Three-Photon Discrete-Energy-Entangled $W$ State in an Optical Fiber

We experimentally demonstrate the generation of a three-photon discrete-energy-entangled $W$ state using multiphoton-pair generation by spontaneous four-wave mixing in an optical fiber. We show that, by making use of prior information on the photon source, we can verify the state produced by this source without resorting to frequency conversion.

Figure 1

(a) Schematic of the experimental setup for generation of the discrete-energy-entangled $W$ state. (b) The setup used to measure coincidences for all possible energy combinations for the three channels $j$, $k$, and $l$, with the filters for measuring the $|Rj,Bk,Rl⟩$ term shown as an example. The filters are chosen to pass either blue or red photons at each channel for the different projection measurements. (c) Nested interferometers used to measure the reduced density matrix. PMF is for polarization-maintaining fiber, BP for bandpass filter, BS1-4 for beam splitter, LC for liquid crystal, $D$ for dichroic mirror, RF for red filter, BF for blue filter, and APD for avalanche photodiode.

Figure 2

(a) Measured probabilities of all possible energy combinations. Note that $|RRB{⟩}_{jkl}$, $|RBR{⟩}_{jkl}$, and $|BRR{⟩}_{jkl}$ are dominant components with about $\frac{1}{3}$ probability, which is as expected for the $|W_1⟩$ state. (b) Logarithmic plot of fourfold coincidence measurements as a function of pump power. The black, blue, and red lines are linear least-squares fits for states $|RBR{⟩}_{jkl}$, $|RRB{⟩}_{jkl}$, and $|BRR{⟩}_{jkl}$, with slopes of $4.02\pm 0.04$, $4.06\pm 0.08$, and $4.00\pm 0.03$, respectively.

Figure 3

(a) Single-photon spectrum of blue (blue solid line) and red (red dashed line) photons. (b) Single-photon interference counts of blue (blue circles) and red (red triangles) photons after the interferometers as a function of voltage across the liquid crystals. The black circles with arrows indicate the voltages across the liquid crystals that are chosen for phases ${\varphi }_B$ and ${\varphi }_R$.

Figure 4

The real (left) and imaginary (right) parts of the reconstructed reduced density matrices for $k$,$l$ (top), $j$,$l$ (middle), and $k$, $j$ (bottom) channels. The error bars represent the uncertainty due to phase instability and statistical noise.