Abstract
We measure the joint Q-function of a multi-spatial-mode field using a charge-coupled device array detector in an unbalanced heterodyne configuration. The intensity pattern formed by interference between a weak signal field and a strong local oscillator is resolved using Fourier analysis and used to reconstruct quadrature amplitude statistics for 22 spatial modes simultaneously. The local oscillator and signal propagate at an angle of 12 mrad thus shifting the classical noise to modes that do not overlap with the signal. In this configuration, balanced detection is not necessary.
Highlights
We measure the joint Q function of a multispatial-mode field using a charge-coupled device array detector in an unbalanced heterodyne configuration
The intensity pattern formed by interference between a weak signal field and a strong local oscillator is resolved using Fourier analysis and used to reconstruct quadrature amplitude statistics for 22 spatial modes simultaneously
The local oscillator and signal propagate at an angle of 12 mrad, shifting the classical noise to modes that do not overlap with the signal
Summary
Balanced homodyne detection (BHD) is the standard measurement technique used to construct the complete quantum-mechanical state of light [2] This technique has one primary weakness: multimode fields or fields in an unknown spatial mode suffer significant losses due to mode mismatch between the local oscillator (LO) and the signal field [2,3]. One of the difficulties of these methods is the need to balance two array detectors and perform pixel-by-pixel subtraction to eliminate the classical intensity noise of the LO [8] These alignment requirements become prohibitive when trying to measure two transverse directions. This difficulty was removed by Beck et al who achieved the same effect with a single array, using unbalanced detection, by arranging the LO and signal fields to isolate the classical LO noise [9]. If the LO is normally incident on the detector and the signal field propagates at a small angle to the LO, the spatial intensity at the detector is given by
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