The present work starts with a historical and conceptual introduction of the foundation of the
entanglement, from the idea of Einstein to the formulation of Bohm, much more experimentally
accessible. For the formation of an entangled state, the description of the nonlinear physical process
SPDC (Spontaneous Parametric Down-Conversion) was given, starting from the classical
Hamiltonian and performing the quantization of the fields exiting the crystal. It was possible to
determine the general structure of the wave function by perturbing the vacuum state. The basic
properties of the density matrix and the qubit, the fundamental unit of quantum computation, have
also been recalled as a prerequisite to the measurements of Bell Inequality and Quantum
Tomography. The second chapter is focusing on the apparatus. This can be thought as divided into
two independent parts. The first, formed by the laser, the temporal precompensation system and the
non-linear crystal, is responsible for the production of entangled photons. The second, formed by
the spatial compensation system, the waveplates, and the beam splitter, can be described as an
operator, according to Jones's matrix calculation, which acts on the wavefunction produced by the
source. Measuring entanglement means detect coincidences, then we explain the dependence of the
counting rate from the apparatus and how we optimized the coincidence rate. Finally, in order to
verify the quantum character of the source, a Bell test was performed and the value of S is
extracted. The reconstruction of the density matrix is presented in the last chapter, using an
analytical analysis of the Bloch hypersphere, from which we found a starting point for a numerical
optimization of the density matrix that better represents our system.
In the last, we characterized the degree of entanglement of the source.
The present work starts with a historical and conceptual introduction of the foundation of the
entanglement, from the idea of Einstein to the formulation of Bohm, much more experimentally
accessible. For the formation of an entangled state, the description of the nonlinear physical process
SPDC (Spontaneous Parametric Down-Conversion) was given, starting from the classical
Hamiltonian and performing the quantization of the fields exiting the crystal. It was possible to
determine the general structure of the wave function by perturbing the vacuum state. The basic
properties of the density matrix and the qubit, the fundamental unit of quantum computation, have
also been recalled as a prerequisite to the measurements of Bell Inequality and Quantum
Tomography. The second chapter is focusing on the apparatus. This can be thought as divided into
two independent parts. The first, formed by the laser, the temporal precompensation system and the
non-linear crystal, is responsible for the production of entangled photons. The second, formed by
the spatial compensation system, the waveplates, and the beam splitter, can be described as an
operator, according to Jones's matrix calculation, which acts on the wavefunction produced by the
source. Measuring entanglement means detect coincidences, then we explain the dependence of the
counting rate from the apparatus and how we optimized the coincidence rate. Finally, in order to
verify the quantum character of the source, a Bell test was performed and the value of S is
extracted. The reconstruction of the density matrix is presented in the last chapter, using an
analytical analysis of the Bloch hypersphere, from which we found a starting point for a numerical
optimization of the density matrix that better represents our system.
In the last, we characterized the degree of entanglement of the source.
This thesis deals with the production of entangled photons using spontaneous parametric down-conversion (SPDC). We start with a short overview of some important theoretical concepts. First we provide a brief reminder of the theory of entanglement. We then discuss how the state of quantum systems can be determined using quantum state tomography. We also explain SPDC, the physical process which we use to produce entangled photons. Finally, we give an overview of the methods which have been used to produce entangled photons in the past, both for two- and three-photon entanglement. \n \nThe first experiment is the design of an efficient source of entangled photon pairs based on a polarizing Sagnac interferometer configuration. With this configuration, we can use quasi-phasematched materials which allow for higher efficiencies than standard bulk nonlinear materials. The source is pumped by a low-power continuous-wave laser diode, and produces degenerate photon pairs at 809nm. It has a spectral brightness of 87,500 pairs/(s mW nm), and the fidelity of the produced quantum states with a Bell state is 98.9%. The source is used for experiments in quantum key distribution, cluster state quantum computing, remote state preparation, state discrimination, and entanglement-enhanced classical communication. \n \nThe second experiment discussed in this thesis is the generation of photon triplets using cascaded SPDC. In this experiment, a primary SPDC source is pumped with a low-power, continuous-wave laser diode, producing photon pairs. Single photons from these pairs serve as the pump for a second down-conversion, resulting in photon triplets. This is the first demonstration of the direct production of photon triplets, and the first observation of SPDC at the single photon level. This method could potentially be used to produce entangled photon triplets without post-selection, and as a source of triggered Bell pairs.
Abstract Using the type-I SPDC process in BBO nonlinear crystal (NLC), we generate a polarization-entangled state near to the maximally-entangled Bell-state with high-visibility (high-brightness) 98.50 ±1.33 % (87.71 ± 4.45 %) for HV (DA) basis. We calculate the CHSH version of the Bell inequality, as a nonlocal realism test, and find a strong violation from the classical physics or any hidden variable theory (HVT), S= 2.71±0.10. Via measuring the coincidence count (CC) rate in the SPDC process, we obtain the quantum efficiency of single-photon detectors (SPDs) around (25.5 ±3.4)% , which is in good agreement to their manufacturer company. As expected, we verify the linear dependency of the CC rate vs. pump power of input CW-laser, which may yield to find the effective second-order susceptibility crystal. Using the theory of the measurement of qubits, includes a tomographic reconstruction of quantum states due to the linear set of 16 polarization-measurement, together with a maximum-likelihood-technique (MLT), which is based on the numerical optimization, we calculate the physical non-negative definite density matrices, which implies on the non-separability and entanglement of prepared state. By having the maximum likelihood density operator, we calculate precisely the entanglement measures such as Concurrence, entanglement of formation, tangle, logarithmic negativity, and different entanglement entropies such as linear entropy, Von-Neumann entropy, and Renyi 2-entropy. Finally, this high-brightness and low-rate entangled photons source can be used for short-range quantum measurements in the Lab.
