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Physical Review A

High-precision many-body Ramsey spectroscopy with composite pulses

Yuehua Pang, Yi Shen, Jiahao Huang, Chaohong Lee

Published Apr 11, 2025• 1 citation
Publisher

Abstract

Ramsey spectroscopy serves as a key tool for frequency measurement. Although entanglement can enhance the measurement precision, the atom-atom interaction required for entanglement generation may lead to a frequency shift. In addition, the spectra also suffer from light shift caused by the interaction between light and atoms. Thus, it is difficult to achieve high precision without inducing additional systematic errors. Here, we propose to realize high-precision entanglement-enhanced Ramsey spectroscopy with composite pulses. First, we utilize spin-squeezed states generated by one-axis twisting (OAT) dynamics to enhance the measurement precision. We find that by applying a suitable pulse after OAT, the resonant frequency can be inferred and the light shift can be reduced by using composite pulses. To increase the signal slope, we use anti-OAT dynamics to perform interaction-based readout after interrogation. By designing suitable composite pulses, it can significantly increase the signal response and further improve the measurement precision. Although both schemes can mitigate the light shift, it cannot be entirely eliminated. Thus, we develop the autobalanced entanglement-enhanced Ramsey spectroscopy. By using combination of different sequences with short and long interrogation times and feedback control, the light shift of both our protocols can be completely suppressed, which increases the measurement accuracy. Besides, we also investigate the effects of background atom-atom interaction and find that it only reduces the measurement precision without introducing additional frequency shift. Our study offers an alternative method for achieving precise frequency measurement, which has the potential to be of significant application in quantum sensors such as atomic clocks.

