Quantum superposition | EPFL Graph Search

Quantum superposition is a fundamental principle of quantum mechanics. In classical mechanics, things like position or momentum are always well-defined. We may not know what they are at any given time, but that is an issue of our understanding and not the physical system. In quantum mechanics, a particle can be in a superposition of different states. However, a measurement always finds it in one state, but before and after the measurement, it interacts in ways that can only be explained by having a superposition of different states. Mathematically, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; conversely, every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation: since the Schrödinger equation is linear, any linear combination of solutions will also be a solutio

Rencontre verticale: toit sur rue, rue sur toit. Superposition, densification et mixité aux Grottes, Genève

Steven Beuc

Le contexte actuel de densification des villes pousse à la recherche de nouvelles formes urbanistiques, architecturales et sociales. A Genève bourgeonnent des surélévations, opérations ponctuelles, constructions spontanées d'un nouveau niveau urbain. Le projet vise à penser la surélévation comme une opération d'ensemble. La superposition d'un nouvel étage à la ville qui ne renierait pas le sol, mais lui offrirait une extension spatiale, enrichissant l'existant par le nouveau. Le quartier des Grottes à Genève, fort de son histoire alternative et appropriative est le terreau de cette mutation urbanistique. Le quartier se présente en son sein comme une petite urbanité, protégée par des fronts marqués de la grande urbanité genevoise. L'extension de la gare Cornavin rapprochera ces deux mondes. Le projet réagit à cette proximité à venir. Deux impulsions naissent dans le tissu hétérogène du quartier et mettent en tension l'espace public de la rue des Grottes. Elles proposent en deux places une escalade de son air, de ses programmes et de ses gens vers un nouvel étage de relation, de rencontre, de vie en communauté. De cette mutation urbanistique naît un hybride architectural qui s'étend de bâtiment à bâtiment, d'îlot à îlot, et de la toiture à la rue. Entre surélévation et franchissement, il tisse des liens autant physiques que sociaux et climatiques. Un monde particulier, un “vivre ensemble” qui lie l'habitat au programme public par l'atelier, le toit au sol par l'espace social.

2013

Unconventional quantum ordered and disordered states in the highly frustrated spin-1/2 Ising-Heisenberg model on triangles-in-triangles lattices

Jana Cisárová

The spin-1/2 Ising-Heisenberg model on two geometrically related triangles-in-triangles lattices is exactly solved through the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the effective spin-1/2 Ising model on a triangular lattice. Basic thermodynamic quantities were exactly calculated within this rigorous mapping method along with the ground-state and finite-temperature phase diagrams. Apart from the classical ferromagnetic phase, both investigated models exhibit several unconventional quantum ordered and disordered ground states. A mutual competition between two ferromagnetic interactions of basically different character generically leads to the emergence of a quantum ferromagnetic phase, in which a symmetric quantum superposition of three up-up-down states of the Heisenberg trimers accompanies a perfect alignment of all Ising spins. In the highly frustrated regime, we have either found the disordered quantum paramagnetic phase with a substantial residual entropy or a similar but spontaneously ordered phase with a nontrivial criticality at finite temperatures. The latter quantum ground state exhibits a striking coexistence of imperfect spontaneous order with partial disorder, which is evidenced by a quantum reduction of the spontaneous magnetization of Heisenberg spins that indirectly causes a small reduction of the spontaneous magnetization of otherwise classical Ising spins. DOI: 10.1103/PhysRevB.87.024421

Amer Physical Soc2013

Tailored-Potential Pyramidal Quantum Dot Heterostructures

Valentina Troncale

Semiconductor quantum dots are usually compared to artificial atoms, because their electronic structure consists of discrete energy levels as for natural atoms. These artificial systems are integrated in solid materials and can be localized with a spatial precision of the order of nanometers. Besides, they conserve their quantum properties even at quite high temperatures (∼ 10 K). These properties make quantum dots one of the most suitable systems for the realization of quantum devices and computers. However, the energy states and the optical properties of quantum dots are much more complicated than for atoms, because a quantum dot is never an isolated potential well. Instead, its electronic structure depends on the crystallin structure of the semiconductor material and on the Coulomb ion-electron and electron-electron correlations. In particular, the presence of several valence bands and their mixing, induced by quantum confinement, gives rise to novel properties which are still not completely understood and exploited in applications. To get a major advance in this field, a full deterministic control of the spatial shape of the quantum confinement is needed, combined with a deeper understanding of the connections between electronic and optical properties. This thesis work has these two main objectives. We realized and experimentally studied different quantum dot systems, in pyramidal hetero-structures grown with MOCVD techniques. These systems allowed the realization of several different geometries for the carrier confining potential, with a precision in the order of nanometers. The optical characterization has been obtained in particular by means of polarization-resolved microphotoluminescence, magneto-photoluminescence, excitation photoluminescence (PLE), and interferometry techniques. For single quantum dots, we have observed and characterized for the first time new excitonic complexes, arising from excited hole states. This allowed a full caracterizatioon of the valence band hole states in our peculiar system. By means of photon correlation measurements, we have also experimentally demonstrated that, even in presence of a large family of exciton states, these quantum dot systems can emit single photons. We have then realized much more complex quantum dot structures, double dot systems (quantum dot molecules) and a completely new system called Dot-in-Dot (DiD). This latter is composed by a small inner dot surrounded by an electrostatic potential well (which can be considered as an outer elongated dot). Such a composite system is characterized by a strong valence band mixing. This state superposition is however very sensitive to small variations of the confining potential. Therefore the degree of valence band mixing can be easily switched by the introduction of a week external field. Since the valence band mixing determines the polarization properties of the emitted light, the DiD changes the polarization properties of its emission spectrum under the action of an external field. In particular, we have experimentally demonstrated this effect for an external static magnetic field, while we have numerically predicted a very similar effect for a static electric field. In the latter case, the polarization switching is a direct consequence of the quantum confined Stark effect induced in the DiD. Hence the DiD appears to be an ideal candidate for realizing emitters of single photons with tunable and controllable polarization.

EPFL2010

Tailored-Potential Pyramidal Quantum Dot Heterostructures

Valentina Troncale

EPFL2010