ standard errors from projection noise.
• Figure 5: (a) SW and RW EIT cooling trajectories for all motional modes using cooling parameters optimized for $R_1$. Corresponding final phonon numbers and cooling rates are listed in Table. \ref{['tab:EITcooling']}. (b) Sideband spectroscopy after RW (top) and SW (bottom) EIT cooling, obtained at fixed $\lambda=729$ nm intensity, and pulse times of 2.8, 30, and 60 $\mu$s for the carrier, axial sidebands, and radial sidebands, respectively. Imbalance in red vs. blue sideband excitation amplitudes are used to infer $\bar{n}$ values reported in (a) Heatingoftrappedion. Error bars in both plots indicate 1$\sigma$ uncertainty.