Spatial spectral holographic (SSH) systems have applications in signal processing including spectrum analysis to optical correlation. Beam splitters and material interactions can affect the phase relationships between fields in separate spots in the material (or fields bypassing the material). Interferometric methods allow for these phase shifts to be exploited for two primary uses: the isolation of fields generated by the material and the amplification of signals and the amplification of signals in the chirped readout of programmed spectra. Stimulated photon echoes are used as the basis of SSH material-based optical systems and have been suggested as a protocol for optical quantum memory. These applications require the stimulated echo field to be isolated from a probe field. Current methods take an angular approach to isolating fields. An alternative approach uses interferometric methods to isolate fields in a way that can be implemented in a photonic integrated circuit. This dissertation will present a mathematical model for the isolation of stimulated photon echoes in both a 2-port Mach-Zehnder interferometer and a 4-port interferometer designed to emulate the isolation achieved via the angular "Box-Geometry" using interferometric methods. Experimental stimulated photon echo studies in a Mach-Zehnder interferometer built around a sample of 0.01% Tm 3+ : LiNbO 3 will demonstrate the principle of interferometric isolation of stimulated photon echoes. Maxwell-Bloch simulations will be used to demonstrate the principle of echo isolation in the 4-port interferometer. Use of the chirped interferometric readout of programmed spectra is demonstrated for SSH grating processing and spectrum analysis is shown in experiments in a sample of 0.01% Tm 3+ : LiNbO 3. Improvements to signal-to-noise ratio over traditional readout are seen by using a strong local oscillator in both applications. In spectrum analysis applications, the recovery of the proper spectral line shape is demonstrated, and SNR improvements are shown for a given read power. In the grating experiments, a non-linear noise floor was shown that created a constraint on the usable read power for these experiments. In this case, the interferometric readout was able to produce an improvement in the signal-to-noise ratio that could not be achieved using a stronger read power.
Programmable photonic integrated circuits are emerging as increasingly large and versatile interferometric processors operating at room temperature. However, their native operations are linear, while many computational tasks require nonlinear input-output transformations that typically rely on nonlinear optical materials or resonant devices. Here, we establish a direct mapping between quantum signal processing (QSP) and the native two-mode operations of programmable interferometric photonic integrated circuits, showing that the
SU(2) structure required by QSP can be realized through programmable phase control and mode mixing. We experimentally demonstrate this correspondence using dual-rail single-photon encoding on a 24-mode programmable photonic integrated circuit, realizing QSP sequences up to depth
L=11 and synthesizing STEP, ReLU and SELU functions through programmable phase control. The optical transformation remains linear, while repeated encoding of the input variable and coherent interference produce a nonlinear dependence of the output probabilities on the encoded variable. Across all accessible circuit depths, the measured responses follow the programmed QSP transformations, with hardware-induced mean squared errors between
10−3 and
10−2, all remaining below the intrinsic finite-depth approximation error. These results establish an algorithm-to-hardware mapping of QSP on programmable photonic processors. They also demonstrate an algorithmic route to programmable nonlinear functions of encoded variables on linear photonic hardware.
Two schemes for interferometric optical phase measurement, with sensitivity limited only by quantum noise in the light, are analyzed. Direct detection is applicable to signals at modulation frequencies away from the technical noise of the light, so that quantum noise dominates the measurement. Alternatively signals otherwise obscured by classical optical noise may be recovered with a phase-modulation technique that shifts the signals to a quantum-noise-limited region of the photocurrent spectrum. The analysis is tested experimentally by using a polarimetric electric-field sensor. In the direct-detection scheme quantum-noise-limited performance produced a phase sensitivity of 0.25 µrad. The indirect scheme allowed subkilohertz signals to be extracted from classical noise 67 dB greater with sensitivity approaching the quantum noise limit.