Lecture

Quantum Transport: Scattering Matrix Approach

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In course

PHYS-744: Advanced Topics in Quantum Sciences and Technologies

This course provides an in-depth treatment of the latest experimental and theoretical topics in quantum sciences and technologies, including for example quantum sensing, quantum optics, cold atoms, theory of quantum measurements and open dissipative quantu ...

Description

This lecture covers the scattering matrix approach to quantum transport, focusing on the conductance distribution and reflection probability. The instructor explains the concept of conductance in terms of scattering matrices and transmission probabilities, highlighting the difference between right-moving and left-moving electrons. The lecture delves into the expression of electrical current in terms of kinetic energy and the Dirac distribution. It also discusses the quantum of conductance and resistance, emphasizing the work of R. Landauer. The presentation concludes with a detailed analysis of the conservation laws and unitarity in quantum transport.

Instructors (5)

Mayeul Sylvain Chipaux

Zoë Holmes

Teaching & PhD PhD Students Ricard Puig, Sacha Lerch, Reyhaneh Aghaei Saem, Shao Hen Chiew, Weijie Xiong, Marc Sanz Drudis, Mehrad Sahebi, Manuel Rudolph Courses Quantum information theory PHYS-550 After recapping the basics of quantum theory from an informationtheoretic perspective, we will cover more advanced topics inquantum information theory. This includes introducing measures of quantum information, and developing a more advanced understanding quantum states, channels and measurement

Vincenzo Savona

Vincenzo Savona studied physics in Pisa at the Scuola Normale Superiore and the University of Pisa, prior to completing his PhD at the EPFL's Institute of Theoretical Physics. Subsequently he did post-doctoral work, first at the EPFL and then in the physics department of the Humboldt University of Berlin. In 2002, he returned to the EPFL to create his own research group, receiving a "professeur boursier" fellowship from the Swiss National Science Foundation. In 2006, he was appointed tenure-track assistant professor at the EPFL and joined the NCCR for Quantum Photonics. In 2010 he was appointed associate professor. Currently he directs the Laboratory of Theoretical Physics of Nanosystems.

Jean-Philippe Brantut

I did my PhD at the Institut d'Optique under the direction of Philippe Bouyer and Alain Aspect, before moving to ETHZ in the group of Tilman Esslinger, first as a post-doc then as a senior scientist. There I developed in particular the method allowing for a quantum simulation of nano-electronic devices with ultracold quantum gases.Since september 2016, I hold the Fondation Sandoz chair in physics of quantum gases at EPFL. There, my group has developed the first cold atoms machine combining Fermi gases with cavity-quantum electrodynamics. We use it to explore new ways of measuring and manipulating quantum matter.

Christophe Marcel Georges Galland

I studied at Ecole Polytechnique in Paris (X2003) and received my PhD in 2010 from ETH Zürich for a thesis in solid-state quantum optics with individual carbon nanotubes, in the Quantum Photonics Group of Prof. Ataç Imamoglu. As a postdoctoral researcher at Los Alamos National Lab (USA) I studied the photophysics of individual nanocrystal quantum dots in the groups of Victor Klimov and Han Htoon. I was investigating the mechanisms responsible for fluorescence fluctuations and how to control them. I then moved to the University of Delaware in the group of Michael Hochberg to work in the emerging field of integrated quantum optics. I was leading international projects such as the realisation of an on-chip source of quantum correlated photons integrating optical filters and demultiplexers. From 2013 to 2016, I was working at EPFL in the group of Prof. Kippenberg in the field of quantum optomechanics with an Ambizione Fellowship of the Swiss National Science Foundation (SNSF). My work focused on the creation of non-classical vibrational states of mesoscopic oscillators and on the amplification of vibrations in molecules. Since May 2017, I am leading the Laboratory of Quantum and Nano-Optics at EPFL as an SNSF-funded professor in the Institute of Physics. My team investigates two main phenomena: (i) the vibrational dynamics of molecules embedded in nanoscale plasmonic cavities, and (ii) non-classical correlations mediated by individual quanta of crystal vibrations at room-temperature. We employ state-of-the-art spectroscopic tools such as femtosecond lasers and single-photon counters to get new insights into sub-nanometer scale dynamics.

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Related concepts (32)

Quantum dot

Quantum dots (QDs) – also called semiconductor nanocrystals, are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology and materials science. When the quantum dots are illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conductance band.

Dirac delta function

In mathematical physics, the Dirac delta distribution (δ distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., ) to its value at zero of its domain (), or as the weak limit of a sequence of bump functions (e.g.

Quantum wire

In mesoscopic physics, a quantum wire is an electrically conducting wire in which quantum effects influence the transport properties. Usually such effects appear in the dimension of nanometers, so they are also referred to as nanowires. If the diameter of a wire is sufficiently small, electrons will experience quantum confinement in the transverse direction. As a result, their transverse energy will be limited to a series of discrete values.

Distribution (mathematics)

Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions (weak solutions) than classical solutions, or where appropriate classical solutions may not exist.

Probability current

In quantum mechanics, the probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability. Specifically, if one thinks of probability as a heterogeneous fluid, then the probability current is the rate of flow of this fluid. It is a real vector that changes with space and time. Probability currents are analogous to mass currents in hydrodynamics and electric currents in electromagnetism. As in those fields, the probability current (i.e.

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