Energy-time entangled photons are critical in many quantum optical phenomena and have emerged as important elements in quantum information protocols. Entanglement in this degree of freedom often manifests itself on ultrafast time scales, making it very difficult to detect, whether one employs direct or interferometric techniques, as photon-counting detectors have insufficient time resolution. Here, we implement ultrafast photon counters based on nonlinear interactions and strong femtosecond laser pulses to probe energy-time entanglement in this important regime. Using this technique and single-photon spectrometers, we characterize all the spectral and temporal correlations of two entangled photons with femtosecond resolution. This enables the witnessing of energy-time entanglement using uncertainty relations and the direct observation of nonlocal dispersion cancellation on ultrafast time scales. These techniques are essential to understand and control the energy-time degree of freedom of light for ultrafast quantum optics.
Energy-time entangled photons are critical in many quantum optical phenomena and have emerged as important elements in quantum information protocols. Entanglement in this degree of freedom often manifests itself on ultrafast time scales, making it very difficult to detect, whether one employs direct or interferometric techniques, as photon-counting detectors have insufficient time resolution. Here, we implement ultrafast photon counters based on nonlinear interactions and strong femtosecond laser pulses to probe energy-time entanglement in this important regime. Using this technique and single-photon spectrometers, we characterize all the spectral and temporal correlations of two entangled photons with femtosecond resolution. This enables the witnessing of energy-time entanglement using uncertainty relations and the direct observation of nonlocal dispersion cancellation on ultrafast time scales. These techniques are essential to understand and control the energy-time degree of freedom of light for ultrafast quantum optics.
Single photons are a natural platform for quantum technologies as they support entanglement in many degrees of freedom and are inherently well protected from a detrimental type of noise called decoherence. In order to fully exploit photons for quantum technologies, it will be necessary to be able to shape, control, and measure their properties in all degrees of freedom: space, time, frequency, and polarization. \n \n The time-frequency degree of freedom of light is of particular interest for quantum information tasks as it supports various encodings, including frequency bins and time bins, and is intrinsically robust for propagation through long-distance fibre links. Applications which harness quantum correlations in this degree of freedom, referred to as energy-time entanglement, include dispersion cancellation and high-dimensional quantum key distribution. However, detection of this entanglement and observation of these effects requires time resolution beyond the capabilities of current photon detectors. Thus, for operations on ultrafast time scales, more powerful and complex methods are required. \n \n In this thesis, we use a nonlinear technique known as optical gating to surpass the limitations in current detectors and measure single photon pairs, improving the time resolution by two orders of magnitude. When a single photon enters a nonlinear medium at the same time as a strong laser pulse, it may upconvert to a higher energy photon. The strong laser pulse effectively acts as an ultrafast shutter or gate and this creates a high resolution snapshot of the photon in time. Optical gating in conjunction with single photon spectrometers then allow us to measure both the spectral and temporal features of photons on subpicosecond time scales. \n \n These high resolution measurements enable us to explore a host of quantum effects which remained previously inaccessible. First, we directly observe energy-time entanglement, analogous to Einstein-Rosen-Podolsky correlations but \\emph{in frequency and time}. Then, with full control over the dispersion of each photon, we observe nonlocal dispersion cancellation on femtosecond time scales. We also explore ultrafast interferometry in the quantum domain by temporally resolving two-photon interference from a Franson interferometer and observe a violation of the CHSH-Bell inequality. Finally, we show that, using these measurements, it is possible to reconstruct a two-photon energy-time entangled state. Such measurement capabilities will be essential to precisely control both the spectral and temporal shape of entangled photons and to develop new applications in quantum state engineering.
Many quantum advantages in metrology and communication arise from interferometric phenomena. Such phenomena can occur on ultrafast timescales, particularly when energy-time entangled photons are employed. These have been relatively unexplored as their observation necessitates time resolution much shorter than conventional photon counters. Integrating nonlinear optical gating with conventional photon counters can overcome this limitation and enable subpicosecond time resolution. Here, using this technique and a Franson interferometer, we demonstrate high-visibility quantum interference with two entangled photons, where the one- and two-photon coherence times are both subpicosecond. We directly observe the spectral and temporal interference patterns, measure a visibility in the two-photon coincidence rate of $(85.3\ifmmode\pm\else\textpm\fi{}0.4)%$, and report a Clauser--Horne--Shimony--Holt--Bell parameter of $2.42\ifmmode\pm\else\textpm\fi{}0.02$, violating the local-hidden variable bound by 21 standard deviations. The demonstration of energy-time entanglement with ultrafast interferometry provides opportunities for examining and exploiting entanglement in previously inaccessible regimes.
