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Physical Review A

Self-generated Floquet modulation in a multiharmonic-dressed alignment-based magnetic-resonance system

Xu‐xing Geng, Kai Jin, Wangwang Tang, Shangqing Liang, Guoqing Yang, Shao‐ping Wu, Guangming Huang, Gao‐xiang Li

Published Aug 15, 2022• 4 citations
Publisher

Abstract

Quantum systems with multiharmonic dressing have been extensively investigated and exhibited various novel phenomena and technologies by virtue of their robust electromagnetic response. Here we mainly investigate the self-generated longitudinal Floquet modulation phenomenon of an alignment-based magnetic-resonance system with pump-probe structure dressed by two different transverse radio-frequency (rf) fields in a warm atomic cesium ensemble, both theoretically and experimentally. The self-generated Floquet modulation includes first and second harmonics, which are contributed to by linear and nonlinear processes from the weak-dressed field, respectively. The self-generated Floquet modulation dresses the alignment absorption spectra into two continua. The asymmetry of each dressed continuum is due to the generalized parity symmetry of the system being broken by the second harmonic modulation. Moreover, the nonlinear modification effect of the weak rf field on the probe verifies the existence of the four-wave mixing process in the rf band. The analytical expression, establishment process, and asymmetry analysis of the continua are given concisely. Our results can be applied to the fields of precision magnetic-field measurement, quantum control, quantum simulation, and so on. In addition, because the physical mechanism is universal, it can be applied not only to an atomic ensemble, but also to solid-state devices.

