Fourier processing of quantum light

It is shown that a classical optical Fourier processor can be used for the shaping of quantum correlations between two or more photons, and the class of filter functions applicable in the multiphoton Fourier space is identified. This concept is experimentally demonstrated by using two types of periodic phase Fourier filters to manipulate the quantum correlations between path-entangled photon pairs. As many more types of filter functions are applicable, this opens up an alternative avenue for the manipulation of correlations between photons, a key ingredient in optical quantum information processing.

Figure 1

Experimental setup. Polarized light from a laser diode (LD) is split into two beams by a half-wave plate (HWP) and a polarizing beam splitter (PBS). The distance between the beams is controlled by a movable retroreflector (RR), and their relative phase is controlled by a movable mirror (M) on a piezoelectric transducer (PZT). The beams undergo down-conversion in a nonlinear crystal (BBO). The pump beams are diverted by a dichroic mirror (DM) and interfered on a camera (CCD). The interference pattern is used together with the PZT for actively stabilizing the relative phase between the beams. The down-converted light goes through a 4-f filter equipped with a spatial light modulator (SLM), and finally detected by two fiber-coupled detectors (D1, D2). Coincidence detection is manifested by a coincidence counting unit (CCU). SF is a spatial filter, QWP is a quarter-wave plate, and BS is a beam splitter. Dark gray (purple) lines represent the pump beams, and light gray (red) lines represent the down-converted light. The inset shows a scheme of a 4-f filter.

Figure 2

(a) Schematic of the beam shaping system with a sinusoidal phase mask applied on the SLM, showing beam propagation and resulting intensity patterns. (b) and (c) Measured output intensity patterns for different values of the phase amplitude $A_p$ for (b) a single input beam and (c) two beams of path-entangled photon pairs.

Figure 3

Experimental observation of nonclassical correlations using a sinusoidal phase mask. (a) Second-order spatial correlation function ${\Gamma }_{q,r}$ of the input state, as measured at the output when no mask was applied. The black frames represent the expected values. (b) A section of the phase pattern created by the applied sinusoidal phase mask in the two-photon Fourier plane. (c)–(f) Resulting correlation patterns for different phases $\phi$ of the input states. Antibunching is observed for (c) $\phi =0$ while for (d) $\phi =\pi$ bunching is observed. For the two intermediate cases (e) $\phi =-\pi /2$ and (f) $\phi =\pi /2$ both effects are seen simultaneously.

Figure 4

Retrieval of phase information using a Zernike-like filter. (a) A section of the additional phase pattern applied on top of the sinusoidal phase [Fig. 3b]. (b) A comparison between the output intensity distribution with (dark red) and without (light blue) the additional phase. The number of each peak is indicated next to it. (c)–(f) Resulting correlation patterns for the same initial phases as in Figs. 3c–3(f). While for (c) $\phi =0$ and (d) $\phi =\pi$ no qualitative change is seen, the two intermediate states (e) $\phi =-\pi /2$ and (f) $\phi =\pi /2$ now show different and opposite correlation patterns, revealing the phase difference between them.