# Winter School on Physics of Small Quantum Systems: Thermal and Topological Phenomena

### 12-16 January 2015

Was organized jointly between the Department of Physics, University of Jyväskylä, and O.V. Lounasmaa Laboratory/Department of Applied Physics, Aalto University. The school took place in the hotel Gustevelund, next to the Tuusula lake, in a region with a rich cultural heritage.

### Topics

- Quantum thermodynamics
- Optomechanics
- Topological superconductors
- Thermal effects in ultracold atom systems
- Fast (radio frequency) measurements

The winter school will focus on the physics of small quantum systems, where thermal and quantum fluctuations affect the dynamics in a significant manner, or where the topological properties of the bulk materials show up as robust and non-trivial surface characteristics. The school will aim to make the connection between the recent theoretical and experimental advances in these fields, bridging many different experimental settings together, ranging from electrical circuits to vibrating wires and to ultracold atom systems.

Exercises - solutions (Brouwer) (Grenier) (Sagawa) (Xuereb) (Sillanpää)

### Slides

Piet Brouwer: Topological superconductors

Charles Grenier 1st lecture, 2nd lecture, 3rd lecture

Takahiro Sagawa: 1st lecture, 2nd lecture, 3rd lecture

André Xuereb: 1st lecture, 2nd lecture, 3rd lecture

Mika Sillanpää: 1st lecture, 2nd lecture

### Lecturers (click on the titles to see the abstracts)

- Piet Brouwer, Freie Universität Berlin:
*Topological superconductors*

Superconductors may be in a nontrivial topological state, in which there are Majorana states at the sample edges or bound to vortices. The simplest topologically nontrivial superconductor is the one-dimensional spinless p-wave superconductor, which has a zero energy Majorana

bound state at each end. Although no known materials are spinless p-wave superconductors, such a system can be realized in principle in spin-orbit coupled nanowires with proximity-induced pairing from a nearby s-wave superconductor. In the three lectures, I plan to discuss the following topics:

* Quick review of BCS mean-field theory of superconductivity

* Spinless p-wave superconductors in one dimension

* Resonant Andreev reflection off Majorana states

* 4 pi Josephson effect

* Symmetry classes D and BDI

* Proposed experimental realizations

* Multichannel wires

* Braiding of Majorana bound states

* Disorder effects - Charles Grenier, ETH Zürich (replaces Corinna Kollath, University of Bonn):
*Thermal effects in ultracold atom systems*- Introduction to ultracold atom gases
- Shaping potentials
- Thermometry, temperature, and entropy
- Thermoelectric effects and their experimental realizations

- Takahiro Sagawa, University of Tokyo:
*Quantum thermodynamics*

- Second law of thermodynamics

- Fluctuation theorems, classical and quantum

- Role of information in thermodynamics

- Paradox of Maxwell daemons

- Experimental realizations - Mika Sillanpää, Aalto University:
*Fast measurements*- Distributed impedance model, transmission line
- Input impedance of transmission line
- Transmission line resonators
- Microwave techniques in practice: network analyzer, spectrum analyzer, cables, connectors, attenuators, circulators, cryogenics.

- André Xuereb, University of Malta:
*Optomechanics*

Optomechanical systems, which deal with the interaction between moving objects and an electromagnetic field, have been attracting much attention over the past couple of decades. Apart from their more practical applications (such as in sensing displacement), they have been proposed as testing grounds for quantum thermodynamics, and for observing departures from quantum mechanics at the mesoscale.

In this set of lectures, I will take you through a tour of the current status of the field, with a focus on its theoretical underpinnings. I will first briefly introduce the theoretical apparatus involved in describing the dynamics of optomechanical systems. I will then discuss the physical implications of the optomechanical interaction, and demonstrate how one can use it to cool the motional degree of freedom, entangle it with the light field, etc. Finally, I will introduce the concept of multi-mode optomechanics and explain the new directions that it makes possible.

Contents (very tentative):- Describing the dynamics of an optomechanical system

- Basic ideas: Radiation pressure

- Links to cold atoms

- Introduction to the Hamiltonian

- Opening the system: Cavity losses and dissipation - Physical implications of the interaction between light and motion

- The various parameter regimes of optomechanics

- Weak coupling: Optomechanical cooling and entanglement

- Strong coupling: Non-Gaussian states and the optomechanical blockade

- Quadratic coupling: QND measurements - Exercises
- The road ahead

- Multimode optomechanics: A run-through

- Quantum thermodynamics with optomechanics

- Testing quantum mechanics with optomechanics

- Describing the dynamics of an optomechanical system

Organizers

- Tero Heikkilä, University of Jyväskylä
- Francesco Massel, University of Jyväskylä
- Teemu Ojanen, Aalto University
- Jukka Pekola, Aalto University
- Mika Sillanpää, Aalto University
- Tapio Ala-Nissilä, Aalto University

For further information of the school, contact qutschool2015 at jyu.fi.

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