Shaping the Ultrafast Temporal Correlations of Thermal-Like Photons

We show that the temporal correlations between two light beams arising from a broadband thermal-like source can be controlled in the femtosecond regime. Specifically, by introducing spectral phase-only masks in the path of one of the beams, we show that the timing and strength of the photon correlations can be programmed on demand. This example demonstrates that the interbeam second-order coherence function propagates as a phase-sensitive ultrafast wave packet in the path towards the detectors, and is thus, susceptible to be modified by acting on just one of the beams. For quite some time, it has been thought that this could only happen with sources showing time-energy entanglement. Our work shows that such a property is due to the existence of a certain type of correlation, but not necessarily the entanglement.

Figure 1

(a) Experimental setup to modify and measure the second-order coherence properties of two beams that, while originating in the same thermal-like source, propagate through different paths. Each beam travels through a different medium which can be described mathematically by a complex transfer function $H(\omega )$. Afterwards, the intensity correlations between the two beams are measured with an ultrafast detector, to yield the second-order correlation function $G^{(2)}(\tau )$. (b) Experimental setup. Filter 1 in the signal arm is a programmable pulse shaper that can modify the amplitude and phase of the input broadband spectrum. In the lower arm, a fiber connector is used. The ultrafast intensity cross correlation is performed in the optical domain with a background-free intensity cross correlator with a controllable motorized delay with 1 fs steps. The setup uses an achromatic lens to focus the reference and signal beams onto a 0.5 mm thick beta-barium borate (BBO) crystal to produce second-harmonic radiation, which is subsequently detected by a photomultiplier tube (PMT). The short length of the beta-barium borate crystal provides broadband phase-matching and femtosecond timing resolution. Further, pol: polarizer; col: fiber collimator. (c) Power spectra (displayed in linear scale) measured at signal and reference arms, respectively.

Figure 2

Measured normalized second-order correlation function $g^{(2)}(\tau )$ when the spectral phase is corrected with the pulse shaper (continuous blue line), compared with the expected $g^{(2)}(\tau )$ trace (dash-dotted red line). When the programmed phase is reversed in sign, the value $g^{(2)}(0)$ drops and the cross correlation broadens (dotted green).

Figure 3

Shaping of the photon temporal correlations. Simulation (left column) and measurement (right column) of the normalized second-order correlation function $g^{(2)}(\tau )$ when the pulse shaper is programmed with the spectral phase $\exp [i\eta \sin (\omega T)]$. The relevant parameters appear in the figure.