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

TL;DR

This paper develops a method using time-dependent density functional theory to analytically inverse engineer and control quantum systems, enabling the design of specific quantum dynamics and operations such as quantum gates.

Contribution

It introduces an analytic reconstruction strategy for quantum control problems using TD(C)DFT maps, demonstrated through examples in real space, lattice, and spin systems.

Findings

Recovered known solutions for driven oscillators.

Designed potentials for prescribed lattice dynamics.

Created control pulses for spin state manipulation.

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 Schr\"odinger 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.