Traditional locking techniques, such as PDH (Pound-Drever-Hall), HC (Hansh-Couillaud), spatial mode interference technique, offset sideband locking technique, quantum noise locking, etc., have been widely applied to laser frequency stabilization and precision optical interferometry measurement. Here, a new technique, which we call phase-sensitive heterodyne locking (PSHL), is investigated by use of frequency-synthesized light to obtain a phase-sensitive high-frequency photoelectric readout to lock the phase of a squeezed light. Comparing with above techniques, there are several kinds of advantages for PSHL to be advocated. Frequency-synthesized light, which allows arbitrary control of the amplitudes and phases of the modulation sidebands relative to the carrier, is derived by the AOM (acousto-optic modulator), not the EOM (electro-optic modulator). Interferometic signals coming from a balanced heterodyne detector are high-frequency AC photoelectric current which can easily get rid of low-frequency classical noise and lead to reach or break through the shot noise limit. A theoretical derivation of the PSHL error signal and the associated stability of the squeezed and anti-squeezed lock points will be carried out in this work.
Shot-noise-limited displacement measurement is difficultly realized by traditional optical interferometry for surface profile detection and MEMS (micro-electro-mechanical systems) manufacture, attributing to low sensitivity of Michelson interferometer and high classical noise of homodyne or direct detector. Aiming at above problems, a dark-end locking method is proposed to enhance sensitivity of phase detecting; a Mach-Zehnder interferometer is utilized to raise recycling efficiency of laser and a LO (local oscillator), dispensing with additional introduction, is obtained in reading out interferometric signal; a balanced heterodyne detector, leading to reach the shot noise limit, is designed to get rid of high low-frequency classical noise. This work will serve as a theoretical guide and experimental support for the forthcoming precision displacement measurement and sub-shot-noise audio-frequency laser interferometry experiments.
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