Figure 1

Experimental layout. Entangled photons down-converted in one crystal are up-converted in the other crystal to produce the SFG photons. The symmetric imaging arrangement was designed to have a focus in the midway between the second and third prisms, creating there a spectral Fourier plane. A computer-controlled spatial light modulator (SLM) located at this plane was used to perform spectral-phase manipulations on the entangled photons. The SFG photons were counted using a single-photon counting module (SPCM-AQR-15 from EG&G), with a dark count of $\sim 50{\mathrm{s}}^{-1}$. This dark count was subtracted from all our measurements, which were performed with integration times of 5–10 s. The entangled-photon beam was filtered out from the SFG photons by a harmonic-separator mirror and filters, and its power was measured by a sensitive InGaAs detector. In order to demonstrate two-photon interference oscillations, a Mach-Zehnder interferometer was placed between the last prism and the SFG crystal.Reuse & Permissions

Figure 2

Direct observation and shaping of the two-photon wave function. The relative delay between the signal and idler photons was induced by varying the slopes of the spectral-phase filter described in (a). (b) The SFG counts (circles) and the calculated second-order correlation function $G^{(2)}(t_s-t_i)=|\psi (t_s,t_i){|}^2$ (line) as a function of the signal-idler delay. Shaping of the two-photon wave function was performed by adding a phase step function in the middle of the signal spectrum, as described in (c). The SFG measurements of the shaped wave function are represented in (d).Reuse & Permissions

Figure 3

Two-photon interference of time and energy entangled photons in a Mach-Zehnder interferometer (see Fig. 1). Interference oscillations of the IR power (a) and the SFG rate (b) as a function of the relative retardation between the interferometer arms. The experimental SFG counts (circles) are compared to the interference oscillations of the two-photon wave function, calculated according to Eq. (8) (line).Reuse & Permissions