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arXiv:2009.10028 · Physical Review A

Population trapping in a pair of periodically driven Rydberg atoms

S. Kumar Mallavarapu, Ankita Niranjan, Weibin Li, Sebastian Wüster, Rejish Nath

Published Feb 26, 2021• 19 citations
arXivHTMLPDF

Abstract

We study the population trapping extensively in a periodically driven Rydberg pair. The periodic modulation of the atom-light detuning effectively suppresses the Rabi couplings and, together with Rydberg-Rydberg interactions, leads to the state-dependent population trapping. We identify a simple yet general scheme to determine population trapping regions using driving-induced resonances, the Floquet spectrum, and the inverse participation ratio. Contrary to the single-atom case, we show that the population trapping in the two-atom setup may not necessarily be associated with level crossings in the Floquet spectrum. Further, we discuss under what criteria population trapping can be related to dynamical stabilization, taking specific and experimentally relevant initial states, which include both product and the maximally entangled Bell states. The behavior of the entangled states is further characterized by the bipartite entanglement entropy.

DOI
10.1103/physreva.103.023335

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We study the population trapping extensively in a periodically driven Rydberg pair. The periodic modulation of the atom-light detuning effectively suppresses the Rabi couplings and, together with Rydberg-Rydberg interactions, leads to the state-dependent population trapping. We identify a simple yet general scheme to determine population trapping regions using driving-induced resonances, the Floquet spectrum, and the inverse participation ratio. Contrary to the single-atom case, we show that the population trapping in the two-atom setup may not necessarily be associated with level crossings in the Floquet spectrum. Further, we discuss under what criteria population trapping can be related to dynamical stabilization, taking specific and experimentally relevant initial states, which include both product and the maximally entangled Bell states. The behavior of the entangled states is further characterized by the bipartite entanglement entropy.
An array of single Rydberg atoms driven by a temporally modulated atom-field detuning is studied. The periodic modulation effectively modifies the Rabi coupling, leading to unprecedented dynamics in the presence of Rydberg-Rydberg interactions, in particular, blockade enhancement, antiblockades, and state-dependent population trapping. Interestingly, the Schrieffer-Wolf transformation reveals a fundamental process in Rydberg gases, correlated Rabi coupling, which stems from the extended nature of the Rydberg-Rydberg interactions. Also, the correlated coupling provides an alternative depiction for the Rydberg blockade, exhibiting a nontrivial behavior in the presence of periodic modulation. The dynamical localization of a many-body configuration in a driven Rydberg lattice is discussed.
Abstract We theoretically propose a protocol for coherent quantum state control in a short periodically driven Rydberg atom array. This Floquet engineering effectively suppresses the Rabi coupling and further reshapes Rydberg–Rydberg interactions, enabling precise control of Rydberg dynamics, including population trapping and blockade dynamics. This capability permits the coherent manipulation of targeted quantum states, such as the population-trapping ground state and entangled states with single or double excitations. A key finding is the robustness of these dynamics against variations in the Rydberg atom interaction, allowing for reliable control even in weak interaction regimes. Floquet spectral analysis further reveals that the stability — and eventual breakdown — of the frozen ground state is fundamentally governed by the splitting, convergence, and spacing of quasienergy levels. Moreover, a systematic analysis of parameter dependence identifies precise operational ranges for quantum state control. These results establish a practical framework for Floquet-engineered quantum manipulation, with promising prospects for quantum information processing applications.
Abstract We study the population dynamics in a two-atom setup in which each atom is driven independently by different light fields, but coupling the same Rydberg state. In particular, we look at how an offset in the Rabi frequencies between two atoms affects the dynamics. We find novel features such as amplifying the Rabi frequency of one atom, together with strong Rydberg-Rydberg interactions freezes the dynamics in the second atom. We analyze this Rydberg-biased freezing phenomenon in detail, with effective Hamiltonians obtained for various limits of the system parameters. In the absence of Rabi-offset, the doubly excited state population exhibits a Lorentzian profile as a function of interaction, whereas for very small offsets it shows splitting and thus peaks. Using an effective Hamiltonian, as well as the perturbation theory in the weak interaction limit, we show that the peak arises from a competition between Rabi-offset and Rydberg-Rydberg interactions when both are sufficiently small, together with the Rydberg blockade at large interactions. The effective Hamiltonians provide us with analytical results for long time dynamics, which are in an excellent agreement with exact numerical solutions. Also, we analyze the growth and the dynamics of quantum correlations such as entanglement entropy/quantum discord for the coherent dynamics. Finally, we extend our studies to the dissipative case in which the spontaneous emission from the Rydberg state is taken into account and in particular, we look at how the Rabi-offset modifies the purity and quantum discord in the steady states. We conclude that the local manipulation of an atom by introducing a Rabi-offset can be a useful tool to control the quantum correlations and in general, the quantum states of the composite two-qubit systems.
We consider a two-level atom driven by modulated light and find that complete population inversion can be induced by light without any resonant frequency component. This is in contrast to the familiar case of monochromatic driving in which complete population inversion is only possible with resonant light. This result concerns experimentally realizable systems and hence the effect of spontaneous emission is also considered. We also relate our work to other recent works on quantum double-well. Analogies with the suppression of quantum tunneling and with the low-frequency radiation generation are discussed. By translating the results from the study of the two-level atom to the theory of optical waveguides, we introduce a new geometric representation for analysing the optical state of a single-mode optical coupler. We find that an optical coupler with out-of-phase index modulations can control and suppress the evanescent power transfer between cores. A new type of optical band-pass filter based on the modulated index coupler is proposed.
Periodic driving enables the engineering of complex quantum matter, yet in interacting systems it generically leads to energy absorption, which limits the lifetime of the engineered states. To address this challenge, dynamical freezing has been proposed as a mechanism for stabilizing non-equilibrium states over parametrically long timescales. While theory predicts robust freezing under simplifying assumptions, realistic platforms inevitably include additional interaction processes that alter its stability. Here, we report the experimental observation of dynamical freezing in programmable Rydberg atom arrays of up to 100 atoms in one and two dimensions. We find that while single-frequency driving produces pronounced suppression of excitation dynamics, the freezing behavior is restricted to a narrow parameter regime due to interaction-induced heating channels present in realistic simulators. Using a perturbative Floquet analysis of the fully interacting atomic system, we identify the dominant microscopic heating processes responsible for this destabilization. Leveraging this understanding, we design a dual-parameter modulation of detuning and Rabi frequency that coherently cancels these absorption pathways and substantially broadens the freezing regime, making it also robust across different geometries. Our results reveal how heating processes shape the stability of dynamical freezing in interacting Floquet systems and demonstrates a route to control driven many-body dynamics in realistic experimental platforms.
We analyze the formation of maximally entangled Rydberg atom pairs subjected to Landau-Zener sweeps of the atom-light detuning. Though the populations reach a steady value at longer times, the phases evolve continuously, leading to periodic oscillations in the entanglement entropy. The local unitary equivalence between the obtained maximally entangled states and the Bell states is verified by computing the polynomial invariants. Finally, we study the effect of spontaneous emission from the Rydberg state of rubidium atoms on the correlation dynamics and show that the oscillatory dynamics persists for high-lying Rydberg states. Our study may offer ways to generate maximally entangled states, quantum gates, and exotic quantum matter in arrays of Rydberg atoms through Landau Zener sweeps.