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Communications Physics

Micromotion shift and dual modulation method in a periodic driving optical lattice clock

Feng Guo, Yan-Hua Zhou, Yanyan Liu, Jiaan Li, Xiaotong Lu, Yanting Zhao, Hong Chang

Published Nov 18, 2025• 1 citation
Publisher

Abstract

Beyond hardware improvements, Floquet Engineering (FE), as a widely used Hamiltonian engineering method, offers new levels of control and promising opportunities for enhancing optical lattice clock performance. However, while FE shapes novel Hamiltonians, its time-periodic nature introduces micromotion, leading to periodic disturbances in the system, such as frequency shifts. In this work, we introduce a dual-modulation (DM) FE method, simultaneously driving the lattice and probing lasers, allowing independent control of atomic motional and electronic degrees of freedom. Using this framework, we theoretically predict and experimentally observe the micromotion shifts. Additionally, by tuning the DM modulation parameters appropriately, we can fully eliminate the Doppler shift caused by the lattice laser modulation. Building on this Doppler-free synchronization modulation, we observe the dynamic localization of atoms in a shallow lattice while eliminating the periodic interference from Doppler shifts. This study proposes a dual-modulation method for optical lattice clocks that synchronously modulates the lattice laser and probing laser to control atomic motion and light-atom interactions independently. The authors derive theoretically and verify experimentally the laws of micromotion shift, and achieving its effective suppression by optimizing modulation parameters.

DOI
10.1038/s42005-025-02341-5

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Beyond hardware improvements, Floquet Engineering (FE), as a widely used Hamiltonian engineering method, offers new levels of control and promising opportunities for enhancing optical lattice clock performance. However, while FE shapes novel Hamiltonians, its time-periodic nature introduces micromotion, leading to periodic disturbances in the system, such as frequency shifts. In this work, we introduce a dual-modulation (DM) FE method, simultaneously driving the lattice and probing lasers, allowing independent control of atomic motional and electronic degrees of freedom. Using this framework, we theoretically predict and experimentally observe the micromotion shifts. Additionally, by tuning the DM modulation parameters appropriately, we can fully eliminate the Doppler shift caused by the lattice laser modulation. Building on this Doppler-free synchronization modulation, we observe the dynamic localization of atoms in a shallow lattice while eliminating the periodic interference from Doppler shifts. This study proposes a dual-modulation method for optical lattice clocks that synchronously modulates the lattice laser and probing laser to control atomic motion and light-atom interactions independently. The authors derive theoretically and verify experimentally the laws of micromotion shift, and achieving its effective suppression by optimizing modulation parameters.
Quantum metrology with ultrahigh precision usually requires atoms prepared in an ultrastable environment with well-defined quantum states. Thus, in optical lattice clock systems deep lattice potentials are used to trap ultracold atoms. However, decoherence, induced by Raman scattering and higher order light shifts, can significantly be reduced if atomic clocks are realized in shallow optical lattices. On the other hand, in such lattices, tunneling among different sites can cause additional dephasing and strongly broadening of the Rabi spectrum. Here, in our experiment, we periodically drive a shallow ^{87}Sr optical lattice clock. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4 Hz linewidth. With careful comparison between the theory and experiment, we demonstrate that the Rabi frequency and the Bloch bands can be tuned, simultaneously and independently. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phases of matter by engineering exotic spin orbit couplings.
The quantum system under periodical modulation is the simplest path to understand the quantum nonequilibrium system because it can be well described by the effective static Floquet Hamiltonian. Under the stroboscopic measurement, the initial phase is usually irrelevant. However, if two uncorrelated parameters are modulated, their relative phase cannot be gauged out so that the physics can be dramatically changed. Here, we simultaneously modulate the frequency of the lattice laser and the Rabi frequency in an optical lattice clock (OLC) system. Thanks to the ultrahigh precision and ultrastability of the OLC, the relative phase could be fine-tuned. As a smoking gun, we observed the interference between two Floquet channels. Finally, by experimentally detecting the eigenenergies, we demonstrate the relation between the effective Floquet Hamiltonian and the one-dimensional topological insulator with a high winding number. Our experiment not only provides a direction for detecting the phase effect but also paves a way in simulating the quantum topological phase in the OLC platform.
The quantum system under periodical modulation is the simplest path to understand the quantum non-equilibrium system, because it can be well described by the effective static Floquet Hamiltonian. Under the stroboscopic measurement, the initial phase is usually irrelevant. However, if two uncorrelated parameters are modulated, their relative phase can not be gauged out, so that it can dramatically change physics. Here, we simultaneously modulate the frequency of lattice laser and Rabi frequency in the optical lattice clock (OLC) system. Thanks to ultra-high precision and ultra-stability of OLC, the relative phase could be fine-tuned. As a smoking gun, we observed the interference between two Floquet channels. At last, we discuss the relation between effective Floquet Hamiltonian and 1-D topological insulator with high winding numbers. Our experiment not only provides a direction for detecting the phase effect, but also paves a way in simulating quantum topological phase in OLC platform.
The quantum metrology with ultra-high precision usually requires the atoms prepared in an ultra-stable environment with well-defined quantum states. Thus, the optical lattice clock system chooses deep lattice potential to trap the ultra-cold atoms. However, building atomic clock in shallow optical lattice can greatly reduce decoherence rate induced by Raman scattering as well as higher order light shift, but tunneling among the lattice sites will cause additional dephasing and strongly broadening of the Rabi spectrum. Here, we periodically drive the shallow 87^{87}87Sr optical lattice clock in the experiment. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4Hz line-width. With careful comparison between the theory and experiment, we demonstrate the Rabi frequency and Bloch bands can be simultaneously and independently tuned by adjusting the driving frequency and amplitude. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phase of matter, such as engineering exotic spin orbit coupling Hamiltonian.
Abstract We investigate Floquet modulation for measuring the probe-induced AC Stark shift coefficient in optical lattice clocks. Periodic frequency modulation allows a high probe intensity to enlarge the measured frequency difference between the settings at low and high probe power while Bessel function dressing maintains a narrow excitation spectrum. This combination improves sensitivity to the coefficient without sacrificing frequency discrimination. We identify modulation conditions that suppress additional frequency shifts while avoiding strong motional resonances. At the same probe intensities and total measurement time, numerical simulations including preparation time show a lower coefficient uncertainty than conventional Rabi inter-rogation with a single π pulse. At high probe intensities, the Floquet coefficient uncertainty approaches a plateau dominated by Rabi frequency calibration.
The concept of “Floquet engineering” relies on an external periodic drive to realize novel, effectively static Hamiltonians. This technique is being explored in experimental platforms across physics, including ultracold atoms, laser-driven electron systems, nuclear magnetic resonance, and trapped ions. The key challenge in Floquet engineering is to avoid the uncontrolled absorption of photons from the drive, especially in interacting systems in which the excitation spectrum becomes effectively dense. The resulting dissipative coupling to higher-lying modes, such as the excited bands of an optical lattice, has been explored in recent experimental and theoretical works, but the demonstration of a broadly applicable method to mitigate this effect is lacking. Here, we show how two-path quantum interference applied to strongly correlated fermions in a driven optical lattice suppresses dissipative coupling to higher bands and increases the lifetime of double occupancies and spin correlations by 2 to 3 orders of magnitude. Interference is achieved by introducing a weak second modulation at twice the fundamental driving frequency with a definite relative phase. This technique is shown to suppress dissipation in both weakly and strongly interacting regimes of an offresonantly driven Hubbard system, opening an avenue to realizing low-temperature phases of matter in interacting Floquet systems.