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Journal of Physics Conference Series

A New Experiment for the Measurement of the g-Factors of 3He+ and 3He2+

Andreas H. Mooser, Alexander Rischka, Antonia Schneider, K. Blaum, S. Ulmer, J. Walz

Published Nov 1, 2018• 12 citations
Publisher

Abstract

We describe a new experiment that aims at a parts per billion measurement of the nuclear magnetic moment of 3 He 2 + and a 100 parts per trillion measurement of the Zeeman effect of the ground-state hyperfine splitting of 3 He+. To enable ultrafast and efficient experiment cycles the experiment relies on new technologies such as sympathetic laser cooling of single 3 He-ions coupled to a cloud of Doppler-cooled 9 Be-ions in a Penning trap or a novel spin-state detection scheme.

DOI
10.1088/1742-6596/1138/1/012004

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A direct, high-precision measurement of the 3He2+ nuclear magnetic moment in a Penning trap will provide the most accurate calibration of 3He probes for nuclear magnetic resonance. The magnetic moment measurement at μTEx is carried out using the so-called continuous Stern-Gerlach effect, in which the spin state of the trapped ion is determined via axial frequency shifts in an inhomogeneous magnetic field. However, its mass and small magnetic moment lead to difficulties in determining the spin state, as the axial frequency shifts are on the order of background frequency fluctuations. These fluctuations can be reduced by lowering the energy of the trapped ion. Since traditional resistive cooling is not sufficient, and a bare helium nucleus cannot be laser cooled directly to reduce its energy, sympathetic cooling of 3He2+ is a well-suited technique. It is achieved by coupling the nucleus to a cloud of Doppler-cooled 9Be+ ions - produced by laser ablation from a solid target - in a coupling trap. To characterise laser cooling of 9Be+ at its 2S1/2 →2 P3/2 transition and to test the available coupling trap, a new cryogenic Penning-trap experiment at μTEx is currently being developed. The experiment uses a pair of Penning traps coupled together over their endcaps forming the coupling trap for sympathetic laser cooling of 3He2+ with 9Be+. The setup, developed and characterized within this thesis, utilises a pulse-tube cooler to reach cryogenic temperatures of 4 K and a permanent magnet capable of generating a magnetic field of 240 mT, with the B2 parameter between ±2 T/m2 over a distance of 5 mm, and 0.75 T/m2 at the trap centre. The choice of a pulse tube cooler and permanent magnet makes the experiment capable of supporting frequent cooling cycles and quick changes. Initially, the experiment is supposed to test the coupling traps and to characterise laser cooling of 9Be+ ions, and in future, offer an adjustable platform for further testing of new components related to high-precision experiments in Penning traps.

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The Zeeman splitting of the metastable 5${\mathit{D}}_{3/2}$ level of $^{138}\mathrm{Ba}^{+}$ in a magnetic field of 6 T has been measured in a laser-microwave double resonance experiment in a Penning ion trap. The magnetic field at the ion's position is determined by the cyclotron frequency of electrons stored in the same trap. From the ratio of both transition frequencies we obtain a ${\mathit{g}}_{\mathit{J}}$ value of 0.799 327 8(3). As a by-product, we confirmed earlier measurements on the 6${\mathit{S}}_{1/2}$ ground-state ${\mathit{g}}_{\mathit{J}}$ factor to 2.002 492 2(10). The precision in both experiments is sufficient to test relativistic many-body calculations. \textcopyright{} 1996 The American Physical Society.

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High precision comparisons of the proton and antiproton g-factor enable stringent tests of CPT symmetry in the baryonic sector. However, current measurement routines suffer from long preparation times and high particle temperatures, which complicate the increase of the precision beyond the parts per billion regime. As a solution, new sympathetic cooling schemes based on co-trapped laser-cooled ions may be used to cool (anti-)protons to the ground state of motion and to significantly decrease particle preparation times. In addition, motional coupling to an auxiliary ion in a double-well potential can be used for the implementation of new readout schemes based on quantum logic spectroscopy for the spin-state of the (anti-)protons. This thesis describes a cryogenic Penning trap system for ground state cooling of single 9Be+ ions, which represents the latest development of the BASE experiment in Hannover towards the implementation of sympathetic cooling schemes and quantum logic spectroscopy of single (anti-)protons. Furthermore, the setup and implementation of lasers systems at 313nm for Doppler cooling, repumping and Raman interactions are described. To this end, an optical platform for laser beam delivery to the vacuum system and an optical phase-locked loop for the stabilization of the relative phase of two lasers at 313 nm are presented. In this work, the laser systems are used for measurements of the optical resonance frequencies for cooling, probing and repumping of 9Be+ ions. In addition, stimulated Raman transitions are demonstrated using two phase-locked lasers at 313nm. In the following, this technique is used for high-precision measurements of the qubit frequency and the magnetic field, as well as themometry measurements with 9Be+ ions. The temperature of the ions after Doppler cooling is measured as a function of the cooling laser parameters and a minimal axial mode temperature of 1.77(10) mK is obtained. The results of this thesis pave the way for sideband spectroscopy and ground state cooling of single 9Be+ ions in Penning traps, which is an essential prerequisite for sympathetic ground state cooling of single (anti-)protons and the application of quantum logic spectroscopy to (anti-)proton g-factor measurements in the future.

