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Journal of Physics D Applied Physics

Floquet-engineered dynamics of Rydberg atom coupling to superconducting circuit: avoided crossings and their facilitation

Yijie Yao, Jiarui Zeng, Yao Yao

Published Jan 23, 2025• 0 citations
Publisher

Abstract

Abstract Avoided crossings are always assumed to be a natural result of degeneracy lift. In order to perform quantum simulations of this, one can utilize a Rydberg atom periodically driven by a microwave field, and by further coupling to a superconducting (SC) quantum circuit, the avoided crossing can be largely enhanced depending on the coupling strength. The entire diagram of transition probability is investigated and the parameter regimes for the facilitation of avoided crossings are determined, which will be extremely useful for realistic experimental designs. We then employ the Floquet theory to calculate the quasi-energy distribution of the Rydberg atom, especially in the blue-detuning regime. The opening and closing of the quasi-energy gap is surprisingly found to be insensitive to the frequency of the SC circuit. The anharmonicity of the circuit is also analyzed.

DOI
10.1088/1361-6463/adad81

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Abstract Avoided crossings are always assumed to be a natural result of degeneracy lift. In order to perform quantum simulations of this, one can utilize a Rydberg atom periodically driven by a microwave field, and by further coupling to a superconducting (SC) quantum circuit, the avoided crossing can be largely enhanced depending on the coupling strength. The entire diagram of transition probability is investigated and the parameter regimes for the facilitation of avoided crossings are determined, which will be extremely useful for realistic experimental designs. We then employ the Floquet theory to calculate the quasi-energy distribution of the Rydberg atom, especially in the blue-detuning regime. The opening and closing of the quasi-energy gap is surprisingly found to be insensitive to the frequency of the SC circuit. The anharmonicity of the circuit is also analyzed.
Synopsis High-order nonlinear multiphoton dynamics of closed and open periodically driven quantum systems are studied within the semiclassical Floquet formalism. Multiphoton up/down frequency conversion in a super-conducting circuit is realized and faithfully reproduced with calculations. The absorption spectra are suppressed at sharp avoided crossings of the Floquet states. We include the effect of coupling to cavity by time evolving the master equation. The characteristics of the time-averaged absorption spectra are investigated by probing details near and around the exceptional points where suppression occurs.
We explore the periodically driven dynamics of two weakly coupled flux qubits and propose a scheme to generate a maximally entangled state based on Floquet engineering. The periodic driving modifies the quasienergy spectrum of the system and induces crossing of quasienergies, and the weak coupling between them lifts the degeneracy of quasienergies. It is found that the phenomena of entanglement resonance of Floquet state appear at certain values of the driving parameters, which could be demonstrated by virtue of the Rabi-frequency spectrum and average concurrence during one driving period. Our scheme relaxes the experimental difficulty in adjusting the static parameters of the system to establish entanglement, and may open interesting perspectives for devising active decoherence-immune quantum-information devices.
Floquet engineering is a powerful method that can be used to modify the properties of interacting many-body Hamiltonians via the application of periodic time-dependent drives. Here, we consider the physics of an inductively shunted superconducting Josephson junction in the presence of Floquet drives in the fluxonium regime and beyond, which we dub the frozonium artificial atom. We find that in the vicinity of special ratios of the drive amplitude and frequency, the many-body dynamics can be tuned to that of an effectively linear bosonic oscillator, with additional nonlinear corrections that are suppressed in higher powers of the drive frequency. By analyzing the inverse participation ratios between the time-evolved frozonium wavefunctions and the eigenbasis of a linear oscillator, we demonstrate the ability to achieve a novel dynamical control using a combination of numerical exact diagonalization and Floquet-Magnus expansion. We discuss the physics of resonances between quasi-energy states induced by the drive and ways to mitigate their effects. We also highlight the enhanced protection of frozonium against external sources of noise present in experimental setups. This work lays the foundation for future applications in quantum memory and bosonic quantum control using superconducting circuits.
We propose a promising hybrid quantum system, where a highly excited atom strongly interacts with a superconducting LCLCLC oscillator via the electric field of capacitor. An external electrostatic field is applied to tune the energy spectrum of the atom. The atomic qubit is implemented by two eigenstates near an avoided-level crossing in the dc Stark map of a Rydberg atom. Varying the electrostatic field brings the atomic-qubit transition on or off resonance with respect to the microwave resonator, leading to a strong atom-resonator coupling with an extremely large cooperativity. Like the nonlinearity induced by Josephson junctions in superconducting circuits, the large atom-resonator interface disturbs the harmonic potential of the resonator, resulting in an artificial two-level particle. Different universal two-qubit logic gates can also be performed on our hybrid system within the space where an atomic qubit couples to a single photon with an interaction strength much larger than any relaxation rates, opening the door to the cavity-mediated state transmission.
We investigate microwave excitation of helium 28 3^{3}3S Rydberg atoms and find that a second microwave field lifts the degeneracy of certain Floquet states describing the 28 3^{3}3S He atom plus single microwave field system. As a result a microwave pulse produces two patterns of Stueckelberg oscillations. They depend sensitively on the frequencies and amplitudes of both microwave fields and are influenced differently by added noise. We present two-frequency Floquet maps showing the origin of the interferences.
Periodic driving can suppress the Josephson nonlinearity of a fluxonium superconducting circuit, producing a nearly harmonic Floquet spectrum at isolated freezing points [K. Lewellen et al., Newton 2, 100434 (2026)]. Here we show that this dynamically frozen behavior does not generically suppress quasiparticle-induced dissipation in the resulting frozonium circuit. We formulate quasiparticle processes in the frozonium using a Floquet framework and analyze both drive-assisted Cooper-pair breaking and tunneling of pre-existing quasiparticles. Pair generation is controlled by gap-breaking thresholds at high drive frequencies, while multiphoton resonances produce pronounced rate enhancements at lower frequencies. Quasiparticle tunneling exhibits connected resonance structures organized by the harmonic Floquet-Magnus spectrum near the freezing point, with resonant hybridization generating characteristic avoided crossings. Our results show that suitable operating regimes must balance dynamical freezing against quasiparticle loss and provide a framework for identifying experimental drive parameters away from harmful resonances.