This chapter presents the basic concepts necessary to use photons as physical implementations of qubits. It starts with a traditional field quantization approach in the optical domain, where it puts an emphasis on how to obtain field modes which can be used as single localizable qubits. After quickly touching on several ways of generating single photon states, it moves to more technical aspects of parametric down conversion, which up to now has been the workhorse for most of the demonstration experiments involving two or a few more qubits in entangled states of high purity. The reader should be able to understand most aspects of contemporary sources of this type. The chapter then finishes by touching upon a few qubit operations with photons, exploring the high temporal correlation of down converted photon pairs, which also allow for at least a partial Bell state analysis.
This chapter presents the basic concepts necessary to use photons as physical implementations of qubits. It starts with a traditional field quantization approach in the optical domain, where it puts an emphasis on how to obtain field modes which can be used as single localizable qubits. After quickly touching on several ways of generating single photon states, it moves to more technical aspects of parametric down conversion, which up to now has been the workhorse for most of the demonstration experiments involving two or a few more qubits in entangled states of high purity. The reader should be able to understand most aspects of contemporary sources of this type. The chapter then finishes by touching upon a few qubit operations with photons, exploring the high temporal correlation of down converted photon pairs, which also allow for at least a partial Bell state analysis.
The natural choice of physical qubit for quantum communication is the photon: a photon can be transmitted quickly from the sender to a distant receiver and the technology for creating, manipulating, distributing, and measuring light pulses is well established. Many of these classical techniques can also be employed for quantum communication protocols. We will therefore focus our attention on optical setups for quantum communication. We will study a number of optical setups in the next few sections and use the conventions introduced in Chapter 4 to analyze them. In particular, we will assume that the qubits are encoded in the degrees of freedom of a single photon. Some of the main technical challenges in quantum communication arise from this need to work with single photon pulses. For instance, photons do not interact with each other in vacuum or linear media, and interactions between two photons in non-linear optical media are relatively small, so that realizing entangling two photon gates via coherent interactions is a challenging task. The quantum communication schemes discussed here circumvent this technical problem to a large extent. They only use non-linear optical materials for parametric down-conversion to create Bell-pairs of photons and then exploit standard linear optical devices and photo-detectors to manipulate them. No further non-linear entangling gates are required. Parametric down-conversion In non-linear optical media a single photon can be down-converted into a pair of photons. In this coherent process the incoming photon is destroyed and two photons of lower energy are created.
Over a century after the modern prediction of the existence of individual particles of light by Albert Einstein, a reliable source of this simple quantum state of one photon does not exist. While common light sources such as a light bulb, LED, or laser can produce a pulse of light with an average of one photon, there is (currently) no way of knowing the number of photons in that pulse without first absorbing (and thereby destroying) them. Spontaneous parametric down-conversion, a process in which one high-energy photon splits into two lower-energy photons, allows us to prepare a single-photon state by detecting one of the photons, which then heralds the existence of its twin. This process has been the workhorse of quantum optics, allowing demonstrations of a myriad of quantum processes and protocols, such as entanglement, cryptography, superdense coding, teleportation, and simple quantum computing demonstrations. All of these processes would benefit from better engineering of the underlying down-conversion process, but despite significant effort (both theoretical and experimental), optimization of this process is ongoing. The focus of this work is to optimize certain aspects of a down-conversion source, and then use this tool in novel experiments not otherwise feasible. Specifically, the goal is to optimize the heralding efficiency of the down-conversion photons, i.e., the probability that if one photon is detected, the other photon is also detected. This source is then applied to two experiments (a single-photon source, and a quantum cryptography implementation), and the detailed theory of an additional application (a source of Fock states and path-entangled states, called N00N states) is discussed, along with some other possible applications.
