I present experimental and theoretical work on extending nonlinear optical effects to the quantum domain. First, I experimentally demonstrate an incoherent nonlinear effect linked to the amplification stage of photon detection in a single-photon counter. The detector, in the high-efficiency regime, does not follow Glauber's quantum mechanical model for photodetection and, as a result, quantum interference effects are observable in the singles rate of one detector. I then go on to theoretically describe and experimentally demonstrate two coherent nonlinear optical effects at the single-photon level. In both experiments, the usually weak nonlinear optical properties of a common nonlinear crystal are enhanced by over 10 orders of magnitude using interference. The first of these coherent processes uses interference to frequency double all photon pairs from a couple of very weak laser beams (containing, on average, less than one photon per pulse). I show how this nonlinearity might be used for �phase-sum� entanglement swapping and an experimental demonstration of Hardy's paradox. The second coherent effect is the dispersive analogue to the first; instead of frequency doubling all of the photon pairs, all photon pairs experience an additional nonlinear phase shift. It is analogous to an immensely enhanced Kerr nonlinearity. This effect is applied to the problem of Bell-state discrimination and can be used to entangle and disentangle the polarization states of a pair of photons under certain conditions. The final experiment in this thesis is a demonstration of a technique for creating coherent superpositions of zero and one photon based on the detection of a single, �trigger� photon.
I present experimental and theoretical work on extending nonlinear optical effects to the quantum domain. First, I experimentally demonstrate an incoherent nonlinear effect linked to the amplification stage of photon detection in a single-photon counter. The detector, in the high-efficiency regime, does not follow Glauber's quantum mechanical model for photodetection and, as a result, quantum interference effects are observable in the singles rate of one detector. I then go on to theoretically describe and experimentally demonstrate two coherent nonlinear optical effects at the single-photon level. In both experiments, the usually weak nonlinear optical properties of a common nonlinear crystal are enhanced by over 10 orders of magnitude using interference. The first of these coherent processes uses interference to frequency double all photon pairs from a couple of very weak laser beams (containing, on average, less than one photon per pulse). I show how this nonlinearity might be used for �phase-sum� entanglement swapping and an experimental demonstration of Hardy's paradox. The second coherent effect is the dispersive analogue to the first; instead of frequency doubling all of the photon pairs, all photon pairs experience an additional nonlinear phase shift. It is analogous to an immensely enhanced Kerr nonlinearity. This effect is applied to the problem of Bell-state discrimination and can be used to entangle and disentangle the polarization states of a pair of photons under certain conditions. The final experiment in this thesis is a demonstration of a technique for creating coherent superpositions of zero and one photon based on the detection of a single, �trigger� photon.
In this thesis I report the first experimental observation of an interaction between a postselected single photon and an electromagnetic field containing a few thousand photons.This is the first observation of the nonlinear interactions due to a single freely propagatingphoton. To achieve this pioneering result, we have theoretically and experimentally studied nonlinear optics at the few-photon level. To the best of our knowledge, the pulse energy levels used for our experiments are the lowest energies used for cross-phase modulation in free space.Photon-photon interaction is vanishingly weak; the strength of this interaction can be enhanced in the presence of a material medium as mediator. In our experiment, we use an atomic coherence effect, namely Electromagnetically-induced Transparency (EIT), to produce a `giant' nonlinear interaction between two optical fields. We have observed a nonlinear phase shift of 18 ± 4 µrad per freely propagating single photon. This is done by sending very weak coherent state pulses into the medium and subsequently detecting single photons, inferring the existence of a photon in the interaction region.The optical setup, electronics and software that have been developed during the completion of this thesis provide the basis for several exciting future light-matter interaction experiments. We have produced phase-stable laser beams to create EIT in our cold Rubidium sample prepared in a Magneto-optical Trap (MOT). The laser system and the improved MOT setup have been built to be stable so that we can do very long data acquisition runs. We also have develop ed to ols and software with high precision and stability such that we can measure phase shifts down to micro-radian level.
Photons are good candidates for carrying quantum information because they are very stable particles: they interact weakly with the medium and barely with each other. However, this has drawbacks when you want to process the information because, in this case, it is preferable to have photon-photon interactions. For example, for applications in quantum repeaters, such interactions would allow deterministic Bell state measurements, increasing the entanglement distribution rate between two remote nodes. Getting two photons to interact with each other efficiently requires mapping them into a nonlinear medium at the single-photon level, that is, a medium that reacts differently when it interacts with a single photon than when it does with two. Such strong nonlinearity has been demonstrated with Rydberg atoms, which are atoms excited to a state with a high principal quantum number.
In this thesis we have performed nonlinear quantum optics experiments using an ensemble of cold Rydberg atoms, where we have studied the properties of the quantum light emitted by these atoms. First, we demonstrated nonlinearities at the single-photon level. To reach this stage, we made several improvements to the previous experimental setup available in the group, of which the implementation of a dipole trap was especially relevant. We evidence quantum nonlinearity by measuring photon antibunching for the transmitted light after interacting with the Rydberg state under electromagnetically induced transparency (EIT). We also showed the generation of single photons on-demand after storing weak coherent states of light pulses as collective Rydberg excitations.
Then, we studied the variation of the light statistic throughout the output pulse after propagating through the medium as Rydberg polaritons, which are superposition states of light and Rydberg excitations. We showed that the properties at the beginning and the end of the pulse were different from those of the steady state. In particular, the light detected after the input pulse was abruptly turned off gave much stronger suppression of two-photon events. Then, we investigated how to exploit this effect to generate single photons on demand. To do this, we analyzed the quality of the single photons detected at the end of the pulse as a function of the detection probability and compared the results with those obtained by storing the input pulse as collective Rydberg excitations. We showed that the photons were generated more efficiently when increasing the detection window at the cost of deteriorating the single photons statistics.
