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Physical Review A

Rosen-Zener-Stückelberg interferometry of ultracold atoms

Sheng-Chang Li, Libin Fu

Published Feb 24, 2020• 7 citations
Publisher

Abstract

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 $2n$ to $5n$ ($n$ 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.

DOI
10.1103/physreva.101.023618

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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.
We adopt a nonlinear two-mode model to investigate the Rosen-Zener-St\"uckelberg (RZS) interferometry of an interacting Bose-Einstein condensate trapped in double-well potential with a periodically modulating barrier. For symmetric potential, we analyze the properties of interference patterns and derive the interference conditions. For asymmetric potential, we explore the resonance structures caused by destructive interference at the weakly coupling limit and obtain the resonance conditions. In particular, we find that the chaotic motions in the asymmetric case with low-frequency modulation, can destroy the formation of interference fringes. In the symmetric case with high-frequency modulation, we see Fano-line-like resonance structures and find that the reso- nance positions exactly correspond to the boundary of macroscopic quantum self-trapping. We show that the nonlinearity can significantly alter both the shape and position of interference fringes and resonance structures. We discuss the experimental feasibility by comparing the solution of the Gross-Pitaevskii equation with both the solution of the two-mode model and the truncated Wigner simulation as well. The results suggest important applications of nonlinear RZS interferometry both in precisely controlling the dynamics and in accurately measuring the parameters of interacting many-body systems.
We propose a time-domain ``interferometer'' based on double-well ultracold atoms through a so-called adiabatic Rosen-Zener process, that is, the barrier between two wells is ramped down slowly, held for a while, and then ramped back. After the adiabatic Rosen-Zener process, we count the particle population in each well. We find that the final occupation probability shows nice interference fringes. The fringe pattern is sensitive to the initial state as well as the intrinsic parameters of the system such as interatomic interaction or energy bias between two wells. The underlying mechanism is revealed and possible applications are discussed.
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 sin2{sin}^{2}sin2-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.
We study undistinguishable two-species Bose-Einstein condensates (BECs) trapped in double wells. In the mean-field approximation we map the quantum system into a classical model and investigate the existence and stability of the fixed point solutions. By appropriately varying the amplitude of the high-frequency periodic modulation on the energy bias between the two wells, we tune the tunneling strength in the adiabatic Rosen-Zener type effectively. Starting from two typical initial states, we study the evolution of the system and find that the interspecies interaction can produce totally distinct results, which is expected to provide a route to manipulate the BEC distribution.
When the level separation of a qubit is modulated periodically across an avoided crossing, tunneling to the excited state—and consequently Landau–Zener–Stückelberg interference—can occur. The types of modulation studied so far correspond to a continuous change of the level separation. Here we study periodic latching modulation, in which the level separation is switched abruptly between two values and is kept constant otherwise. In this case, the conventional approach based on the asymptotic Landau–Zener formula for transition probabilities is not applicable. We develop a novel adiabatic-impulse model for the evolution of the system and derive the resonance conditions. Additionally, we derive analytical results based on the rotating-wave approximation (RWA). The adiabatic-impulse model and the RWA results are compared with those of a full numerical simulation. These theoretical predictions are tested in an experimental setup consisting of a transmon whose flux bias is modulated with a square wave form. A rich spectrum is observed, with distinctive features correspoding to two regimes: slow-modulation and fast-modulation. These experimental results are shown to be in very good agreement with the theoretical models. Also, differences with respect to the well known case of sinusoidal modulation are discussed, both theoretically and experimentally.