DOI
10.1103/physreva.106.023108

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Quantum systems with multiharmonic dressing have been extensively investigated and exhibited various novel phenomena and technologies by virtue of their robust electromagnetic response. Here we mainly investigate the self-generated longitudinal Floquet modulation phenomenon of an alignment-based magnetic-resonance system with pump-probe structure dressed by two different transverse radio-frequency (rf) fields in a warm atomic cesium ensemble, both theoretically and experimentally. The self-generated Floquet modulation includes first and second harmonics, which are contributed to by linear and nonlinear processes from the weak-dressed field, respectively. The self-generated Floquet modulation dresses the alignment absorption spectra into two continua. The asymmetry of each dressed continuum is due to the generalized parity symmetry of the system being broken by the second harmonic modulation. Moreover, the nonlinear modification effect of the weak rf field on the probe verifies the existence of the four-wave mixing process in the rf band. The analytical expression, establishment process, and asymmetry analysis of the continua are given concisely. Our results can be applied to the fields of precision magnetic-field measurement, quantum control, quantum simulation, and so on. In addition, because the physical mechanism is universal, it can be applied not only to an atomic ensemble, but also to solid-state devices.
A longitudinal radio-frequency (rf) magnetic field resonating at the Larmor frequency along the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction in the presence of a static transverse magnetic field s investigated. Optical-radio-frequency double resonance in 85Rb^{85}\mathrm{Rb}85Rb characterizes the strength of an external magnetic field through the precession frequency of 85Rb^{85}\mathrm{Rb}85Rb atoms. The measurements are carried out in a paraffin-coated 85Rb^{85}\mathrm{Rb}85Rb cell with a spin alignment configuration. An intriguing discovery of magnetic resonance peaks is observed at subharmonics of the Larmor frequency, accompanied by the emergence of nonlinear effects in the vicinity of the resonance. Notably, when the Larmor frequency reaches zero, the optical rotation signals induced by the rf magnetic field demonstrate a superposition of high-order harmonics of the rf frequency. Based on the simplified density matrix formalism and perturbation treatment, analytical expressions for the optical rotation are consistent with experimental outcomes. These findings hold the potential of extending our understanding on unveiling the dynamics of population and coherence among Zeeman sublevels, thereby advancing our knowledge in the field of alignment magnetometry.
Periodically driven systems, so-called Floquet systems, exhibit novel and exotic phases of matters inaccessible in static counterparts. The associated flexibility offered by Floquet engineering has helped gain insight into synthetic dimensions of quantum systems, non-equilibrium dynamics, and topology. Here, we apply the technique of Floquet engineering to the coherent dressing of spin states, aiming to provide a new dimension in the spin manipulation. We use an anti-relaxation coated 87 Rb vapor cell interacting with a transverse radio-frequency magnetic field, which is resonant with the Larmor precession and excites the coherence between adjacent Zeeman sublevels. The narrow linewidth of the natural resonance promises the successful observation of a radio-frequency dressed spin state via electromagnetically induced transparency spectroscopy. In this configuration, we create a Floquet system by adding a longitudinal oscillating magnetic field to periodically drive Zeeman levels. We experimentally observe the Floquet engineered coherent dressing spectroscopy, featuring a series of sidebands in frequency space with weight factor in terms of Bessel function, as expected by our theoretical model. Our method can be applied to coherent dressed states of natural and artificial atoms, offering the possibilities of quantum bit control and quantum sensing.
Multiphoton nonlinear frequency mixing effects on coherent electromagnetically induced absorption spectra of 85Rb^{85}\mathrm{Rb}85Rb atoms using two orthogonal linear polarizations of strong-coupling and weak probe beams are investigated theoretically and experimentally with respect to an applied longitudinal magnetic field and coupling powers. Herein, we confirm that at least five-photon interactions in solving density matrix equations for the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of 85Rb^{85}\mathrm{Rb}85Rb atoms are required to explain experimentally observed coherent electromagnetically induced absorption spectra when a quantum axis is selected as the propagation direction of co-propagating coupling and probe laser beams. Distinct calculated spectral differences owing to variations in the magnetic field and coupling power between three- and five-photon interactions are confirmed. The obtained asymmetrical spectral shapes match very well with those calculated from five-photon interactions considering the off-resonant ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=2,3$ transitions. Genuine coherent spectral shapes are observed with a single laser combined with two acousto-optic modulators, wherein the spectral resolution is limited because of the decoherence rate between Zeeman sublevels in the ground state from transit-time relaxation.
Dressed states are eigenstates of the full Hamiltonian which also includes the interaction of the atoms with the driving field. From this point of view, photons of the field interacting with the atom externally induce quantum coherence, and thus modify the inherent properties of atomic system, such as Mollow triplets in the resonance fluorescence spectrum. Because of the rigorous requirement on the ratio of driving strength to the intrinsic linewidth, the associated demonstrations in neutral atoms are restricted to optical dressing in a cavity quantum electrodynamics system and microwave dressing in the Rydberg excitation. Here, we report the realization of coherent dressing of a ground state driven by a radio-frequency magnetic field in an antirelaxation coated warm vapor cell. We reveal the properties of the radio-frequency dressed states, a linear scaling in the resonance splitting, and the improved resonance linewidth. Such a system is robust to the variation of detection frequency and atom number and is able to determine the driving frequency. It thus may emerge as a unique and versatile tool in quantum metrology, for instance, rf atomic magnetometry in a large detection frequency range. Published by the American Physical Society 2024
The application of nonresonant electromagnetic fields, a technique known as 'dressing', provides critical control over the properties of fundamental quantum systems. We investigate the time evolution of a dressed-atom coherent spin ensemble, effectively representing a qubit, driven by a non-resonant electromagnetic field with two components, one along the quantisation static magnetic field and the other one orthogonal to it. While this second component produces a Larmor precession of the spin, the longitudinal dressing modifies the instantaneous field value, leading to a frequency modulated temporal evolution of the spin. This dual-dressing configuration represents an extension of the Landau-Zener multipassage interferometry in the presence of an additional dressing field controlling the tunneling process by its amplitude and phase. Our measurement of the qubit coherence introduces additional features to the transition probability readout of standard interferometry. The coherence time evolution is characterized by oscillations at several frequencies, each of them produced by a different quantum contribution. Such frequency description introduces a new picture of the qubit multipassage evolution. Our tuning-dressed configuration expands the toolbox for quantum state manipulation and quantum control applications. The experiments are performed in rubidium and caesium atomic magnetometers, confined in a magneto-optical trap and in a vapour cell, respectively. Static fields in the μT range and kHz oscillating fields with large Rabi frequencies are applied. Because the present low-frequency dressing operation does not fall within the standard Floquet engineering paradigm based on the high-frequency expansion, we develop an ad-hoc dressing perturbation treatment. Numerical simulations support the adiabatic and non-adiabatic qubit evolution.
The application of a periodic nonresonant drive to a system allows the Floquet engineering of effective fields described by a broad class of quantum simulated Hamiltonians. The Floquet evolution is based on two different elements. The first one is a time-independent or stroboscopic evolution with an effective Hamiltonian corresponding to the quantum simulation target. The second element is the time evolution at the frequencies of the nonresonant driving and of its harmonics, denoted as micromotion. We examine experimentally and theoretically the harmonic dual-dressing Floquet engineering of a cold atomic two-level sample. Our focus is the dressing operation with small bare energies and large Rabi frequencies, where frequencies and amplitudes of the stroboscopic/micromotion time evolutions are comparable. At the kHz range of our dressed atom oscillations, we probe directly both the stroboscopic and micromotion components of the qubit global time evolution. We develop ad-hoc monitoring tools of the Floquet space evolution. The direct record of the time evolution following a pulsed excitation demonstrates the interplay between the two components of the spin precession in the Floquet space. From the resonant pumping of the dressed system at its evolution frequencies, Floquet eigenenergy spectra up to the fifth order harmonic of the dressing frequency are precisely measured as function of dressing parameters. Dirac points of the Floquet eigenenergies are identified and, correspondingly, a jump in the dynamical phase shift is measured. The stroboscopic Hamiltonian eigenfrequencies are measured also from the probe of the micromotion sidebands.These monitoring tools are appropriate for quantum simulation/computation investigations. Our results evidence that the stroboscopic phase shift of the qubit wavefunction contains an additional information that opens new simulation directions.