In this thesis, I present experimental and theoretical work which assesses and develops a range of tools that are required for performing quantum information processing, particularly in photonic systems. I investigate the three degrees of freedom of a single photon—its polarisation, spatialmomentum and time-frequency distributions. For polarisation, I show that using wave plates to implement arbitrary, single-qubit rotations is more complicated than is commonly appreciated. In the spatial-momentum and time-frequency domains, I develop ways to perform tomographic analysis of quantum states, and I report the first demonstrations of these techniques. In the time-frequency domain, the tomography technique utilises entanglement in the photon polarisation as a resource to store and provide access to the time-frequency information. In my first two experiments, I use spontaneous parametric down-conversion to produce entanglement between pairs of single photons in all three degrees of freedom. I demonstrate the first characterisation of entanglement in spatial modes and the time-frequency domain, the first quantitative measurement of entangled qutrit states, and the highest quality entangled states yet measured in both polarisation and spatial modes. I also report the first realisation of complete hyperentanglement, and a full, black-box tomography of a 36-dimensional two-photon state—the largest system to be characterised in this way to date. In my final experiment, I model and implement a new architecture for a controlled-Z gate which is much simpler to align than previous implementations. This gate requires only one non-classical interference condition, the visibility of which is the main limitation to its performance. I show that the gate operates effectively as a means of both creating entanglement and discriminating between the four elements in a basis of maximally entangled, Bell-type states. Indeed, its observed performance as a Bell analyser would be sufficient to build a quantum state teleporter which would guarantee that the recipient would be left with a better copy of an unknown input state than any eavesdropper. In a series of numerical simulations, I investigate some of the practicalities that arise when using tomographic reconstruction techniques, including how to estimate errors, which measurements to make and what is actually the optimal reconstruction. In particular, I show that tomographies perform better when based on the results from over-complete sets of measurements. Finally, I discuss the important issue of how to compare two processes, particularly when trying to assess the quality of a measured process by comparing it to some expected ideal. Judging possible candidate measures against a set of experimentally and theoretically motivated
For any communication, the conveyed information must be carried by some physical system. If this system is a quantum system rather than a classical one, its behavior will be governed by the laws of quantum mechanics. Hence, the properties of quantum mechanics, such as superpositions and entanglement, are accessible, opening up new possibilities for transferring information. The exploration of these possibilities constitutes the field of quantum communication. The key ingredient in quantum communication is the qubit, a bit that can be in any superposition of 0 and 1, and that is carried by a quantum state. One possible physical realization of these quantum states is to use single photons. Hence, to explore the possibilities of optical quantum communication, photonic quantum states must be generated, transmitted, characterized, and detected with high precision. This thesis begins with the first of these steps: the implementation of single-photon sources generating photonic qubits. The sources are based on photon-pair generation in nonlinear crystals, and designed to be compatible with fiber optical communication systems. To ensure such a compatibility and to create a high-quality source, a theoretical analysis is made, optimizing the coupling of the photons into optical fibers. Based on the theoretical analysis, a heralded single-photon source and a two-crystal source of entangled photons-pairs are experimentally implemented. The source of entangled photons is further developed into a compact source with a narrow bandwidth compatible with standard telecommunication wavelength-division multiplexers, and even further developed to a more stable one-crystal source. The sources are to be used for quantum communication in general and quantum cryptography in particular. Specifically, a heralded single-photon source is implemented and then used for a full test of a decoy-state quantum cryptography protocol.
