SLIDE 1 Tunnęłing dyńamics of bosońic Josephson juńctions assistęd by a cavity fiełd
Gergely Szirmai, Giovanni Mazzarella, Luca Salasnich Wigner Research Centre, Budapest University of Padova Quantum T echnologies Conference VI, June 26, 2015
- Phys. Rev. A 91, 023601 (2015)
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BEC inside a double well
Interacting Bose gas
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BEC inside a double well
Interacting Bose gas 2-mode approximation
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BEC inside a double well
Interacting Bose gas Bose-Einstein condensate
4 real parameters, but only 2 independent imbalance relative phase
2-mode approximation
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Bosonic Josephson Junction
Effective Hamiltonian
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Why is it called bosonic Josephson Junction?
Bosonic Josephson Junction
Effective Hamiltonian
SLIDE 7 INSULATOR SUPERCONDUCTOR 2 1
It is a tunneling phenomena of a matter wave, just like in the case of a superconducting Josephson Junction. Why is it called bosonic Josephson Junction?
Bosonic Josephson Junction
Effective Hamiltonian
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Semiclassical dynamics
Classical equations of motion
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Semiclassical dynamics
Classical equations of motion Fixed point classification of the solutions
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x y
pumping laser double well EM field profile
A BEC inside a double well (coherent population transfer between the wells) And a cavity outside
BEC + double well + cavity
The cavity field is super- imposed to the double-well potential and affects the atomic tunneling. The dynamically changing spatial distribution of the atoms can shift the cavity in and out of resonance. At resonance the photon number is hugely enhanced and the atomic tunneling becomes amplified.
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BEC + double well + cavity
Full Hamiltonian Cavity photons Josephson junction Atom-light interaction (photon scattering)
Cavity-laser detuning: Pump strength: Cavity photon #: AC-Stark shift: Cavity-assisted tunneling:
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Semiclassical dynamics 2
Bose-Einstein condensate
4 real parameters, but only 2 independent imbalance relative phase
Cavity coherent state Classical equations of motion
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Josephson oscillations
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Anti-self trapping
SLIDE 15 Summary / outlook
Addition of the cavity field 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)
