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arXiv:2510.19362

Dipole-Dipole Interactions of Floquet States

Tim Ehret, Vyacheslav Shatokhin, Andreas Buchleitner

Published Oct 22, 2025• 0 citations
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Abstract

We formulate a Floquet-Markov Lindblad master equation for translationally cold two-level atoms driven by a strong monochromatic wave and coupled to a common electromagnetic bath. The resulting dipole-dipole interaction reproduces the anisotropic Heisenberg model.
DOI
10.48550/arxiv.2510.19362

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We formulate a Floquet-Markov master equation, which combines an open quantum system approach with Floquet theory, for two spatially separated two-level atoms driven by a strong electromagnetic field and coupled to a common electromagnetic bath. This equation features a modified form of dipole-dipole interactions compared to the case of weakly driven atoms, giving rise to new, previously undescribed shifts of the Floquet quasienergies. We provide a detailed physical interpretation of the modified dipole-dipole interactions of two-level atoms, discuss their manifestations in two-atom resonance fluorescence, and extract the distance dependence of the dipole-dipole force between the atoms. The extensive discussion of two-level atoms is complemented by a brief study of one-dimensional hydrogen atoms (otherwise essentially described without approximations), with focus on the dipole-dipole interactions of periodically driven atoms whose electronic degrees of freedom are locked in non-dispersive wave packet states.
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The dynamics of open quantum systems is commonly described by quantum master equations derived under the assumption of weak system-bath coupling and a separation of timescales between system and bath. When the system is additionally subjected to a periodic driving, the validity of the resulting Floquet master equations is further restricted to regimes of weak or high-frequency driving. Here, we benchmark a set of commonly used Floquet master equations for a model of two locally driven spins coupled to a shared Ohmic reservoir at finite temperature. We systematically probe the accuracy of the equations as a function of the driving parameters, thus identifying limits of their applicability. Dynamical maps predicted by each master equation are compared against numerically exact non-Markovian simulations, tracking the full relaxation dynamics. We find that the accuracy of each master equation closely reflects the assumptions underlying its derivation. For the Floquet-Lindblad equation, errors can be strongly amplified near resonances where the secular approximation breaks down, while approaches that avoid the secular approximation perform better and exhibit a more systematic dependence of the error on driving frequency and amplitude.