Direct Frequency-Comb-Driven Raman Transitions in the Terahertz Range

C. Solaro, S. Meyer, K. Fisher, M. V. DePalatis, and M. Drewsen

Phys. Rev. Lett. 120, 253601 – Published 19 June 2018

Abstract

We demonstrate the use of a femtosecond frequency comb to coherently drive stimulated Raman transitions between terahertz-spaced atomic energy levels. More specifically, we address the $3 d {{}^{2}D}_{3 / 2}$ and $3 d {{}^{2}D}_{5 / 2}$ fine structure levels of a single trapped ${}^{40}{Ca}^{+}$ ion and spectroscopically resolve the transition frequency to be $ν_{D} = 1, 819, 599, 021, 534 \pm 8 Hz$ . The achieved accuracy is nearly a factor of five better than the previous best Raman spectroscopy, and is currently limited by the stability of our atomic clock reference. Furthermore, the population dynamics of frequency-comb-driven Raman transitions can be fully predicted from the spectral properties of the frequency comb, and Rabi oscillations with a contrast of 99.3(6)% and millisecond coherence time have been achieved. Importantly, the technique can be easily generalized to transitions in the sub-kHz to tens of THz range and should be applicable for driving, e.g., spin-resolved rovibrational transitions in molecules and hyperfine transitions in highly charged ions.

Received 19 December 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.253601

Physics Subject Headings (PhySH)

Atomic spectra Coherent control Light-matter interaction Quantum information with trapped ions

Trapped ions

Femtosecond laser spectroscopy Raman spectroscopy

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

C. Solaro^*, S. Meyer, K. Fisher, M. V. DePalatis, and M. Drewsen^†

Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark

^*solaro@phys.au.dk
^†drewsen@phys.au.dk

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Vol. 120, Iss. 25 — 22 June 2018

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Images

Figure 1
Schematic of the experimental setup and the relevant electronic levels of the ${Ca}^{+}$ ion. The 397 nm beam, propagating along the $(1 / \sqrt{2}) (\hat{y} + \hat{z})$ direction, is $π$ polarized with respect to the external magnetic field ${\vec{B}}_{ext}$ . The 866, 854, and 729 nm beams, propagating along $\hat{z}$ , have a linear polarization rotated by 45° with respect to ${\vec{B}}_{ext}$ . The ac-Stark-shift laser beam, propagating along $\hat{y}$ , has a linear polarization rotated to maximize the ac-Stark shift on the selected Zeeman sublevels of the $D_{3 / 2}$ state. The frequency comb beam propagates along $\hat{z}$ with a well-defined linear polarization ${\vec{E}}_{comb}$ set by a rotatable Glan-Taylor polarizer.
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Figure 2
(a) Evolution of the population of the $D_{5 / 2}$ state versus duration of the frequency comb’s pulse train. Points correspond to the experimental data, while the solid line is a fit to the data with 99.3(6)% contrast, an exponential decay time of 3.2(2) ms and a Rabi frequency of $Ω_{R} = 2 π \times 4.121 (3) kHz$ . Note that the contrast, depending also on state initialization, is a lower estimate to the Raman transfer efficiency. (b) Typical spectra of the $| J, m_{j} ⟩ : | \frac{5}{2}, - \frac{3}{2} ⟩ \to | \frac{3}{2}, - \frac{3}{2} ⟩$ transition performed at two different comb’s intensities and with ${\vec{E}}_{comb} ∥ {\vec{B}}_{ext}$ . The measured spectra are shifted from the expected transition frequency (calculated by taking the linear Zeeman shift into account) by $δ ν_{D}^{ac} = 9.873 (12) kHz$ (black points) and $δ ν_{D}^{ac} = 4.253 (8) kHz$ (red squares) due to the comb’s ac-Stark shift induced by off-resonant coupling to the $P_{1 / 2, 3 / 2}$ states. Solid curves are ${sinc}^{2}$ fits to the data.
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Figure 3
(a) Measured transition frequency versus the differential ac-Stark shift induced by the frequency comb on the $| S_{1 / 2}, - \frac{1}{2} ⟩ \leftrightarrow | D_{5 / 2}, - \frac{5}{2} ⟩$ transition ( $δ ν_{729}^{ac} \propto I$ ). Blue squares (red points) correspond to a comb polarization rotated by $θ = 78 (1) °$ ( $θ = 88 (1) °$ ) from the quantization axis. Solid lines show the linear fit to the data used to extrapolate the fine structure level separation to zero intensity. The measured frequency is extracted from the average of the resonance frequencies of the $| \frac{5}{2}, \frac{1}{2} ⟩ \to | \frac{3}{2}, \frac{1}{2} ⟩$ and $| \frac{5}{2}, - \frac{1}{2} ⟩ \to | \frac{3}{2}, - \frac{1}{2} ⟩$ transitions. The spread along the $x$ axis is mainly due to pointing instabilities of the frequency comb beam. (b) Absolute frequency measurements on different dates used to determine the fine structure level separation ${\bar{ν}}_{D} = 1, 819, 599, 021, 555 \pm 8 Hz$ . The dashed lines correspond to the 8 Hz standard deviation of the mean.
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Figure 4
Top (bottom): Evolution of the population of the $| D_{5 / 2} ⟩$ state versus duration of the Ti:sapphire frequency comb’s pulse train without (with) GDD compensation. Lines are fit to the experimental data [19].
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