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arXiv:2111.11504 · AIP Advances

Resolved-sideband micromotion sensing in Yb+ on the 935 nm repump transition

Connor Goham, J. Britton

Published Nov 1, 2022• 4 citations
arXivHTMLPDF

Abstract

Ions displaced from the potential minimum in an RF Paul trap exhibit excess micromotion. A host of well-established techniques are routinely used to sense (and null) this excessive motion in applications ranging from quantum computing to atomic clocks. The rich atomic structure of Yb+, a heavy ion, includes low-lying 2D3/2 states that must be repumped to permit Doppler cooling, typically using a 935 nm laser coupled to the 3D[3/2]1/2 states. In this article, we demonstrate the use of this transition to make resolved-sideband measurements of 3D micromotion in 172Yb+ and 171Yb+ ions. Relative to other sensing techniques, our approach has very low technical overhead and is distinctively compatible with surface-electrode ion traps.

DOI
10.1063/5.0128113

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arXiv:2406.14204•Jun 20, 2024•1 citation
Ions displaced from the potential minimum in an RF Paul trap exhibit excess micromotion. A host of well-established techniques are routinely used to sense (and null) this excessive motion in applications ranging from quantum computing to atomic clocks. The rich atomic structure of Yb+, a heavy ion, includes low-lying 2D3/2 states that must be repumped to permit Doppler cooling, typically using a 935 nm laser coupled to the 3D[3/2]1/2 states. In this article, we demonstrate the use of this transition to make resolved-sideband measurements of 3D micromotion in 172Yb+ and 171Yb+ ions. Relative to other sensing techniques, our approach has very low technical overhead and is distinctively compatible with surface-electrode ion traps.
Resolved-sideband micromotion sensing in trapped 171^{171}171Yb+^++ ions using Lindblad/Rate equation
We have investigated excess micromotion for a Yb +^++ ion in a Paul trap. In the presence of light modulated by excess micromotion, we calculate the cooling florescence spectrum of the 369.53 nm transition by finding the steady periodic state solution of the Lindblad master equation including the time-dependent Hamiltonian. We have shown that applying a 369.53 nm laser for specific RF parameters does not resolve efficiently micromotion sidebands. To sense well-resolved sidebands micromotion, we solve the Lindblad equation for the four-level optical transitions of the cooling cycle by incorporating the introduced time-dependent Hamiltonian and the branching ratio for spontaneous decay rates at the low intensity limit. However, in the weak-driving regime the rate equation under adiabatic approximation is implemented to detect the excess micromotion effects on the cooling florescence as a function of the repump detuning. This steady state florescence rate of P-state based on the rate equation approach leads to results in agreement with the Lindblad master equation, but with much less computational effort and no numerical issues. We show that by scanning the detuning of the repump laser, the cooling spectrum could be applied as an efficient micromotion sensor at Ωc/r=0.1ΓP/B\Omega _\mathrm{{c/r}}=0.1 \Gamma _\mathrm{{P/B}}Ωc/r​=0.1ΓP/B​ . Our comprehensive discussion provides a theoretical and practical framework to predict the accurate experimental observations of sideband micromtion sensing in the trapped Yb +^++ ion which can be used and also extended.
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.
As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low 10−18 range, motional frequency shifts account for a considerable fraction of the uncertainty budget. Micromotion, a driven motion fundamentally connected to the principle of the Paul trap, is a particular concern in these systems. In this article, we experimentally investigate at this level three common methods for minimizing and determining the micromotion amplitude. We develop a generalized model for a quantitative application of the photon-correlation technique, which is applicable in the commonly encountered regime where the transition linewidth is comparable to the rf drive frequency. We show that a fractional frequency uncertainty due to the 2nd-order Doppler shift below |Δν/ν|=1×10−20 can be achieved. The quantitative evaluation is verified in an interleaved measurement with the conceptually simpler resolved sideband method. If not performed deep within the Lamb-Dicke regime, a temperature-dependent offset at the level of 10−19 is observed in resolved sideband measurements due to sampling of intrinsic micromotion. By direct comparison with photon-correlation measurements, we show that the simple to implement parametric heating method is sensitive to micromotion at the level of |Δν/ν|=1×10−20 as well.
In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a measurement technique for micromotion amplitude. Micromotion is directly observed using a time-resolving, single-photon-sensitive camera that provides both fluorescence and position data for each ion on the nanosecond time scale. Micromotion amplitude and phase for each ion in the crystal are measured, allowing this method to be sensitive to tilts and shifts of the ion chain from the null of the radio-frequency quadrupole potential in the linear trap. Spatial resolution makes this micromotion detection technique suitable for complex ion configurations, including two-dimensional geometries. It does not require any additional equipment or laser beams, and the modulation of the cooling lasers or trap voltages is not necessary for detection as it is in other methods.
We present the design of a compact optical clock based on the 2 S 1/2 → 2 D 3/2 435.5 nm transition in 171 Yb + . The ion trap will be based on a micro-fabricated circuit, with surface electrodes generating a trapping potential to localize a single Yb ion a few hundred μ m from the electrodes. We present our trap design as well as simulations of the resulting trapping pseudo-potential. We also present a compact, multi-channel wavelength meter that will permit the frequency stabilization of the cooling, repumping and clear-out lasers at 369.5 nm, 935.2 nm and 638.6 nm needed to cool the ion. We use this wavelength meter to characterize and stabilize the frequency of extended cavity diode lasers at 369.5 nm and 638.6 nm.
Laser cooling typically requires one or more repump lasers to clear dark states and enable recycling transitions. Here, we have achieved cooling of Be+ ions using a single laser beam, facilitated by one-dimensional heating through micromotion. By manipulating the displacement from the trap's nodal line, we precisely controlled the ion micromotion direction and speed, reaching up to 3144 m/s, which corresponds to a 7.1 GHz Doppler frequency shift in our experiment. This approach eliminates the necessity of a 1.25 GHz offset repump laser while keeping the Be+ ions cold in the perpendicular direction. Measurements were taken using cooling laser detuning and imaging of ion trajectories. Molecular dynamics simulations, based on machine learned time-dependent electric field E(X, Y, Z, t) inside the trap, accurately reproduced the experimental observation, illuminating the relationship between the direction of micromotion and the trapping electric filed vector. This work not only provides a robust method for managing the micromotion velocity of ions but also sheds light on laser cooling complex systems that require multiple repumping lasers. Additionally, it offers a method for controlling energy in the context of ion-molecule collision investigations.