Entangled photons are a crucial resource for linear optical quantum communication and quantum computation. Besides the remarkable progress of photon state engineering using atomic memories (Kimble (2008); Yuan et al. (2008)) the majority of current experiments is based on the production of photon pairs in the process of spontaneous parametric down-conversion (SPDC), where the entangled photon pair is concluded from post-selection of randomly occurring coincidences. Here we present new insights into the heralded generation of photon states (Barz et al. (2010); Wagenknecht et al. (2010)) that are maximally entangled in polarization (Schrodinger (1935)) with linear optics and standard photon detection from SPDC (Kwiat et al. (1995)). We utilize the down-conversion state corresponding to the generation of three pairs of photons, where the coincident detection of four auxiliary photons unambiguously heralds the successful preparation of the entangled state (Śliwa & Banaszek (2003)). This controlled generation of entangled photon states is a significant step towards the applicability of a linear optics quantum network (Nielsen & Chuang (2000)), in particular for entanglement distribution (Bennett et al. (1996)), entanglement swapping (Kaltenbaek et al. (2009); Pan et al. (1998)), quantum teleportation (Bouwmeester et al. (1997)), quantum cryptography (Bennett & Brassard (1984); Ekert (1991); Jennewein et al. (2000)) and scalable approaches towards photonics-based quantum computing schemes (Browne & Rudolph (2004); Gottesman & Chuang (1999); Knill et al. (2001)).
Entangled photons are a crucial resource for linear optical quantum communication and quantum computation. Besides the remarkable progress of photon state engineering using atomic memories (Kimble (2008); Yuan et al. (2008)) the majority of current experiments is based on the production of photon pairs in the process of spontaneous parametric down-conversion (SPDC), where the entangled photon pair is concluded from post-selection of randomly occurring coincidences. Here we present new insights into the heralded generation of photon states (Barz et al. (2010); Wagenknecht et al. (2010)) that are maximally entangled in polarization (Schrodinger (1935)) with linear optics and standard photon detection from SPDC (Kwiat et al. (1995)). We utilize the down-conversion state corresponding to the generation of three pairs of photons, where the coincident detection of four auxiliary photons unambiguously heralds the successful preparation of the entangled state (Śliwa & Banaszek (2003)). This controlled generation of entangled photon states is a significant step towards the applicability of a linear optics quantum network (Nielsen & Chuang (2000)), in particular for entanglement distribution (Bennett et al. (1996)), entanglement swapping (Kaltenbaek et al. (2009); Pan et al. (1998)), quantum teleportation (Bouwmeester et al. (1997)), quantum cryptography (Bennett & Brassard (1984); Ekert (1991); Jennewein et al. (2000)) and scalable approaches towards photonics-based quantum computing schemes (Browne & Rudolph (2004); Gottesman & Chuang (1999); Knill et al. (2001)).
The generation of high purity single photons and entangled photon pairs is a crucial first step in many quantum optics experiments, including those that require quantum teleportation [1], entanglement swapping [2], and the generation of multi-photon entanglement [3]. The most widely used and established approach for creating photon pairs is spontaneous parametric down conversion (SPDC) - where pump photons undergo a non-linear optical process to create a down-converted photon pair [4]. Traditionally, the generation of high-purity heralded single photons required severe spectral filtering, introducing additional loss. However, through careful engineering of spectral correlations of the down-converted photon pairs one can circumvent the need for filtering and avoid the accompanying reduction in heralding efficiency.
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.
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.
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.
Quantum states of photons such as entangled and single photons are indispensable components for applications in optical quantum information processing. Being able to generate and manipulate quantum states of photons on a chip is a crucial step towards realizing real-world quantum information processing systems such as an optical quantum computer. In this thesis, theoretical and experimental research was carried out for on-chip generation of quantum states of photons via the nonlinear process of spontaneous parametric down-conversion (SPDC), including polarization entangled photons, hyperentangled photons and heralded pure single photons. A majority of the study was based on III-V semiconductor AlGaAs, which could lead to monolithic integration of pump lasers and enable electrically pump sources operating at room temperature. The generation of cross-polarized entangled photons via a type-II SPDC in an AlGaAs Bragg reflection waveguide (BRW) was first investigated. The lack of material birefringence enables the direct generation of wavelength-multiplexed polarization entangled photons with a concurrence of at least 0.77 in a bandwidth of 95 nm. Second, a technique using concurrent type-0 and type-I processes on an AlGaAs chip to generate polarization entangled photon was developed. This technique allows the generation of both co-polarized and cross-polarized entangled photons on the same chip without the need of off-chip compensation, interferometer and bandpass filter. Third, a technique of generating hyperentangled photons on an AlGaAs chip was developed by utilizing spatial modes of different guiding mechanisms. High quality entanglement could be achieved with bandpass filtering of a few nanometers without off-chip phase compensation. Four, a generic technique using nonlinear photonic nanowires to engineer two-photon quantum states was proposed. Via dispersion engineering which controls the group velocity of each mode, maximally entangled polarization entangled photons and pure heralded single photons can be generated on-chip. Design examples were applied to III-V semiconductor and ferroelectric materials. Last, a strategy to enhance the bandwidths of wavelength conversion and SPDC spectrum was developed by tapering the waveguides. Combined with further integration of pump lasers, photonic circuits and detectors, the techniques developed in this thesis provides a viable route to achieve fully integrated generation and manipulations of photonic quantum qubits.
Entangled states of photons form the backbone of many quantum technologies. Due to the lack of effective photon-photon interactions, the generation of these states is typically probabilistic. In the prevailing but fundamentally limited generation technique, known as postselection, the target photons are measured destructively in the generation process. By contrast, in the alternative approach-heralded state generation-the successful creation of a desired state is verified by the detection of ancillary photons. Heralded state generation is superior to postselection in several critical ways: it enables free usage of the prepared states, allows for the success probability to be arbitrarily increased via multiplexing, and provides a scalable route to quantum information processing using photons. Here, we review theoretical proposals and experimental realisations of heralded entangled photonic state generation, as well as the impact of realistic experimental errors. We then discuss the wide-ranging applications of these states for quantum technologies, including resource states in linear optical quantum computing, entanglement swapping for repeater networks, fundamental physics, and quantum metrology.