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Physical Review Letters

Nondestructive Control of the Rovibrational Ground State of a Single Molecular Hydrogen Ion in a Penning Trap

C. M. König, F. Heiße, Jonathan Morgner, Tim Sailer, B. Tu, D. Bakalov, K. Blaum, Stephan Schiller, Sven Sturm

Published Apr 24, 2025• 7 citations
Publisher

Abstract

In this work, we demonstrate a new method for quantum state control and nondestructive internal quantum state readout of a single HD^{+} ion in the rovibrational ground state in a Penning trap. Furthermore, we demonstrate a measurement of the magnetic trapping field with the same ion to sub-ppb uncertainty. This could enable nondestructive, high-precision spectroscopy of the hyperfine, Zeeman, and rovibrational level structure of single molecular ions. In particular, this technique can be applied to H_{2}^{+} as well as to its antimatter equivalent, H[over ¯]_{2}^{-}, with the potential for high-precision tests of charge-parity-time reversal symmetry beyond current sensitivities [Phys. Scr. T 1995, 423 (1995)PHSTBO0031-894910.1088/0031-8949/1995/T59/060, Phys. Rev. A 98, 010101 (2018)PLRAAN2469-992610.1103/PhysRevA.98.010101].

DOI
10.1103/physrevlett.134.163001

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•Jan 1, 2013•2 citations
In this work, we demonstrate a new method for quantum state control and nondestructive internal quantum state readout of a single HD^{+} ion in the rovibrational ground state in a Penning trap. Furthermore, we demonstrate a measurement of the magnetic trapping field with the same ion to sub-ppb uncertainty. This could enable nondestructive, high-precision spectroscopy of the hyperfine, Zeeman, and rovibrational level structure of single molecular ions. In particular, this technique can be applied to H_{2}^{+} as well as to its antimatter equivalent, H[over ¯]_{2}^{-}, with the potential for high-precision tests of charge-parity-time reversal symmetry beyond current sensitivities [Phys. Scr. T 1995, 423 (1995)PHSTBO0031-894910.1088/0031-8949/1995/T59/060, Phys. Rev. A 98, 010101 (2018)PLRAAN2469-992610.1103/PhysRevA.98.010101].
In this thesis I describe how we achieve control over the quantum state of a single H2+ hydrogen molecular ion. Scientific progress is based on the comparison of theories with experimental measurements. For the simplest molecular quantum systems, such as the hydrogen molecular ions H2+ or HD+, the theoretical predictions of quantum electrodynamics are very accurate. In order to test the theory or to extract fundamental constants from the combination of theory and experiments, the experiments must also achieve high precision. In the recent past, hydrogen molecular ions were mainly measured in ensembles. For example, measurements exist both on molecular beams and with dissociative detection in ion traps. However, the spectroscopy of single ions is one of the most precise measurement methods in physics, which was demonstrated by the spectroscopy of a single ytterbium ion in an ion trap. To perform spectroscopy of a single ion in this way, it must have a suitable energy structure for laser cooling, state preparation and fluorescence detection. This is not the case for many ions, including H2+. Quantum logic spectroscopy (QLS) is a technique that makes it possible to perform measurements on an ion without such an energy structure. The ion to be measured (spectroscopy ion) is trapped in an ion trap with a second ion (helper ion), which has the properties described in the previous paragraph. The shared modes of motion between the two ions allow cooling, preparation and detection of the spectroscopy ion via the helper ion. This was demonstrated with an aluminum spectroscopy ion co-trapped with a magnesium helper ion. QLS can also be used for molecules. This has been shown with MgH+, CaH+ and N2+. We implement QLS to enable spectroscopy of a single H2+ ion. For this we trap H2+ together with a 9Be+ ion. We cool the joint motion of the ions to their ground state. We combine buffer gas cooling with a laser and microwave pulse based state preparation sequence to prepare the H2+ molecule in a pure quantum state. This allows us to perform high contrast QLS on a single H2+ ion. Furthermore, we can change and control the quantum state in the hyperfine structure using microwave pulses. We demonstrate the power of our technique by performing microwave spectroscopy on a magnetic field insensitive hyperfine transition. We use QLS to read out the result of the measurement. Within half an hour, we can achieve a statistical uncertainty of 2 Hz. This paves the way for future high-precision measurements on H2+. The techniques described here could potentially be applied to other light molecular ions.
Science is founded on the benchmarking of theoretical models against experimental measurements, with the challenge that, for all but the simplest systems, the calculations required for high precision become extremely challenging. H 2 + is the simplest stable molecule, and its structure is calculable to high precision. However, studying H 2 + experimentally presents significant challenges: Standard control methods such as laser cooling are not applicable due to the long lifetimes of its rotational and vibrational states. Here, we solve this issue by combining buffer gas cooling to quench the H 2 + rovibrational excitation with quantum logic operations between H 2 + and a cotrapped “helper” ion to control the molecule’s hyperfine structure. This enables us to perform pure quantum state preparation, coherent control, and nondestructive readout, which we use to demonstrate high-resolution microwave spectroscopy in the hyperfine structure of H 2 + with a precision of 2 Hz. Our results pave the way for high-precision spectroscopy of H 2 + in both the microwave and optical domains. Because of the wide applicability of buffer gas cooling, our method provides a general tool for molecular ion species that are hard to control with quantum logic tools alone.
