TOPO OPOLOGICA OGICAL L DR DRIVING IVING FIEL FIELDS DS Dr. - PowerPoint PPT Presentation

SPIN SPIN RES RESON ONANCE ANCE UNDER UNDER TOPO OPOLOGICA OGICAL L DR DRIVING IVING FIEL FIELDS DS Dr. Andrés Reynoso LABORATORY OF PHOTONICS AND OPTO-ELECTRONICS (LPO) Centro Atomico Bariloche ARGENTINA San Carlos de Bariloche, Argentina, (photo taken by S. Cutts) reynos eynoso@ca o@cab.cnea.go b.cnea.gov.ar .ar

Background and credits I Motivation: Geometrical phases in Rashba rings II Proposal: Driven two-level system (TLS) Summary

BACK CKGR GROUN OUND D AND AND CR CRED EDITS ITS Copenhagen Sydney Bariloche

BACK CKGR GROUN OUND D AND AND CR CRED EDITS ITS Copenhagen Bariloche PhD 2009 Instituto Balseiro Centro Atomico Bariloche Spin orbit coupling (SOC) in 2D semiconductors Anomalous Josephson effect due to interplay between SOC and magnetic fields People Syndey Bariloche Bariloche: Carlos Balseiro, Gonzalo Usaj, Grenoble: Denis Feinberg, Michel Avignon

BACK CKGR GROUN OUND D AND AND CR CRED EDITS ITS Copenhagen Copenhagen Postdoc 2009-2011 Niels Bohr International Academy Double quantum dots in carbon nanotubes, interplay hyperfine, external and SOC fields with valley physics Anomalous Josephson effect due to interplay between SOC and magnetic fields Syndey Bariloche People Copenhagen: Karsten Flensberg,

BACK CKGR GROUN OUND D AND AND CR CRED EDITS ITS Sydney Postdoc 2011-2014 Quantum group – The Univ. of Sydney Copenhagen Floquet systems, closed & open Topological Superconductors interplay between SOC and magnetic fields. Majora Fermions People Sydney: Andrew Doherty, Sevilla: Diego Frustaglia Sydney Bariloche

BACK CKGR GROUND OUND AND AND CRE CREDITS DITS Copenhagen Bariloche now! CONICET research position. Lab of Photonics and Opto-electronics (LPO) Centro Atómico Bariloche -New lines @ Theory for our Lab’s experiments , For example cavity optomechanics, Raman spectroscopy, Applied plasmonics, Quantum cascade devices for infared, etc. Floquet systems, SOC interplay with magnetic fields and superconductivity, topological effects. People Syndey Bariloche Bariloche: Alex Fainstein, Axel Bruchhausen, M.L.Pedano, G. Rozas; Sevilla: Diego Frustaglia , JP Baltanás; Paris: Quantronics, Leandro Tosi, Cristian Urbina; Japan: Henri Saarikoski, Junsaku Nitta, Oxford: S. Poncé, F. Giustino

BACK CKGR GROUN OUND D AND AND CR CRED EDITS ITS Copenhagen Bariloche now! CONICET research position. Lab of Photonics and Opto-electronics (LPO) Centro Atómico Bariloche -New lines @ Theory for our Lab’s experiments , For example cavity optomechanics, Raman spectroscopy, Applied plasmonics, Quantum cascade devices for infared, etc. Floquet systems, SOC interplay with magnetic fields and superconductivity, topological effects. People Syndey Bariloche Bariloche: Alex Fainstein, Axel Bruchhausen, An example of the M.L.Pedano, G. Rozas; Sevilla: Diego Frustaglia LPO research , JP Baltanás; Paris: Quantronics, Leandro Tosi, Cristian Urbina; Japan: Henri Saarikoski, Junsaku Nitta, Oxford: S. Poncé, F. Giustino

BACK CKGR GROUN OUND D AND AND CR CRED EDITS ITS Copenhagen Sydney Bariloche

Background and credits I Motivation: Geometrical phases in Rashba rings II Proposal: Driven two-level system (TLS) Summary

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS 2 Di 2 Dimen mension sional E al Electr lectron on Gase Gases (2DEGs) s (2DEGs)

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS Rash Rashba ba spin spin-orb orbit co it coup upli ling ng (RSOC (RSOC)     H .[ V r ( ) p ] SO 2 2 2 m c Relativistic effect      H ( p p ) SO y x x y Rashba E. I., Sov. Phys. Solid State, 2 1109 (1960). It can be modified with  gate voltages 0.51 meV nm GaAs/AlGaAs Nitta et al . PRL 78 (1997) 510 meV nm InSb/InAlSb Miller et al PRL 90 076807 (2003)

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS Free ee spa space ce solution f solution for or the the R RSOC SOC Hamil Hamilton tonian ian Spin is  to the k-vector Fermi surface

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS The he RSOC RSOC Ring Ring

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS The he RSOC RSOC Ring Ring + + a comp a competing eting inplan inplane e fi field. eld. GO GOAL: AL: Stu Study dy the the effec ef ect of t of c cha hang nging ing the the topo topolog logy y of of th the e driving driving

I MOTIVATION: GEOMETRICAL PHASES IN RASHBA RINGS The he RSOC RSOC Ring Ring + + a comp a competing eting inplan inplane e fi field. eld.

Background and credits I Motivation: Geometrical phases in Rashba rings II Proposal: Driven two-level system (TLS) Summary

II PROPOSAL: DRIVEN TWO-LEVEL SYSTEM (TLS)

II PROPOSAL: DRIVEN TWO-LEVEL SYSTEM (TLS) 1- Schroedinger equation 2- Floquet quasi-energy state (FQE) 3- Equation for the FQE Fourier expansion for H and the FQEs in order to solve (3)

II PROPOSAL: DRIVEN TWO-LEVEL SYSTEM (TLS) We know TOTAL PHASE @ period T = DYNAMIC PHASE @ period T + GEOMETRICAL PHASE @ period T Exact evolution of a FQE Quasi-energy phase times T  From this we directly get TOTAL PHASE @ period T Mean energy @ period T of a FQS  From this we directly get DYNAMIC PHASE @ period T

II PROPOSAL: DRIVEN TWO-LEVEL SYSTEM (TLS)

II PROPOSAL: DRIVEN TWO-LEVEL SYSTEM (TLS)

II PROPOSAL: DRIVEN TWO-LEVEL SYSTEM (TLS)

II PROPOSAL: DRIVEN TWO-LEVEL SYSTEM (TLS)

II PROPOSAL: DRIVEN TWO-LEVEL SYSTEM (TLS)

Background and credits I Motivation: Geometrical phases in Rashba rings II Proposal: Driven two-level system (TLS) Summary

SUMMARY

SUMMARY