Experimental study of balanced optical homodyne and heterodyne detection by controlling sideband modulation

We experimentally study optical homodyne and heterodyne detections with a same setup, which is flexible to manipulate the signal sideband modulation. When the modulation only generate a single signal sideband, the light field measurement by mixing the single sideband at $\omega_{0}+\Omega$ with a strong local oscillator at the carrier frequency $\omega_{0}$ on a beam splitter become balanced heterodyne detection. When two signal sidebands at $\omega_{0}\pm\Omega$ are generated and the relative phase of the two sidebands is locked, this measurement corresponds to optical balanced homodyne detection. With this setup, we may confirm directly that the signal-to-noise ratio with heterodyne detection is two-fold worse than that with homodyne detection. This work will have important applications in quantum state measurement and quantum information.