Observation of spatial quantum correlations in the macroscopic regime

Spatial quantum correlations in the transverse degree of freedom promise to enhance optical resolution, image detection, and quantum communications through parallel quantum information encoding. In particular, the ability to observe these spatial quantum correlations in a single shot will enable such enhancements in applications that require real-time imaging, such as particle tracking and in situ imaging of atomic systems. Here, we report on measurements in the far field that show spatial quantum correlations in single images of bright twin beams with ${10}^8$ photons in a 1-$\mu \mathrm{s}$ pulse using an electron-multiplying charge-coupled-device camera. A four-wave mixing process in hot rubidium atoms is used to generate narrowband, bright pulsed twin beams of light. Owing to momentum conservation in this process, the twin beams are momentum correlated, which leads to spatial quantum correlations in the far field. We show around 2 dB of spatial quantum noise reduction with respect to the shot-noise limit. The spatial squeezing is present over a large range of total number of photons in the pulsed twin beams.

Figure 1

Schematic of experimental setup for the four-wave mixing and characterization of spatial quantum correlations in the far field present in bright twin light beams with an EMCCD camera. PBS: polarizing beam splitter. The inset shows the double-$\mathrm{\Lambda }$ energy-level scheme for the FWM.

Figure 2

Cross-correlation plots between (a) probe and conjugate pulses and (b) two coherent-state pulses.

Figure 3

Experimentally observed noise ratio for twin beams and coherent-state pulses at different binnings. The number of binned pixels given along the $x$ axes represent the number of pixels used along each side of the square binning region. (a) Noise ratios for (i) coherent-state pulses and pulsed twin beams (ii) without and (iii) with background correction. For the twin-beam traces conjugate images are rotated ${180}^{\circ }$ with respect to the probe images. (b) Noise ratio without rotation of the conjugate images. Error bars in (a) and (b) represent the standard deviation of the mean noise ratio over 100 shots. (c) Noise ratio of trace (ii) in (a), with error bars representing the standard deviation of the noise ratio over the 100 shots.

Figure 4

Experimentally observed noise ratio for twin beams and coherent-state pulses as a function of total photocounts in the 1-$\mu \mathrm{s}$ probe beam pulse. The different traces correspond to (i) coherent-state pulses, (ii) pulsed twin beams without background subtraction, and (iii) pulsed twin beams with background subtraction. Error bars represent the standard deviation of the mean noise ratio over the 100 acquired shots.

Figure 5

(a) Timing sequence of the pump and input probe pulses used to acquire probe and conjugate images in two consecutive frames of the EMCCD. (b) Two consecutive frames (frame size $170\times 512$ pixels) acquired by the EMCCD camera. Each frame contains an image of the probe (right) and an image of the conjugate (left). The time interval between these two frames is $\sim 60\mu \mathrm{s}$.