Two-photon Doppler-free spectroscopy of the 6s squared; 1S 0 to 6s23s; 1S 0 Rydberg transition for quantum sensing in ytterbium

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Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Two-photon Doppler-free spectroscopy of the 6s squared; 1S 0 to 6s23s; 1S 0 Rydberg transition for quantum sensing in ytterbium".

Mira: Here's the gist of the paper. Two-photon Doppler-free spectroscopy of the 6s23s1S0 → 6s23s1S0 Rydberg transition in Yb facilitates quantum sensing applications such as a two-photon clock, electrometer, or BBR thermometer Transition Selection and Advantages The unique level structure of Yb places the 6s6p1P1 state’s energy at ≈49.7% of the ionization energy, which facilitates two-photon Doppler-free excitation of the 6s23s1S0 Rydberg state from the 6s21S0 ground state at a relatively low optical intensity This J = 0 → J = 0 transition is immune to first-order Zeeman and electric quadrupole shifts, has reduced sensitivity to higher-order Zeeman shifts, and is further predicted to have relatively low sensitivity to density shifts The 6sns1S0 states are nondegenerate, immune to first-order Zeeman and electric quadrupole shifts, are not part of a fine structure manifold, with higher-order Zeeman shifts consequently being suppressed Theoretical Calculations and State Properties Configuration interaction (CI) theory is employed to compute relevant properties of the 6s23s1S0 Rydberg state for sensing, including the C6 coefficient, dc polarizability, blackbody radiation (BBR) shift, and BBR depopulation rate The CI calculations support a suppressed C6 coefficient, consistent with extrapolated results from Ref.

29: The second-order Zeeman shift for this transition is dominated by the Rydberg state, which itself is estimated to be dominated by the diamagnetic contribution Experimental Demonstration and Characterization The authors demonstrate two-photon Doppler-free spectroscopy of the 6s21S0 → 6s23s1S0 transition in Yb Experimental spectra estimate the natural linewidth (lifetime) of the 6s23s1S0 state to be 90 kHz (1.8 µs) Three distinct detection channels are demonstrated: trap-loss spectroscopy, lattice-trapped metastable state population, and fluorescence spectroscopy The measured linewidth for the Doppler-free feature is 187(3) kHz, corresponding to a 14× reduction compared to the Doppler-broadened profile Sensing Applications and Performance Metrics The transition is proposed for several sensing applications, including a two-photon clock, voltage reference, or free-space BBR thermometer The transition shares features with the wellestablished two-photon (778 nm) clock operated on the 5S1/2 → 5D5/2 transition in Rb The dc Stark shift for a nondegenerate state can be expressed as ∆Edc = −1/2αdcE squared where E is an applied electric field The Yb natural linewidth observed in this work is ≈ 50× smaller than in Ref.

5: The transition possesses a large probe ac Stark shift that if uncontrolled will limit the performance of a quantum sensor Multiple techniques can be applied to mitigate the probe Stark shifts The authors estimate the spectroscopy beam to have an ≈ 1.0 mm 1/e2 intensity diameter based on the measured two-photon ac Stark shift The work provides a practical step towards realizing quantum sensors with this transition The natural lifetime of the 6s23s1S0 state is compatible with CI results but is incompatible with extrapolation of the Ref.

71: data In general, the CI results demonstrate reasonable agreement with the available lifetime data, to the extent that the available data allows us to say as much The spectral dependence of the underlying ac Stark shift must be considered when using Rydberg atoms for BBR sensing The clock frequency scales predominantly as T 4, while the “sense” frequency scales predominantly as T squared The fractional clock error is calculated to be 7 × 10-19 for Yb with ρ1 = ρ2 = 0.5, T1 = 300 K, and T2 = 305 K Appendix Details The appendix contains tables of calculated energy levels, lifetimes, C6 coefficients, dc polarizabilities, BBR shifts, BBR depopulation rates, and THz sensing frequencies The CI method is applied for both Jπ = 0+ and Jπ = 1- symmetries to evaluate the properties of the states The results are compiled in Table VI The C6 coefficients exhibit order-of-magnitude agreement between the ab initio CI and modified CI results The modified CI results “feel” the influence of 4f-excited perturber state, despite the absence of such states from the divalent CI computational approach The BBR-related properties δEBBR, SBBR, and γBBR are calculated assuming a BBR temperature of 300 K The C6 coefficient for the 6s23s1S0 state is estimated to be 7.6 × 10 13 a.u.