DOI
10.1103/physreva.111.042611

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Ramsey spectroscopy serves as a key tool for frequency measurement. Although entanglement can enhance the measurement precision, the atom-atom interaction required for entanglement generation may lead to a frequency shift. In addition, the spectra also suffer from light shift caused by the interaction between light and atoms. Thus, it is difficult to achieve high precision without inducing additional systematic errors. Here, we propose to realize high-precision entanglement-enhanced Ramsey spectroscopy with composite pulses. First, we utilize spin-squeezed states generated by one-axis twisting (OAT) dynamics to enhance the measurement precision. We find that by applying a suitable pulse after OAT, the resonant frequency can be inferred and the light shift can be reduced by using composite pulses. To increase the signal slope, we use anti-OAT dynamics to perform interaction-based readout after interrogation. By designing suitable composite pulses, it can significantly increase the signal response and further improve the measurement precision. Although both schemes can mitigate the light shift, it cannot be entirely eliminated. Thus, we develop the autobalanced entanglement-enhanced Ramsey spectroscopy. By using combination of different sequences with short and long interrogation times and feedback control, the light shift of both our protocols can be completely suppressed, which increases the measurement accuracy. Besides, we also investigate the effects of background atom-atom interaction and find that it only reduces the measurement precision without introducing additional frequency shift. Our study offers an alternative method for achieving precise frequency measurement, which has the potential to be of significant application in quantum sensors such as atomic clocks.
Sophisticated Ramsey-based interrogation protocols using composite laser pulse sequences have been recently proposed to provide next-generation high-precision atomic clocks with a near perfect elimination of frequency shifts induced during the atom-probing field interaction. We propose here a simple alternative approach to the autobalanced Ramsey interrogation protocol and demonstrate its application to a cold-atom microwave clock based on coherent population trapping (CPT). The main originality of the method, based on two consecutive Ramsey sequences with different dark periods, is to sample the central Ramsey fringes with frequency jumps finely adjusted by an additional frequency-displacement concomitant parameter, scaling as the inverse of the dark period. The advantage of this displaced frequency-jump Ramsey method is that the local oscillator (LO) frequency is used as a single physical variable to control both servo loops of the sequence, simplifying its implementation and avoiding noise associated with controlling the LO phase. When tested using a CPT cold-atom clock, the DFJR scheme reduces the sensitivity of the clock frequency to variations of the light shifts by more than an order of magnitude compared with the standard Ramsey interrogation. This simple method can be applied in a wide variety of Ramsey-spectroscopy based applications including frequency metrology with CPT-based and optical atomic clocks, mass spectrometry, and precision spectroscopy.
Probing an atomic resonance without disturbing it is an ubiquitous issue in physics. This problem is critical in high-accuracy spectroscopy or for the next generation of atomic optical clocks. Ultra-high resolution frequency metrology requires sophisticated interrogation schemes and robust protocols handling pulse length errors and residual frequency detuning offsets. This review reports recent progress and perspective in such schemes, using sequences of composite laser-pulses tailored in pulse duration, frequency and phase, inspired by NMR techniques and quantum information processing. After a short presentation of Rabi technique and NMR-like composite pulses allowing efficient compensation of electromagnetic field perturbations to achieve robust population transfers, composite laser-pulses are investigated within Ramsey's method of separated oscillating fields in order to generate non-linear compensation of probe-induced frequency shifts. Laser-pulses protocols such as hyper-Ramsey, modified hyper-Ramsey, generalized hyper-Ramsey and hybrid schemes as auto-balanced Ramsey spectroscopy are reviewed. These techniques provide excellent protection against both probe induced light-shift perturbations and laser intensity variations. More sophisticated schemes generating synthetic frequency-shifts are presented. They allow to reduce or completely eliminate imperfect correction of probe-induced frequency-shifts even in presence of decoherence due to the laser line-width. Finally, two universal protocols are presented which provide complete elimination of probe-induced frequency shifts in the general case where both decoherence and relaxation dissipation effects are present by using exact analytic expressions for phase-shifts and the clock frequency detuning. These techniques might be applied to atomic, molecular and nuclear frequency metrology, Ramsey-type mass spectrometry as well as precision spectroscopy.
Abstract Light shifts induced during atom–light interactions significantly affect the medium- and long-term frequency stability of atomic clocks. Here, we employ composite laser pulse sequences to mitigate interrogation-induced light shifts in a cold-atom coherent-population-trapping clock. We obtain the anti-symmetry error signal via modulating the local oscillator phase in the free-evolution time of Ramsey interferometry. Utilizing this signal, we employ two feedback loops to simultaneously eliminate light shifts and stabilize the clock frequency using the auto-balanced Ramsey (ABR) spectroscopy scheme. Our experimental results demonstrate that this approach can reduce the clock frequency’s sensitivity to variations in light shifts by implementing four Ramsey sub-sequences. Furthermore, we show that the ABR spectroscopy scheme enhances the long-term frequency stability of the atomic clock when the averaging time τ > 5000 s.
A new class of atomic interferences using ultranarrow optical transitions are pushing quantum engineering control to a very high level of precision for the next generation of sensors and quantum gate operations. In such context, we propose a new quantum engineering approach to Ramsey-Bord\'e interferometry introducing multiple composite laser pulses with tailored pulse duration, Rabi field amplitude, frequency detuning and laser phase step. We explore quantum metrology with hyper-Ramsey and hyper-Hahn-Ramsey clocks below the ${10}^{\ensuremath{-}18}$ level of fractional accuracy by fine-tuning control of light excitation parameters leading to spinor interferences protected against light-shift coupled to laser-probe field variation. We review cooperative composite pulse protocols to generate robust Ramsey-Bord\'e, Mach-Zehnder, and double-loop atomic sensors shielded against measurement distortion related to Doppler and light shifts coupled to pulse area errors. Fault-tolerant autobalanced hyperinterferometers are introduced eliminating several technical laser pulse defects that can occur during the entire probing interrogation protocol. Quantum sensors with composite pulses and ultracold atomic sources should offer a new level of high accuracy in the detection of acceleration and rotation inducing phase shifts, a strong improvement in tests of fundamental physics with hyperclocks while paving the way to a new conception of atomic interferometers tracking space-time gravitational waves with very high sensitivity.
Everyone is trying to make frequency measurements as accurate as possible. But what if the measurement process itself becomes a major source of error? This issue is particularly relevant in the context of state-of-the-art atomic clocks where errors at the 18th decimal place are not negligible anymore. In order to spectroscopically interrogate an atomic clock transition without compromising the clock's accuracy, we devise a perturbation-immune version of Ramsey's method of separated oscillatory fields. By actively balancing the spectroscopic responses from phase-congruent Ramsey probe cycles of unequal durations, we eliminate a wide variety of interrogation-induced line shifts often encountered in high precision spectroscopy, among them, in particular, light shifts, phase chirps, and transient Zeeman shifts. We experimentally demonstrate autobalanced Ramsey spectroscopy on the light shift prone171Yb+electric octupole optical clock transition and show that interrogation defects are not turned into clock errors. This opens up frequency accuracy perspectives below the 10-18level for the Yb+system and for other types of optical clocks. Further applications of this simple and universal approach include next generation coherent population trapping clocks and perturbation-immune readout of quantum sensors. Future long-term clock comparisons searching for physics beyond the standard model will also benefit from this technique.
Optical clock interrogation protocols, based on laser-pulse spectroscopy, suffer from probe-induced frequency shifts and their variations induced by laser power. The original hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not fully eliminate the shift, especially when decoherence and relaxation by spontaneous emission or collisions are present. We propose to solve the fundamental problem of frequency shifts induced by the laser probe by deriving the exact canonical form of a multipulse generalized hyper-Ramsey resonance, including decoherence and relaxation. We present a universal interrogation protocol based on composite laser-pulse spectroscopy with phase modulation eliminating probe-induced frequency shifts at all orders in the presence of various dissipative processes. Unlike frequency shift extrapolation based methods, a universal interrogation protocol based on $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/4$ and $\ifmmode\pm\else\textpm\fi{}3\ensuremath{\pi}/4$ phase-modulated resonances is proposed which does not compromise the stability of the optical clock while maintaining an ultrarobust error signal gradient in the presence of substantial uncompensated ac Stark shifts. Such a scheme can be implemented in two flavors: either by inverting clock state initialization or by pulse order reversal even without a perfect quantum state initialization. This universal interrogation protocol can be applied to atomic, molecular, and nuclear frequency metrology, mass spectrometry, and the field of precision spectroscopy. It might be designed using magic-wave-induced transitions, two-photon excitation, and magnetically induced spectroscopy or it might even be implemented with quantum logic gate circuit and qubit entanglement.