Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations

We present the key elements required for continuous variable parallel quantum information protocols based on spatial multimode quantum correlations. We describe techniques for encoding, combining and detecting spatial quantum information with high efficiency in the individual transverse modes. Until now, the missing feature for the implementation of such protocols was the generation of squeezing in higher order transverse Hermite-Gauss modes. We experimentally demonstrate squeezing in selective modes by fine-tuning the phase matching condition of the nonlinear ${\chi }^{(2)}$ material and the cavity resonance condition of an optical parametric amplifier. Combined, these results open the way to practical multimode optical quantum information systems.

Figure 1

Practical spatial multimode systems: (a) single quantum information channel including modulation, propagation, and detection scheme in the case of information encoded on a ${\mathrm{TEM}}_{mn}$ mode; (b) measurement of the spatial properties of a test sample using lossless combiners and multimode detectors (MMD). SQZ: squeezed. HD: homodyne detection.

Figure 2

Top: Scheme for single pass SHG measurement in the case of ${\mathrm{TEM}}_{10}$ fundamental mode operation. Below: SH profiles generated in the crystal far field for three phase matching temperatures with a (a) ${\mathrm{TEM}}_{10}$ and (b) ${\mathrm{TEM}}_{20}$ pump profile. The cross-section traces show excellent between experimental results and theory fits.

Figure 3

Experimental setup to generate ${\mathrm{TEM}}_{n0}$ transverse mode squeezing. An OPA is seeded with an infrared misaligned ${\mathrm{TEM}}_{00}$ beam. The cavity is then locked to the ${\mathrm{TEM}}_{n0}$ mode and pumped with a SH ${\mathrm{TEM}}_{00}$ beam. The ${\mathrm{TEM}}_{n0}$ squeezed beam thereby produced is analyzed using spatial homodyne detection, whose ${\mathrm{TEM}}_{n0}$ LO is created from a misaligned ring cavity. Transverse beam profiles are represented in the case of ${\mathrm{TEM}}_{10}$ mode squeezing.

Figure 4

Squeezing and antisqueezing spectra measured in the (a) ${\mathrm{TEM}}_{00}$, (b) ${\mathrm{TEM}}_{10}$, (c) ${\mathrm{TEM}}_{20}$ modes. All traces are taken with a resolution bandwidth of 30 kHz and a video bandwidth of 30, over more than 1 min. For (b), we also present the results obtained with a coherent copropagating ${\mathrm{TEM}}_{00}$ mode. The insets show the noise properties at 4.45 MHz, normalized to the QNL (ii), when the LO phase is (i) scanned, or (iii) locked to the squeezing quadrature.