Abstract
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×π radians (16°) 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.
Highlights
Semiconductor quantum dots (QDs) are an excellent solid-state platform for opto-electronic, photonic, and quantum information processing devices due to their large oscillator strength and discrete density of states [1]
Phase-sensitive nonlinear spectroscopy techniques are widely implemented to explore these dynamics through demodulation of the complex optical signal field into its quadrature components; complete reconstruction of the optical response requires measuring both the amplitude and phase of each quadrature, which is often lost in standard detection methods
When applying a B = 1.5 T magnetic field in the Faraday configuration, the sideband modulation depth increases by nearly a factor of two and the lineshapes are asymmetric, leading to a dispersive profile of ΔPSB [Fig. 3(b)]; since both sidebands can have amplitude and phase modulation components, in principle, the origin of the asymmetry cannot be determined from measurements of the power spectrum alone owing to the lack of phase information
Summary
Semiconductor quantum dots (QDs) are an excellent solid-state platform for opto-electronic, photonic, and quantum information processing devices due to their large oscillator strength and discrete density of states [1]. An enhanced technique that is widely employed is to heterodyne the transmitted probe field with a strong local oscillator (LO) and detect the power in the radio-frequency beatnote between the probe and LO This measurement provides the time average of the in-phase (I) and quadrature (Q) components of the signal while suppressing noise from scatter of the pump field [14,17]. Advantages of heterodyne pump-probe spectroscopy include shot-noise limited detection of a weak probe beam, separation of colinear, co-polarized pump and probe beams, and detection of the amplitude and phase of the transmitted probe Despite these advantages, measurements of the power in I and Q do not provide any details of their dynamics, which prevents full demodulation of the nonlinear signal unless initial assumptions about the optical response are made. The ability to control the QD’s optical amplitude and phase response may find applications as a highly configurable single element quadrature modulator, which may facilitate novel optical modulation schemes such as Hilbert transformation for faint photonic communications [19]
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