Continuous sampling of the squeezed-state nonclassicality

Abstract

We report the direct -continuous in phase -sampling of a regularized P function, the so-called nonclassicality quasiprobability, for squeezed light. Through their negativities, the resulting phasespace representation uncovers the quantum character of the state. In contrast to discrete phaselocked measurements, our approach allows an unconditional verification of nonclassicality by getting rid of interpolation errors due to fixed phases. To realize the equal phase distribution of measured quadratures, a data selection is implemented with quantum random numbers created by measuring the vacuum noise. The continuously measured squeezed field was generated in an optical parametric amplifier. Suitable pattern functions for obtaining the regularized P function are investigated. The significance of detecting negativities in our application is determined. The sampling of nonclassicality quasiprobabilities is shown to be a powerful and universal method to visualize quantum effects within arbitrary quantum states.

Preparation of arbitrary quantum states with regular P functions

“…One clearly observes the typical shape of the regularized P function of a squeezed vacuum state; see Ref. [23]. In particular, we reach a high statistical significance of eight standard deviations for the negativity of this function.…”

“…It was shown in Ref. [35] and later confirmed in experiment [23], that a larger value of q leads to a clearly improved statistical significance of the negativity of the regularized P function, P w , sampled from a fixed amount of data in balanced homodyne detection. In fact, the significance is maximal in the limit q → ∞.…”

“…The usefulness of quasiprobabilities to certify nonclassicality has been demonstrated for various states [22,36]. Moreover, different experimental schemes for the reconstruction of quasiprobabilities have been analyzed [12,23,[37][38][39][40][41]. Among those, we consider the balanced and the unbalanced homodyne detection in the following.…”

Quasiprobability distributions for quantum-optical coherence and beyond

“…Their construction requires to find a sufficiently smooth kernel K which, most importantly, is nonnegative for all arguments [55,56]. Applying this approach to experimental data even reveals the nonclassicality of squeezed states via regular quasiprobabilities with negativities [57,58], which is impossible using s-parametrized distributions.…”

Quasiprobability representation of quantum coherence

“…For this reason, regularization methods have been introduced [55,56] and generalized to multipartite and time-dependent systems [30,57]. This allows for the direct experimental sampling of regular negative quasiprobabilities of quantum light [58,59]. Notably, such irregularity problems do not occur in discrete-variable systems.…”