Frequency locking of an optical cavity using linear–quadratic Gaussian integral control

Abstract

We show that a systematic modern control technique such as linear–quadratic Gaussian (LQG) control can be applied to a problem in experimental quantum optics which has previously been addressed using traditional approaches to controller design. An LQG controller which includes integral action is synthesized to stabilize the frequency of the cavity to the laser frequency and to reject low frequency noise. The controller is successfully implemented in the laboratory using a dSpace digital signal processing board. One important advantage of the LQG technique is that it can be extended in a straightforward way to control systems with multiple measurements and multiple feedback loops. This work is expected to pave the way for extremely stable lasers with fluctuations approaching the quantum noise limit and which could be potentially used in a wide range of applications.

Digital locking of a three-mirror ring cavity

“…The error signal follows the step input without oscillations in the steady state. This is in contrast to the closed-loop step response presented in [11], [12] which showed undesired steady state oscillations in the frequency close to the first resonance in the frequency response for the plant. The closed-loop step response using the digital PI controller is also presented for comparison.…”

“…A simple third-order model is obtained for the cavity using system identification methods, leading to a fourth-order model for the integral LQG controller. This is in contrast to the results presented in [11], [12] where a 13 th -order model is used for the plant, leading to a 15 thorder controller. This is further reduced to a sixth-order controller using model reduction techniques for the purpose of implementation.…”

“…al. implemented an integral LQG control scheme to lock a two-mirror optical cavity in [11], [12]. Here, the controller was designed by considering a state space model for the cavity-actuator system obtained using subspace system identification methods.…”

“…The transmitted beam (Tx output), is detected at the transmitted port by a photodetector at the output of mirror m2. The error signal is detected at mirror m3 using a homodyne detection scheme; see e.g., [11], [12]. The error signal is connected to a dSpace R analog-to-digital convertor (ADC) port which digitizes the signal to be used by the controller programmed in Matlab R RTI.…”

Precision charge drive with low frequency voltage feedback for linearization of piezoelectric hysteresis

“…Piezoelectric actuators are utilized in a wide range of industrial, scientific and commercial applications including scanning probe microscope positioning systems [1,2], fuel injection valves [3], and laser beam manipulation [4]. Although piezoelectric actuators have a number of desirable characteristics, a major disadvantage is the hysteresis exhibited at high electric fields [5,6].…”