Proposal for exploring macroscopic entanglement with a single photon and coherent states

Entanglement between macroscopically populated states can easily be created by combining a single photon and a bright coherent state on a beamsplitter. Motivated by the simplicity of this technique, we report on a method using displacement operations in the phase space and basic photon detections to reveal such an entanglement. We show that this eminently feasible approach provides an attractive way for exploring entanglement at various scales, ranging from 1 to 1000 photons. This offers an instructive viewpoint to gain insight into why it is hard to observe quantum features in our macroscopic world.

Figure 1

Creation and detection of macro entanglement by combining a single-photon Fock state $|1\rangle$ and a coherent state $|\sqrt{2}\alpha \rangle$ on a 50:50 beamsplitter.

Figure 2

Behavior of the negativity of the state ${\overline{\rho }}_{\mathrm{out}}$ as a function of the phase noise variance (rad) for various ${\left|\alpha \right|}^2=\{1,10,100\}$ (from top to bottom). The full line is the numerical calculation, the dashed line is a semianalytical bound, and the dot-dashed line is a fully analytical bound. (See the main text for details.)