Direct Sampling of Negative Quasiprobabilities of a Squeezed State

Although squeezed states are nonclassical states, so far, their nonclassicality could not be demonstrated by negative quasiprobabilities. In this work we derive pattern functions for the direct experimental determination of so-called nonclassicality quasiprobabilities. The negativities of these quantities turn out to be necessary and sufficient for the nonclassicality of an arbitrary quantum state and are therefore suitable for a direct and general test of nonclassicality. We apply the method to a squeezed vacuum state of light that was generated by parametric down-conversion in a second-order nonlinear crystal.

Figure 1

Simplified sketch of the experimental setup. A spatially filtered continuous-wave field at 1064 nm served as a local oscillator (LO) for balanced homodyne detection (BHD) and a phase-locked second harmonic field at 532 nm as the pump for the parametric squeezed light source (OPA). MC, spatial mode cleaner; PZT, piezoelectrically actuated mirror for adjusting the quadrature amplitude phase of the BHD.

Figure 2

Absolute value of the significance $\Sigma (w)$ of the negativity of the quasiprobability versus the filter width $w$.

Figure 3

Nonclassicality quasiprobability for a squeezed vacuum state. The data are directly sampled from our balanced homodyne data and clearly show negative values.

Figure 4

Cross section of the nonclassicality quasiprobability for our squeezed vacuum state. Note that the uncertainty in the data is less than the linewidth chosen here.