Tunn ing dy amics of boso ic Josephson ju ctions assist d by a - PowerPoint PPT Presentation

Tunn ęł ing dy ń amics of boso ń ic Josephson ju ń ctions assist ę d by a cavity fi e ł d Phys. Rev. A 91, 023601 (2015) Gergely Szirmai, Giovanni Mazzarella, Luca Salasnich Wigner Research Centre, Budapest University of Padova Quantum T echnologies Conference VI, June 26, 2015

BEC inside a double well Interacting Bose gas

BEC inside a double well Interacting Bose gas 2-mode approximation

BEC inside a double well Interacting Bose gas 2-mode approximation Bose-Einstein condensate 4 real parameters, imbalance but only 2 independent relative phase

Bosonic Josephson Junction E ff ective Hamiltonian

Bosonic Josephson Junction E ff ective Hamiltonian Why is it called bosonic Josephson Junction?

Bosonic Josephson Junction E ff ective Hamiltonian Why is it called bosonic Josephson Junction? INSULATOR 1 2 It is a tunneling phenomena of a matter wave, just like in the case of a superconducting Josephson Junction. SUPERCONDUCTOR

Semiclassical dynamics Classical equations of motion

Semiclassical dynamics Classical equations of motion Fixed point classi fi cation of the solutions

BEC + double well + cavity A BEC inside a double well (coherent population transfer double well between the wells) And a cavity outside The cavity fi eld is super- imposed to the double-well potential and a ff ects the atomic tunneling. EM field profile The dynamically changing spatial distribution of the atoms can shift the cavity in and out of resonance. At resonance the photon pumping laser number is hugely enhanced and y the atomic tunneling becomes ampli fi ed. x

BEC + double well + cavity Full Hamiltonian Josephson junction Cavity photons Cavity-laser detuning: Pump strength: Atom-light interaction (photon scattering) Cavity photon #: AC-Stark shift: Cavity-assisted tunneling:

Semiclassical dynamics 2 Bose-Einstein condensate 4 real parameters, imbalance but only 2 independent relative phase Cavity coherent state Classical equations of motion

Josephson oscillations

Anti-self trapping

Summary / outlook Addition of the cavity fi eld is similar to add a new mass to a pendulum Dynamics changes drastically. A new separatrix appears. Possibility of chaos. The cavity is an open system, what happens if we allow photon loss? Phys. Rev. A 91 , 023601 (2015)