Demonstration of a Raman Velocity Filter in Collinear Laser Spectroscopy: Towards Applications for sub-ppm High-Voltage Measurements

TL;DR

This work addresses the energy-width limitation in collinear laser spectroscopy for high-precision high-voltage measurements. It combines theory (two-level reduction) and full four-level simulations to design Raman-based velocity filtering in Sr$^+$, and demonstrates the first velocity-selective Raman transition in CLS. Experimentally, a Raman velocity filter is realized, achieving a ground-state Lamb dip and reducing the effective energy width to about $0.15$ eV, with Lamb-dip widths near $1$ MHz, consistent with simulations that include spatial beam effects. The results validate Raman transitions as a practical route toward sub-ppm metrology and outline path improvements (beam overlap, laser stability, alternate ion sources) for future high-precision voltage standards.

Abstract

Raman transitions have a wide range of applications in atomic physics and have recently been proposed as a means for improving high-precision high-voltage measurements. Here, we present a theoretical analysis and a first experimental demonstration of $5s\,^2\mathrm{S}_{1/2} \rightarrow 4d\,^2\mathrm{D}_{3/2,5/2}$ Raman transitions in $^{88}$Sr$^+$ ions in collinear laser spectroscopy. For the theoretical description the three-level system is reduced to an effective two-level system, in order to estimate the experimental parameters, while the role of the spatial laser intensity distribution in combination with the radial extension of the ion beam are elucidated by performing simulations of the full four-level system. Experimentally, we realized the first velocity-selective Raman transition in collinear laser spectroscopy. Using a $^{88}$Sr$^+$ ion beam, we demonstrate a reduction in the energy width to less than $200\,$meV, which is about an order of magnitude reduction compared to the usage of an optical dipole transition as in previous works. We also investigate two-photon Rabi oscillations and show that their observed collapse is consistent with the simulations.

Figures (12)

• Figure 1: Raman transition in a three-level $\Lambda$-scheme. The arrows indicate the coupling of the laser $j \in \{1,2\}$ (frequency $\omega_{\mathrm{L}j}$ , wavevector $\Vec{k}_{Lj}$) to the dipole transition between the levels $\ket{n}$, $n \in \{1,2\}$ and $\ket{3}$ with the Rabi frequency $\Omega_{nj}$ and the single-photon detuning $\Delta_{nj}$. The full blue and red arrows indicate the couplings driving the Raman transition, while the dashed arrows correspond to the interactions that only result in additional AC-Stark shifts. Also indicated are the ion momenta in the different basis states, which have been included to account for Doppler-shifts and photon recoils.
• Figure 2: Fine structure level scheme of Sr$^+$. The arrows indicate different dipole transitions with their respective wavelength. Also indicated are life times $\tau$ of the different states and the branching ratios of the different decay paths. The life times and branching ratios were taken from NIST_ASD.
• Figure 3: a) Schematics of the COALA beamline. The ions are produced in the surface ionization source (SIS) placed on a high voltage $U_\mathrm{acc}=20\,$kV, accelerated to ground potential and superimposed with the laser beams using electrostatic ion optics. All lasers are operated at a fixed frequency. Two interaction regions, the dedicated drift tube (IR1) and an einzel lens (IR2), are used to drive Raman transitions via Doppler tuning by floating the interaction regions to $U_\mathrm{pump,1}$ and $U_\mathrm{pump,2}$ respectively. The fluorescence detection region (FDR) is equipped with photomultiplier tubes, used to detect the 408-nm photons from the $\mathrm{P}_{3/2}\rightarrow\mathrm{S}_{1/2}$ decay. b) Measurement scheme for a single Raman transition, shown for the $\mathrm{S}_{1/2}\rightarrow\mathrm{D}_{3/2}$ transition. Initially, the ground state is populated. Spectroscopy is performed on the Raman transition via Doppler tuning by scanning $U_\mathrm{pump,1}$. A fixed voltage $U_\mathrm{FDR}$ is applied to the FDR to probe the $\mathrm{D}_{3/2}$ state by resonantly driving $\mathrm{D}_{3/2}\rightarrow\mathrm{P}_{3/2}$ dipole transition and detecting the 408-nm photons emitted from the subsequent $\mathrm{P}_{3/2}\rightarrow\mathrm{S}_{1/2}$ decay. c) Measurements scheme for Doppler-free collinear Raman spectroscopy, shown for a $\mathrm{S}_{1/2}\rightarrow\mathrm{D}_{5/2}$ and a consecutive $\mathrm{S}_{1/2}\rightarrow\mathrm{D}_{3/2}$ transition. In a first Raman transition, driven at fixed $U_\mathrm{pump,1}$, ions of one velocity are selected and transferred to the $\mathrm{D}_{5/2}$ state. To perform a Doppler-free measurement the interaction potential $U_\mathrm{pump,2}$ of a second $\mathrm{S}_{1/2}\rightarrow\mathrm{D}_{3/2}$ Raman transition is scanned. The second transition is detected by probing the $\mathrm{D}_{3/2}$ state like in b). Ions of the velocity transferred out of the ground state in the first interaction are not transferred in the second interaction, as indicated by the grayed out transitions. Thus they do not contribute to the PMT signal, resulting in a Doppler-free Lamb dip in the resonance spectrum.
• Figure 4: Simulations of the energy dependent population transfer for a $3\pi$$\mathrm{S}_{1/2}\rightarrow\mathrm{D}_{5/2}$ Raman transition. The dotted lines indicate simulations without spatial intensity distribution ($w_i=0$), solid lines simulations with beam diameters according to Tab. \ref{['tab:params']} ($w_i\neq0$). The different colors show simulations for different variations in the two-photon detuning $\Delta \delta \in \{0,\, 0.2\,\mathrm{MHz},\, 2\,\mathrm{MHz}\}$, induced by according laser line-widths or variations in the interaction potential $\Delta U \in \{0,\, 0.01\,\mathrm{V},\,0.1\,\mathrm{V}\}$.
• Figure 5: Simulated population transfer across the the ion-beam cross-section including spatial intensity distributions for a $3\pi$$\mathrm{S}_{1/2}\rightarrow\mathrm{D}_{5/2}$ Raman transition in a Gaussian beam profile according to Tab. \ref{['tab:params']}. The phase of the Raman transition decreases with the distance from the beam center, reflecting the spatial intensity distribution of the laser beams, resulting in a local minimum ($2\pi$-pulse) and a second local maximum ($1\pi$-pulse). In the second maximum the population transfer does not reach $1$ due to a smaller AC-Stark shift compared to the beam center.