Observation of Genuine Tripartite Non-Gaussian Entanglement from a Superconducting Three-Photon Spontaneous Parametric Down-Conversion Source

Abstract

The generation of entangled photons through Spontaneous Parametric Down-Conversion (SPDC) is a critical resource for many key experiments and technologies in the domain of quantum optics. Historically, SPDC was limited to the generation of photon pairs. However, the use of the strong nonlinearities in circuit quantum electrodynamics has recently enabled the observation of Three-Photon SPDC (3P-SPDC). Despite great interest in the entanglement structure of the resultant states, entanglement between photon triplets produced by a 3P-SPDC source has still has not been confirmed. Here, we report on the observation of genuine tripartite non-Gaussian entanglement in the steady-state output field of a 3P-SPDC source consisting of a superconducting parametric cavity coupled to a transmission line. We study this non-Gaussian tripartite entanglement using an entanglement witness built from three-mode correlation functions, and observe a maximum violation of the bound by 23 standard deviations of the statistical noise. Furthermore, we find strong agreement between the observed and the analytically predicted scaling of the entanglement witness. We then explore the impact of the temporal function used to define the photon mode on the observed value of the entanglement witness.

Figures (4)

• Figure 1: Three-photon spontaneous parametric down-conversion (3P-SPDC) in a superconducting cavity. (a) Circuit model. The short circuit at one end of a meandered $\lambda/4$ CPW resonator (green) is replaced by an asymmetric SQUID that creates a tunable boundary condition for the resonator modes. The SQUID is flux-coupled to a static DC coil (blue) and an AC pump line (red). The other end of the cavity is capacitively coupled to an output transmission line. (b) Cartoon of 3P-SPDC in the cavity with heterodyne measurement of the three propagating output modes defined by a temporal mode function. High-frequency pump photons (red) are split into entangled photon triplets inside the cavity at distinct frequencies (green) which couple to the continuum of the output line with coupling strengths ${\gamma_i}$. We convert the propagating modes into discrete modes, ${\hat{A}_i}$, with a temporal mode function $f(t)$, lastly measuring their voltage quadratures ${\hat{X}_i}$ and ${\hat{P}_i}$.
• Figure 2: Measured entanglement witness, $W$, for three-mode states generated from 3P-SPDC as a function of their measured average photon number, $\langle \hat{N}_{\textrm{tot}} \rangle$, which is varied by changing the pump amplitude. The error bars show one standard deviation of statistical error, $\sigma$, above and below the mean. We observe $W>0$, indicating genuine tripartite non-Gaussian entanglement, over nearly an order of magnitude of $\langle \hat{N}_{\textrm{tot}} \rangle$ before entanglement is no longer detected. At the maximum value of $W$, we violate the bound by more than $15\sigma$. We compare the measured witness values against stochastic trajectories simulations and an analytically predicted scaling law, Eq. \ref{['witness_form']}. Simulation results are plotted on the right axis, rescaled by a fitted factor of 1.9.
• Figure 3: Measured correlators as a function of the normalized three-photon drive strength, $g/g_{\text{min}}$. We estimate $g_{\text{min}} = 0.057$ MHz supplementary. Dotted lines are the linear (a) and quadratic (b),(c) scalings of the correlators predicted by perturbation theory in equations (\ref{['pt_1']}-\ref{['pt_3']}) with fitted multiplicative factors.
• Figure 4: Entanglement witness, $W$, as a function of width, $\Delta T$, of the temporal mode function for Gaussian (red) and boxcar (blue) mode functions. Markers are experimental data, solid lines are theoretical predictions. The width of the Gaussian mode function is defined as the full-width-half-maximum value, while the boxcar width is defined by the edges of the boxcar. $W$ grows rapidly for small $\Delta T$, until it reaches a maximum. The maximum values are achieved when $\Delta T$ is significantly larger than the cavity lifetimes ($0.12-0.25 \, \mu$s). We see that larger values of $W$ are obtained with the Gaussian mode function, in agreement with previous works ChalmersFiltersLu2021.