Exact Classification of Landau-Majorana-Stückelberg-Zener Resonances by Floquet Determinants

Recent experiments have shown that Landau-Majorana-Stückelberg-Zener (LMSZ) interferometry is a powerful tool for demonstrating and exploiting quantum coherence not only in atomic systems but also in a variety of solid state quantum systems such as spins in quantum dots, superconducting qubits, and nitrogen vacancy centers in diamond. In this Letter, we propose and develop a general (and, in principle, exact) theoretical formalism to identify and characterize the interference resonances that are the hallmark of LMSZ interferometry. Unlike earlier approaches, our scheme does not require any approximations, allowing us to uncover important and previously unknown features of the resonance structure. We also discuss the experimental observability of our results.

Figure 1

Left: $P_2(nT)$ with $n=10$ as a function of drive amplitude $A$ and detuning $ϵ$ for monochromatic driving from numerical solution of Schrödinger equation with $\phi =-\pi /2$, and $h=5\omega$. Right: red squares and green diamonds mark real and complex roots of FD, respectively.

Figure 2

$P_2(T)$ from numerical solution with $h=5\omega$, $ϵ=\omega$, $\phi =-\pi /2$. Red squares, green diamonds, and purple circles mark real, complex, and accidental resonances obtained from the FD, respectively.

Figure 3

$P_2(T)$ from numerical solution with $h=5\omega$, $ϵ=\sqrt{2}\omega$, $\phi =-\pi /2$. Red squares, green diamonds, and purple circles mark real, complex, and accidental resonances obtained from the FD, respectively.

Figure 4

$P_2(T)$ as a function of $A$ and $ϵ$ for the parameters of Fig. 1. Real (red squares) and complex (green diamonds) resonances only occur for $2ϵ/\omega =\mathrm{\text{integer}}$, while accidental (purple circles) resonances occur for nonintegral values of $2ϵ$.