Demonstrating<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-type entanglement of Dicke states in resonant cavity quantum electrodynamics

Abstract

Nonlinearity and entanglement are two important properties by which physical systems can be identified as nonclassical. We study the dynamics of the resonant interaction of up to $N=3$ two-level systems and a single mode of the electromagnetic field sharing a single excitation dynamically. We observe coherent vacuum Rabi oscillations and their nonlinear $\sqrt{N}$ speedup by tracking the populations of all qubits and the resonator in time. We use quantum state tomography to show explicitly that the dynamics generates maximally entangled states of the $W$ class in a time limited only by the collective interaction rate. We use an entanglement witness and the 3-tangle to characterize the state whose fidelity $F=78%$ is limited in our experiments by crosstalk arising during the simultaneous qubit manipulations which is absent in a sequential approach with $F=91%$.