# Ultracold atoms in optical resonators

### Research objectives

- simulation of artificial, long-range interactions
- supersolidity
- quantum phase transitions in non-equilibrium systems

Schematic plot of a Bose-Einstein condensate (BEC) interacting with a single mode optical cavity. The cavity mode is described by a cos(*kx*) function along the cavity axis while it has a Gaussian envelope in the transverse direction. The BEC wave function evolves dynamically in time due to the interaction with the radiation field. The figure illustrates self-organization. A quasi homogeneous BEC (which has a shape of an elongated ellipsoid with its semi major axis well exceeding the optical wavelength) is illuminated by a pumping laser perpendicular to the cavity axis. When the intensity of the pump laser is below a threshold value (left panel) the BEC wave function remains homogeneous and incapable of scattering a classical field into the resonator. However, above threshold intensity (right panel) the BEC self-organizes into a one-wavelength pattern that scatters photons constructively into the resonator and thus stabilizes the optical potential supporting the Bragg lattice.

### Participants

Peter Domokos

(group leader)

Dávid Nagy

(postdoc)

Gergely Szirmai

(postdoc)

András Vukics

(postdoc)

Gábor Kónya

(PhD student)

### Collaborators

- Prof. Helmut Ritsch, Universität Innsbruck
- Prof. Tilman Esslinger, ETH Zürich

### References

- D. Nagy, G. Szirmai, and P. Domokos: Critical exponent of a quantum-noise-driven phase transition: The open-system Dicke model, Phys. Rev. A
**84**, 043637 (2011) - D. Nagy, G. Konya, G. Szirmai, and P. Domokos: Dicke-Model Phase Transition in the Quantum Motion of a Bose-Einstein Condensate in an Optical Cavity, Phys. Rev. Lett.
**104**, 130401 (2010)