Fault-tolerant dynamically-decoupled hyper-Ramsey spectroscopy of ultra-narrow clock transitions

TL;DR

The paper tackles the vulnerability of hyper-Ramsey spectroscopy to laser-intensity noise, decoherence, and frequency drifts in ultra-narrow clock transitions. It introduces dynamically decoupled hyper-Ramsey (DD-HR) by embedding rotary Hahn-echo refocusing pulses and Eulerian pulse circuits to render AC-Stark shifts negligible while suppressing low-frequency noise. It provides analytic expressions for HR and DD-HR transition probabilities, demonstrates robustness to large pulse-area variations and decoherence, and extends the framework to advanced dynamical-decoupling families (PDD, CPMG, WAHAHA, TM, UDD) and composite pulses. An experimental demonstration on a superconducting qubit confirms the predicted robustness and fidelity, highlighting the potential of fault-tolerant, noise-resilient quantum sensors for precision metrology and new-physics searches.

Abstract

Hyper-Ramsey protocols effectively reduce AC-Stark shifts in probing ultra-narrow optical clock transitions but they remain sensitive to laser intensity noise, decoherence, frequency drifts, and low-frequency perturbations. We address these limitations by incorporating dynamical decoupling, using sequences of rotary Hahn-echo pulses that toggle the probe frequency detuning and phase between opposite signs. Implementing time-optimized Eulerian cycling circuits of multiple refocusing pulses, we generate high-contrast hyper-Ramsey interferences that are completely free from AC-Stark shifts and robust against environmental noise and laser probe parameters imperfections. We demonstrate the robustness of our dynamically-decoupled hyper-Ramsey interrogation scheme by implementing it directly at the pulse level on a superconducting quantum processing unit. Fault tolerant dynamically-decoupled SU(2) hyper-clocks are a significant step toward universal, noise resilient quantum sensors, enabling fault-tolerant metrology for searches about new physics beyond the Standard Model.

Figures (17)

• Figure 1: (a) Classes of HR and DDHR protocols based on phase-shifted refocusing pulses encapsulated by Ramsey pulses to probe a two-level quantum system. Signs of laser probe frequency detunings are indicated as $\pm$ exponents. (b) Definitions of Laser parameters including amplitude $\Omega_{l}$, relative phase $\varphi_{l}$ and frequency detunings $\widetilde{\delta}_{l}$ of the l-th pulse where $\widetilde{\delta}_{l}=\delta_{l}-\Delta_{LS}$ (see schematics), light-shift $\Delta_{LS}$ and probe drift (or distortion) $\varepsilon_{P}$.
• Figure 2: (a) HR3$_{\pi}$ quantum interferences versus clock detuning $\delta/2\pi$. (b) DDHR3$_{\pi}$ quantum interferences versus clock detuning $\delta/2\pi$. Laser parameters are $\Omega=\pi/2\tau$ with a pulse duration $\tau=10$ ms and a fixed free evolution time T$=200$ ms. No residual light-shift and no laser probe frequency offset or drift are assumed to be present.
• Figure 3: Excitation profile of HR3$_{\pi}$ and DDHR3$_{\pi}$ interferences versus a variation of the pulse area $\Omega\tau=q\frac{\pi}{2}$ over the entire sequence of pulses at resonance. Other parameters are identical to Fig. \ref{['fig:interferences']}. No decoherence.
• Figure 4: Light-shift and decoherence effects on the central fringe frequency-shift. The DDHR3$_{\pi}$ (filled red stars) central fringe frequency-shift versus a residual probe-induced light-shift $\Delta_{LS}/2\pi$ is insensitive to decoherence. The HR3$_{\pi}$ (blue solid dots) central fringe frequency-shift is robust to a residual probe-induced light-shift $\Delta_{LS}/2\pi$ without decoherence but is compromized by introducing a decoherence term up to $\gamma_{c}/2\pi=100$ mHz (green solid dots). Other parameters are identical to Fig. \ref{['fig:interferences']} including a variation of pulse areas by $\pm10\%$ ($\Omega=q\frac{\pi}{2\tau}$ where q$=0.9,1.0,1.1$).
• Figure 5: Interference contrast and sensitivity of the central fringe to a probe-induced frequency drift or offset $\varepsilon_{P}/2\pi$. (a) HR3$_{\pi}$ (blue solid dots), DD-HR3$_{\pi}$ (filled red stars) and DDD-HR3$_{\pm\pi/4}$ (open red stars) central fringe frequency-shift versus a residual probe-induced frequency drift $\varepsilon_{P}/2\pi$. (b) The inset shows how the DD-HR3$_{\pi}$ protocol efficiently eliminates the linear dependence on $\varepsilon_{P}/2\pi$ compared to the HR3$_{\pi}$ original scheme. Other parameters are identical to Fig. \ref{['fig:interferences']}. No decoherence.