Efficient Generation of Entangled Photon-Pairs The first experiments with correlated photons have been performed in the context of EPR-Bell experiments on the realistic and local properties of quantum mechanics. The source used there produced pairs of polarization entangled photons from a 2-photon decay of Calcium atoms. The technical requirements of these experiments were high (vacuum systems, stronge dye-lasers, etc.) whereas the efficiency of the source was quite low. An important step forward was the introduction of spontaneous parametric down conversion (SPDC), which has become the most common source in quantum optics for generating correlated or entangled photon pairs. In this process photons of an intense pump laser convert to photon pairs in an optical nonlinear crystal. Conservation of energy and momentum leads to strong correlations between the generated photons. With this kind of two-photon source it was possible to realize or improve many experiments on the foundations of quantum mechanics addressing the EPR-Paradoxon and in the new field of quantum information. But again, more advanced experiments and applications suffer from the limited ef- ficiency of the fluorescence process. Many photon pairs are lost by spatial and spectral filtering, which is necessary to achieve polarization entanglement and long coherence times. Different techniques have been implemented to increase the number of photon pairs using two-crystal arrangements, focusing techniques or periodically poled crystals. Most of these methods have the disadvantage that no entangled photons have been observed. It is the aim of this work to increase the yield and to improve the mode definition of entangled photon pairs generated by resonant enhancement of the pump mode and the fluorescence modes. As a first step a linear cavity for the pump mode was realized. Since the conversion probability is proportional to the pump power it was possible to increase the photon pair count rate by factor of 7 over the previous source. Besides the possibility of further improvement on already established pair correlation experiments, such an enhancement allows to build a compact source for photon pairs, in which an expensive argon-ion laser is replaced by a cheap diode laser. Among other applications such sources are of strong interest for quantum cryptography. 3 In many quantum information experiments optical fibers are use to carry the photons over long distance. Therefore, light from the parametric down-conversion source has to be efficiently coupled into fibers. In the second part we report on a new method to optimize collection efficiency by matching the angular distribution of the parametric fluorescence to the spatial mode of an optical fiber. By using this technique, we detected 366500 polarization-entangled photon pairs per second in the near-infrared region in single-mode optical fibers for 465 mW pump power (at 351.1 nm) with a 2 mm BBOcrystal. The entanglement of the photon pairs was verified by measuring polarization correlations of more than 96% in a HV-basis and in a ±45◦-basis. To our knowledge, such enormous count rates of highly entangled photon pairs have not been reached yet with any other technique. In the third part of this thesis we investigated the process of parametric downconversion in a cavity which is resonant to certain longitudinal down-conversion modes only. The idea of placing the parametric down-conversion source inside a cavity is not new. Such a device is usually referred to as a single or double resonant optical parametric oscillator (OPO) and is mainly used to generate squeezed quantum states. In that kind of application the system is operating close to but still under the threshold of oscillation. In our application the situation is quite different. The system is operating far below threshold so that mainly spontaneous emission occurs. In that mode correlations between single photons can still be observed. But bouncing the light back and forth inside the cavity increases the interaction length and hence enhances the signal levels of the down-conversion fields. Further, by resonating two certain modes only, the bandwidth is reduced by orders of magnitude and the coherence time is found to be inverse proportional to the bandwidth. A similar experiment has already been realized with a type-I parametric down-converter in the resonator. We have tried to realize a compact double resonant OPO far below threshold with a type-II parametric down-converter in a high-finesse cavity to realize a bright source of entangled photon pairs with extremely narrow bandwidth.
One of the main issues in the domain of quantum information and communication is the generation, manipulation and detection of several qubits on a single chip. Several approaches are currently investigated for the implementation of qubits on different types of physical supports and a variety of quantum information technologies are under development: for quantum memories, spectacular advances have been done on trapped atoms and ions, while to transmit information, photons are the ideal support thanks to their high speed of propagation and their almost immunity against decoherence. My thesis work has been focused on the conception, fabrication and characterization of a miniaturized semiconductor source of entangled photons, working at room temperature and telecom wavelengths. First the theoretical concepts relevant to understand the work are described (chapter 1). Then the conception and fabrication procedures are given (chapter 2). Chapter 3 presents the optoelectronics characterization of the device under electrical pumping, and chapter 4 the results on the optical losses measurements and the nonlinear optical characterization (second harmonic generation, spontaneous parametric down conversion and joint spectral intensity reconstruction). Chapters 5 and 6 focus on the characterization of the quantum state generated by a passive sample (demonstration of indistinguishability and energy-time entanglement) and its utilization in a multi- user quantum key distribution protocol (polarization entanglement). Finally the work on the first electrically driven photon pairs source emitting in the telecom range and working at room temperature is presented (chapter 7).