QUEST - Centre for Quantum Engineering and Space-Time Research Multi-resonant spinor dynamics in a Bose-Einstein condensate Jan Peise B. Lücke, M.Scherer, O. Topic, W. Ertmer, C. Klempt Institute of Quantum Optics, Leibniz Universität Hannover G. Gebreyesus, F. Deuretzbacher, L. Santos Institute of Theoretical Physics, Leibniz Universität Hannover J. Arlt QUANTOP, Institut for Fysik og Astronomi, Aarhus Universitet, Denmark

QUEST - Centre for Quantum Engineering and Space-Time Research LightAtoms OpticsAtom optics Coherent opticsAtom optics with Bose-Einstein condensates Non-classical optics Non-classical atom optics Light and atoms for interferometry 2

QUEST - Centre for Quantum Engineering and Space-Time Research Parametric amplification vs. spin dynamics Optical parametric amplification Coherent pump Non-linear crystal Signal and idler beam Spinor Bose-Einstein condensate 87 Rb BEC in m F =0 Spin dynamics Atoms in m F =±1 3

QUEST - Centre for Quantum Engineering and Space-Time Research Introduction Experimental setup Spin dynamic resonances Spin dynamics via microwave dressing Content 4

QUEST - Centre for Quantum Engineering and Space-Time Research 87 Rb atoms in a dipole trap 87 Rb F=2 m F =

QUEST - Centre for Quantum Engineering and Space-Time Research Absorption detection m F =-1 m F =0 m F =1 6

QUEST - Centre for Quantum Engineering and Space-Time Research Introduction Experimental setup Spin dynamic resonances Spin dynamics via microwave dressing Content 7

QUEST - Centre for Quantum Engineering and Space-Time Research Simplified model for spin dynamics  E 0; 1  E 0; -1 Effective potential for mF=+/-1 atoms Multiresonant spinor dynamics in a Bose-Einstein condensate, Klempt et al., Phys. Rev. Lett. 103, (2009) 8

QUEST - Centre for Quantum Engineering and Space-Time Research Spin dynamic resonances in a cylindrical trap Effective potential with cylindrical symmetry magnetic field population in m F = ±1 9

QUEST - Centre for Quantum Engineering and Space-Time Research magnetic field population in m F = ±1 Spatial modes populated by spin dynamics magnetic field Spontaneous Breaking of Spatial and Spin Symmetry in Spinor Condensates Scherer, et.al, Phys. Rev. Lett.,105, (2010) 10

QUEST - Centre for Quantum Engineering and Space-Time Research Introduction Experimental setup Spin dynamic resonances Spin dynamics via microwave dressing Content 11

QUEST - Centre for Quantum Engineering and Space-Time Research Instability rates Instability rate Maximal for Instability rate Im[E] In F=1: 12

QUEST - Centre for Quantum Engineering and Space-Time Research Spin dynamics in F=1 F=2 U 1 >0 F=1 U 1 <0 Zeeman splitting in F=1  E 0; 1  E 0; Frequency Magnetic field

QUEST - Centre for Quantum Engineering and Space-Time Research Dressed states Bare states Reminder Ω resonant Rabi frequency ω laser frequency ω0 atomic frequency Hamiltonian Dressed states AC Stark shift 14

QUEST - Centre for Quantum Engineering and Space-Time Research Microwave dressing Resonance frequency Hz F=1 F=2 m F =-2m F =-1m F =0m F =1m F =2 Fixed magnetic field No spin dynamics 15

QUEST - Centre for Quantum Engineering and Space-Time Research Spin dynamics via microwave dressing 16

QUEST - Centre for Quantum Engineering and Space-Time Research Thank you for your attention. 17