3D imaging of the biphoton spatiotemporal wave packet

TL;DR

This work tackles the challenge of fully characterizing the joint spatiotemporal structure of biphoton states produced by SPDC. It introduces and demonstrates a self-referenced, all-optical method titled 3D imaging of photonic wave packets (3D-JSTA) to reconstruct the three-dimensional joint amplitude $ψ(k_s,k_i)$, capturing spatial–spatial, spectral–spectral, and spatiotemporal correlations. The biphoton state is shaped by the interplay of the phase-matching function and the pump envelope, described by $ψ(k_s,k_i)$ under Δq and Δν constraints, enabling nontrivial nonlocal correlations. The experimental results reveal both local and nonlocal spatiotemporal correlations and show that the pump’s spectral dispersion critically influences the joint spectral phase, highlighting the need for complete pump characterization to access higher-dimensional photonic states for quantum communication and computation.

Abstract

Photons are among the most important carriers of quantum information owing to their rich degrees of freedom (DoFs), including various spatiotemporal structures. The ability to characterize these DoFs, as well as the hidden correlations among them, directly determines whether they can be exploited for quantum tasks. While various methods have been developed for measuring the spatiotemporal structure of classical light fields, owing to the technical challenges posed by weak photon flux, there have so far been no reports of observing such structures in their quantum counterparts, except for a few studies limited to correlations within individual DoFs. Here, we propose and experimentally demonstrate a self-referenced, high-efficiency, and all-optical method, termed 3D imaging of photonic wave packets, for comprehensive characterization of the spatiotemporal structure of a quantum light field, i.e., the biphoton spatiotemporal wave packet. Benefiting from this developed method, we successfully observe the spatial-spatial, spectral-spectral, and spatiotemporal correlations of biphotons generated via spontaneous parametric down-conversion, revealing rich local and nonlocal spatiotemporal structure in quantum light fields. This method will further advance the understanding of the dynamics in nonlinear quantum optics and expand the potential of photons for applications in quantum communication and quantum computing.

Figures (5)

• Figure 1: Experimental setup and schematic diagram of biphoton spatiotemporal correlations. As shown in (a), a laser pulse from Rega 9000 is firstly spatially filtered and spectrally dispersed by the beam shaping and spectral control module, then split by a PBS into two beams, one for pumping a cpKTP(custom-poled KTP) crystal to generate the spatiotemporally correlated photon pairs as shown in inset (b), another for pumping the PCF to implement the spectral shearing as shown in inset (c). The biphoton generated in type-II SPDC are in collinear configuration but have perpendicular polarization to each other, as shown by the two red cones in (b). The spatiotemporal correlation is sketched as their correlated spatial intensity distribution varying with the different time, as shown by the different color spots representing the frequencies on the gray temporal slices. To observe these correlations, one photon is directly collected by a fiber coupler and guided to the SNSPD after passing through a 4-km long DCF, while the other passes through the spectral shearing interferometer (SSI), as shown by the bottom dashed box in (a). Within the SSI, the photon's amplitude is split into two portions, one undergoes a 25-cm long PCF and, in the presence of the pump pulse, its spectrum is shifted by $\Omega$ due to the nonlinear cross-phase modulation(XPM), the other just propagates in free space with an adjustable temporal delay $\tau$. The two portions of amplitude are coherently recombined before entering the fiber coupler and subsequent DCF and SNSPD. The concept of the spectral shearing process is illustrated in (c), with the inset diagramming the photon's original (red) and shifted (blue) spectrum. At the detection stage, the spatial imaging is implemented by scanning the fiber couplers and, the two DCFs map the photons' frequencies to their arrival times at the detectors which are captured by the coincidence counts with picoseconds resolution. The joint spatial--spectral measurement is finally implemented. (d) and (e) diagram the joint spectral interference patterns of signal (d) or idler (e) photons, respectively, after passing through SSI. The tilted interference fringes indicate the existence of joint spectral phase correlations.
• Figure 2: Biphoton joint spatial correlations. The spatial intensity distribution of the signal photons while the idler photon are post-selected at (a) (-0.5, -0.5) mm, (b) (0, 0) mm and (c) (+0.5, +0.5) mm three specific spatial positions. The spectral dimension is neglected for clarity. The inset in the lower-right corner illustrate the corresponding spatial phase distribution.
• Figure 3: Biphoton joint spectral correlations. Measurement process of the joint spectral phase gradient along the signal axis(a-d) and idler axis(e-h) when both of them are post-selected in the central spatial positions. The reconstructed joint spectral and temporal amplitude are illustrated in (i-k). (a) and (e) show the spectra of the signal and idler photons before(red) and after(blue) spectral shearing. (b) and (f) display the Fourier transformation of the joint spectral interference patterns without spectral shearing(shown in the insets), along the signal and idler axes, respectively. The peak location of the side-lobes denote the temporal delay between the two arms of SSI. (c) and (g) show joint spectral interference patterns with spectral shearing of signal and idler photons. with calibrated frequency shift and temporal delay, the joint spectral phase gradients along the signal and idler axes are quantitatively determined, as shown in (d) and (h), respectively. The arrows indicate the gradient direction. (i) The joint spectral phase distribution reconstructed from the two-dimensional gradient field composed of (d) and (h). (j) The directly measured joint spectral intensity. (k) The joint temporal intensity obtained by Fourier transforming the joint spectral complex amplitude composed of (i) and (j) from the spectral domain to the temporal domain.
• Figure 4: Single photon spatiotemporal correlations. The spatiotemporal iso-intensity envelope of the signal photons with idler photons post-selected at the central spatial position. Colors represent the corresponding phase distributions along the iso-intensity contour.
• Figure 5: Biphoton spatiotemporal correlations. The iso-intensity envelopes of signal photons are shown for idler photons post-selected at spatial positions of (a) (-0.5, -0.5) mm, (b) (0, 0) mm, and(c) (+0.5, +0.5) mm, and temporal positions of -1.5 ps(red), 0 ps(green) and +1.5 ps(blue). Each iso-intensity envelope is normalized to its maximum value and projected onto the $x-t$ and $y-t$ planes. Additionally, the total spatial intensity distribution of the signal photons is illustrated on the $x-y$ plane.