Quantum Interferometry with Microwave-Dressed Spinor Bose-Einstein Condensates in the Regime of Long Evolution Times

We recently achieved all-optical generation of Na spinor Bose-Einstein condensates (BEC) in our crossed far-off resonant trap at 1064 nm. Using our BEC, we experimentally investigate atom interferometry based on spin-exchange collisions in the regime of long evolution times where the Bogoliubov and truncated Wigner approximations break down, and compare the results with our numerical simulations. Spin-exchange collisions in the F= 1 spinor Bose-Einstein condensate can be precisely controlled by microwave dressing, and generate pairs of entangled atoms with magnetic quantum numbers $m_F$= +1 and $m_F$= -1 from pairs of $m_F$= 0 atoms. Spin squeezing created by the collisions can reduce the noise in an atom interferometer below the shot noise limit. For long evolution times, $t\gg h/c$, where $c$ is the spin-dependent interaction energy, $c\simeq h\cdot30$ Hz, there are large numbers of atoms with $m_F$= +1 or $m_F$= -1 in the arms of the interferometer, allowing for easier detection via Stern-Gerlach time-of-flight absorption imaging.