Finally, we investigated the indistinguishability of the photons emitted by our Rydberg atomic ensemble, a crucial property for using Rydberg atoms as nodes in quantum networks. We also compared the single photons generated after storage under EIT conditions with those obtained using a two-photon Raman excitation to the Rydberg state. We measured the indistinguishability by making them interfere with weak coherent states of light in a Hong-Ou-Mandel experiment. And we showed that, although we obtained better photon statistics under EIT conditions, the indistinguishability from those obtained with Raman excitation was significantly higher.
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.
This PhD thesis treats applications of nonlinear optical effects for quantum information processing. The two main applications are four-wave mixing in the form of Bragg scattering (BS) for quantum-state-preserving frequency conversion, and sum-frequency generation (SFG) in second-order nonlinear materials for heralded entanglement. BS is shown to be separable in the input and output modes in the low-conversion regime, the regime of small pump powers or short interaction times. The selective frequency conversion of a signal is found to only depend on one of the pumps, while the temporal output of the converted idler depends on the other pump. This allows for temporal-mode-multiplexing. When the effects of nonlinear phase modulation (NPM) are included, the phases of the natural input and output modes are changed, reducing the separability. These effects are to some degree mediated by pre-chirping the pumps. In the high-conversion regime without the effects of NPM, exact Green functions for BS are derived. In this limit, separability is possible for conversion efficiencies up to 60 %. However, the system still allows for selective frequency conversion as well as re-shaping of the output. One way to obtain a 100 % conversion efficiency is to use multiple stages of frequency conversion, but this setup suffers from the combined effects of NPM. This problem is circumvented by using asymmetrically pumped BS, where one pump is continuous wave. For this setup, NPM is found to only lead to linear phase shifts of the input and output modes, corresponding to shifts of the central frequencies of the fields. The trade-off is that one is only able to select which signals are converted, or change the shape of the output idler. Finally, entanglement swapping using SFG was investigated. Considering two pairs of entangled photons, the process of up-converting one photon from each pair leads to heralded entangled pairs by successful detection of the up-converted photon. It was seen that this was indeed possible in the case of anti-correlated phasematching in the up-conversion crystal. Possible ways of increasing the probability of an up-conversion event were investigated briefly.
The creation and manipulation of biphotons is important for many applications in quantum optics and quantum information. Topics that benefit from efficient biphoton sources range from the most fundamental quantum science experiments to the highly applied fields of quantum communication and quantum computation. Biphoton sources have long been hailed as one of the leading methods for creating entangled photon pairs for tests of Bell's inequality, creating heralded photon pairs that are used in on-demand single-photon sources and heralded measurement techniques, and for quantum communication protocols to name a few. Specifically for quantum communication, biphoton sources are commonly used for cutting edge quantum key distribution (QKD) protocols. In the first part of the thesis, I focus on realizing an efficient biphoton source that produces high yield photon pairs. More specifically, I develop an optimized biphoton source using the nonlinear optical process of spontaneous parametric down-conversion in a second-order nonlinear crystal. I develop a formalism for predicting the two important metrics of a biphoton source: the heralding efficiency and joint count rate. I show how, from a large parameter space, one can tailor the phase matching of the nonlinear interaction to create a high quality biphoton source that produces both high heralding efficiency and high joint count rate. I achieve heralding efficiencies of 86$\\pm5\\%$ and joint count rates of 2.58$\\pm0.6kHzpermWpumppower.Ishowthatusingacollinearnondegenerategeometryallowsforheraldingefficienciesofupto99.7\\%$ assuming no loss in the system. I verify the theoretical model with experimental results and find good agreement. In the second part of the thesis I turn to manipulating the single photons born from the biphoton source for applications in creating single-photon spectrometers and time-frequency QKD systems. The security of QKD is only guaranteed if the two parties have access to a set of states called mutually unbiased states. I create a set of these states in time and their conjugate states in the frequency basis and show that I can manipulate single photon correlations in time and frequency so that an eavesdropper can be detected if she localizes a photon to a 1 ns time interval. Additionally, in these experiments, I stretch a single photon wavepacket of 5-ps-width to a wavepacket of 8.3-ns-width and subsequently recompress it to at least the resolution of the detectors (sim 300 ps). This demonstrates a stretch factor of >1600 for a single-photon pulse using a group velocity dispersive material. To my knowledge, this is the largest reported stretch factor for a single-photon wavepacket produced by a biphoton source. The ability to stretch and recompress a single photon by this amount has applications in creating high-resolution, high-efficiency, single-photon spectrometers as well as advancing time-frequency QKD systems and other temporal pulse shaping applications.
Summary form only given. In any optical system, quantum and classical theory yield identical predictions for the mean intensity. The quantum mechanical predictions diverge from the classical theory only for higher order correlations. For this reason, typical quantum-interference experiments are performed by measuring coincidence rates between two or more detectors. The usual approximation, following Glauber, is that a single-photon counter fires at a rate proportional to the intensity, or number of incident photons per unit time. This approximation is so good and so entrenched that one routinely assumes that all singles-detection rates are insensitive to quantum effects. However, if one of these detectors fires, it cannot fire again for a characteristic time, called the dead-time. This characteristic of the detectors makes them highly nonlinear over times shorter than the dead-time, and thus sensitive to the higher order intensity correlations. In other words the detector has a different response for two photons arriving at different times, than for two photons arriving at the same time. We use the process of spontaneous parametric-downconversion (SPDC) to create correlated photon-pairs and send them through a polarization-based Hong-Ou-Mander interferometer. This quantum interferometer allows us to change the photon statistics without changing the intensity of the beams.