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arXiv:2503.12197 · APL Quantum

Floquet engineering clock transitions in magnetic molecules

Andrew Cupo, Shuanglong Liu, Silas Hoffman, X.-G. Zhang, Hai‐Ping Cheng

Published Oct 6, 2025• 0 citations
arXivHTMLPDF

Abstract

We theoretically study Floquet engineering of magnetic molecules via a time-periodic magnetic field that couples to the emergent total electronic spin of the metal center. By focusing on the low-lying energy levels using an S = 1 spin Hamiltonian containing the zero-field and Zeeman terms, we demonstrate their continuous tunability under the Floquet field. Remarkably, under the action of linearly polarized Floquet controls, the energy levels of a clock transition qubit retain their stability against variations in an external static magnetic field. This property is closely linked to having a net-zero total Zeeman shift, which results from both static and effective dynamical contributions. Furthermore, using second-order Van Vleck degenerate perturbation theory, we derived an effective Hamiltonian analytically, which explicitly shows the dependence of the renormalized zero-field tensor on the driving field. Based on our theoretical predictions, experimentalists will be able to dynamically tune qubit energy gaps to values that are useful in their specific laboratory settings, while retaining the spin decoherence suppressing effect of maintaining a clock transition.

DOI
10.1063/5.0283275

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We theoretically study Floquet engineering of magnetic molecules via a time-periodic magnetic field that couples to the emergent total electronic spin of the metal center. By focusing on the low-lying energy levels using an S = 1 spin Hamiltonian containing the zero-field and Zeeman terms, we demonstrate their continuous tunability under the Floquet field. Remarkably, under the action of linearly polarized Floquet controls, the energy levels of a clock transition qubit retain their stability against variations in an external static magnetic field. This property is closely linked to having a net-zero total Zeeman shift, which results from both static and effective dynamical contributions. Furthermore, using second-order Van Vleck degenerate perturbation theory, we derived an effective Hamiltonian analytically, which explicitly shows the dependence of the renormalized zero-field tensor on the driving field. Based on our theoretical predictions, experimentalists will be able to dynamically tune qubit energy gaps to values that are useful in their specific laboratory settings, while retaining the spin decoherence suppressing effect of maintaining a clock transition.
Holonomic quantum computing functions by transporting an adiabatically degenerate manifold of computational states around a closed loop in a control-parameter space; this cyclic evolution results in a non-Abelian geometric phase which may couple states within the manifold. Realizing the required degeneracy is challenging and typically requires auxiliary levels or intermediate-level couplings. One potential way to circumvent this is through Floquet engineering, where the periodic driving of a nondegenerate Hamiltonian leads to degenerate Floquet bands, and subsequently non-Abelian gauge structures may emerge. Here we present an experiment in ultracold Rb87 atoms where atomic spin states are dressed by modulated RF fields to induce periodic driving of a family of Hamiltonians linked through a fully tuneable parameter space. The adiabatic motion through this parameter space leads to the holonomic evolution of the degenerate spin states in SU(2) , characterized by a non-Abelian connection. We study the holonomic transformations of spin eigenstates in the presence of a background magnetic field, characterizing the fidelity of these single-qubit gate operations. Results indicate that while the Floquet engineering technique removes the need for explicit degeneracies, it inherits many of the same limitations present in degenerate systems. Published by the American Physical Society 2024
Coherent control of interacting spin systems under time-periodic driving is a central challenge in spin-based quantum technologies. Here we demonstrate the applicability of a full Floquet-space formalism, adapted from Nuclear Magnetic Resonance (NMR) methodologies, to model the dynamics of driven coupled electron spins in the presence of a static magnetic field B0 and a transverse oscillating field B1. The framework explicitly includes isotropic exchange coupling J and the chiral Dzyaloshinskii-Moriya antisymmetric exchange interaction (DMI), and its numerical convergence is systematically validated with respect to Fourier-space truncation. In the non-interacting limit, the expected driven-spin dynamics is recovered, with the oscillation periodicity governed by B1. Exchange coupling alone does not modify the collective spin expectation values under the chosen initial condition, consistent with symmetry considerations. In contrast, increasing DMI generates a finite Sy component, suppresses Sz, and produces tilted, elliptical Bloch-sphere trajectories, reflecting the emergence of chiral spin-spin correlations. These effects are pronounced for open boundary conditions, while remaining nearly negligible in the periodic boundary case. When exchange coupling and DMI coexist, the dynamics becomes strongly perturbed and multi-frequency in nature. Together, these results demonstrate that full Floquet-space modeling provides a robust and predictive framework for analyzing and engineering coherent dynamics in driven interacting spin systems beyond simple coherent-rotation regimes.
Abstract In recent years, there has been an intense search for materials realizing the Kitaev quantum spin liquid model. A number of edge-shared compounds with strong spin-orbit coupling, such as RuCl3 and iridates, have been proposed to realize this model. Nevertheless, an effective spin Hamiltonian derived from the microscopic model relevant to these compounds generally contains terms that are antagonistic toward the quantum spin liquid. This is consistent with the fact that the zero magnetic field ground state of these materials is generally magnetically ordered. It is a pressing issue to identify protocols to drive the system to the limit of the Kitaev quantum spin model. In this work, we propose Floquet engineering of these Kitaev quantum magnets by coupling materials to a circularly polarized laser. We demonstrate that all the magnetic interactions can be tuned in situ by the amplitude and frequency of the laser, hence providing a route to stabilize the Kitaev quantum spin liquid phase.
Recent advances in quantum technologies have enabled the precise control of single trapped molecules on the quantum level. Exploring the scope of these new technologies, we studied theoretically the implementation of qubits and clock transitions in the spin, rotational, and vibrational degrees of freedom of molecular nitrogen ions including the effects of magnetic fields. The relevant spectroscopic transitions span six orders of magnitude in frequency, illustrating the versatility of the molecular spectrum for encoding quantum information. We identified two types of magnetically insensitive qubits with very low ("stretched"-state qubits) or even zero ("magic" magnetic-field qubits) linear Zeeman shifts. The corresponding spectroscopic transitions are predicted to shift by as little as a few mHz for an amplitude of magnetic-field fluctuations on the order of a few mG, translating into Zeeman-limited coherence times of tens of minutes encoded in the rotations and vibrations of the molecule. We also found that the Q(0) line of the fundamental vibrational transition is magnetic-dipole allowed by interaction with the first excited electronic state of the molecule. The Q(0) transitions, which benefit from small systematic shifts for clock operation and is thus well suited for testing a possible variation in the proton-to-electron mass ratio, were so far not considered in single-photon spectra. Finally, we explored possibilities to coherently control the nuclear-spin configuration of N2+ through the magnetically enhanced mixing of nuclear-spin states.
Floquet engineering in quantum simulation employs externally applied high-frequency pulses to dynamically design steady-state effective Hamiltonians. Such protocols can be used to enlarge the space of Hamiltonians but approximations often limit pulse profile shapes and therefore the space of available effective Hamiltonians. We consider a nonstroboscopic high-frequency expansion formalism for Floquet engineering. We generalize the pulse profiles available by rigorously keeping all necessary terms to lowest order in inverse frequency expansions used to derive the effective Hamiltonians. Our approach allows wide tunability in application of external driving fields. We apply our method to long-range interacting XXZ spin Hamiltonians. We model an example application where we derive conditions on specific pulse shapes to engineer effective Ising models from XXZ models. Our method allows the space of continuous pulse profiles, relevant to experimental control fields, to better and more accurately explore possible effective Hamiltonians available for Floquet engineering.
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.