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arXiv:2002.10827 · Physical review. B./Physical review. B

Landau-Zener-Stückelberg interferometry in dissipative circuit quantum electrodynamics

Mariano Bonifacio, Daniel Domı́nguez, María José Sánchez

Published Jun 15, 2020• 17 citations
arXivHTMLPDF

Abstract

We study Landau-Zener-St\"uckelberg (LZS) interferometry in a cQED architecture under the effects of dissipation. To be specific, we consider a superconducting qubit driven by a $\mathrm{dc}+\mathrm{ac}$ signal and coupled to a transmission line resonator, but our results are valid for general qubit-resonators devices. To take the environment into account, we assume that the resonator is coupled to an Ohmic quantum bath. The Floquet-Born-Markov master equation is numerically solved to obtain the dynamics of the system for an arbitrary amplitude of the drive and different timescales. We unveil important differences in the resonant patterns between the strong coupling and ultrastrong coupling regimes in the qubit-resonator interaction, which are mainly due to the magnitude of photonic gaps in the energy spectrum of the system. We identify in the LZS patterns the contribution of the qubit gap and the photonic gaps, showing that for large driving amplitudes the patterns present a weaving structure due to the combined intercrossing of the different gaps contributions.

DOI
10.1103/physrevb.101.245415

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We study Landau-Zener-St"uckelberg (LZS) interferometry in a cQED architecture under the effects of dissipation. To be specific, we consider a superconducting qubit driven by a dc+ac\mathrm{dc}+\mathrm{ac}dc+ac signal and coupled to a transmission line resonator, but our results are valid for general qubit-resonators devices. To take the environment into account, we assume that the resonator is coupled to an Ohmic quantum bath. The Floquet-Born-Markov master equation is numerically solved to obtain the dynamics of the system for an arbitrary amplitude of the drive and different timescales. We unveil important differences in the resonant patterns between the strong coupling and ultrastrong coupling regimes in the qubit-resonator interaction, which are mainly due to the magnitude of photonic gaps in the energy spectrum of the system. We identify in the LZS patterns the contribution of the qubit gap and the photonic gaps, showing that for large driving amplitudes the patterns present a weaving structure due to the combined intercrossing of the different gaps contributions.
We study Landau-Zener-St\"uckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from an LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also show that the presence of a resonant mode in the quantum bath can impede the dynamic transition when the resonant frequency is of the order of the qubit gap. Our results are obtained by a numerical calculation of the finite time and the asymptotic stationary population of the qubit states, using the Floquet-Markov approach to solve a realistic model of the flux qubit considering up to ten energy levels.
An entangled state generation protocol for a system of two qubits driven with an ac signal and coupled through a resonator is introduced. We explain the mechanism of entanglement generation in terms of an interplay between unitary Landau-Zener-Stuckelberg (LZS) transitions induced for appropriate amplitudes and frequencies of the applied ac signal and dissipative processes dominated by photon loss. In this way, we found that the steady state of the system can be tuned to be arbitrarily close to a Bell state, which is independent of the initial state. Effective two-qubit Hamiltonians that reproduce the resonance patterns associated with LZS transitions are derived.
In this work we propose a way to unveil the type of environmental noise in strongly driven superconducting flux qubits through the analysis of the Landau-Zener-St\"uckelberg (LZS) interferometry. We study both the two-level and multilevel dynamics of the flux qubit driven by a dc+ac\mathrm{dc}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\mathrm{ac}dc+ac magnetic field. We find that the LZS interference patterns exhibit well-defined multiphoton resonances whose shape strongly depends on the timescale and the type of coupling to a quantum bath. For the case of transverse system-bath coupling, the nnn-photon resonances are narrow and nearly symmetric with respect to the dc magnetic field for almost all timescales, while in the case of longitudinal coupling they exhibit a change from a wide symmetric to an antisymmetric shape for times of the order of the relaxation time. We find this dynamic behavior relevant for the interpretation of several LZS interferometry experiments in which the stationary regime is not completely reached.
We demonstrate amplification (and attenuation) of a probe signal by a driven two-level quantum system in the Landau-Zener-St\"uckelberg-Majorana regime by means of an experiment, in which a superconducting qubit was strongly coupled to a microwave cavity, in a conventional arrangement of circuit quantum electrodynamics. Two different types of flux qubit, specifically a conventional Josephson junctions qubit and a phase-slip qubit, show similar results, namely, lasing at the working points where amplification takes place. The experimental data are explained by the interaction of the probe signal with Rabi-like oscillations. The latter are created by constructive interference of Landau-Zener-St\"uckelberg-Majorana (LZSM) transitions during the driving period of the qubit. A detailed description of the occurrence of these oscillations and a comparison of obtained data with both analytic and numerical calculations are given.
Superconducting circuit quantum electrodynamics (QED) architecture composed of superconducting qubit and resonator is a powerful platform for exploring quantum physics and quantum information processing. By employing techniques developed for superconducting quantum computing, we experimentally investigate phase-sensitive Landau–Zener–Stückelberg (LZS) interference phenomena in a circuit QED. Our experiments cover an extensive range of LZS transition parameters and demonstrate the LZS induced Rabi-like oscillation as well as phase-dependent steady-state population.
Landau–Zener–Stückelberg (LZS) interference of continuously driven superconducting qubits is studied. Going beyond the second order perturbation expansion, we find a time dependent stationary population evolution as well as unsymmetrical microwave driven Landau–Zener transitions, resulting from the nonresonant terms which are neglected in rotating-wave approximation. For the low-frequency driving, the qubit population at equilibrium is a periodical function of time, owing to the contribution of the nonresonant terms. In order to obtain the average population, it is found that the average approximation based on the perturbation approach can be applied to the low-frequency region. For the extremely low frequency which is much smaller than the decoherence rate, we develop noncoherence approximation by dividing the evolution into discrete time steps during which the coherence is lost totally. These approximations present comprehensive analytical descriptions of LZS interference in most of parameter space of frequency and decoherence rate, agreeing well with those of the numerical simulations and providing a simple but integrated understanding to system dynamics. The application of our models to microwave cooling can obtain the minimal frequency to realize effective microwave cooling.