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Journal of Experimental and Theoretical Physics Letters

Optical Spectroscopy and Measurement of Ion Heating Rates in a Planar Trap

Ilya Gerasin, A. Russkikh, Nikita O. Zhadnov, K. S. Kudeyarov, Igor V. Sherstov, Ilya A. Semerikov, N. Kolachevsky

Published Jul 1, 2026• 0 citations
Publisher

Abstract

The experiment including the trapping of a single $$^{{171}}{\text{Y}}{{{\text{b}}}^{ + }}$$ ion into a planar Paul trap, spectroscopy of the quadrupole $${{{\text{|}}}^{2}}{{S}_{{1/2}}},F = 0\rangle \leftrightarrow {{{\text{|}}}^{2}}{{D}_{{3/2}}},F = 2\rangle $$ transition, observation of Rabi oscillations at this transition, and measurement of secular frequencies has been reported. The ion heating rates have been determined to be $$\bar {n}$$ = (840 ± 100) s –1 . This result is an important step towards a scalable ion quantum computer.

DOI
10.1134/s0021364026607177

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The experiment including the trapping of a single 171Yb+^{{171}}{\text{Y}}{{{\text{b}}}^{ + }}171Yb+ ion into a planar Paul trap, spectroscopy of the quadrupole |2S1/2,F=0⟩↔|2D3/2,F=2⟩{{{\text{|}}}^{2}}{{S}_{{1/2}}},F = 0\rangle \leftrightarrow {{{\text{|}}}^{2}}{{D}_{{3/2}}},F = 2\rangle |2S1/2​,F=0⟩↔|2D3/2​,F=2⟩ transition, observation of Rabi oscillations at this transition, and measurement of secular frequencies has been reported. The ion heating rates have been determined to be nˉ\bar {n}nˉ = (840 ± 100) s –1 . This result is an important step towards a scalable ion quantum computer.
We experimentally demonstrate laser spectroscopy of the electric-quadrupole transition 6s2S1/2−−5d2D3/26s{}^{2}{S}_{1/2}--5d{}^{2}{D}_{3/2}6s2S1/2​−−5d2D3/2​ of a single trapped 171Yb{}^{171}\mathrm{Yb}171Yb ion. The probed transition has a natural linewidth of 3.1 Hz, and is at a wavelength of 435.5 nm. A 171Yb{}^{171}\mathrm{Yb}171Yb ion is laser cooled to the range of the Doppler limit in a radio-frequency Paul trap. The $F=0--{F}^{\ensuremath{'}}=2,$ ${m}_{{F}^{\ensuremath{'}}}=0$ hyperfine component of the 2S1/2−−2D3/2{}^{2}{S}_{1/2}{--}^{2}{D}_{3/2}2S1/2​−−2D3/2​ transition is excited by a laser source whose frequency is controlled by an optical reference cavity of high intrinsic stability. The recoilless carrier component of the vibrational sideband spectrum is resolved with a minimum linewidth of approximately 80 Hz, corresponding to a fractional frequency resolution of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}.$ This resolution limit is attributed to laser frequency instability. The effective decoherence rates of the residual ion motion are inferred from the observation that the axial and two radial low-frequency first-order secular-vibration sidebands show minimum linewidths in the range of 0.2--1 kHz. Prospects for an optical frequency standard based on the investigated atomic system are discussed.
Trapped ions in linear Paul traps are largely isolated from interaction with the environment. This property of trapped ions make them a primary choice for quantum technology. \nOver the last decade, trapped atomic ions in linear radio frequency Paul traps have shown to be an important tool to implement quantum algorithms. The scalability of linear ion \ntraps is required to handle large numbers of qubits, in order to implement useful quantum computation. Advance micro-fabrication technology allows the realisation of scalable ion traps. Further developments of micro-trap designs, for the purpose of scalable quantum technology, requires inter-disciplinary investigations of ion traps. Micro-scale ion trap designs typically require a versatile experimental setup. The first part of this thesis describes such an experimental setup including a chip bracket that can host macroscopic ion traps as well as advanced symmetric and asymmetric ion trap chips with up to 90 control electrodes. The system provides versatile optical access for both type of traps and the vacuum chamber is designed in a way so the ion traps can be replaced within a short amount of time. To test the working of the setup, a macroscopic ion trap with an ion-electrode distance of 310±10 μm is used to trap ytterbium ions (Yb+). The trap is characterised by measuring the heating rate, (n•), and spectral noise density SE(ω). A \nphotoionisation technique is used to ionise the different isotopes of Yb in our trap. Isotope selective photoionisation requires exact measurements of 1So↔1P1 transition for the different Yb isotopes. A technique to measure these resonant frequencies is described. \nThis technique works by observing and aligning fluorescence spots and by using this technique, the 1So↔1P1 transition frequencies for stable isotopes of Yb were measured with an accuracy of 60 MHz. These new measured transition frequencies for stable Yb isotopes differ from previously published work by 