Hydrogen molecular ions play an important role for accurate quantum electrodynamics calculations of rovibrational energy levels [1] and the comparison with laser spectroscopy results [2] allowed probing fundamental physics constants and laws. Advances are driven by an accurate control of the external and internal molecular degrees of freedom with a wide range of techniques [3]. Experimental setups with HD+ions are based on ions in a linear Paul trap and sympathetically cooled to the Lamb-Dick confinement regime by a laser-cooled atomic ion (Be+). Optical transitions allowed rotational cooling [4] and state-resolved detection by resonant-enhanced-multiphoton dissociation (REMPD) [5]. This contribution reports numerical results on the use of a two-photon rotational transition in the terahertz frequency range for preparation of trapped HD+ions in the rovibrational ground state and for high-resolution spectroscopy.
Manipulating the motion of individual trapped ions at the single quantum level has become standard practice in radio-frequency ion traps, enabling sweeping advances in quantum information processing and precision metrology. The key step for motional-state engineering is ground-state cooling. Full motional control also bears great potential to explore another regime of sensitivities for fundamental physics tests in Penning traps. Here we demonstrate the key enabling step by implementing resolved-sideband cooling on the axial mode of a single Be + 9 ion in a 5 Tesla cryogenic Penning trap. The system has been developed for the implementation of high-precision antimatter experiments to test the fundamental symmetries of the standard model with the highest accuracy in the baryonic sector. We measure an axial phonon number of n ¯ z = 0.10 ( 4 ) after cooling and demonstrate that the axial heating rate in our system is compatible with the implementation of quantum logic spectroscopy of (anti-)protons. Published by the American Physical Society 2024
Resolved-sideband cooling of a single 9^99Be+^++ ion in a Penning trap
Manipulating individual trapped ions at the single quantum level has become standard practice in radio-frequency ion traps, enabling applications from quantum information processing to precision metrology. The key ingredient is ground-state cooling of the particle's motion through resolved-sideband laser cooling. Ultra-high-presicion experiments using Penning ion traps will greatly benefit from the reduction of systematic errors offered by full motional control, with applications to atomic masses and ggg-factor measurements, determinations of fundamental constants or related tests of fundamental physics. In addition, it will allow to implement quantum logic spectroscopy, a technique that has enabled a new class of precision measurements in radio-frequency ion traps. Here we demonstrate resolved-sideband laser cooling of the axial motion of a single 9^99Be+^++ ion in a cryogenic 5 Tesla Penning trap system using a two-photon stimulated-Raman process, reaching a mean phonon number of nˉz=0.10(4)\bar{n}_z = 0.10(4)nˉz​=0.10(4). This is a fundamental step in the implementation of quantum logic spectroscopy for matter-antimatter comparison tests in the baryonic sector of the Standard Model and a key step towards improved precision experiments in Penning traps operating at the quantum limit.
The search for a permanent electron electric dipole moment (eEDM) serves as a test of fundamental symmetry violations and of physics beyond the Standard Model. Trapped molecular ions in the 3Δ1 metastable electronic state are suitable candidates for an eEDM search due to their large effective electric fields and long electron spin coherence times. This thesis presents the quantum state manipulation and coherent spectroscopy of trapped HfF+ molecular ions in rotating bias fields for an eEDM search. The quantum state manipulation, which involves preparation of a large fraction of molecular ions in a single desired quantum state as well as rotational-state-resolved detection, is complicated by the lack of HfF+ spectroscopic information prior to the start of this thesis. We performed state preparation by first state-selectively autoionizing neutral HfF such that 35% of the HfF+ are formed in a single rovibrational level of the electronic ground state 1Σ+, and then transferring those ions into the desired Stark levels of a single hyperfine-rovibrational manifold of the 3Δ1 state. Rotational-state-resolved detection is accomplished by both laser-induced fluorescence and resonance-enhanced multi-photon photodissociation, where the latter is preferred as the state detection method of choice because its efficiency is two orders of magnitude higher compared to fluorescence. With the quantum state manipulation techniques developed, we performed Ramsey spectroscopy of the trapped HfF+ ions in the presence of rotating bias electric and magnetic fields, demonstrating electron spin coherence times as long as 150 ms. Finally, we present a preliminary measurement of the eEDM at the |de| < 10-25 e cm level.