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The comparison of the g-factors of the proton and the antiproton is a stringent test of CPT invariance. The state-of-the-art method for the determination of the (anti-)proton's g-factor is the application of the continuous Stern-Gerlach effect. With this method, precisions in the low parts per billion regime could be achieved. However, preparation times for cold enough particles are on the order of minutes to hours. The implementation of sympathetic cooling using a co-trapped atomic ion could lead to preparation times in the milliseconds regime. Furthermore, the applicability of sympathetic cooling would enable an alternative readout scheme using quantum logic methods. This thesis presents a Penning trap system that is designed for ground state cooling, adiabatic transport, and motional coupling of single 9Be+ ions. It has been built in a modular manner, giving the option of adapting it for motional coupling and sympathetic cooling of single (anti-)protons. In the course of this work, the prerequisites for motional coupling of 9Be+ ions have been fulfilled: A cloud of 9Be+ ions was cooled to a temperature of 1.7~mK applying Doppler cooling. The achieved temperature is about three times the Doppler limit which is 0.5~mK for beryllium ions. Furthermore, a scheme for reproducible loading of the trap and reducing the particle number was developed. Finally, first transport in our apparatus was demonstrated with clouds of beryllium ions. The method used for that is directly applicable to single ions. The results of this work pave the way towards adiabatic transport of single 9Be+ ions, which is crucial for sympathetic cooling of (anti-)protons in a double-well potential as well as for implementing quantum logic spectroscopy with single (anti-)protons.

