Encoding information in the time–frequency domain demonstrates its potential for quantum information processing. It offers a novel scheme for communications with large alphabets, computing with large quantum systems, and new approaches to metrology. It is then crucial to secure full control on the generation of time–frequency quantum states and their properties. Here, the authors present an overview of the theoretical background and the technical aspects related to the characterization of time–frequency properties of two-photon states. The authors provide a detailed account of the methodologies that have been implemented for measuring frequency correlations and for the retrieval of the full spectral wavefunction. This effort has benefited enormously from the adaptation of classical metrology schemes to the needs of operating at the single-photon level.
Encoding information in the time–frequency domain demonstrates its potential for quantum information processing. It offers a novel scheme for communications with large alphabets, computing with large quantum systems, and new approaches to metrology. It is then crucial to secure full control on the generation of time–frequency quantum states and their properties. Here, the authors present an overview of the theoretical background and the technical aspects related to the characterization of time–frequency properties of two-photon states. The authors provide a detailed account of the methodologies that have been implemented for measuring frequency correlations and for the retrieval of the full spectral wavefunction. This effort has benefited enormously from the adaptation of classical metrology schemes to the needs of operating at the single-photon level.
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.
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.
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.
Light, which is composed of discrete quanta, or photons, is one of the most fundamental concepts in physics. Being an elementary entity, the behaviour of photons is governed by the rules of quantum mechanics. The ability to create, manipulate and measure quantum states of light is not only useful in foundational tests of quantum theory, but also in a wide range of quantum technologies – which aim to utilize non-classical properties of quantum systems to perform tasks not possible with classical resources. Only recently has it been possible to control the properties of number states of light, which have a fixed photon-number. Two-photon states are central to testing fundamental physical theories (such as locality and reality) and the implementation of quantum information technologies. The versatility of photon-pair states is en- abled by the potential entanglement properties it can posses. Thus controlling the correlations between photons is crucial to both pure and applied physics. To produce a single photon, a photon-pair state can be used. Detection of one photon indicates its twin’s existence. Many applications, such as optical quantum computation, require pure indistinguishable single photons. Heralding single pho- tons from a photon-pair will, in general, produce single photons in a mixed quantum state due to correlations within the pair. A common approach to creating photon-pairs is through the nonlinear sponta- neous four-wave mixing interaction in optical fibres. This thesis presents a theoreti- cal and experimental implementation of a scheme to tailor the spectral correlations within the pairs. Emphasis is placed on engineering the two-photon state such that they are completely uncorrelated. Spatial entanglement is naturally avoided due to the discrete nature of the optical fibre modes. Spectral correlations are eliminated by careful choice of dispersion characteristics and conditions. The purity of the photons generated by this scheme is demonstrated by means of two-photon inter- ference from independent sources. We measure a purity of (85.9 ± 1.6)% with no spectral filtering, exhibiting the usefulness of this source for quantum technologies and applications.
Developing techniques for characterizing quantum mechanical systems has been a major topic of research, especially in recent years, as quantum technologies, such as quantum communication and quantum cryptography, have grown to become an important asset in modern society. Although techniques such as quantum state tomography is an effective method to characterize a system consisting of two-level systems, the characterization of continuous degree of freedom such as space or frequency stills represents a time-consuming task as the state space scales exponentially with the dimension of the system. In this work, we show an indirect approach for measuring properties of high-dimensional degrees of freedom by coupling them to two-dimensional subsystems that can be measured efficiently via quantum state tomography. In our case, the property of interest is the correlation factor of the joint spectral amplitude describing the two-photon frequency states, which are coupled to the polarization degree of freedom using a completely positive trace-preserving map, called a dephasing channel. The action of the map on the polarization state induces a decoherence effect that depends on the initial frequency state, thus allowing to retrieve information about the frequency correlation factor by only measuring the decoherence in the polarization state. In the experimental part, we produced a pair of photons using spontaneous parametric down-conversion and characterized the joint spectral intensity with stimulated emission tomography. The decoherence was controlled with a birefringent material that acts as a dephasing channel. The polarization state was measured after the dephasing channel for two different initial frequency configurations using quantum state tomography. The bounds for the frequency correlation factor were calculated from the fidelity of the two polarization states and the generalized data processing inequality. The results of this work show that the polarization decoherence can be used as a tool to measure the frequency correlation factor of the joint spectral amplitude.
Quantum optics plays a central role in the study of fundamental concepts in quantum mechanics, and in the development of new technological applications. Typical experiments employ sources of photon pairs generated by parametric processes such as spontaneous parametric down-conversion and spontaneous four-wave-mixing. The standard characterization of these sources relies on detecting the pairs themselves and thus requires single photon detectors, which limit both measurement speed and accuracy. Here it is shown that the two-photon quantum state that would be generated by parametric fluorescence can be characterised with unprecedented spectral resolution by performing a classical experiment. This streamlined technique gives access to hitherto unexplored features of two-photon states and has the potential to speed up design and testing of massively parallel integrated nonlinear sources by providing a fast and reliable quality control procedure. Additionally, it allows for the engineering of quantum light states at a significantly higher level of spectral detail, powering future quantum optical applications based on time-energy photon correlations.