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.
In the past two decades, the union of quantum mechanics and information science has led to significant progress in our understanding of the quantum world and in our ability to coherently control individual quantum systems. New technologies have appeared, and some of them, such as quantum key distribution (QKD), are now commercially available. We are now envisioning quantum networks that could allow us to communicate over intercontinental scales, as the internet does, but with a provable security. An open question in this framework is how to certify that a given quantum network performs well, i.e. how to detect entanglement between 2, 5, 10 or 100 nodes located far away from each other. Bell tests are appealing for such a task as they allow one to certify the presence of entanglement deviceindependently, i.e. without assumptions on the Hilbert space dimension or on the proper alignment of the measurement devices. In the first chapter, I start by examining in depth the most standard approach to perform a Bell test in which a source based on spontaneous parametric down conversion (SPDC) is used to create photon pairs entangled in polarization. I show, in particular, that in this case the Bell inequality violation is fundamentally limited by vacuum and multi-photon emissions. In the second part of this thesis, I show how to overcome this limitation by using the SPDC source to create single photon entanglement, i.e. entanglement between two paths sharing a single photon, or two-mode squeezed states. Here, the non local content of the states is revealed using photon counting techniques preceded by small displacements in phase space. In the third part, I show how these measurements can be used for an optomechanical Bell test. This opens the way for device-independent quantum information processing with optomechanical systems and might be relevant to test collapse models in a theory independent manner. In the fourth chapter, the same measurements are used to build up a witness that can reveal genuine path entanglement. This witness has triggered an experiment which highlights its potential for network certification. I conclude the thesis by showing how path entanglement can be revealed with the human eye by exploiting these displacement operations.
Multi-particle entangled states are becoming more and more interesting for different applications in quantum information, such as quantum multi-particle teleportation, entangled based cryptography and quantum communication schemes based on multi-particle states, but also for fundamental reasons such as testing local realism by means of the Greenberger-Horne-Zeilinger states (GHZ) arguments . The advantage of multiparticle entanglement versus the most common two particle one lies in the fact that the greater the number of particles involved in the entangled state, the more clearly the quantum effects are exhibited. Our final goal is to exploit the multi-photon entangled states for quantum metrology. By the interaction of those states with nanostructures (mostly nanoholes, but in a future also nanospheres), we expect to reach sub-wavelength sensitivity phase measurements beating the Standard Quantum Limit as well as to detect plasmonic effects. In this thesis we present our work consisting on designing and building an experimental setup for the generation of states of 4-photon entangled in the transverse linear momentum. In the first part we explain some basics in the form of a technical introduction. We then adapt a general theoretical model to our particular case, explaining the physics of the process of generation of entangled states of photons. We proceed explaining the details of our setup, as well as the procedure of measurement. We then present the results of our tests in a "standard" 2-photon regime to show the correct functioning of the setup itself. Some more sophisticated measurements using structured light in the form of a first-order Hermite-Gaussian mode has been performed to generate entanglement in higher spatial modes are also presented. We conclude with theoretical and experimental details regarding the 4-photon experiments feasible with our setup. Our source is based on Spontaneous Parametric Down-Conversion (SPDC). In the last two decades it has been extensively studied for the generation of two-photon entangled states, since Kwiat et al. published in 1995 the new scheme based on polarization entangled photons. Most of the studies regarding entangled states involving more than two photons are indeed based on quantum correlations in the polarization or in the path of the down converted beams. The great advantage of entangling a spatial degree of freedom (as we do) is related to the dimensionality of the Hilbert space in which the state is defined. In the particular case of linear momentum, which is a continuous variable, we are dealing with infinite dimensions. Since in each dimension of the state one quanta of information can be encoded, the advantage of having multidimension entanglement for the field of quantum communication and computing is clear. The specs of our setup include a periodically-poled KTP crystals offering high conversion efficiency and cut for type-0 SPDC. The photons generated are well known to be inherently entangled in different degrees of freedom such as polarization, energy-time, linear momentum, and orbital angular momentum. Since each single SPDC event generates one photon pair, in order to reach four photon we entangle two consecutive SPDC events per each state. Furthermore, it is possible to manipulate (to enhance) the dimensionality of the entanglement by properly tailoring the pump spatial profile. The key point for the generation of four-photon entangled states is that, under some conditions, two consecutive pairs generated via SPDC cannot be described as two independent pairs but necessarily as a four-photon state showing genuine entanglement. This can happen when using a pulsed laser to generate the entangled photons; in particular, in the regime in which the coherence time of the down-converted photons τc is (much) longer than the temporal length of the pumping pulse Δt. In this condition the emission of a second pair is stimulated by the presence of the first one. That effect can be ultimately seen as a constructive multi-particle interference effect, the deep origin of which has to be sought in the boson statistic of photons.
Quantum computation and quantum communication require sources of entangled photons, especially from low-cost diode lasers. This study considered a polarization entangled photons pulse source produced via a spontaneous parametric down-conversion process in the type-I phase-matching of two nonlinear crystals, incorporating a continuous wave laser diode operating in pulse mode as a pump. The generated photons were measured based on visibility as a function of the pump frequency and collection apertures. A polarization correlation between photon pairs of approximately 93% and a Bell parameter S value of 2.56 ± 0.05 were obtained using the source described here.