[ANGLÈS] In this thesis we tried to investigate the non-linear effects introduced by a generalized interaction of a two-level atom coupled to two photons. Scattering matrices were used to calculate the non-linear effects introduced and the dependence of outgoing frequencies of quantum light on these effects was found. It was seen as quite opposed to typical classical theories, that the non-linear susceptibility for an atom dictates very precise output frequencies from it. As a next step this work probes into quantum computing in which the two-photon bound state problem was mathematically established to show that a single two-level atom cannot be used in realization of non-linear logical operations in quantum computations. In the end a possible intuitive solution, involving dissimilar decay rates in three level systems, was thought of and shown that it can be effectively applied to quantum logic.
[ANGLÈS] In this thesis we tried to investigate the non-linear effects introduced by a generalized interaction of a two-level atom coupled to two photons. Scattering matrices were used to calculate the non-linear effects introduced and the dependence of outgoing frequencies of quantum light on these effects was found. It was seen as quite opposed to typical classical theories, that the non-linear susceptibility for an atom dictates very precise output frequencies from it. As a next step this work probes into quantum computing in which the two-photon bound state problem was mathematically established to show that a single two-level atom cannot be used in realization of non-linear logical operations in quantum computations. In the end a possible intuitive solution, involving dissimilar decay rates in three level systems, was thought of and shown that it can be effectively applied to quantum logic.
One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally very difficult. We therefore employ linear optics with projective measurements to generate these non-linearities. The downside is that the measurement-induced nonlinearities achieved with linear optics are less versatile and the success rate can be quite low. This project is mainly the result of a literature study but also a theoretical work on the physics behind quantum optical multiports which is essential for realizing two-photon gates. By applying different postcorrection techniques we increase the probability of success in a modifed non-linear sign shift gate which is foundational for the two photon controlled-NOT gate. We prove that it's not possible to correct the states by only using a single beam splitter. We show that it might be possible to increase the probability of success using a more complex setup with at least two error-correcting beam splitters.
Realising a platform for efficiently guiding and manipulating light at the singlephoton level lies at the heart of optical quantum information processing. In this thesis we aid in the pursuit of this goal by analysing few-photon transport properties in photonic devices while keeping in mind possible applications and experimental challenges. We especially focus on single and two-photon transport properties in one-dimensional waveguides coupled to (artificial) atoms modelled as two and three-level emitters. We begin by introducing key concepts relevant for this thesis and then explain how to model such waveguide geometries. We show how directional-dependent coupling between a waveguide and a localized quantum system can be modelled from a chain of harmonic oscillators by allowing the system to couple to more than one site. Using the input-output formalism and scattering matrix theory we determine a general form for the single and two-photon S-matrices for a waveguide coupled to a two-level system. We also explain how to engineer a quantum optical Fanoresonance waveguide geometry and calculate how this modifies the S-matrices, the few-photon scattering probabilities, and the scattered output spectra. We show that the nonlinear effects in such a system generates highly correlated directional scattering probabilities. We device a protocol that can generate maximal entanglement between two spectrally distinct solid-state emitters by the use of multi-photon scattering. The results also reveal a rich structure for multi-photon states interacting with non-identical emitters. As a final investigation, we quantify how spectral diffusion in quantum dots affects finite-width single and two-photon scattering. Single-photon scattering probabilities are described by a simple convolution but this is not the case for a two-photon state scattering off a two-level emitter. We show that the effect of spectral wandering depletes the nonlinear scattering properties, but that it affects co and counter-propagating output probabilities differently.
Optical emitters strongly coupled to photons propagating in one-dimensional waveguides are a promising platform for optical quantum information processing. Here, we present a theoretical study of the scattering of two indistinguishable photons on a single two-level atom in a Hong-Ou-Mandel setup. By computing the dynamics, we can describe the system at any time of the scattering event. This allows us to highlight the one-to-one correspondence between the saturation of the atom and the effective interaction induced between the photons. Furthermore, we discuss the integrability of the atomic beam splitter and provide an intuitive picture for the correlations observed between the outgoing photons.
