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Physical Review A

Accurate classification and selective observation of Rosen-Zener-Stückelberg resonances

Sheng-Chang Li, Libin Fu

Published Sep 14, 2020• 2 citations
Publisher

Abstract

Rosen-Zener-St\"uckelberg (RZS) interferometry has provided an important tool for presenting and describing the quantum coherence in many systems, especially in ultracold atomic systems. In this paper we propose a Floquet matrix method to recognize the resonances induced by destructive RZS interference of a periodically driving two-level system with a ${sin}^{2}$-type field. It is shown that the RZS resonances can be precisely distinguished into two classes: Regular resonance and accidental resonance. The former corresponds to the degenerate points in quasienergy spectrum and can be divided into integer resonance and half-integer resonance, while the latter is characterized by the eigenstate of a Floquet matrix with half of the components equaling to zero. We further discuss the possibility of experimentally observing these resonances. Particularly, it is found that a selective observation of different types of resonances can be realized in most cases by adjusting the time interval of periodic measurements.

DOI
10.1103/physreva.102.033323

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We investigate the Rosen-Zener-St\"uckelberg interferometry of ultracold atoms in a sinusoidal-type periodical modulated, symmetrical double-well potential. Periodical modulation of the trapping potential barrier leads to an analog of light-assisted Rosen-Zener tunneling, with distinct signatures of the energy gap visible in the amount of particles transferred from one well to the other. Time-averaged atomic occupations in one well show nice interference patterns for multiple-period modulation. The condition for constructive interference is given by the requirements satisfied by the St\"uckelberg phase. Both integer and noninteger resonances ranging from 2n2n2n to 5n5n5n (nnn is a positive integer) are predicted at certain modulating amplitudes. In particular, we find that the resonance profiles can change from a Fano-like line shape with weak modulation to a Lorentzian-like line shape with strong modulation. Our theory is generic for many other forms of periodical modulation fields and can be used to realize a time-domain multiple-slit interferometer.
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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.
We investigate Landau-Zener-St\"uckelberg-Majorana (LZSM) interferometry in a nonlinear two-level system subjected to a sinusoidal driving field. A comprehensive analysis for the interference patterns is shown from which we can analytically obtain the condition of constructive and destructive interferences in some cases. In the presence of nonlinear interaction, the level structure is changed, which can lead to an asymmetric deformation of the interference patterns and a significant position shift of the interference fringes. Our findings suggest an application of the nonlinear LZSM interferometry in accurately calibrating the parameters characterizing a nonlinear two-level system, as well as its coupling with the driven fields.
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