Paper summary: Kai: So we're looking at this paper about two-photon Doppler-free spectroscopy of the 6s squared; 1S zero to 6s23s; 1S zero Rydberg transition for quantum sensing in ytterbium <ref:2610.22574#pg1,two-photon Doppler-free spectroscopy of the 6s>. It looks like they found a way to excite this state from the ground state at a relatively low optical intensity using two photons, and that's the main thing they're focusing on for quantum sensing applications.

Mira: Yeah, what makes it interesting is how they use the unique level structure of ytterbium. They place the energy of that 6s6p 1P1 state at about forty-nine point seven percent of the ionization energy, which really helps facilitate this two-photon Doppler-free excitation from the 6s21S0 ground state at a low optical intensity <ref:2610.22574#pg1,of the ionization energy, which>.

Lev: From my side, I see the J=zero to J=zero transition they're looking at <ref:2610.22574#pg1>. They say it's immune to first-order Zeeman and electric quadrupole shifts, and it also has reduced sensitivity to higher-order Zeeman shifts, which is a big deal for keeping errors down.

Kai: That’s the part where they really highlight why this transition is promising for sensing. They predicted that it should also have relatively low sensitivity to density shifts, which means it might be good for situations where you have high particle density in your measurement setup.

Mira: The theoretical work they did using configuration interaction theory is pretty deep here. They compute properties like the C6 coefficient, the dc polarizability, and blackbody radiation shift for that 6s23s 1S0 Rydberg state, which tells us a lot about how it will behave in different environments <ref:2610.22574#pg1>.

Lev: I'm looking at those calculations too. They support a suppressed C6 coefficient, which is consistent with what they found in prior work by citing Ref: twenty-nine <ref:2610.22574#pg3>. And the second-order Zeeman shift is dominated by the Rydberg state itself, which they estimate is dominated by the diamagnetic contribution.

Kai: So, experimentally, they actually demonstrated this two-photon Doppler-free spectroscopy of that 6s21S0 to 6s23s 1S0 transition in ytterbium <ref:2610.22574#pg1,two-photon Doppler-free spectroscopy of>. They measured a natural linewidth for that Rydberg state to be ninety kHz, which is about eighteen microseconds.

Mira: And they showed three different detection channels for this measurement: trap-loss spectroscopy, lattice-trapped metastable state population, and fluorescence spectroscopy. The measured linewidth for the Doppler-free feature was one hundred eighty seven thousand kHz, which is a fourteen times reduction compared to the Doppler broadened profile.

Lev: That reduction factor is significant if you think about what real hardware would need to do to maintain that level of coherence for sensing. But I have to ask, how does this measured linewidth compare to what the theory predicted for that state?

Kai: Well, they estimated the spectroscopy beam would have an intensity diameter of about one point zero millimeter one/e2 based on the two-photon ac Stark shift they measured <ref:2610.22574#pg1>. That gives us a concrete idea of the experimental setup required.

Mira: They also mention that this transition shares features with the well-established two-photon clock operating on the 5S1/two to 5D5/two transition in rubidium. And for a nondegenerate state, they express the dc Stark shift as delta E dc equals negative one over two alpha dc E squared, where E is an applied electric field.

Lev: If we look at the clock frequency scaling, it scales predominantly as T to the fourth power, while the "sense" frequency scales predominantly as T to the second power. That distinction is important for how you'd design a sensor based on this.

Kai: It sounds like they are pointing toward several potential sensing applications: a two-photon clock, an electrometer, or even a free-space blackbody radiation thermometer using this transition in ytterbium.

