Dynamics of observables and exactly solvable quantum problems: Using time-dependent density-functional theory to control quantum systems

M. Farzanehpour and I. V. Tokatly
Phys. Rev. A 93, 052515 – Published 24 May 2016

Abstract

We use analytic (current) density-potential maps of time-dependent (current) density-functional theory [TD(C)DFT] to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schrödinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time-dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum not gate.

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  • Received 29 June 2015
  • Revised 23 February 2016

DOI:https://doi.org/10.1103/PhysRevA.93.052515

©2016 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

M. Farzanehpour1,* and I. V. Tokatly1,2,†

  • 1Nano-Bio Spectroscopy group and ETSF Scientific Development Centre, Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, E-20018 San Sebastián, Spain
  • 2IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain

  • *m.farzanehpour@gmail.com
  • ilya.tokatly@ehu.es

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Issue

Vol. 93, Iss. 5 — May 2016

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