Optical quantum computing, quantum information and quantum communication protocols rely on the generation of qubits encoded in optical systems, many of which can be generate via the process of spontaneous parametric down-conversion. In this thesis, we investigate down-converted states, in the context of quantum computing and quantum information. In the high gain regime, a type I down-converted state can be described as a single-mode squeezed vacuum state. We present an analysis of photon-subtracted squeezed vacuum states as a resource for teleportation of coherent state qubits and propose proof-of-principle experiments for the demonstration of coherent-state teleportation and entanglement swapping. In the low gain regime, the output state of a type II parametric down-converter can be approximated as containing pairs of single photons, which can be used to herald the presence of one- or two- photon Fock states in one mode, conditional on the detection of the same number of photons in the other mode. We explore the effects of spectral filtering and inefficient detection, of the heralding mode, on the count rate, g(2) and purity of the heralded state, as well as the fidelity between the resulting state and an ideal Fock state. We also develop a technique for controlling the joint spectral profile of the down-converted photons. By exploiting the dependence of the effective nonlinearity of a periodically poled crystal on its poling order, we tailor the nonlinearity profile and therefore the phase matching function of the down-converted photons. Finally, we consider the validity of the Taylor series expansion of the unitary operator which governs the evolution of the fields within the crystal, in comparison to the strictly correct time-ordered Dyson series expansion.
Optical quantum computing, quantum information and quantum communication protocols rely on the generation of qubits encoded in optical systems, many of which can be generate via the process of spontaneous parametric down-conversion. In this thesis, we investigate down-converted states, in the context of quantum computing and quantum information. In the high gain regime, a type I down-converted state can be described as a single-mode squeezed vacuum state. We present an analysis of photon-subtracted squeezed vacuum states as a resource for teleportation of coherent state qubits and propose proof-of-principle experiments for the demonstration of coherent-state teleportation and entanglement swapping. In the low gain regime, the output state of a type II parametric down-converter can be approximated as containing pairs of single photons, which can be used to herald the presence of one- or two- photon Fock states in one mode, conditional on the detection of the same number of photons in the other mode. We explore the effects of spectral filtering and inefficient detection, of the heralding mode, on the count rate, g(2) and purity of the heralded state, as well as the fidelity between the resulting state and an ideal Fock state. We also develop a technique for controlling the joint spectral profile of the down-converted photons. By exploiting the dependence of the effective nonlinearity of a periodically poled crystal on its poling order, we tailor the nonlinearity profile and therefore the phase matching function of the down-converted photons. Finally, we consider the validity of the Taylor series expansion of the unitary operator which governs the evolution of the fields within the crystal, in comparison to the strictly correct time-ordered Dyson series expansion.
This thesis presents experimental progress towards highly efficient generation of cavity- enhanced, narrow-band multiphotons using spontaneous parametric downconversion. It also suggests theoretical proposals for new applications of multiphoton sources in quantum information technology. Photons prepared in Fock states, with a well-defined number of particles, are the essence of the quantum nature of light, and their unique nonclassical properties help us to develop quantum information technology. The generation of Fock states has been most commonly achieved by using spontaneous parametric down-conversion (SPDC) through the χ(2) nonlinearity in bulk crystals. During the SPDC process the nonlinear crystal emits photon-number correlated modes, and a photon-number- resolving measurement in one mode heralds the preparation of the other mode in a Fock state. The fidelity and the success rate of Fock state generation is limited by the multimode nature of SPDC emission. In this thesis, I will investigate the use of cavity-enhanced SPDC modes for higher fidelity photon pair generation, in which the well defined mode of the cavity is enhanced and results in the narrow-band source of the heralded single-photons with up to 80% heralding efficiency. The heralding efficiency is defined as the ratio between number of coincidences and single events on the heralding mode. The photon-number-resolving ability of high-quantum-efficiency transition edge sensors is used for the heralding and detection. We further discuss the feasibility of Fock state generation with higher photon numbers upon improving the data acquisition and analysis techniques. We also demonstrate and implement an interferometry scheme that exploit the phase of the photon and is capable of reading boundless bits of digital information using a single photon. This thesis also introduces new theoretical proposals for using Fock states to obtain quantum advantages for various quantum information applications, here to increase the efficiency in reading out information stored in a classical digital memory and to discriminate optical phases with lower error rates than is feasible with classical protocols.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems3. We focus here on the use of a continuous-wave optical parametric oscillator3,4. This system is based on a non-linear χ2 crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states5. Generating directly such states is a difficult task and would require strong χ3 non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics(1,2). Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems(3). We focus here on the use of a continuous-wave optical parametric oscillator(3,4). This system is based on a non-linear χ(2) crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states(5). Generating directly such states is a difficult task and would require strong χ(3) non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.
This thesis presents a study of photon generation and conversion processes in nonlinear optics. Our results extend beyond the first order perturbative regime, in which only pairs of photons are generated in spontaneous parametric down-conversion or four wave mixing. They also allow us to identify the limiting factors for achieving unit efficiency frequency conversion, and to correctly account for the propagation of bright nonclassical photon states generated in the nonlinear material. This is done using the Magnus expansion, which allows us to incorporate corrections due to time-ordering effects in the time evolution of the state, while also respecting the quantum statistics associated with squeezed states (in photon generation) and single photons or coherent states (in photon conversion). We show more generally that this expansion should be the preferred strategy when dealing with any type of time-dependent Hamiltonian that is a quadratic form in the creation and annihilation operators of the fields involved. Using the Magnus expansion, simple figures of merit to estimate the relevance of these time-ordering corrections are obtained. These quantities depend on the group velocities of the modes involved in the nonlinear process and provide a very simple physical picture of the interactions between the photons at different times. These time-ordering effects are shown to be important only when the photons and pump beam overlap within the nonlinear material for a significant amount of time. We also discuss the possibility of preparing Fock states with many photons using parametric down-conversion sources and realistic photon-number-resolving detectors. After discussing photon generation processes, we study photon conversion processes in which a nonlinear material and a classical strong pump field are used modify the frequency of a second incoming low-intensity field. We show that time-ordering effects limit the efficiency of this conversion process, re-examine strategies to get around this problem, and show that it should be possible to have a clear observation of modified upconversion probabilities due to these effects, and thus have an experimental demonstration of time-ordering effects in nonlinear optics.
The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when pumped by a laser, produce pairs of single photons via the process of spontaneous parametric down conversion (SPDC). This process is mediated by the second order nonlinear susceptibility of the material. When pumped in a high gain regime, these crystals give rise to optical parametric amplification, which is a viable source of squeezed light. The vast majority of research in this area has focused on crystals that are seeded by vacuum in their two modes. This dissertation concerns the field of quantum nonlinear optics. It is an investigation into the processes that occur when nonlinear materials interact with the electromagnetic field on the single photon level. I have focused on seeding nonlinear crystals with quantum states of light, including single photons and entangled states. This process results in various states directly applicable to interferometry, imaging, and cryptography. Another application investigated is an absolute radiance measurement via stimulated parametric down conversion resulting from non-vacuum seeding of a nonlinear crystal. Additionally, other nonlinear processes, including four-wave mixing, nonlinear magneto-optical effects and coherent population trapping in warm atomic vapor involving quantum states of light are investigated. The process of seeding third-order nonlinear interactions, such as in atomic vapors, gives rise to a variety of interesting, nonclassical phenomena such as entangled image transfer and nonlocal imaging. Strong analogies between SPDC and four-wave mixing are drawn. I also experimentally show an all optical pi-only phase shift of one light beam via another in warm Cesium vapor.
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.