Coherent excitation of bound electron quantum state with quantum electron wavepackets

TL;DR

This paper introduces a quantum model for coherently exciting a bound electron using shaped quantum electron wavepackets, demonstrating control over quantum states and potential for quantum engineering.

Contribution

It develops an analytical model for TLS excitation via multi-particle quantum electron beams, validated by density matrix simulations, showing quadratic growth in transition probability.

Findings

Transition probability grows quadratically with correlated wavepackets.

Full Rabi oscillations can be achieved in the system.

Quantum state engineering of TLS is possible with shaped electron wavepackets.

Abstract

We present a fully quantum model for the excitation of a bound electron based on the free-electron bound-electron resonant interaction (FEBERI) scheme. The bound electron is modeled as a quantum two-level system (TLS) at any initial quantum (qubit) state, and the free electron is presented as a pre-shaped quantum electron wavepacket (QEW). In the case that the QEW is short or modulated at optical frequency, the TLS quantum state may be coherently controlled with multiple modulation-correlated QEWs. For this case, we derive the transition probability of the TLS due to interaction with a multi-particle beam based on an analytical approximate solution of the Schrodinger equation that amounts to using Born's probabilistic interpretation of the quantum electron wavefunction. We verify the credibility of the analytical model at its validity ranges using a fully quantum density matrix computation procedure. It is shown that the transition probability can grow quadratically with the number of correlated QEWs, and theoretically - exhibit full Rabi oscillation. The study indicates a possibility of engineering the quantum state of a TLS by utilizing a beam of shaped QEWs.