Time-resolved measurement of Landau-Zener tunneling in different bases

Abstract

A comprehensive study of the tunneling dynamics of a Bose-Einstein condensate in a tilted periodic potential is presented. We report numerical and experimental results on time-resolved measurements of the Landau-Zener tunneling of ultracold atoms introduced by the tilt,which experimentally is realized by accelerating the lattice. The use of different protocols enables us to access the tunneling probability, numerically as well as experimentally, in two different bases, namely, the adiabatic basis and the diabatic basis. The adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic one to the free-particle momentum eigenstates. Our numerical and experimental results are compared with existing two-state Landau-Zener models

Quantum driving protocols for a two-level system: From generalized Landau-Zener sweeps to transitionless control

“…The full dynamics of the Wannier-Stark system can be locally approximated by a simple two-state model, with an effective Hamiltonian brought into the form of Eq. (1) by subtracting the quadratic term in the momentum [29]. The time dependence of is induced through a variation of the quasimomentum q of the condensate by the force F .…”

“…The dynamics of ultracold atoms in a tilted optical lattice can be described by the well-known Wannier-Stark Hamiltonian [29]. Under the action of the force F , the quasimomentum of a condensate initially prepared atq = 0 in the n = 0 energy band scans the lower band in an oscillating motion with the Bloch period given by T Bloch = 2πh/(F d L ).…”

“…The experimental protocols are carried out using the techniques previously developed by us and described in detail in [28,29]. The force is experimentally implemented by accelerating the optical lattice [33].…”

“…Section II briefly introduces the quantum driving of our two-level paradigmatic quantum system and also the quantum speed limit. Starting from the linear LZ as a reference protocol investigated in [28,29], we explored generalized LZ protocols where ω is fixed and is scanned nonlinearly (Sec. III).…”

Wave-function-renormalization effects in resonantly enhanced tunneling

“…Such a decay * Present address: Museo Storico della Fisica e Centro Studi e Ricerche "Enrico Fermi", Piazza del Viminale 1, 00184 Rome, Italy. was examined in different theoretical analyses [5,6,14] and measured in experimental investigations with ultracold atoms [12,13,15,16]. In this study we scrutinize the time behavior of the tunneling probability and use its remarkable features at short and intermediate times in order to extract information about wave-function-renormalization effects.…”