Kerr-induced non-Gaussianity of ultrafast bright squeezed vacuum

TL;DR

This work demonstrates a deterministic route to bright non-Gaussian light by applying Kerr nonlinearity to bright squeezed vacuum (BSV). By sampling the Husimi function with a single-shot f-2f interferometer, the authors observe an intensity-dependent phase that deforms the initial Gaussian Husimi distribution into an 'S' shape, evidencing non-Gaussianity. They show that, due to inevitable losses, BSV becomes a mixture of pure squeezed coherent states, with some components remaining highly Kerr-sensitive and capable of exhibiting Wigner negativity under Kerr evolution if purified. The results bridge ultrafast nonlinear optics and quantum optics, enabling high-photon-number non-Gaussian states for quantum information and metrology applications, while outlining paths toward purity-distillation of such states.

Abstract

Non-Gaussian states of light are a critical resource for fault-tolerant quantum computing and enhanced metrology, but are typically faint and often obtained via post-selection. Here, we demonstrate the deterministic generation of a bright non-Gaussian state by introducing a Kerr nonlinearity to a macroscopic state of light called bright squeezed vacuum (BSV). To characterize the resulting state, we use a single-shot f-2f interferometer to sample its Husimi function. We observe a clear transformation from a 2D Gaussian distribution to an 'S'-shaped non-Gaussian profile, which is the direct statistical evidence of the intensity-dependent nonlinear phase. The negativity of the Wigner function, which is an intrinsic property of any pure non-Gaussian state, cannot be observed because BSV is a mixed state even under minute optical loss. However, we show that BSV can be considered as a mixture of pure squeezed coherent states, for some of which Kerr-induced Wigner-function negativity is quite tolerant to loss. This work bridges the gap between quantum optics and ultrafast nonlinear optics, opening a path to quantum applications that require high photon flux.

Figures (4)

• Figure 1: (a) Experimental setup. OPA 1 and OPA 2, 3-mm BBO crystals; DM1 and DM2, dichroic mirrors; ND, neutral density filter; SHG, second-harmonic generation. (b) Two typical single-shot spectra with spectral fringes (incoherent background is subtracted). Each single-shot spectrum contains information about the amplitude $|\alpha_{2\omega}|$ and relative phase $\phi_{2\omega}$ of the second-harmonic pulse of BSV.
• Figure 2: (a-c) Experimental and (d-f) simulated Husimi functions for different strengths of the Kerr interaction. The radial coordinate is normalized to the mean amplitude.
• Figure 3: Schematic representation of BSV as a mixture (red ellipse) of squeezed coherent states (blue ellipses) in phase space. The dashed circle represents the vacuum state (the shot-noise uncertainty).
• Figure 4: Transformation of the Wigner function due to the Kerr nonlinearity described by unitary transformation $\hat{S}_{\operatorname{Kerr}}$ for (a) a coherent state with $|\alpha|^2=200$ and (b) a phase-squeezed state with the same mean number of photons and degree of squeezing 8 dB. (c) Simulated Wigner negativity volume vs. the number of photons $|\alpha|^2$ for the fixed Kerr phase $\phi_{\operatorname{Kerr}} = 2 \chi t |\alpha|^2 = 0.6$. Circles correspond to the lossless case, triangles assume a 5%-loss before the Kerr interaction and 5% loss after it. Lines visualize an exponential fit of the points.