Quantum Homodyne Tomography of a Two-Photon Fock State

We present a continuous-variable experimental analysis of a two-photon Fock state of free-propagating light. This state is obtained from a pulsed nondegenerate parametric amplifier, which produces two intensity-correlated twin beams. Counting two photons in one beam projects the other beam in the desired two-photon Fock state, which is analyzed by using a pulsed homodyne detection. The Wigner function of the measured state is clearly negative. We developed a detailed analytic model which allows a fast and efficient analysis of the experimental results.

Figure 1

Experimental setup and Wigner function of the two-photon state propagating in the experiment (corrected for homodyne detection losses, see text).

Figure 2

Experimental quadrature measurements and quadratures reconstructed using our model (see text).

Figure 3

Wigner functions of the measured uncorrected states, reconstructed by a standard Radon transform, compared to those obtained using the model described in the text.

Figure 4

Experimental Wigner functions corrected for losses in the homodyne detection, reconstructed by a standard maximal-likelihood (MaxLike) method, compared to those obtained using the model described in the text.

Figure 5

Main density matrix coefficients of the states conditioned on 0, 1, and 2 photons (corrected for detection losses).

Figure 6

Modeling of the experiment.