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arXiv:2408.13407 · Physical Review A

Electromagnetically-induced-transparency cooling with a tripod structure in a hyperfine trapped ion with mixed-species crystals

Jenny J. Wu, Pan‐Yu Hou, Stephen D. Erickson, A. D. Brandt, Yong Wan, Giorgio Zarantonello, Daniel C. Cole, A. C. Wilson, D. H. Slichter, Dietrich G. Leibfried

Published Apr 10, 2025• 4 citations
arXivHTMLPDF

Abstract

Cooling of atomic motion is a crucial tool for many branches of atomic physics, ranging from fundamental physics explorations to quantum information and sensing. For trapped ions, electromagnetically-induced-transparency (EIT) cooling has received attention for the relative speed, low laser power requirements, and broad cooling bandwidth of the technique. However, in applications where the ion used for cooling has hyperfine structure to enable long coherence times, it is difficult to find a closed three-level system in which to perform standard EIT cooling. Here, we demonstrate successful EIT cooling on $^{25}\mathrm{Mg}^{+}$ by the addition of an extra laser frequency; this method can be applied to any ion with nonzero nuclear spin. Furthermore, we simultaneously EIT cool all axial modes in mixed-species crystals $^{9}\mathrm{Be}^{+}\text{\ensuremath{-}}^{25}\mathrm{Mg}^{+}$ and $^{9}\mathrm{Be}^{+}\text{\ensuremath{-}}^{25}\mathrm{Mg}^{+}\text{\ensuremath{-}}^{9}\mathrm{Be}^{+}$ through the $^{25}\mathrm{Mg}^{+}$ ion. This demonstrates the viability of EIT cooling in architectures where the laser-cooled species can host high-fidelity hyperfine qubits.

