Quantum tomography in position and momentum space

TL;DR

This paper presents a quantum tomography method for continuous variable systems in position and momentum space, using a two-level probe interacting with a harmonic oscillator to reconstruct wavefunctions and density matrices.

Contribution

It introduces a novel tomography technique applicable to various physical systems with high quantum control, enabling wavefunction and density matrix reconstruction.

Findings

Method successfully reconstructs pure state wavefunctions.

Method enables direct measurement of mixed state density matrices.

Applicable to multiple physical systems with high quantum control.

Abstract

We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in position and momentum variables, during a tunable time span. We study two cases: the reconstruction of the wavefunctions of pure states and the direct measurement of the density matrix of mixed states. We show that our method can be applied to several physical systems where high quantum control can be experimentally achieved.