Realizing a sensitive photon-number-dependent phase shift is crucial for both classical and quantum photonics. Such a capability could revolutionize classical and quantum photonic machine learning and enable photon-photon gate operations. Achieving this requires efficient light-matter interaction, a challenge addressed by recent advancements in coupling quantum dots (QDs) to nanophotonic devices, leading to near-deterministic single-photon coupling. This research investigates the feasibility and characteristics of a single-photon phase shift using a QD embedded within a waveguide. The use of a waveguide architecture is particularly attractive due to its potential for scalability in the construction of larger quantum photonic circuits, a critical need for applications like quantum neural networks. Strong optical nonlinearities are achieved using single emitters like QDs embedded in photonic waveguides or cavities, exploiting tight light confinement to maximize light-matter coupling efficiency. In waveguide geometries, the deterministic reflection of narrow-band single-photon wavepackets upon resonant interaction with a two-level quantum emitter, contrasted with the partial transmission of two-photon wavepackets due to emitter saturation, allows for deterministic quantum operations like photon sorting. Even moderate nonlinear interactions, as opposed to optimal π or π/2 phase shifts, have been proposed to enhance measurement-based quantum computing and implement quantum neural networks. Previous demonstrations of emitter-induced phase shifts using atomic ensembles, trapped atoms, or ions, suffered from limitations in light confinement, resulting in small phase shifts (a few degrees). High-finesse cavities or nanophotonic equivalents can enhance light-atom coupling but add experimental complexity. Solid-state emitters like QDs offer better integration with nanophotonic structures, but significant phase shifts have mainly been shown in nanocavities, limited by the narrow cavity linewidth. Nanophotonic waveguides offer a balance—weaker Purcell enhancement but near-unity photon-emitter coupling efficiency, though previously limited to a few degrees due to restricted coupling efficiency. Single QDs in waveguides offer high single-mode coupling and narrow emission lines, promising substantial phase shifts. Most previous studies focused on measuring intensity modifications (transmission or reflection), but direct measurement of the phase response requires interferometric techniques. Prior phase shift measurements included direct Mach-Zehnder interferometry with single atoms (limited by coupling efficiency) and heterodyne detection-like schemes with single organic molecules (achieving smaller phase shifts) and indirect measurements using Floquet theory fitting, which can be challenging with QDs' multiple transitions. This study aims to address these gaps by directly measuring the single-photon phase shift induced by a QD in a nanophotonic waveguide using interferometry.

The paper extensively reviews previous work on achieving nonlinear phase shifts using various systems and techniques. It highlights the limitations of free-space approaches, the complexities of cavity-based methods, and the challenges of achieving significant phase shifts using molecules in waveguides. The authors emphasize the potential of using quantum dots (QDs) embedded in nanophotonic waveguides due to their high single-mode coupling efficiency and narrow linewidths. The literature review also points to the need for direct interferometric measurements of the phase shift to accurately quantify the nonlinear interaction, contrasting this approach with previous methods relying on intensity measurements or indirect inference techniques. Existing interferometric measurements using Mach-Zehnder setups with atoms had limitations in coupling efficiency. Heterodyne methods with molecules provided some progress, but the paper stresses the novelty of their approach which directly measures the total transmission response across a QD resonance in a waveguide. The study also considers previous work on chiral quantum optics which suggests the possibility of even larger phase shifts through directional coupling, highlighting that the achievement of high directionality is crucial for optimal phase shift.

