Quantum entanglement plays a prominent role in both foundational physics and emerging quantum technologies. Light is especially promising as a platform for experimental realizations of high-dimensional entanglement, for which the time-frequency degree of freedom provides a natural encoding. Here, we propose and demonstrate a technique to determine the full quantum state of a pair of photons entangled in the time-frequency domain. Our approach, based on spectral shearing interferometry, is entirely self-referenced. To test our system, we measure a photon-pair source with nonlocal spectral phase that results in entanglement between the photons, in which the time when either photon is detected is correlated with the frequency of the other photon. The results demonstrate an effective new tool for exploring the temporal and spectral characteristics of multipartite quantum systems exhibiting high-dimensional entanglement.
Quantum entanglement plays a prominent role in both foundational physics and emerging quantum technologies. Light is especially promising as a platform for experimental realizations of high-dimensional entanglement, for which the time-frequency degree of freedom provides a natural encoding. Here, we propose and demonstrate a technique to determine the full quantum state of a pair of photons entangled in the time-frequency domain. Our approach, based on spectral shearing interferometry, is entirely self-referenced. To test our system, we measure a photon-pair source with nonlocal spectral phase that results in entanglement between the photons, in which the time when either photon is detected is correlated with the frequency of the other photon. The results demonstrate an effective new tool for exploring the temporal and spectral characteristics of multipartite quantum systems exhibiting high-dimensional entanglement.
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.
The ability to characterize the complete quantum state of light is essential for both fundamental and applied science. For single photons the quantum state is provided by the mode that it occupies. The spectral temporal mode structure of light has recently emerged as an essential means for quantum information science. Here we experimentally demonstrate a self-referencing technique to completely determine the pulse-mode structure of single photons by means of spectral shearing interferometry. We detail the calibration and resolution of the measurement and discuss challenges and critical requirements for future advances of this method.
Time-frequency entangled photons ("biphotons") exhibit joint spectral and temporal correlations that are unattainable with classical light. Besides being deployed for tests of quantum nonlocality, these photonic states are desirable for a unique range of applications that can significantly impact communications and computation. In this dissertation, we describe novel schemes based on spectral and temporal domain processing for manipulating and characterizing broadband biphotons. Implementing frequency-dependent filters, first, we present and demonstrate a technique for controlling the relative delay between a pair of entangled photons, relying on pump frequency tuning and the quantum concept of nonlocal dispersion cancellation. Next, we demonstrate near-field frequency-to-time mapping, a technique adopted from classical photonics, for arbitrary control of biphoton temporal correlations. Subsequently, we generate temporal correlation trains by creating biphoton frequency combs through programmable spectral amplitude shaping and demonstrate the temporal Talbot effect with entangled photons for the first time. Moreover, in the absence of fast single-photon detectors, we show how electro-optic phase modulation (originally a time-dependent operation) can be used to examine the coherence of biphoton frequency combs. Lastly, we introduce a scheme based on electro-optic intensity modulation, another time-domain operation, for improving the resolution in biphoton temporal correlation measurements. Overall, our body of work could provide additional insight into the manipulation and characterization of biphoton states, as well as contribute towards the improvement of quantum technologies.
Temporal-spectral modes of light provide a fundamental window into the nature of quantum systems and offer a robust means for information encoding. Methods to precisely characterize the temporal-spectral state of light at the single-photon level thus play a central role in understanding single-photon sources and their applications in emerging optical quantum technologies. Here we demonstrate an optical reference-free method, which melds techniques from ultrafast metrology and single-photon spectral detection, to characterize the pulse-mode structure of heralded single photons.
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.
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.