Bloch sphere | EPFL Graph Search

In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch. Quantum mechanics is mathematically formulated in Hilbert space or projective Hilbert space. The pure states of a quantum system correspond to the one-dimensional subspaces of the corresponding Hilbert space (and the "points" of the projective Hilbert space). For a two-dimensional Hilbert space, the space of all such states is the complex projective line \mathbb{CP}^1. This is the Bloch sphere, which can be mapped to the Riemann sphere. The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors |0\rangle and |1\rangle, respectively, which in turn might correspond e.g. to the sp

Coherent oscillations between orbital angular momentum polariton states in an elliptic resonator

Benoît Marie Joseph Deveaud, François Morier-Genoud, Gaël Nardin, Barbara Pietka

We optically excited the eigenmodes of an elliptic resonator in a semiconductor microcavity. Using a pulsed excitation, we created a superposition of eigenmodes, and imaged the temporal evolution of the coherent emission pattern. A semiconductor quantum well was embedded in the microcavity structure. The system was operated in the strong light matter coupling regime, where the eigenmodes are hybrid half-photonic half-excitonic quasiparticles called exciton polaritons. Oscillations between orbital angular momentum states (or vortex states) were observed, and turned out to be remarkably well described within the Poincaré sphere representation.

2011

Mesoscopic magnetic systems: From fundamental properties to devices

Dirk Grundler

Research into mesoscopic magnetic systems, which incorporate magnetic elements with dimensions ranging from a few nm up to a few 10s of micrometer, has been spurred on by the developments in their fabrication, characterisation, and control. Electron beam and optical lithography are key methods for their fabrication because they can be used to create tailor- made planar arrangements of elements or more complex layered structures. These can be further transformed into high quality three-dimensional mesoscale architectures using strain engineering based origami approaches. Further methods include fabrication of magnetic nano- and micro-objects on curved templates prepared using ion beam erosion techniques or via self-assembly of non-magnetic particles, which does not require expensive equipment. In addition, direct write methods such as focused electron or ion beam induced deposition, along with two photon laser lithography, provide a means to create geometrically curved and three dimensional structures. The characterisation of the magnetic states can be performed with electrical measurements or using various magnetic microscopy, tomography, and scattering methods. These characterisation methods can then be used to observe the behaviour of complex magnetic textures including magnetic domain walls, vortices, Bloch points, and skyrmions. The control of the magnetic states, which is important for applications, can be achieved with a variety of external stimuli including magnetic or electric fields, spin currents, strain, photons and heat. This results in magnetization dynamics that can happen at timescales ranging from minutes down to less than a picosecond. Mesoscopic magnetic systems and their magnetic configurations are therefore not only of fundamental interest, but have the potential to be implemented in a wide range of device applications including ferro-, ferri- and antiferromagnetic spintronics, computation, magnonics, mechanically flexible and printable human-machine interfaces, electromobility, and medical applications including small-scale machinery. This Special Topic on mesoscopic magnetic systems includes, but is not restricted to, articles in the areas of current interest outlined below, which include experiments, theory and simulations in this fascinating field. We hope to have captured the variety of exciting areas in this Special Topic and that this will provide inspiration for the future, either in terms of fundamental science and discovery, or for more applied work to create novel devices.

2021

Mesoscopic magnetic systems: From fundamental properties to devices

Dirk Grundler

2021