The experiment utilized a ~3 m long Mach-Zehnder interferometer built on a closed-cycle cryostat to cool a GaAs photonic crystal waveguide with an embedded InGaAs QD to 4 K. A continuous-wave laser was sent through one arm of the interferometer, interacting with the QD, and then interfered with a reference arm (local oscillator). The interferometer's visibility (0.65) was mainly limited by mode matching. To stabilize the interferometer, a second (locking) laser was employed with fast feedback corrections using a piezoelectric transducer (PZT) and a field-programmable gate array (FPGA). The locking laser, far-detuned to avoid interaction with the QD, was filtered from the signal using a grating filter before detection by a single-photon avalanche photodiode (SPAD). To probe the phase shift, the resonant laser frequency was swept across the QD resonance, while the locking laser frequency remained fixed. The QD resonance frequency was tuned using the DC-Stark effect with an applied voltage. The 'on' and 'off' resonance cases (with and without applied voltage) were compared to directly measure the QD-induced phase shift. Data were acquired and fitted to identify intensity and phase changes near the QD resonance. For each power level, the maximum observed phase shift was determined, and the nonlinear behavior as the QD saturated was investigated. The experimental parameters were used to estimate the saturation photon flux. The waveguide used had a radius of 70 nm and a lattice constant of 250 nm, similar to previous designs. The bandgap was positioned to minimize Purcell enhancement while maintaining a high β-factor. Light coupling was achieved via shallow-etched grating couplers with >25% efficiency, suppressing grating back reflections. The interferometer was locked using the PZT-mounted mirror and the FPGA-based feedback loop to compensate for phase changes not originating from the quantum emitter. The locking laser was significantly more powerful than the resonant laser and was blue-detuned to avoid interacting with the QD. The chosen wavelength ensured good transmission in the sample.

The researchers directly measured a single-photon phase shift induced by a quantum dot (QD) in a nanophotonic waveguide using an interferometric method. They observed a maximal phase shift of φ_max,2 = (−0.19 ± 0.03)π radians (approximately 34 degrees) for one of the two dipole transitions of the QD neutral exciton. This is significantly larger than previous direct measurements using Mach-Zehnder interferometry. The phase shift was found to be nonlinear, exhibiting saturation at a mean photon flux of approximately 0.39 photons interacting with the QD during its lifetime. This saturation behavior demonstrates a nonlinear response to changes in the input laser power, which is consistent with theoretical calculations and is critical for potential quantum gate applications. The observed phase shifts were limited by the QD's coupling efficiency and decoherence, suggesting that future experiments with fully lifetime-limited QD transitions should enable even larger phase shifts approaching π/2. Furthermore, the theoretical analysis demonstrates that chiral coupling could lead to maximum phase shifts of π, further enhancing the potential of this system for quantum gate implementation. The study also highlights that the abrupt phase response towards saturation in a chiral waveguide offers potential for use as an all-optical phase switch, and that this system may also be used for highly sensitive measurements of environmental decoherence processes. The linewidths of the two quantum dot dipole transitions were measured to be 1.95 ± 0.05 GHz and 1.45 ± 0.05 GHz wide.

The direct observation of a substantial single-photon phase shift in a waveguide using a single quantum dot represents a significant advancement in quantum nonlinear optics. The measured phase shift of approximately 34 degrees is considerably larger than previously reported direct measurements, and the nonlinear response nearing saturation at the single-photon level confirms the potential for quantum gate applications. The limitations due to the QD's coupling efficiency and decoherence suggest avenues for future improvement. The theoretical exploration of chiral configurations, which could potentially yield even larger phase shifts, emphasizes the importance of controlling the light-matter interaction geometry. The findings directly address the need for a highly efficient and scalable approach to realize quantum optical nonlinearities, crucial for building complex quantum photonic circuits. The reported methodology offers a robust and accurate way to measure phase shifts, circumventing limitations of previous intensity-based measurements. The compatibility of this system with photonic integrated circuits suggests its suitability for scalable quantum technologies, including quantum machine learning and quantum computation.

This research successfully demonstrates a direct, interferometric measurement of a significant single-photon phase shift induced by a single quantum dot in a nanophotonic waveguide. The observed phase shift and its nonlinear power dependence showcase the potential of this system for various applications, including high-efficiency optical switching and quantum information processing. Future improvements in QD quality and exploration of chiral configurations promise even larger phase shifts, bringing the realization of deterministic quantum phase gates closer to reality. The method established here provides a powerful tool for investigating the fundamental physics of light-matter interaction and for developing advanced quantum photonic devices.

The main limitations of the current study stem from the imperfections of the quantum dot used. The observed phase shift was somewhat lower than the theoretical maximum due to the QD emission line not being fully lifetime-limited. Improvements in QD fabrication techniques aimed at reducing decoherence and increasing coupling efficiency would directly improve the phase shift achievable. Additionally, while the theoretical analysis indicates the potential for even larger phase shifts in chiral waveguides, such configurations with both high β-factor and high directionality require further experimental investigation.