Nonclassical properties and quantum resources of hierarchical photonic superposition states

TL;DR

This paper introduces hierarchical quantum superposition states of coupled oscillators, analyzes their nonclassical properties, and explores their potential for quantum metrology and entanglement, with practical generation methods proposed.

Contribution

The paper defines a new class of hierarchical superposition states, analyzes their properties, and proposes feasible methods for their generation using current quantum optical technology.

Findings

Hierarchical superposition states exhibit strong nonclassical features.

These states are useful for high-precision quantum metrology.

Proposed generation methods are practical with existing technology.

Abstract

We motivate and introduce a class of "hierarchical" quantum superposition states of $N$ coupled quantum oscillators. Unlike other well-known multimode photonic Schr\"{o}dinger cat states such as entangled coherent states, the hierarchical superposition states are characterized as two-branch superpositions of tensor products of single-mode Schr\"{o}dinger cat states. In addition to analyzing the photon statistics and quasiprobability distributions of prominent examples of these nonclassical states, we consider their usefulness for high-precision quantum metrology of nonlinear optical Hamiltonians and quantify their mode entanglement. We propose two methods for generating hierarchical superpositions in $N=2$ coupled microwave cavities which exploit currently existing quantum optical technology for generating entanglement between spatially separated electromagnetic field modes.