Single photons provide a natural platform for quantum communication and quantum networking, as they can be entangled in many degrees of freedom and maintain coherence over long-distance links. However, while their minimal interactions with the environment isolate them from detrimental noise, it can make them difficult to measure and manipulate. In particular, manipulation on the ultrafast timescale is necessary to fully exploit the energy-time (or spectral) photonic degree of freedom. Full control over the spectral properties of single photons is key to many quantum technologies and opens the door to natural high-dimensional quantum encodings. \n \nIn this thesis, we theoretically and experimentally examine the use of nonlinear optical processes mediated by strong laser pulses as a method to control the spectral properties of ultrafast single photons. By mixing single-photon pulses with strong escort pulses that have been shaped through dispersion in a nonlinear crystal, the shape of the escort is imprinted on the photon, resulting in a custom-tailored upconverted pulse. We theoretically examine this process for quadratic spectral phases and show that it has the potential to be simultaneously effective and efficient for the customization of single-photon spectral waveforms, and can be performed in an entanglement-conserving manner. \n \nWe then experimentally demonstrate the range of this technique through three applications. First, we show that sum-frequency generation with shaped pulses can be used to coherently measure time-bin encoded photons with bin separations on the order of picoseconds, well below the timing resolution of our detectors. Secondly, we show that this technique can be adapted to convert a train of pulses to a frequency comb, which can be read out in a straightforward manner using diffraction-based spectrometry. We also show here that this process can be performed in a polarization-maintaining fashion, and demonstrate that entanglement with a partner photon is conserved with high fidelity. Finally, we show that this process can be viewed as a time lens, which modulates a temporal waveform in an analogous fashion to a lens focusing a beam of light. We apply the time lens to a photon from an energy-time entangled pair, and show negative magnification of the joint spectrum through a reversal of the spectral correlations. Such processes could find application in quantum state engineering and high-speed single-photon measurement.
The generation of ultrafast laser pulses and the reconstruction of their electric fields is essential for many applications in modern optics. Quantum optical fields can also be generated on ultrafast timescales; however, the tools and methods available for strong laser pulses are not appropriate for measuring the properties of weak, possibly entangled pulses. Here, we demonstrate a method to reconstruct the joint-spectral amplitude of a two-photon energy-time entangled state from joint measurements of the frequencies and arrival times of the photons, and the correlations between them. Our reconstruction method is based on a modified Gerchberg-Saxton algorithm. Such techniques are essential to measure and control the shape of ultrafast entangled photon pulses.
The time-energy entanglement of down-converted photon pairs is particularly difficult to characterize because direct measurements of photon arrival times are limited by the temporal resolution of photon detection. Here, we explore an alternative possibility of characterizing the temporal coherence of two-photon wave functions using single-photon interference with weak coherent light. Specifically, this method makes use of the fact that down conversion generates a coherent superposition of vacuum and two-photon states, so that the coincidence count rates for photon pairs after interference with weak coherent light are given by a superposition of the two-photon wave function from the down conversion with the product wave function defined by the weak coherent references. By observing the frequency-dependent interference pattern, it is possible to reconstruct the amplitudes and the phases of the two-photon wave function within the bandwidth of the reference pulses used in the single-photon interferences. The correlated single-photon interferences therefore provide a direct map of the entangled two-photon wave function generated in the down-conversion process.
Quantum correlations of ultrafast quantum optical states in the time–frequency domain manifest prominently on femtosecond time scales, an elusive challenging regime. We develop a new method to probe the time–frequency mode structure of ultrafast two-photon states utilizing dual-comb-based asynchronously overlapping pulses with single-photon frequency upconversion through femtosecond optical sampling. This method enables quick, highly precise joint temporal intensity measurements over a broad temporal dynamic range with only a single linear scanning stage. We demonstrate full characterization of time–frequency entangled two-photon states in both time and frequency domains. We quantified the time–frequency mode structure in both time and frequency domains through Schmidt decomposition, resulting in temporal and spectral purities of 87.7% and 76.9%, respectively, for heralded single-photons without any spectral filtering. Furthermore, through the simple control of pump spectral bandwidth, we demonstrate the ability to tailor time–frequency entanglement, verifying the two-dimensional Fourier duality. This method paves the way for a substantial upgrade to ultrafast quantum optical techniques, enabling a rapid, detailed, and multi-dimensional characterization of entangled states with potential applications in quantum metrology and photon-deficient fluorescence imaging.