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Concept# Quantum

Summary

In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.
For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and descr

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'Albert Einstein' (ˈaɪnstaɪn ; ˈalbɛʁt ˈʔaɪnʃtaɪn; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely held to be one of the great

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PHYS-207(a): General physics : quanta

Ce cours est une introduction à la mécanique quantique. En partant de son développement historique, le cours traite les notions de complémentarité quantique et le principe d'incertitude, le processus de mesure, l'équation de Schrödinger, ainsi que des éléments de physique atomique et moléculaire.

CS-308: Quantum computation

The course introduces teh paradigm of quantum computation in an axiomatic way. We introduce the notion of quantum bit, gates, circuits and we treat the most important quantum algorithms. We also touch upon error correcting codes. This course is independent of COM-309.

PHYS-426: Quantum physics IV

Introduction to the path integral formulation of quantum mechanics. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented, including non-perturbative effects, such as tunneling and instantons.

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We study causality in gravitational systems beyond the classical limit. Using on-shell methods, we consider the 1-loop corrections from charged particles to the photon energy-momentum tensor - the self-stress - that controls the quantum interaction between two on-shell photons and one off-shell graviton. The self-stress determines in turn the phase shift and time delay in the scattering of photons against a spectator particle of any spin in the eikonal regime. We show that the sign of the beta-function associated to the running gauge coupling is related to the sign of time delay at small impact parameter. Our results show that, at first post-Minkowskian order, asymptotic causality, where the time delay experienced by any particle must be positive, is respected quantum mechanically. Contrasted with asymptotic causality, we explore a local notion of causality, where the time delay is longer than the one of gravitons, which is seemingly violated by quantum effects.

2022The exceptional performance of self-assembled Quantum Dot (QD) materials renders them extremely appealing for their use as optical communications devices. As lasers, they feature reduced and temperature independent threshold current and proper emission wavelength at the fiber telecommunication windows. These characteristics, together with the low linewidth enhancement factor and broad spectrum, make QD materials extremely attractive for application as light emitters or amplifiers. There exist, nevertheless, several unclear issues which prevent QDs from conquering the new generation of optoelectronic devices. Their differential efficiency is lower than expected. The output power of QD lasers is lower than that of their quantum well counterpart. Still, it is their dynamics which has incited the majority of studies. The modulation bandwidth of these devices seems to be limited by the relaxation of carriers from the upper energetic layers to the low levels within the dot. Besides, the electron-hole interaction is widely unknown, the extent of the electron-hole Coulombic attraction is not yet established. Throughout this thesis I present a theoretical and experimental study of the gain and phase dynamics of quantum dot lasers. I explain the appearance of different decay times observed in pump and probe experiments in QD amplifiers as a result of the different electron and hole relaxation times, by means of an electron-hole rate-equation model. The ultrafast hole relaxation first leads to an ultrafast recovery of the gain, which is then followed by electron relaxation and, on the nanosecond timescale, radiative and non-radiative recombinations. The phase dynamics is slower and is affected by thermal redistribution of carriers within the dot. Our results corroborate with spectral measurements of the dephasing and gain in QD amplifiers. Additionally, our work is compared with existing pump and probe results. Exploiting the capacity of QD lasers to emit at two different wavelengths corresponding to the ground state (GS) and excited state (ES), I present a theoretical study of the QD dynamics, based on a linearization of the QD rate-equations. The results predict the existence of single oscillation frequency of GS and ES, meaning that both states are highly coupled. In order to verify our theory, we perform two kinds of experiments. By modulating these lasers at high frequency, we measure separately the dynamics of GS and ES. However, in contradiction to our theory, two different modulation frequencies are found. Additional temporally-resolved measurements of the laser dynamics reveal a surprising effect. By injecting a sub-bandgap pump in an InAs/InGaAs QD laser, the emitted photons are depleted. Through additional transmission and photocurrent measurements, we relate this observation with carrier photoexcitation, which was so far only theoretically addressed. The role of carrier photoexcitation in our experimental laser dynamics is further supported by a rate-equation model. Impelled by this finding, we study the effect of carrier photoexcitation in the static and dynamic characteristics. We find that carrier photoexcitation reduces the efficiency of QD lasers, which is one of the major QD handicaps, and depletes the GS lasing after the ES threshold, as observed experimentally. Moreover, by adding carrier photoexcitation to our linearization of the rate-equations, we find that the theory predicts the appearance of two lasing resonance frequencies, in agreement with our previous experimental results. Additionally, we deal with the improvement of carrier relaxation. In tunnel injection devices, carriers are given an additional path towards the ground state of the dot by growing a quantum well layer close to the QD active plane. Through the quantum-mechanical tunneling effect, carriers relax from the nearby quantum well layer to the QDs, which speeds up relaxation. We aim at the increase of the modulation bandwidth while keeping the good performances quantum dot lasers have exhibited, such as low and temperature insensitive threshold current and proper emission wavelength. In the final part of this work, we present dynamical measurements of 1.5 µm InAs/InP tunnel injection and non-tunnel injection QD lasers, which display remarkable static characteristics. After proving with static measurements that tunnel injection is actually taking place in these structures, we show several dynamic measurements. Pump and probe measurements on QD devices show that the tunnel injection samples exhibit a slightly faster relaxation time than the non-tunnel injection samples used as reference, meaning that relaxation time is improved with tunnel injection. However, by probing the device with an ultrafast pump no improvement of the dynamic characteristics is observed. These results confirm that the laser dynamic properties of InP QD lasers, both standard and tunnel-injection designs, are actually not limited by relaxation of carriers. We point towards the size distribution of these quantum dash-like structures as the limiting factor of the modulation frequency.

Several applications are pushing the development of high performance mode-locked lasers: generation of short pulses for extremely high bit rate transmission at 100 Gb/s and beyond, all-optical clock recovery at 40 Gb/s and beyond, generation of millimeter wave signals through mode-beating on a high speed photodiode, optical sampling for analog-to-digital conversion, and generation of wavelength-division-multiplexing channels. This paper will report on new advances in InP-based quantum dash mode-locked lasers, which largely surpass the performance of their bulk or quantum well counterparts in terms of the mode-beating spectral purity and the bandwidth of optical spectrum. In particular, we will describe the quantum dash nanostructures used for the mode-locked lasers and the dependence of the mode-locking properties on detailed quantum dash structures. We will demonstrate that these quantum dash lasers can be actively mode-locked, generating sub-picosecond or picosecond pulses at different repetition frequencies with extremely low timing jitter. They can also be used to achieve all-optical clock recovery, with timing jitter compliant with International Telecommunication Union (ITU) standards even for highly degraded input optical signal-to-noise ratio. Finally, we demonstrate that, owing to the very wide and flat optical spectrum and the low relative-intensity noise level of the mode-locked laser, error-free transmission over 50 km single mode fiber has been achieved for eight wavelength division multiplexing ITU channels at 10 Gb/s with a channel spacing of 100 GHz. (C) 2009 Alcatel-Lucent.

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