Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum walks in weak electric fields and Bloch oscillations
197
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we will call an electric TBH; this phenomenon will be referred to as TBH Bloch oscillations. A similar phenomenon is known to show up in so-called electric discrete-time quantum walks (DQWs); this phenomenon will be referred to as DQW Bloch oscillations. This similarity is particularly salient when the electric field of the DQW is weak. For a wide, i.e., spatially extended initial condition, one numerically observes semi-classical oscillations, i.e., oscillations of a localized particle, both for the electric TBH and the electric DQW. More precisely: The numerical simulations strongly suggest that the semi-classical DQW Bloch oscillations correspond to two counter-propagating semi-classical TBH Bloch oscillations. In this work it is shown that, under certain assumptions, the solution of the electric DQW for a weak electric field and a wide initial condition is well approximated by the superposition of two continuous-time expressions, which are counter-propagating solutions of an electric TBH whose hopping amplitude is the cosine of the arbitrary coin-operator mixing angle. In contrast, if one wishes the continuous-time approximation to hold for spatially localized initial conditions, one needs at least the DQW to be lazy, as suggested by numerical simulations and by the fact that this has been proven in the case of a vanishing electric field.
rate research
Read More
We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $Phi$, e.g., on whether $Phi/(2pi)$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.
Describing a particle in an external electromagnetic field is a basic task of quantum mechanics. The standard scheme for this is known as minimal coupling, and consists of replacing the momentum operators in the Hamiltonian by modified ones with an added vector potential. In lattice systems it is not so clear how to do this, because there is no continuous translation symmetry, and hence there are no momenta. Moreover, when time is also discrete, as in quantum walk systems, there is no Hamiltonian, only a unitary step operator. We present a unified framework of gauge theory for such discrete systems, keeping a close analogy to the continuum case. In particular, we show how to implement minimal coupling in a way that automatically guarantees unitary dynamics. The scheme works in any lattice dimension, for any number of internal degree of freedom, for walks that allow jumps to a finite neighborhood rather than to nearest neighbours, is naturally gauge invariant, and prepares possible extensions to non-abelian gauge groups.
We report on the experimental realization of electric quantum walks, which mimic the effect of an electric field on a charged particle in a lattice. Starting from a textbook implementation of discrete-time quantum walks, we introduce an extra operation in each step to implement the effect of the field. The recorded dynamics of such a quantum particle exhibits features closely related to Bloch oscillations and interband tunneling. In particular, we explore the regime of strong fields, demonstrating contrasting quantum behaviors: quantum resonances vs. dynamical localization depending on whether the accumulated Bloch phase is a rational or irrational fraction of 2pi.
We examine phenomenon of electromagnetic transparency in semiconductor superlattices (having various miniband dispersion laws) in the presence of multi-frequency periodic and non-periodic electric fields. Effects of induced transparency and spontaneous generation of static fields are discussed. We paid a special attention on a self-induced electromagnetic transparency and its correlation to dynamic electron localization. Processes and mechanisms of the transparency formation, collapse, and stabilization in the presence of external fields are studied. In particular, we present the numerical results of the time evolution of the superlattice current in an external biharmonic field showing main channels of transparency collapse and its partial stabilization in the case of low electron density superlattices.
The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