DOI
10.1103/physreva.111.043109

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Cooling of atomic motion is a crucial tool for many branches of atomic physics, ranging from fundamental physics explorations to quantum information and sensing. For trapped ions, electromagnetically-induced-transparency (EIT) cooling has received attention for the relative speed, low laser power requirements, and broad cooling bandwidth of the technique. However, in applications where the ion used for cooling has hyperfine structure to enable long coherence times, it is difficult to find a closed three-level system in which to perform standard EIT cooling. Here, we demonstrate successful EIT cooling on 25Mg+^{25}\mathrm{Mg}^{+}25Mg+ by the addition of an extra laser frequency; this method can be applied to any ion with nonzero nuclear spin. Furthermore, we simultaneously EIT cool all axial modes in mixed-species crystals 9Be+\ensuremath-25Mg+^{9}\mathrm{Be}^{+}\text{\ensuremath{-}}^{25}\mathrm{Mg}^{+}9Be+\ensuremath-25Mg+ and 9Be+\ensuremath-25Mg+\ensuremath-9Be+^{9}\mathrm{Be}^{+}\text{\ensuremath{-}}^{25}\mathrm{Mg}^{+}\text{\ensuremath{-}}^{9}\mathrm{Be}^{+}9Be+\ensuremath-25Mg+\ensuremath-9Be+ through the 25Mg+^{25}\mathrm{Mg}^{+}25Mg+ ion. This demonstrates the viability of EIT cooling in architectures where the laser-cooled species can host high-fidelity hyperfine qubits.
We report the electromagnetically induced transparency (EIT) cooling of ^{137}Ba^{+} ions with a nuclear spin of I=3/2, which are a good candidate of qubits for future large-scale trapped-ion quantum computing. EIT cooling of atoms or ions with a complex ground-state level structure is challenging due to the lack of an isolated Λ system, as the population can escape from the Λ system to reduce the cooling efficiency. We overcome this issue by leveraging an EIT pumping laser to repopulate the cooling subspace, ensuring continuous and effective EIT cooling. We cool the two radial modes of a single ^{137}Ba^{+} ion to average motional occupations of 0.08(5) and 0.15(7), respectively. Using the same laser parameters, we also cool all the ten radial modes of a five-ion chain to near their ground states. Our approach can be adapted to atomic species possessing similar level structures. It allows engineering of the EIT Fano-like spectrum, which can be useful for simultaneous cooling of modes across a wide frequency range, aiding in large-scale trapped-ion quantum information processing.
We report the electromagnetically-induced-transparency (EIT) cooling of a large trapped ^{171}Yb^{+} ion chain to the quantum ground state. Unlike conventional EIT cooling, we engage a four-level tripod structure and achieve fast sub-Doppler cooling over all motional modes. We observe simultaneous ground-state cooling across the complete transverse mode spectrum of up to 40 ions, occupying a bandwidth of over 3 MHz. The cooling time is observed to be less than 300 μs, independent of the number of ions. Such efficient cooling across the entire spectrum is essential for high-fidelity quantum operations using trapped ion crystals for quantum simulators or quantum computers.
Motional modes of trapped-ion crystals in Penning traps can now be cooled to near their ground states via electromagnetically induced transparency (EIT) cooling. Numerical simulations are valuable tools for interpreting EIT cooling results and optimizing experimental protocols, but existing molecular dynamics codes are limited to the simulation of Doppler cooling. In this work, we fill this gap by implementing a semiclassical model of EIT cooling in a novel MD code. By simultaneously evolving the ions' internal quantum states and classical motion, we are able to calculate the instantaneous EIT laser forces acting on the ions. We first validate our code by comparing the single-ion cooling rate to fully quantum simulation results. Next, we analyze cooling of the drumhead modes in planar ion crystals, quantifying the effects of planar ion motion and a finite laser beam width. Finally, we demonstrate efficient EIT cooling of the axial modes in 3D ellipsoidal crystals containing up to 500 ions. Such crystals are a promising platform for future quantum sensing experiments with enhanced sensitivity. We find that the mode spectra of 3D crystals can be engineered to enable sympathetic cooling of the low-frequency E×B\boldsymbol{E}\times\boldsymbol{B}E×B modes. This numerical framework provides a powerful tool for modeling sub-Doppler cooling techniques and for optimizing future quantum sensing and quantum information experiments.
We theoretically propose and experimentally demonstrate a parallel electromagnetically induced transparency (parallel EIT) cooling technique for ion crystals in the Paul trap. It breaks the stringent cooling requirements of the standard EIT cooling, thus allowing, in principle, to simultaneously cool the motional mode spectrum with an arbitrary range. Experimentally a large cooling range over 5 MHz is proved by using a single trapped 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ ion. We also observe simultaneous near-ground-state cooling for all motional modes of a 4-ion chain with the best average phonon number of about 0.2. For cooling a large number of modes, we only need to modulate the probe beam of the standard EIT cooling with several rf frequencies. This cooling scheme has no selectivity for the types of ions (e.g., 171Yb+{}^{171}{\mathrm{Yb}}^{+}171Yb+, 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+), therefore it would be a powerful tool for initialization of all kinds of operational trapped-ion quantum computers or simulators.
Trapped ions are a powerful and flexible platform used for scientific applications ranging from studies of fundamental physics and precision spectroscopy to quantum simulation and quantum information processing. These applications are enabled by the excellent control that can be exerted over the long-lived atomic states of trapped ions using electromagnetic fields. In crystals containing multiple ions, the shared motion is used as a mediator to couple the atomic states of distant ions. This thesis focuses on improving the control over ion motion, and in particular for crystals that contain multiple ion species. The first set of experiments discussed in this thesis is the application of a ground-state cooling method known as electromagnetically-induced-transparency (EIT) cooling to 25Mg+. This ion has a complex hyperfine structure which enables the implementation of a long-lived qubit. By demonstrating EIT cooling on 25Mg+, it is shown that such qubit ions are also compatible with this resource-efficient sub-Doppler cooling method. The normal modes of trapped-ion motion are well-described by quantum harmonic oscillators, and the second set of experiments described in this thesis covers the direct, rapid, and parametric coupling between two harmonic oscillators in the motion modes of multi-ion crystals. This coupling can be used to indirectly cool ion modes that are otherwise difficult or inefficient to cool. It can also be used to perform mid-circuit non-destructive readout of trapped-ion motion, which is useful for the study of states encoded in the ion motion, such as those used for bosonic error correction.
We theoretically and experimentally investigate double-electromagnetically-induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for ^{171}Yb^{+} ions with a clock state, for which EIT cooling has not been realized like many other ions with a simple Λ scheme. A cooling rate of n[over ¯][over ˙]=34(±1.8) ms^{-1} and a cooling limit of n[over ¯]=0.06(±0.059) are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12-ion crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences.