NOON states with ultracold bosonic atoms via resonance- and chaos-assisted tunneling

We investigate theoretically the generation of microscopic atomic NOON states, corresponding to the coherent

|N, 0> + |0, N> superposition with N ∼ 5 particles, via collective tunneling of interacting ultracold bosonic

atoms within a symmetric double-well potential in the self-trapping regime. We show that a periodic driving

of the double well with suitably tuned amplitude and frequency parameters allows one to substantially boost this

tunneling process without altering its collective character. The timescale to generate the NOON superposition,

which corresponds to half the tunneling time and would be prohibitively large in the undriven double well for

the atomic populations considered, can thereby be drastically reduced, which renders the realization of NOON

states through this protocol experimentally feasible. Resonance- and chaos-assisted tunneling are identified as

key mechanisms in this context. A quantitative semiclassical evaluation of their impact on the collective tunneling

process allows one to determine the optimal choice for the driving parameters in order to generate those NOON

states as fast as possible.