Mira: They also discuss the dc polarizability scaling as n star to seven within a given series, which is favorable for getting a strong response in some applications. However, they caution that higher-lying states suffer from increased sensitivity to density-dependent van der Waals interactions, which scale much more steeply with n star to eleven.

Lev: So the authors admit that there are trade-offs here between signal strength and noise sensitivity related to those van der Waals interactions as you go up in the Rydberg series. That’s a necessary caveat for any practical realization of this concept.

Kai: And they did estimate the fractional clock error for ytterbium with rho one equals rho two equals zero point five, T1 equal to three hundred Kelvin, and T2 equal to three hundred five Kelvin to be seven times ten to the minus nineteen.

Mira: That level of error is what you're aiming for in a quantum sensor application. It’s a very small number compared to what we usually see in atomic measurements right now.

Lev: From an engineering standpoint, achieving that kind of clock stability means you need incredible control over the environment and the laser intensity to manage those Stark shifts they mentioned earlier.

Kai: They did suggest that if you don't control the probe ac Stark shift, it could limit how good your quantum sensor performance actually is, so mitigating those shifts with different techniques is something they highlight.

Mira: The paper provides a practical step toward realizing these quantum sensors with this transition in ytterbium. It shows that the transition itself has a large probe ac Stark shift if left uncontrolled, which is a factor you have to manage.

Lev: The natural lifetime of the 6s23s 1S0 state they inferred from their linewidth measurements is ninety kHz, which they found compatible with their configuration interaction calculations <ref:2610.22574#pg1>. But they also admit that it's incompatible with some extrapolation of data from a reference paper by citing Ref: seventy-one.

Kai: So, the natural lifetime measurement is a bit of a point of discussion between the experimental measurement and the theoretical extrapolation. It shows where we need to be careful with our assumptions.

Mira: The spectral dependence of that underlying ac Stark shift needs to be considered if you're using Rydberg atoms for blackbody radiation sensing, because that affects how accurate those measurements are going to be.

Lev: Overall, the work provides a practical path forward, but it clearly shows the remaining challenges in managing the noise sources and achieving the desired performance metrics for a real quantum sensor based on this transition in ytterbium.

Conclusion: Kai: So this paper is about using two photons to measure a specific transition in ytterbium to build quantum sensors and that's what they're calling "Two-photon Doppler-free spectroscopy of the 6s squared; 1S zero to 6s23s; 1S zero Rydberg transition" <ref:2610.22574#pg1,Two-photon Doppler-free spectroscopy of the 6s>.

Mira: Yeah, it focuses on how this specific state in ytterbium behaves when you excite it using two photons at a low optical intensity.

Lev: It's about finding a way to probe that state without the usual Doppler broadening, which is a big technical hurdle for these kinds of measurements.

Kai: They found that because of the way ytterbium's energy levels are spaced, this specific transition has some advantages in terms of being less sensitive to certain types of shifts like Zeeman effects and density shifts.

Mira: The theory they used, configuration interaction theory, helped them calculate how this state will behave in different environments, giving them things like the C6 coefficient and the blackbody radiation shift.

Lev: And they found that these theoretical calculations give a decent picture of what to expect when you try to run this on real hardware, though there's always that gap between calculation and reality.

Kai: So for someone just listening, it means they're exploring a path toward building things like quantum clocks or thermometers using these ytterbium states.

Mira: They’ve also looked at how the clock frequency scales with temperature versus how the sensing frequency scales, which is important when you think about applying this to a thermometer.

Lev: The fractional error they calculated for the clock part is around seven times ten to the minus nineteen, which is pretty tight for what we're aiming for in real hardware.

Kai: It shows that this transition might be a viable candidate if we can manage those probe ac Stark shifts they mentioned, because they said that's a big thing to control for the sensor performance.

Mira: That probe shift could really limit how good the sensor ends up being if we don't get it under control with some mitigation techniques.

Lev: So the next step is figuring out exactly what kind of experimental setup you need to build to actually realize this level of precision and see those results in a lab.