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arXiv:2502.13973 · Journal of Experimental and Theoretical Physics Letters

Theory of Composite Ramsey Sequences of Radiofrequency Pulses beyond the Rotating Wave Approximation

Valeriy I. Yudin, Прудников Олег Николаевич, А. В. Тайченачев, M. Yu. Basalaev, Vitalii G Pal'chikov, Sergei N Bagayev

Published Jul 1, 2024• 0 citations
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Abstract

We develop a theory of composite Ramsey sequences of rf pulses interacting with the Zeeman structure at the long-lived atomic level, beyond the rotating wave approximation. Such sequences are proposed in experiments to detect the violation of local Lorentz invariance [R. Shaniv, R. Ozeri, M.S. Safronova, S.G. Porsev, V.A. Dzuba, V.V. Flambaum, and H. Häffner, Phys. Rev. Lett. 120, 103202 (2018)]. Based on Fourier analysis, we have shown that taking into account non-resonant contributions leads to a radical change in the dynamics of the quantum system (with respect to the rotating wave approximation) in the case when the number of Ramsey pulses exceeds several tens. As a result, the effectiveness of using such rf pulses sequences to test local Lorentz invariance has not yet been fully determined and requires additional research.

DOI
10.1134/s0021364024602033

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We develop a theory of composite Ramsey sequences of rf pulses interacting with the Zeeman structure at the long-lived atomic level, beyond the rotating wave approximation. Such sequences are proposed in experiments to detect the violation of local Lorentz invariance [R. Shaniv, R. Ozeri, M.S. Safronova, S.G. Porsev, V.A. Dzuba, V.V. Flambaum, and H. Häffner, Phys. Rev. Lett. 120, 103202 (2018)]. Based on Fourier analysis, we have shown that taking into account non-resonant contributions leads to a radical change in the dynamics of the quantum system (with respect to the rotating wave approximation) in the case when the number of Ramsey pulses exceeds several tens. As a result, the effectiveness of using such rf pulses sequences to test local Lorentz invariance has not yet been fully determined and requires additional research.
Trapped-ion quantum sensors have become highly sensitive tools for the search of physics beyond the Standard Model. Recently, stringent tests of local Lorentz-invariance (LLI) have been conducted with precision spectroscopy in trapped ions (Pruttivarasin et al 2015 Nature 517 592-5, Megidish et al 2019 Phys. Rev. Lett. 122 123605, Sanner et al 2019 Nature 567 204-8, Dreissen et al 2022 Nat. Commun. 13 1-6) . We here elaborate on robust radio-frequency composite-pulse spectroscopy at second long coherence times in the magnetic sublevels of the long-lived 2F7/2 state of a trapped 172Yb+ ion which is scalable to spatially extended multi-ion systems. We compare two Ramsey-type composite rf pulse sequences, a generalized spin-echo (GSE) sequence (Shaniv et al 2018 Phys. Rev. Lett. 120 103202) and a sequence based on universal rotations with 10 rephasing pulses (UR10) (Genov et al 2017 Phys. Rev. Lett. 118 133202) that decouple the energy levels from magnetic field noise, enabling robust and accurate spectroscopy. Both sequences are characterized theoretically and experimentally in the spin- 1 / 22 S1/2 electronic ground state of 172Yb+ and results show that the UR10 sequence is 38 (13) times more robust against pulse duration (frequency detuning) errors than the GSE sequence. We extend our simulations to the eight-level manifold of the 2F7/2 state, which is highly sensitive to a possible violation of LLI, and show that the UR10 sequence can be used for high-fidelity Ramsey spectroscopy in noisy environments. The UR10 sequence is implemented experimentally in the 2F7/2 manifold and a coherent signal of up to 2.5 s is reached. In (Dreissen et al 2022 Nat. Commun. 13 1-6) we have implemented this sequence and used it to perform the most stringent test of LLI in the electron-photon sector to date with a single Yb+ ion. Due to the high robustness of the UR10 sequence, it can be applied on larger ion crystals to improve tests of Lorentz symmetry further. We demonstrate that the sequence can also be used to extract the quadrupole moment of the meta-stable 2F7/2 state, obtaining a value of Θ = - 0.0298 (38)ea02 which is in agreement with the value deduced from clock measurements (Lange et al 2020 Phys. Rev. Lett. 125 143201).
