Finite quantum systems - from semiconductor quantum dots and wires to ultra-cold atomic quantum gases

Stephanie Reimann and Andreas Wacker, Lund University, Sweden

Abstract:

Finite quantum systems from semiconductor quantum dots and wires to ultra-cold atomic quantum gases (S.M. Reimann and A. Wacker, Lund University, Sweden).

Experimental methods in quantum optics as well as semiconductor physics have made it possible to create quantum-confined droplets of fermions or bosons [1,2]. These artificial many-body systems can nowadays be manipulated with unprecedented control down to the single-electron or single-atom level [3,4]. Despite the close connection between cold and ultra-cold atomic gases and electrons in nanostructured quantum systems, research efforts in these fields have advanced mostly independently of each other. The lectures will highlight the many similarities between these a priori rather different quantum systems where the quantum many-body properties lead to complex and sometimes unexpected phenomena. The first part of the lectures will discuss the many-particle properties of finite quantum systems (days 1-3, lectured by S.M. Reimann), while the second half (days 4-5, lectured by A. Wacker) will give an overview to quantum transport through finite systems such as quantum dots or wires. A short introduction to the physics of semiconductor nanostructures and the electronic structure of quantum dots and quantum wires will be given, where electron-electron interactions dominate the transport properties. Concepts such as shell structure and Hund's rules, as well as Wigner-localization in strongly-correlated systems, will be dicussed. A brief overview of the different computational techniques for finite quantal systems, ranging from configuration-interaction calculations to the density functional approach, and the Gross- Pitaevskii method for bosons, will be given. A very interesting quantum phenomenon is the formation of vortices in a Bose-Einstein condensate that is brought to rotation (see picture). We will take this example to discuss the suprising similarities between boson-and fermion systsems confined in a harmonic trap [2]. We further discuss the quantum-gas analogue of a quantum wire, where one can study a similar scenario for the quantum transport [5,6]: Attractive interactions may lead to a complete suppression of current in the low-bias range, a total current blockade. We demonstrate this effect for the example of ultracold quantum gases with dipolar interactions. The lectures will close with a brief summary and an outlook on future "atomtronics" systems [7,8] at the borderline between semiconductor physics and quantum optics, also considering thermal transport [9,10].

Overview on the themes of the lectures: Quantum dot "artificial atoms" and semiconductor nanowrires, Shell structure in finite-fermion systems, Many-body quantum physics of finite fermion and boson systems-from Hund's rules, to Wigner crystals, Electronic-structure calculations for nanostructures, Exact approaches-from configuration-interaction calculations to quantum Monte Carlo, Density-functional theory, Quantum-Hall physics in small fermion droplets, Vortices in rotating atomic condensates, Concepts to treat transport through interacting systems, Relevance of coherence for transport through small systems, Thermoelectric transport and its atomic analogies.

References and Reading Material:

[1] S.M. Reimann and M. Manninen, "Electronic structure of quantum dots", Rev. Mod. Phys. 74, 1283-1342 (2002).
[2] H. Sarrikoski, S.M. Reimann, A. Harju and M. Manninen, "Vortices in quantum droplets: Analogies between boson and fermion systems", Rev. Mod. Phys. 82, 2785 (2010)
[3] F. Serwane, G. Zurn, T. Lompe, T.B. Ottenstein, A.N. Wenz, and S. Jochim, "Deterministic Preparation of a Tunable Few-Fermion System", Science 332, 6027 (2011)
[4] G. Zurn, A.N. Wenz, S. Murmann, A. Bergschneider, T. Lompe and S. Jochim, "Pairing in Few- Fermion Systems with Attractive Interactions", Phys. Rev. Lett. 111, 175302 (2013)
[5] L.H. Kristinsdottir, O. Karlstrom, J. Bjerlin, J.C. Cremon, P. Schlagheck, A. Wacker and S.M. Reimann, "Total Current Blockade in an Ultracold Dipolar Quantum Wire", Phys. Rev. Lett. 110, 085303 (2013).
[6] L.H. Kristinsdottir, J.C. Cremon, H.A. Nilsson, H.Q. Xu, L. Smauleson, H. Linke, A. Wacker, and S.M. Reimann, "Signatures of Wigner localization in epitaxially grown nanowires", Phys. Rev. B 83, 041101 (2011).
[7] R.A. Pepino, J. Cooper, D.Z. Anderson and M.J. Holland, "Atomtronic Circuits of Diodes and Transistors", Phys. Rev. Lett. 103, 140405 (2009).
[8] S. Krinner, D. Stadler, D. Husmann, J.P. Brantut, and T. Esslinger , "Observation of quantized conductance in neutral matter", Nature 517, 7532 (2015).
[9] O. Karlstrom, H. Linke, G. Karlstrom, and A. Wacker, "Increasing thermoelectric performance using coherent transport", Phys. Rev. B 84, 113415 (2011)
[10] J.P. Brantut, C. Grenier, J. Meineke, D. Stadler, S. Krinner, C. Kollath, T. Esslinger, and A. Georges, "A Thermoelectric Heat Engine with Ultracold Atoms", Science 342, 6159 (2013)