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Modeling of lock-in channels vs microwave carrier frequency, where the in-phase channel is optimized as the microwave error signal. An array representing the different regions in a cell with a light-intensity gradient is combined to obtain the total signal. The top panel shows the zero-crossing region of the middle panel, with both axes magnified. The arrow indicates the quadrature channel output at the in-phase channel zero-crossing.
Experimental setups with different light-shift suppression methods. DL, diode laser; FR, Faraday rotator; PE, pellicle; PO, polarizer; LCW, liquid crystal wave; BS, beam shaper; NDF, neutral density filter; BE, beam expander; I, iris; O, oven; H, horn; HC, Helmholtz coils; L, lens; PD, photodetector; CP, current preamplifier; LA, lock-in amplifier; PID, PID controller; FS, frequency synthesizer; FC, frequency counter; and FG, function generator.
Comparison of laser frequency error signals illustrating that the quadrature method locks to the same frequency as the conventional method, which is a zero-shift frequency. The signal-to-noise ratio of the quadrature method improved at higher temperatures due to increased cell optical thickness.
Comparison of clock frequency stability with and without the quadrature method of light-shift suppression.
Quadrature channel error signals for experiment and modeling vs lock-in phase with the local oscillator locked. The different curves denote different fixed laser detuning from the zero-shift frequency.
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