In this dissertation, we shall focus on theoretically studying quantum nonlinear optical schemes to construct a conditional phase gate at the single-photon level. With an aim to develop analytical models, we shall carry out a rigorous quantized multimode field analysis of some of these schemes involving only the interacting field operators. More specifically, we shall first study the three-wave mixing process involving two single-photons in a second-order nonlinear medium (x(2)) under two different cases viz. when the photons are traveling with equal velocities and when they are traveling with different velocities, and explore the possibility of using them for building a conditional phase phase gate. Finally, we shall study the interaction of single-photon wavepackets with a realistic atomic system viz. an ensemble of five-level atoms, to construct a phase gate. We will particularly look at the "giant Kerr" effect in electromagnetically induced transparency to explore the possibility of using this scheme for achieving a conditional phase shift and to understand how the bandwidth gets restricted naturally in such an atomic system.
Mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons enables the realization of optical nonlinearities which can modify light on the level of individual photons.This novel approach forms the basis of a growing Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional π-phase shifts.This thesis reports on two experiments investigating strong photon-photon interactions mediated by Rydberg interactions.First, applying a ladder-type EIT scheme to Rydberg atoms in D-states with high principal quantum number results in the Rydberg interaction mediated nonlinearity accompanied by a time-dependent decay of transmission of probe light through the medium.In a joint experimental and theoretical analysis, this effect is attributed to the dephasing of propagating polaritons into stationary Rydberg excitations caused by the state mixing interaction occurring with Rydberg D-state atoms.Second, via a two-photon Raman excitation scheme Rydberg atoms are efficiently excited in a small atomic cloud.As the size of the Rydberg blockade exceeds the dimension of the medium, only a single Rydberg excitation can be present at a time.By fast engineered dephasing this Rydberg excitation is decoupled from the light field.Measurement of the transmitted light and the amount of excited Rydberg atoms gives evidence for the realization of a deterministic single-photon absorber.
In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices, it is crucial to fully understand the non-equilibrium dynamics of strongly interacting photons. Employing both numerical and analytical approaches we map out the full scattering dynamics for two photons scattering on a two-level emitter in a one-dimensional waveguide. The strongest non-linear interaction arise when the emitter is excited the most, which occurs for incoming photon pulses with a spectral bandwidth comparable to the emitter linewidth. For two identical, counter-propagating photons, the emitter works as a non-linear beam splitter, as the emitter induces strong directional correlations between the scattered photons. Even though the non-linearity also alters the pulse spectrum due to a four-wave mixing process, we demonstrate that input pulses with a Gaussian spectrum can be mapped to the output with up to 80 % fidelity. Using two identical two-level emitters, we propose a setup for a deterministic controlled-phase gate, which preserves the properties of the two incoming photons with almost 80 %, limited by spectral changes induced by the non-linearity and phase modulations upon scattering. Another setup for a controlled-phase operation is suggested with two coupled ring resonators exploiting a strong second-order material non-linearity. By dynamically trapping the first of two temporally separated photons in the non-linear resonator, the scattering of the second photon is altered. Due to the trapping, the undesired aforementioned non-linear effects are avoided, but the gate performance is now limited by the capturing process. Semiconductor quantum dots (QDs) are promising for realizing few-photon non-linearities in solid-state implementations, although coupling to phonon modes in the surrounding lattice have significant influence on the dynamics. By accounting for the commonly neglected asymmetry between the electron and hole wavefunction in the QD, we show how the phonon-assisted transition rate to a slightly detuned optical mode may be suppressed. This is achieved by properly matching the electrical carrier confinement with the deformation potential interaction, where the suppression only occurs in materials where the deformation potential interaction shifts the electron and hole bands in the same direction. We demonstrate also how the phonon-induced effects may be altered by placing the QD inside an infinite slab, where the confinement of the phonons is modified instead. For a slab thickness below ∼ 70 nm, the bulk description of the phonon modes may be insufficient. The QD decay rate may be strongly increased or decreased, depending on how the detuning between the QD and the optical mode matches the phonon modes in the slab.