•Jan 1, 2021•0 citations
We describe a new experiment that aims at a parts per billion measurement of the nuclear magnetic moment of 3 He 2 + and a 100 parts per trillion measurement of the Zeeman effect of the ground-state hyperfine splitting of 3 He+. To enable ultrafast and efficient experiment cycles the experiment relies on new technologies such as sympathetic laser cooling of single 3 He-ions coupled to a cloud of Doppler-cooled 9 Be-ions in a Penning trap or a novel spin-state detection scheme.
A direct, high-precision measurement of the 3He2+ nuclear magnetic moment in a Penning trap will provide the most accurate calibration of 3He probes for nuclear magnetic resonance. The magnetic moment measurement at μTEx is carried out using the so-called continuous Stern-Gerlach effect, in which the spin state of the trapped ion is determined via axial frequency shifts in an inhomogeneous magnetic field. However, its mass and small magnetic moment lead to difficulties in determining the spin state, as the axial frequency shifts are on the order of background frequency fluctuations. These fluctuations can be reduced by lowering the energy of the trapped ion. Since traditional resistive cooling is not sufficient, and a bare helium nucleus cannot be laser cooled directly to reduce its energy, sympathetic cooling of 3He2+ is a well-suited technique. It is achieved by coupling the nucleus to a cloud of Doppler-cooled 9Be+ ions - produced by laser ablation from a solid target - in a coupling trap. To characterise laser cooling of 9Be+ at its 2S1/2 →2 P3/2 transition and to test the available coupling trap, a new cryogenic Penning-trap experiment at μTEx is currently being developed. The experiment uses a pair of Penning traps coupled together over their endcaps forming the coupling trap for sympathetic laser cooling of 3He2+ with 9Be+. The setup, developed and characterized within this thesis, utilises a pulse-tube cooler to reach cryogenic temperatures of 4 K and a permanent magnet capable of generating a magnetic field of 240 mT, with the B2 parameter between ±2 T/m2 over a distance of 5 mm, and 0.75 T/m2 at the trap centre. The choice of a pulse tube cooler and permanent magnet makes the experiment capable of supporting frequent cooling cycles and quick changes. Initially, the experiment is supposed to test the coupling traps and to characterise laser cooling of 9Be+ ions, and in future, offer an adjustable platform for further testing of new components related to high-precision experiments in Penning traps.
The Zeeman splitting of the metastable 5D3/2{\mathit{D}}_{3/2}D3/2​ level of 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ in a magnetic field of 6 T has been measured in a laser-microwave double resonance experiment in a Penning ion trap. The magnetic field at the ion's position is determined by the cyclotron frequency of electrons stored in the same trap. From the ratio of both transition frequencies we obtain a gJ{\mathit{g}}_{\mathit{J}}gJ​ value of 0.799 327 8(3). As a by-product, we confirmed earlier measurements on the 6S1/2{\mathit{S}}_{1/2}S1/2​ ground-state gJ{\mathit{g}}_{\mathit{J}}gJ​ factor to 2.002 492 2(10). The precision in both experiments is sufficient to test relativistic many-body calculations. \textcopyright{} 1996 The American Physical Society.
We report an improved measurement of the Land\'e gJ{g}_{J}gJ​ factor of the 5D5/25{D}_{5/2}5D5/2​ state of singly ionized barium. Measurements were performed on single Doppler-cooled 138{}^{138}138Ba+{}^{+}+ ions in linear Paul traps using two similar, independent apparatuses. Transitions between Zeeman sublevels of the 6S1/26{S}_{1/2}6S1/2​ and 5D5/25{D}_{5/2}5D5/2​ states were driven with two independent, stabilized radio-frequency synthesizers using a dedicated electrode within each ion trap chamber. State detection within each Zeeman manifold was achieved with a frequency-stabilized fiber laser operating at 1.76 $\ensuremath{\mu}$m. By calculating the ratio of the two Zeeman splittings, and using the measured Land\'e gJ{g}_{J}gJ​ factor of the 6S1/26{S}_{1/2}6S1/2​ state, we find a value of 1.200 372(4stat)(7sys)({4}_{\mathrm{stat}})({7}_{\mathrm{sys}})(4stat​)(7sys​) for gD5/2{g}_{{D}_{5/2}}gD5/2​​.
High precision comparisons of the proton and antiproton g-factor enable stringent tests of CPT symmetry in the baryonic sector. However, current measurement routines suffer from long preparation times and high particle temperatures, which complicate the increase of the precision beyond the parts per billion regime. As a solution, new sympathetic cooling schemes based on co-trapped laser-cooled ions may be used to cool (anti-)protons to the ground state of motion and to significantly decrease particle preparation times. In addition, motional coupling to an auxiliary ion in a double-well potential can be used for the implementation of new readout schemes based on quantum logic spectroscopy for the spin-state of the (anti-)protons. This thesis describes a cryogenic Penning trap system for ground state cooling of single 9Be+ ions, which represents the latest development of the BASE experiment in Hannover towards the implementation of sympathetic cooling schemes and quantum logic spectroscopy of single (anti-)protons. Furthermore, the setup and implementation of lasers systems at 313nm for Doppler cooling, repumping and Raman interactions are described. To this end, an optical platform for laser beam delivery to the vacuum system and an optical phase-locked loop for the stabilization of the relative phase of two lasers at 313 nm are presented. In this work, the laser systems are used for measurements of the optical resonance frequencies for cooling, probing and repumping of 9Be+ ions. In addition, stimulated Raman transitions are demonstrated using two phase-locked lasers at 313nm. In the following, this technique is used for high-precision measurements of the qubit frequency and the magnetic field, as well as themometry measurements with 9Be+ ions. The temperature of the ions after Doppler cooling is measured as a function of the cooling laser parameters and a minimal axial mode temperature of 1.77(10) mK is obtained. The results of this thesis pave the way for sideband spectroscopy and ground state cooling of single 9Be+ ions in Penning traps, which is an essential prerequisite for sympathetic ground state cooling of single (anti-)protons and the application of quantum logic spectroscopy to (anti-)proton g-factor measurements in the future.
The comparison of the g-factors of the proton and the antiproton is a stringent test of CPT invariance. The state-of-the-art method for the determination of the (anti-)proton's g-factor is the application of the continuous Stern-Gerlach effect. With this method, precisions in the low parts per billion regime could be achieved. However, preparation times for cold enough particles are on the order of minutes to hours. The implementation of sympathetic cooling using a co-trapped atomic ion could lead to preparation times in the milliseconds regime. Furthermore, the applicability of sympathetic cooling would enable an alternative readout scheme using quantum logic methods. This thesis presents a Penning trap system that is designed for ground state cooling, adiabatic transport, and motional coupling of single 9Be+ ions. It has been built in a modular manner, giving the option of adapting it for motional coupling and sympathetic cooling of single (anti-)protons. In the course of this work, the prerequisites for motional coupling of 9Be+ ions have been fulfilled: A cloud of 9Be+ ions was cooled to a temperature of 1.7~mK applying Doppler cooling. The achieved temperature is about three times the Doppler limit which is 0.5~mK for beryllium ions. Furthermore, a scheme for reproducible loading of the trap and reducing the particle number was developed. Finally, first transport in our apparatus was demonstrated with clouds of beryllium ions. The method used for that is directly applicable to single ions. The results of this work pave the way towards adiabatic transport of single 9Be+ ions, which is crucial for sympathetic cooling of (anti-)protons in a double-well potential as well as for implementing quantum logic spectroscopy with single (anti-)protons.