Adaptive Quantum Optics with Spatially Entangled Photon Pairs

Light shaping facilitates the preparation and detection of optical states and underlies many applications in communications, computing, and imaging. In this Letter, we generalize light shaping to the quantum domain. We show that patterns of phase modulation for classical laser light can also shape higher orders of spatial coherence, allowing deterministic tailoring of high-dimensional quantum entanglement. By modulating spatially entangled photon pairs, we create periodic, topological, and random patterns of quantum illumination, without effect on intensity. We then structure the quantum illumination to simultaneously compensate for entanglement that has been randomized by a scattering medium and to characterize the medium’s properties via a quantum measurement of the optical memory effect. The results demonstrate fundamental aspects of spatial coherence and open the field of adaptive quantum optics.

Figure 1

Schematic of the experiment. (a) Spatially entangled photon pairs are generated by type-I SPDC in a $\beta$-barium borate (BBO) crystal pumped by a collimated continuous-wave laser at 403 nm. Near-degenerate down-converted photons are selected via spectral filters (SF) at $806\pm 1.5\mathrm{nm}$. Lenses $L_1$ and $L_2$ image the output surface of the crystal onto the SLM. Pairs of photons are emitted with respective angles denoted ${\mathit{\theta }}_{\mathbf{1}}$ and ${\mathit{\theta }}_{\mathbf{2}}$. $L_3$ and $L_4$ image the modulated photons into another optical plane (dashed line), where a scattering medium can be inserted. $L_5$ forms an image of the angular spectrum $\mathit{\theta }=({\theta }_x,{\theta }_y)$ of photon pairs onto an EMCCD camera. The camera enables both direct and correlation intensity measurements. The thin scattering medium (b) consists of a layer of Parafilm placed on a glass microscope slide. Scale bar is 2 cm. For clarity, the SLM is represented in transmission, while it operates in reflection.

Figure 2

Structuring entanglement by wave front shaping. Direct intensity images $I$ (column 2) and joint probability distributions $\mathrm{\Gamma }$ (column 3 and 4) are measured under photon-pair illumination using an EMCCD camera [20, 21]. Without shaping (a1), anticorrelations in the angular spectrum are visible on a conditional image $\mathrm{\Gamma }({\mathit{\theta }}_1|{\mathit{\theta }}_A)$ (a3) [taken for an arbitrarily chosen position ${\mathit{\theta }}_A=(1.6\mathrm{mrd},1.1\mathrm{mrd})$] and on the sum-coordinate projection of $\mathrm{\Gamma }$ (a4). A sine phase mask (b1) programmed on the SLM tailors the spatial structure of entanglement into a comblike pattern, visible on both the conditional image (b3) and on the sum-coordinate projection (b4). A helical SLM phase pattern (c1) produces a ring structure in the sum coordinate projection (c4) with a ring diameter 1.93 mrad (green scale bar). The same experiment performed under classical illumination creates a ring in the direct image (c3) with half the diameter 1.04 mrad (white scale bar). All direct images recorded under quantum illumination (a2), (b2), and (c2) are independent of the programmed phase patterns. Angular unit is mrad.

Figure 3

Focusing entanglement through a thin scattering medium. Conditional image $\mathrm{\Gamma }({\mathit{\theta }}_1|\mathbf{0})$ measured without the medium (a) shows an intense probability peak at ${\mathit{\theta }}_1=\mathbf{0}$. After insertion of the medium, the peak disappears and is replaced by a two-photon speckle pattern (b). Programming the optimized phase pattern (c), previously determined using classical coherent light, allows refocusing of the entanglement at the output of the medium (d). The shape of the direct intensity image measured at the output (insets) is not affected by the presence of the medium or by the shaping process.

Figure 4

Characterization of the optical memory effect using quantum illumination. The joint probability distribution of photon pairs is projected onto two columns of pixels located at ${\theta }_{x_1}=-0.07$ mrd and ${\theta }_{x_2}=0.07$ mrd on the direct image (a). Without the scattering medium (b), $\mathrm{\Gamma }({\theta }_{y_1},{\theta }_{y_2}|{\theta }_{x_1}=-0.07,{\theta }_{x_2}=0.07)$ shows an intense antidiagonal that reflects the anticorrelation in the angular spectrum of photon pairs. With the medium (c), the optimization technique reconstructs anticorrelations between pairs only in a limited angular range $\mathrm{\Delta }{\theta }_y$, seen as a reduction of the diagonal length. Programming the optimal phase pattern onto the SLM effectively transforms the thin scattering medium into a transparent medium but with a limited field of view (d). Fitting the focusing ratio $\mathrm{\Gamma }({\theta }_{x_1}=0,{\theta }_y|{\theta }_{x_2}=0,-{\theta }_y)/\mathrm{\Gamma }(\mathbf{0}|\mathbf{0})$ (red circles) with its corresponding theoretical model (red line) gives $\mathrm{\Delta }{\theta }_y=1.01\pm 0.1$ mrd (e). Classical measurement of the memory effect is represented on the same graph (blue circle) together with its corresponding theoretical model (blue line). For clarity, error bars are shown above the graphs.