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arXiv:0804.4538 · New Journal of Physics

Nonlinear Landau–Zener processes in a periodic driving field

Qi Zhang, Peter Hänggi A, Jiangbin Gong

Published Jul 3, 2008• 30 citations
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Abstract

Effects of a periodic driving field on Landau–Zener (LZ) processes are studied using a nonlinear two-mode model that describes the mean-field dynamics of a many-body system. A variety of different dynamical phenomena in different parameter regimes of the driving field are discussed and analyzed. These include shifted, weakened, or enhanced phase dependence of nonlinear LZ (NLZ) processes, nonlinearity-enhanced population transfer in the adiabatic limit and Hamiltonian chaos on the mean-field level. The emphasis of this work is based on how the impact of a periodic driving field on LZ processes with self-interaction differs from those without self-interaction. Apart from gaining knowledge of driven NLZ processes, our findings can be used to gauge the strength of nonlinearity and for efficient manipulation of the mean-field dynamics of many-body systems.

DOI
10.1088/1367-2630/10/7/073008

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Effects of a periodic driving field on Landau–Zener (LZ) processes are studied using a nonlinear two-mode model that describes the mean-field dynamics of a many-body system. A variety of different dynamical phenomena in different parameter regimes of the driving field are discussed and analyzed. These include shifted, weakened, or enhanced phase dependence of nonlinear LZ (NLZ) processes, nonlinearity-enhanced population transfer in the adiabatic limit and Hamiltonian chaos on the mean-field level. The emphasis of this work is based on how the impact of a periodic driving field on LZ processes with self-interaction differs from those without self-interaction. Apart from gaining knowledge of driven NLZ processes, our findings can be used to gauge the strength of nonlinearity and for efficient manipulation of the mean-field dynamics of many-body systems.
We investigate the dynamics of Landau-Zener (LZ) transitions in an anisotropic, dissipative three-level LZ model (3-LZM) using the numerically accurate multiple Davydov D2Ansatz in the framework of the time-dependent variational principle. It is demonstrated that a non-monotonic relationship exists between the Landau-Zener transition probability and the phonon coupling strength when the 3-LZM is driven by a linear external field. Under the influence of a periodic driving field, phonon coupling may induce peaks in contour plots of the transition probability when the magnitude of the system anisotropy matches the phonon frequency. The 3-LZM coupled to a super-Ohmic phonon bath and driven by a periodic external field exhibits periodic population dynamics in which the period and amplitude of the oscillations decrease with the bath coupling strength.
We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These photon-induced sideband transitions are a signature of the photon-assisted tunneling in our many-body LZ process. In the Rabi regime, where the system is dominated by the intermode coupling, the system can be looked as an ensemble of identical noninteracting single-particle LZ systems and the photon-induced sideband transitions are similar to the ones in single-particle LZ systems. In the Fock regime, where the system is dominated by the interparticle interaction, we develop an analytical theory for understanding the sideband transitions, which is confirmed by our numerical simulation. Furthermore, we discuss the quantization of the driving field. In the effective model of the quantized driving field, the sideband transitions can be understood as the LZ transitions between states of different ``photon'' numbers.
We study the motion of a cold atom in a frequency-modulated standing laser wave. If the detuning between the atomic electronic transition and the field is large, the atom moves in a modulated optical potential demonstrating known classical nonlinear effects such as chaos and nonlinear resonances. If the atom-field detuning is small, then two optical potentials emerge in the system, and the atom performs Landau-Zener (LZ) tunnelings between them. It is a radically non-classical behavior. However, we show that classical nonlinear structures in system's phase space (KAM-tori and chaotic layers) survive. Quantum effect of LZ tunnelings only induces small random jumps of trajectories between these structures (dynamical tunneling).
In this work, we investigate the influence of colored noise originating from a heat bath on nonlinear Landau-Zener (LZ) tunneling. The nonlinearity might arise intrinsically from many-body mean-field atomic self-interactions or Kerr nonlinearities in optical systems. Contrary to the well-established picture of thermally enhanced quantum tunneling within the linear LZ paradigm, ensemble statistics of our numerical simulations demonstrate that nonlinearity can give rise to thermally suppressed LZ tunneling: the tunneling probability of the nonlinear LZ system decreases as the amplitude of the colored noise increases beyond a critical value. Analytically, the Wiener-Hermite expansion facilitates elucidation of the intrinsic mechanism accounting for the nonmonotonic dependence of tunneling probability on noise amplitude. We compare these behaviors with stochastic resonance responses and clarify that the two phenomena stem from distinct physical mechanisms. In addition, we obtain approximate solutions in the weak- and strong-noise limits and discuss the implications of our theory.
This paper presents nonlinear Landau–Zener (LZ) tunneling of an electron spin in an accelerating optical parabolic potential, manifested in a heterostructure quantum wire subjected to a periodic magnetic field comprising a spike and a homogeneous part. In this context, driving the two states of a pure nonlinear two-level quantum bit (qubit) system through an avoided level crossing can result in nontrivial dynamics, especially with and without considering a parabolic confinement potential characterized by a curvature confinement potential. We report two striking nonadiabatic and adiabatic scenarios in low modulation frequency limit which appear when such strength modulation occurs. Firstly, the changes of the amplitude of the driving field without considering a parabolic confinement potential act as a perturbation which mixes the spin states. Here, the dynamical evolution of the tunneling probabilities of the nonadiabatic populations under investigation is analyzed. Secondly, for strong fields and strong dependence of a parabolic confinement potential, the two diabatic states do not cross but present anti-crossing phenomenon as the time tends to infinity, describing an adiabatic transition. However, if the field strength in a wire is weak enough, the level separation of a qubit state switches abruptly around the crossing point, and LZ tunneling applies to the whole dynamical range, from adiabatic to fully nonadiabatic crossing. Locally, the tunneling process can be seen as a two-level system (TLS) undergoing a Rabi oscillation. These results open new prospects for the use of quantum interferences in spin–based devices.
We present a detailed analysis of the Landau–Zener problem for an interacting Bose–Einstein condensate in a time-varying double-well trap, especially focusing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity and thus fundamentally alters the dynamics. It is shown that essentially all the features of the Landau–Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase-space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility of exploiting Landau–Zener sweeps to generate squeezed states for spectroscopic tasks is analyzed in detail. Moreover, we study the influence of phase noise and propose a Landau–Zener sweep as a sensitive yet readily implementable probe for decoherence, since the noise has significant effect on the transition rate for slow parameter variations.