Optical amplitude and phase modulation dynamics at the single-photon   level in a quantum dot ridge waveguide
  The amplitude and phase of a material's nonlinear optical response provide insight into the underlying electronic dynamics that determine its optical properties. Phase-sensitive nonlinear spectroscopy techniques are widely implemented to explore these dynamics through demodulation of the complex optical signal field into its quadrature components; however, complete reconstruction of the optical response requires measuring both the amplitude and phase of each quadrature, which is often lost in standard detection methods. Here, we implement a heterodyne-detection scheme to fully reconstruct the amplitude and phase response of spectral hole-burning from InAs/GaAs charged quantum dots. We observe an ultra-narrow absorption profile and a corresponding dispersive lineshape of the phase, which reflect the nanosecond optical coherence time of the charged exciton transition. Simultaneously, the measurements are sensitive to electron spin relaxation dynamics on a millisecond timescale, as this manifests as a magnetic-field dependent delay of the amplitude and phase modulation. Appreciable amplitude modulation depth and nonlinear phase shift up to 0.09$\times\pi$ radians (16$\deg$) are demonstrated, providing new possibilities for quadrature modulation at faint photon levels with several independent control parameters, including photon number, modulation frequency, detuning, and externally applied fields. 
Galan Moody, Corey McDonald, Ari Feldman, Todd Harvey, Richard P.   Mirin, and Kevin L. Silverman
cond-mat.mes-hall physics.optics