Two-parameter estimation with three-mode NOON state in a symmetric three-well system

Abstract

We propose a theoretical scheme to realize two-parameter estimation via a Bose-Einstein condensates confined in a symmetric triple-well. The three-mode NOON state is prepared adiabatically as the initial state. Two phase differences between the wells are two parameters to be estimated. With the help of classical and quantum Fisher information, we study the sensitivity of the triplewell on estimating two phase parameters simultaneously. The result shows that the precision of simultaneous estimation of two parameters in a triple-well system can reach the Heisenberg scaling.

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

“…A notable exception is Ref. [11] where the production of triple-NOON states of the form e iϕ1 |N, 0, 0 + e iϕ2 |0, N, 0 + e iϕ3 |0, 0, N was theoretically investigated for a gas of ultracold bosonic atoms. A key ingredient in those bosonic quantum gases is the presence of atom-atom interaction, which induces a spectral separation of NOON states from other states with identical total population of the modes.…”

“…It also comes into play in Ref. [11] where an adiabatic transition to the triple-NOON state was investigated in a symmetric three-site system considering bosonic atoms that exhibit an attractive mutual interaction. This proposal is intriguing but may be challenging to implement in practice, as extremely low temperatures as well as very slow parameter variations would be required.…”