Bose–Einstein condensate sub-wavelength confinement via superoscillations

Optical lattices are essential tools in the field of ultra-cold atomic physics. In this study, we theoretically demonstrate that sub-wavelength confinement can be achieved in these lattices through superoscillations. This generic wave phenomenon occurs when a local region of the wave oscillates faster than any of the frequencies in its global Fourier decomposition. To illustrate this, we consider a one-dimensional tri-chromatic optical potential confining a spinless Bose–Einstein condensate of 87Rb atoms. By numerically optimizing the relative phases and amplitudes of the optical trap’s frequency components, it is possible to generate superoscillatory spatial regions. Such regions contain multiple density peaks at sub-wavelength spacing. This work establishes superoscillations as a viable method of confining a Bose–Einstein condensate in a blue-detuned optical lattice at the sub-wavelength scale.