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Ultrafast Metrology in the Quantum Domain

Jean-Philippe W. MacLean

Published Feb 15, 2019• 1 citation
OpenAlex

Abstract

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.

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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.
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.
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.
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.
Quantum physics holds promise to revolutionise a number of technologies by enabling performance beyond what is feasible with classical resources, such as secure communications, precision measurement and high-speed simulation and computation. To realise this, quantum information must be encoded into one of the physical degrees of freedom of light. The time-frequency (TF) domain provides a infinite-dimensional space which is naturally compatible with integrated optical platforms. Additionally, future quantum networks will require coherent coupling of quantum systems that do not necessarily exhibit TF mode overlap. The ability to generate, coherently control and measure a variety of TF states of quantum light is therefore a necessary step towards implementing optical quantum technologies. Developing the building blocks for future optical quantum applications calls for an assortment of methods for measuring the properties of TF states of quantum light. Whilst much progress has been made towards this goal recently, deficiencies with existing methods remain. Efficient spectrally-resolved detection away from the telecoms wavelength range and a robust approach to single-photon state characterisation that is sensitive to the spectral phase have so far proven challenging. Additionally, accessing quantum advantages requires measurements that are sensitive to the nonclassical correlations that can exist between separate subsystems. However, until now a flexible approach to determining the full quantum state of systems of multiple time/frequency entangled photons has been lacking. Here we develop a toolbox of techniques for the measurement of TF quantum states of light for few-photon systems, and apply these to the task of precision measurement. Firstly, we propose, construct and demonstrate efficient single-photon spectrometers based on dispersive time-to-frequency mapping, using chirped fibre Bragg gratings to apply the necessary group delay dispersion. We use two such devices operating in coincidence to realise a full phase-sensitive reconstruction of the TF state of a single photon, by spectrally resolving the output of a nonclassical interference process with an external reference. We also demonstrate a complementary, optical reference-free method. This characterisation tool, an implementation of electro-optic spectral shearing interferometry with coincident spectrally-resolved single-photon detection, melds techniques from ultrafast metrology and quantum optics. We proceed to demonstrate the flexibility of this device by reconstructing a wide range of test pulses generated with a pulse shaper. By implementing this technique in conjunction with spectrally-resolved detection of a second photon, we realise complete characterisation of the TF wave function of a spectrally-entangled broadband photon pair. This method is robust to a wide range of inputs and is generalisable to spectrally mixed states and across a wide range of wavelengths, including to spectrally non-degenerate photon pairs. To demonstrate, we generate an entangled photon pair with controllable TF entanglement and perform a full reconstruction. Lastly, we present a new technique for using TF entangled photon pairs to realise quantum-enhanced measurement of a time delay in a quantum channel in the presence of environmental noise. This scheme is based on entanglement-enhanced rejection of background light. A simple experiment demonstrating the feasibility of such a measurement is presented.
Ultrafast quantum optics with time-frequency entangled photons is at the forefront of progress towards future quantum technologies. However, to unravel the time domain structure of entangled photons and exploit fully their rich dimensionality, a single-photon detector with sub-picosecond temporal resolution is required. Here, we present ultrafast single-photon detection using an optical Kerr gate composed of a photonic crystal fiber (PCF) placed inside a Sagnac interferometer. A near-rectangle temporal waveform of a heralded single-photon generated via spontaneous parametric down-conversion is measured with temporal resolution as high as 224 ± 9 fs. The large nonlinearity and long effective interaction length of the PCF enables maximum detection efficiency to be achieved with only 30.5 mW gating pulse average power, demonstrating an order-of-magnitude improvement compared to optical gating with sum-frequency generation. Also, we discuss the trade-off relationship between detection efficiency and temporal resolution.
To fully utilize the energy-time degree of freedom of photons for optical quantum-information processes, it is necessary to control and characterize the temporal quantum states of the photons at extremely short time scales. For measurements of the temporal coherence of the quantum states beyond the time resolution of available detectors, two-photon interference with a photon in a short-time reference pulse may be a viable alternative. In this paper, we derive the temporal measurement operators for the bunching statistics of a single-photon input state with a photon from a weak coherent reference pulse. It is shown that the effects of the pulse shape of the reference pulse can be expressed in terms of a spectral filter selecting the bandwidth within which the measurement can be treated as an ideal projection on eigenstates of time. For full quantum tomography, temporal coherence can be determined by using superpositions of reference pulses at two different times. Moreover, energy-time entanglement can be evaluated based on the two-by-two entanglement observed in the coherences between pairs of detection times.