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arXiv:2411.06026 · Physical Review Letters

Sub-Doppler Cooling of a Trapped Ion in a Phase-Stable Polarization Gradient

Ethan Clements, Felix Knollmann, Sabrina Corsetti, Zhaoyi Li, Ashton Hattori, Milica Notaros, Reuel B. Swint, Tal Sneh, May E. Kim, Aaron D. Leu, Patrick T. Callahan, Thomas Mahony, Gavin N. West, Cheryl M. Sorace-Agaskar, Dave Kharas, Robert McConnell, Colin Bruzewicz, Isaac L. Chuang, Jelena Notaroš, John Chiaverini

Published Nov 7, 2025• 6 citations
arXivHTMLPDF

Abstract

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing tailorable light-matter interactions in the sub-wavelength regime. In this Letter, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of 2π×1.45 MHz we achieve ⟨n⟩=1.56±0.07 in 150 μs and cooling rates of ∼0.3 quanta/μs. We examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a multilevel model. Cooling is fast and power efficient, with lower average motional Fock state occupation when compared to simulated operation under the corresponding running wave configuration. Our results demonstrate a well-controlled test bed for studying the dynamics of multilevel atomic systems in a phase-stable polarization gradient.

DOI
10.1103/fy3t-f1hz

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Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing tailorable light-matter interactions in the sub-wavelength regime. In this Letter, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of 2π×1.45 MHz we achieve ⟨n⟩=1.56±0.07 in 150 μs and cooling rates of ∼0.3 quanta/μs. We examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a multilevel model. Cooling is fast and power efficient, with lower average motional Fock state occupation when compared to simulated operation under the corresponding running wave configuration. Our results demonstrate a well-controlled test bed for studying the dynamics of multilevel atomic systems in a phase-stable polarization gradient.
Trapped ions are a promising modality for quantum systems, with demonstrated utility as the basis for quantum processors and optical clocks. However, traditional trapped-ion systems are implemented using complex free-space optical configurations, whose large size and susceptibility to vibrations and drift inhibit scaling to large numbers of qubits. In recent years, integrated-photonics-based systems have been demonstrated as an avenue to address the challenge of scaling trapped-ion systems while maintaining high fidelities. While these previous demonstrations have implemented both Doppler and resolved-sideband cooling of trapped ions, these cooling techniques are fundamentally limited in efficiency. In contrast, polarization-gradient cooling can enable faster and more power-efficient cooling and, therefore, improved computational efficiencies in trapped-ion systems. While free-space implementations of polarization-gradient cooling have demonstrated advantages over other cooling mechanisms, polarization-gradient cooling has never previously been implemented using integrated photonics. In this paper, we design and experimentally demonstrate key polarization-diverse integrated-photonics devices and utilize them to implement a variety of integrated-photonics-based polarization-gradient-cooling systems, culminating in the first experimental demonstration of polarization-gradient cooling of a trapped ion by an integrated-photonics-based system. By demonstrating polarization-gradient cooling using an integrated-photonics-based system and, in general, opening up the field of polarization-diverse integrated-photonics-based devices and systems for trapped ions, this work facilitates new capabilities for integrated-photonics-based trapped-ion platforms.
Laser cooling is fundamental to quantum computing and metrology using atomic systems. Precise control often requires cooling atoms' motional degrees of freedom to the quantum ground state, imposing operation time and architectural limitations particularly in large-scale systems. Here we demonstrate how the integrated optical control of interest for scaling trapped-ion systems additionally enables laser cooling that bypasses limitations of conventional schemes. Leveraging multi-channel integrated delivery of ultraviolet to infrared wavelengths for calcium ion control including in passively phase-stable ultraviolet standing waves (SWs), we experimentally verify a long-standing prediction by Cirac et al., realizing Doppler cooling to below the conventional Doppler limit at a SW node. We also present the first realization of ground-state cooling via electromagnetically induced transparency (EIT) using a ``probe" beam delivered as a SW with atoms positioned at a node, predicted to enable multi-mode sub-recoil-limit laser cooling. We demonstrate cooling of motional modes spanning an approximately 5 MHz bandwidth from the Doppler temperature to near the ground state within 150~\textmu s, reaching nˉ≈0.05\bar n \approx 0.05nˉ≈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 work leverages capabilities enabled by integrated optical delivery to demonstrate fast cooling of multiple modes to the quantum ground state, and more broadly how scalable approaches to optical control can enable enhancements in fundamental atomic functionalities.
We propose a sub-Doppler cooling scheme for trapped-ion crystals in Paul traps. The combination of a hollow tweezer and microwave drive creates an effective two-level system which is cooled through attractive Sisyphus cooling. For 171Yb+{}^{171}\rm{Yb}^+171Yb+ ions, we numerically identify optimal parameters for one- and two-ion crystals, and investigate the cooling rate in ion crystals with up to three ions. Our cooling scheme utilizes a single ion addressed with a tweezer to achieve sub-Doppler cooling of the NNN axial motional modes perpendicular to the tweezer propagation direction, does not rely on the Lamb-Dicke regime and uses off-resonant light. We reach 1/e1/e1/e cooling times for the center of mass mode of τcom<2τ_{\rm com}<2τcom​<2 ms, and a steady-state excitation number of nˉcom≈0.7\bar{n}_{\rm{com}}\approx 0.7nˉcom​≈0.7. Our scheme is well-suited as an intermediate stage between Doppler cooling and ground-state sideband cooling, and can be readily realized in trapped-ion platforms.
Abstract We implement three-dimensional polarization gradient cooling (PGC) of trapped ions. Counter-propagating laser beams near 393 nm impinge in lin ⊥ lin configuration, at a frequency below the S 1/2 to P 3/2 resonance in 40 Ca + . Our measurements demonstrate that cooling with laser beams detuned to lower frequencies from the resonance is robust against an elevated phonon occupation number and works continuously in the crossover from regular Doppler cooling to detunings of tens of linewidths. It is thus robust against heating events and also works well for an initial ion motion far out of the Lamb–Dicke regime. We show that PGC performance strongly depends on residual micromotion (MM) and find PGC working for a MM modulation index β ⩽ 0.1. Still, we find that the spectral impurity of the laser field affects both, cooling rates and cooling limits. Thus, a Fabry–Pérot cavity filter is employed to efficiently suppress amplified spontaneous emission of the diode laser. We demonstrate mean phonon numbers for a single ion of 5.4(4) at a trap frequency of 2 π × 285 kHz and 3.3(4) at 2 π × 480 kHz, in the axial and radial directions, respectively.
Using a laser polarization gradient, we realize 3D Sisyphus cooling of ^{171}Yb^{+} ions confined in and near the Lamb-Dicke regime in a linear Paul trap. The cooling rate and final mean motional energy of a single ion are characterized as a function of laser intensity and compared to semiclassical and quantum simulations. Sisyphus cooling is also applied to a linear string of four ions to obtain a mean energy of 1-3 quanta for all vibrational modes, an approximately order of magnitude reduction below Doppler cooled energies. This is used to enable subsequent, efficient sideband laser cooling.
Efficient Three-Dimensional Sub-Doppler Cooling of 40^{40}40Ca+^++ in a Penning Trap
We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a 40^{40}40Ca+^++ ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a 1/e cooling time constant of 108(8) μμμs, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 μμμs as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially-propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of $ω_z = 2π~\times~$221 kHz, which places the motion well outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic oscillator motion of the trapped ion.