Trapping and Ground-State Cooling of a Single ${\mathrm{H}}_{2}^{+}$

Trapping and Ground-State Cooling of a Single $H_{2}^{+}$

N. Schwegler, D. Holzapfel, M. Stadler, A. Mitjans, I. Sergachev, J. P. Home, and D. Kienzler

Phys. Rev. Lett. 131, 133003 – Published 27 September 2023

Abstract

We demonstrate co-trapping and sideband cooling of a $H_{2}^{+} - {}^{9}{Be}^{+}$ ion pair in a cryogenic Paul trap. We study the chemical lifetime of $H_{2}^{+}$ and its dependence on the apparatus temperature, achieving lifetimes of up to $11_{- 3}^{+ 6} h$ at 10 K. We demonstrate cooling of two of the modes of translational motion to an average phonon number of 0.07(1) and 0.05(1), corresponding to a temperature of 22(1) and $55 (3) μ K$ , respectively. Our results provide a basis for quantum logic spectroscopy experiments of $H_{2}^{+}$ , as well as other light ions such as ${HD}^{+}$ , $H_{3}^{+}$ , and ${He}^{+}$ .

Received 14 December 2022
Revised 24 April 2023
Accepted 24 July 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.133003

Physics Subject Headings (PhySH)

Atom & ion cooling Atom & ion trapping & guiding Chemical reactions Cooling & trapping Molecule trapping & guiding Quantum control Quantum metrology

Ionized molecules Ions Trapped ions

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

N. Schwegler ^*, D. Holzapfel , M. Stadler , A. Mitjans , I. Sergachev , J. P. Home , and D. Kienzler ^†

Institute for Quantum Electronics, Department of Physics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland

^*snick@phys.ethz.ch
^†daniel.kienzler@phys.ethz.ch

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Vol. 131, Iss. 13 — 29 September 2023

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Figure 1
Example of sideband spectroscopy scans on ${}^{9}{Be}^{+}$ probing the axial mode frequencies to distinguish $H_{2}^{+} - {}^{9}{Be}^{+}$ , $H_{3}^{+} - {}^{9}{Be}^{+}$ , and ${}^{9}{Be}^{+}$ . The detuning of the Raman lasers from the carrier transition is denoted $Δ ω$ and the measured ${}^{9}{Be}^{+}$ $| ↓ ⟩$ probability $P_{↓}$ . The solid lines represent a running average over three points to guide the eye. The vertical dashed lines mark the calculated frequency of the in- and out-of-phase axial mode of $H_{2}^{+} - {}^{9}{Be}^{+}$ and $H_{3}^{+} - {}^{9}{Be}^{+}$ based on the axial frequency of a single ${}^{9}{Be}^{+}$ ( $2 π \times 1.1 MHz$ ) confined in the same trapping potential. Different frequency ranges use different probe duration to optimize signal strength. The sets for $H_{2}^{+} - {}^{9}{Be}^{+}$ and $H_{3}^{+} - {}^{9}{Be}^{+}$ are taken a few minutes apart, during which $H_{2}^{+}$ underwent a chemical reaction to $H_{3}^{+}$ . The mass changed from 2 to 3 u, which shifts (b) the axial in-phase mode at $2 π \times 1.3 MHz$ by $- 2 π \times 25 kHz$ , and the axial out-of-phase mode is shifted from (d) $2 π \times 3.4$ to (c) $2 π \times 2.8 MHz$ . A single ${}^{9}{Be}^{+}$ shows a resonance in scan (a) only, giving us a means of detecting loss of $H_{2}^{+}$ . The duration to complete one set of data containing all four scans is 80 s.
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Figure 2
Survival probability $P_{Surv}$ of $H_{2}^{+} - {}^{9}{Be}^{+}$ measured for different cryostat temperatures. For clarity, the data at 22 K (19 K, 17 K) is offset by 10 s (20 s, 30 s). A chemical reaction $H_{2}^{+} + H_{2} \to H_{3}^{+} + H$ is marked with a circle, while ion loss is marked with a cross. The data is not preprocessed and no additional loss mechanisms are observed.
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Figure 3
(a) Lifetime $τ$ of $H_{2}^{+} - {}^{9}{Be}^{+}$ and (b) partial $H_{2}$ density $n_{H_{2}}$ for different cryostat temperatures, extracted from the data shown in Fig. 2. The error bars on the $y$ axis show the 68% confidence interval and are derived assuming an exponential distribution. The error bars on the temperature values indicate the standard deviation of the measured temperatures and are limited by the precision of the temperature control loop.
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Figure 4
Red and blue sidebands of the axial in- and out-of-phase modes of motion of $H_{2}^{+} - {}^{9}{Be}^{+}$ probed using the stimulated Raman transition on ${}^{9}{Be}^{+}$ . The detuning of the Raman lasers from the corresponding sideband transition is denoted $Δ ω$ and the measured ${}^{9}{Be}^{+}$ $| ↓ ⟩$ probability $P_{↓}$ . The fits (solid lines) are used to extract the contrast and determine the average phonon number. We obtain for the in-phase mode (a) $\bar{n} = 10 (5)$ after Doppler cooling and (c) $\bar{n} = 0.07 (1)$ after sideband cooling. For the out-of-phase mode we obtain (b) $\bar{n} = 2.4 (5)$ after Doppler cooling and (d) $\bar{n} = 0.05 (1)$ after sideband cooling. For the dataset (c) the out-of-phase mode is Doppler cooled, while for the dataset (d) both the in- and out-of-phase mode are cooled to the ground state simultaneously. In the latter case, the temperature of the in-phase mode is similar to the one obtained from (c).
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Physical Review Letters

Trapping and Ground-State Cooling of a Single H2+

N. Schwegler, D. Holzapfel, M. Stadler, A. Mitjans, I. Sergachev, J. P. Home, and D. Kienzler

Phys. Rev. Lett. 131, 133003 – Published 27 September 2023

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Trapping and Ground-State Cooling of a Single $H_{2}^{+}$