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Journal of Physics Conference Series

Floquet formalism for multiphoton dynamics in superconducting quantum circuits

Hossein Zolfghari Jooya, H. R. Sadeghpour

Published Jan 1, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/1412/9/092005

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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.
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This Letter demonstrates control over multiphoton absorption processes in driven two-level systems, which include, for example, superconducting qubits or laser-irradiated graphene, through spectral shaping of the driving pulse. Starting from calculations based on Floquet theory, we use differential evolution, a general purpose optimization algorithm, to find the Fourier coefficients of the driving function that suppress a given multiphoton resonance in the strong field regime. We show that the suppression of the transition probability is due to the coherent superposition of high-order Fourier harmonics which closes the dynamical gap between the Floquet states of the two-level system.
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.
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.
Abstract We propose a versatile scheme for multiphoton frequency up/down conversion in flux superconducting qubit circuits, driven by a pair of microwaves tuned near and far off the qubit resonance. Flux qubits can be engineered with strong anharmonicity such that the two lowest eigenstates are energetically well separated from the higher ones. We demonstrate the high order non-linear transitions between the two lowest levels in the three-photon regime, by coupling the qubit to bichromatic microwave fields with the same Rabi frequencies. Both up and down conversions are presented and accurately interpreted with many-mode Floquet formalism. An intuitive graph theoretic approach elucidates the physics of multiphoton pumping and population trapping. The analytical solutions also illustrate how controllability is achievable for desired single- or multiphoton pumping processes in a wide range of frequencies. The proposed design and theoretical approach are applicable in maintaining the inter-connectivity of future superconducting quantum machines.
We study driven and open quantum systems described by a time-periodic Lindblad master equation. In closed systems, the stroboscopic dynamics can always be described by an effective time-independent Floquet Hamiltonian; this idea is the basis of Floquet engineering. However, in the presence of dissipation, the existence of an effective time-independent Floquet Lindbladian is not guaranteed due to the non-unitary nature of the evolution. Using Floquet theory, we construct a well-defined time-independent Floquet Lindbladian in an extended Sambe-Liouville space, transforming the initial time-dependent problem to a static and non-Hermitian eigenvalue problem. For harmonic driving, we introduce a matrix continued fraction method to nonperturbatively resum multiphoton processes and construct an effective Floquet Lindbladian acting only on the physical Liouville space. Compared to other high-frequency expansions, this method has the advantage of providing the whole infinite series expansion at once. Using a resolvent formalism, we show how to obtain a spectral Floquet representation of correlation functions of an open quantum system. As an application, we consider a dissipating two-level system in a linearly polarized field and calculate its resonance fluorescence spectrum. Furthermore, we consider a parametrically driven quantum dot with pump and loss for which we calculate its spectral function and current-voltage characteristics.