Line search by quantum logic spectroscopy enhanced with squeezing and statistical tests

TL;DR

The paper tackles the challenge of fast, high-confidence searches for narrow optical transitions in trapped ions and highly charged species by scanning broad frequency bandwidths. It introduces two complementary approaches—motional squeezing and statistically postprocessing via hypothesis testing—within a quantum logic spectroscopy framework. The authors demonstrate that each method independently enhances search speed and that their combination yields an order-of-magnitude improvement under realistic noise and SPAM conditions, with an optimal squeezing around 8 dB. The proposed framework reduces practical search times from months toward about a week, offering a general strategy for noisy, bandwidth-rich signal searches in precision metrology.

Abstract

In quantum logic spectroscopy, internal transitions of trapped ions and molecules can be probed by measuring the motional displacement caused by an applied light field of variable frequency. This provides a solution to ``needle in a haystack'' problems, such as the search for narrow clock transitions in highly charged ions, recently discussed by S. Chen et al. (Phys. Rev. Applied 22, 054059). The main bottleneck is the search speed over a frequency bandwitdh, which can be increased by enhancing the sensitivity of displacement detection. In this work, we explore two complementary improvements: the use of squeezed motional states and optimal statistical postprocessing of data using a hypothesis testing framework. We demonstrate that each method independently provides a substantial boost to search speed. Their combination effectively mitigates state preparation and measurement errors, improving the search speed by an order of magnitude and fully leveraging the quantum enhancement offered by squeezing.

Figures (5)

• Figure 1: Quantum logic spectroscopy protocol. (a) A spectroscopy ion with the sought-for electronic transition (blue, right) is trapped together with a logic ion (red, left), forming an ion crystal. (b) The unknown transition frequency $\omega_0$ is probed with an ODF interaction, parametrized by the interrogation detuning $\Delta$. (c) When tuned close to the transition, the ODF produces motional displacement and diffusion (yellow arrows) in the squeezed motional wave packet of the ion crystal's normal mode. The packet is then "unsqueezed", amplifying the displacement signal, which is then detected using the logic ion. (d) The ODF frequency detuning $\Delta$ is scanned step-wise. To detect the presence of the transition from the displacement signal, hypothesis testing is performed on the data from $L$ neighbouring frequency points.
• Figure 2: (a) Excitation profile of the ODF interaction for different interrogation times. The dashed horizontal lines in (a) correspond to the excitation due to the background noise in the absence of the transition. (b) FWHM of the excitation profile. (c) Background noise in the absence of the excitation.
• Figure 3: (a) Decision errors for searching a narrow transition using a Neyman-Pearson hypothesis test. For a fixed parameter set $L=5, M=8, t=35T, \Delta_s=8\Omega$, the tunable test parameter $\Phi$ is striking the balance between the errors of two types (s. Tab. \ref{['tab:errors']}). Dashed lines represent noisy test with $10\%$ SPAM error. (b) The two considered positions of the signal lineshape with respect to the grid of interrogated frequencies. See text for details.
• Figure 4: Bandwidth search speed $v$ for different frequency steps $\Delta_s$ and interrogation times $t$. Each plot corresponds to a particular number of measurements $M$ and number of frequencies $L$ passed to the statistical test. Dashed white line is the FWHM of the signal lineshape.
• Figure 5: Optimal bandwidth search speed versus the amount of squeezing used in the detection protocol. Hypothesis test analyzes data from single ($L=1$, red curves) or multiple ($L=3$, blue curve) interrogated frequencies. The dashed line corresponds to no SPAM errors, for the solid line $10\%$ chance of a bit-flip error in the data is assumed.