Abstract In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2 F 7/2 manifold of an Yb + ion, extending the coherence time from 200 μ s to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2 F 7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10 −21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.
Abstract Trapped-ion quantum sensors have become highly sensitive tools for the search of physics beyond the Standard Model. Recently, stringent tests of local Lorentz-invariance (LLI) have been conducted with precision spectroscopy in trapped ions (Pruttivarasin et al 2015 Nature 517 592–5, Megidish et al 2019 Phys. Rev. Lett. 122 123605, Sanner et al 2019 Nature 567 204–8, Dreissen et al 2022 Nat. Commun. 13 1–6) . We here elaborate on robust radio-frequency composite-pulse spectroscopy at second long coherence times in the magnetic sublevels of the long-lived 2 F 7 / 2 state of a trapped 172Yb+ ion which is scalable to spatially extended multi-ion systems. We compare two Ramsey-type composite rf pulse sequences, a generalized spin-echo (GSE) sequence (Shaniv et al 2018 Phys. Rev. Lett. 120 103202) and a sequence based on universal rotations with 10 rephasing pulses (UR10) (Genov et al 2017 Phys. Rev. Lett. 118 133202) that decouple the energy levels from magnetic field noise, enabling robust and accurate spectroscopy. Both sequences are characterized theoretically and experimentally in the spin- 1 / 2 2 S 1 / 2 electronic ground state of 172Yb+ and results show that the UR10 sequence is 38 (13) times more robust against pulse duration (frequency detuning) errors than the GSE sequence. We extend our simulations to the eight-level manifold of the 2 F 7 / 2 state, which is highly sensitive to a possible violation of LLI, and show that the UR10 sequence can be used for high-fidelity Ramsey spectroscopy in noisy environments. The UR10 sequence is implemented experimentally in the 2 F 7 / 2 manifold and a coherent signal of up to 2.5 s is reached. In (Dreissen et al 2022 Nat. Commun. 13 1–6) we have implemented this sequence and used it to perform the most stringent test of LLI in the electron–photon sector to date with a single Yb+ ion. Due to the high robustness of the UR10 sequence, it can be applied on larger ion crystals to improve tests of Lorentz symmetry further. We demonstrate that the sequence can also be used to extract the quadrupole moment of the meta-stable 2 F 7 / 2 state, obtaining a value of Θ = − 0.0298 ( 38 ) e a 0 2 which is in agreement with the value deduced from clock measurements (Lange et al 2020 Phys. Rev. Lett. 125 143201).
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.
The coherent interaction of Rydberg atoms with microwave fields in the ultrastrong-driving regime, in which the Rabi frequency is of the same order of magnitude as the transition frequency, has been studied for states with principal quantum number n=105n=105n=105 in helium. Experiments were performed in pulsed supersonic beams, and the effects of the ultrastrong 1.280 GHz microwave driving field, tuned to near resonance with the $1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}\ensuremath{\rightarrow}1s105p\phantom{\rule{0.16em}{0ex}}^{3}P$ transition, were identified from Autler-Townes splittings of the $1s3p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ transition by cw laser spectroscopy. The microwave field strength was calibrated in situ in the apparatus from Autler-Townes splittings measured in the weak-driving regime in which the rotating-wave approximation holds. The results of the experiments were compared to the energy-level structure of the atoms in the presence of the microwave field calculated using Floquet methods. From this comparison, the microwave-field strengths for which the rotating-wave approximation and the two-level approximation break down have been identified. The feasibility of implementing microwave traps for Rydberg atoms and molecules, which operate in the ultrastrong-driving regime, has been evaluated.
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.