Upper-bounded and sliced Jaynes- and anti-Jaynes-Cummings Hamiltonians and Liouvillians in cavity quantum electrodynamics

TL;DR

This paper introduces a method to engineer specialized Hamiltonians and Liouvillians in cavity QED, enabling precise control over quantum states for applications like Fock state generation and optical state truncation.

Contribution

It presents a novel protocol to create upper-bounded and sliced Jaynes-Cummings Hamiltonians and Liouvillians, expanding control in cavity quantum electrodynamics.

Findings

Engineered Hamiltonians confined to specific Fock subspaces.

Built Liouvillians for state manipulation independent of Hamiltonian engineering.

Applications include steady Fock state generation and quantum scissors devices.

Abstract

In this paper, we present a protocol to engineer upper-bounded and sliced Jaynes-Cummings and anti-Jaynes-Cummings Hamiltonians in cavity quantum electrodynamics. In the upper-bounded Hamiltonians, the atom-field interaction is confined to a subspace of Fock states ranging from $\left\vert 0\right\rangle $ up to $\left\vert 4\right\rangle $, while in the sliced interaction the Fock subspace ranges from $\left\vert M\right\rangle $ up to $\left\vert M+4\right\rangle $. We also show how to build upper-bounded and sliced Liouvillians irrespective of engineering Hamiltonians. The upper-bounded and sliced Hamiltonians and Liouvillians can be used, among other applications, to generate steady Fock states of a cavity mode and for the implementation of a quantum-scissors device for optical state truncation.