660 MHz. Furthermore, this technique can also be used to obtain the transition frequencies at different laser-atomic beam angles, typical for non-perpendicular laser-atomic beam angles. The second part of this thesis discusses the optimisation of surface trap geometries as they are being used to implement scalable ion trap designs which consist of a large number of trapping zones. The trap depth in surface traps is low compared to symmetric traps of similar dimensions. How to optimise the trap geometry to achieve maximum trap depth for a given ion height above the trap electrodes, is discussed. Fast and adiabatic ion shuttling operations in one dimension as well as ion separation and recombination processes are important for many quantum information implementations. The maximum speed of separation of trapped ions for adiabatic shuttling operations depends on the secular frequencies, the trapped ion experiences in the process. It will be shown how such ion trap structures have to be designed for fast ion separation process and linear shuttling. Numerical results of adiabatic shuttling operations for trapped ions in such trap structures are also presented.
The present decade has seen great advances in optical frequency standards following the development of femtosecond laser frequency combs. With this technology, combined with a stable and narrow probe laser source (50-100 Hz linewidth), we made a systematic study of the 5s 2S1/2-4d 2D5/2 (S-D) transition frequency of the 88Sr+ ion as a function of the quantization axis in the trap. This study revealed the presence of systematic shifts caused by residual micromotion in our rf Paul trap and led to an evaluation of those shifts. Also, a method was developed based on the measurement of the Zeeman spectrum of the clock transition to cancel the electric quadrupole shift caused by patch potentials on the trap electrodes. From these results, we also determined the absolute frequency of the S-D clock transition frequency at 674 nm with a fractional frequency uncertainty of 3.4 × 10-14. We have since made improvements to our probe laser system and have observed 5 Hz Fourier transform limited linewidths on a Zeeman component of the S-D transition of the 88Sr+ ion. To observe such a narrow transition it is essential to have a known and well behaved drift of the laser frequency during the few minutes it takes to measure the ion resonance using the quantum jump signal. Our approach to minimize the drift rate and its sensitivity to temperature fluctuations has been to stabilize the cavity at the temperature where its coefficient of thermal expansion is zero. We will present an overview of our recent progress made on the frequency standard based on the laser-cooled and trapped single ion of 88Sr+.
We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.
A single 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ ion is confined in a linear Paul trap and Doppler-cooled on the S1/2{S}_{1/2}S1/2​ to P1/2{P}_{1/2}P1/2​ dipole transition. Then the narrow quadrupole S1/2{S}_{1/2}S1/2​ to D5/2{D}_{5/2}D5/2​ transition at 729 nm is probed. The observed spectrum is interpreted in terms of the Zeeman substructure superimposed with oscillation sidebands due to the harmonic motion in the trap. The height of the motional sidebands provides a sensitive method to determine the ion's temperature and thus allows us to test sub-Doppler laser cooling schemes needed for quantum state preparation and quantum computation. We also observe the dynamics induced by Rabi oscillations on a carrier transition and interpret it in terms of the thermal state which is reached after Doppler cooling.
We compare the frequencies of the $6s\text{ }^{2}S_{1/2}(F=0)\ensuremath{\rightarrow}5d\text{ }^{2}D_{3/2}(F=2)$ reference transition in 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ for two single ions stored in independent traps. The quadrupole moment of the 5d 2D3/25d\text{ }^{2}D_{3/2}5d 2D3/2​ state is measured to be $9.32(48)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{C}\text{ }\mathrm{m}}^{2}$ and from the quadratic Stark shift the relevant scalar and tensor polarizabilities are determined to be ${\ensuremath{\alpha}}_{S}({S}_{1/2})\ensuremath{-}{\ensuremath{\alpha}}_{S}({D}_{3/2})=\ensuremath{-}6.9(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{J}\text{ }\mathrm{m}}^{2}/{\mathrm{V}}^{2}$ and ${\ensuremath{\alpha}}_{T}({D}_{3/2})=\ensuremath{-}13.6(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{J}\text{ }\mathrm{m}}^{2}/{\mathrm{V}}^{2}$, respectively. In the absence of external perturbations we find a mean frequency difference between the two trapped ions of 0.26(42) Hz, corresponding to a relative difference of $3.8(6.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. This is comparable to the agreement found in the most accurate comparisons between cesium fountain clocks.