Abstract
We report an experimental demonstration of generation and measurement of sub-wavelength phase structure of a Bose-Einstein condensate (BEC) with two-dimensional optical lattice. This is implemented by applying a short lattice pulse on BEC in the Kapitza-Dirac (or Raman-Nath) regime, which, in the classical picture, corresponds to phase modulation imprinted on matter wave. When the phase modulation is larger than 2π in a lattice cell, the periodicity of phase naturally forms the sub-wavelength phase structure. By converting the phase information into amplitude, we are able to measure the sub-wavelength structure through the momentum distribution of BEC via the time-of-flight absorption image. Beyond the classical treatment, we further demonstrate the importance of quantum fluctuations in the formation of sub-wavelength phase structure by considering different lattice configurations. Our scheme provides a powerful tool for exploring the fine structure of a lattice cell as well as topological defects in matter wave.
Highlights
We report an experimental demonstration of generation and measurement of sub-wavelength phase structure of a Bose-Einstein condensate (BEC) with two-dimensional optical lattice
We have experimentally realized the sub-wavelength phase structure in BEC with 2D optical lattices. This is implemented by applying a short lattice pulse in the Kapitza-Dirac regime, such that in the classical picture the lattice potential imprints a phase modulation on matter wave
The www.nature.com/scientificreports sub-wavelength phase structure in our work can be connected to the topological defects in matter wave[38,39,40], such as phase steps or vortices, which could be detected in the momentum space
Summary
We report an experimental demonstration of generation and measurement of sub-wavelength phase structure of a Bose-Einstein condensate (BEC) with two-dimensional optical lattice This is implemented by applying a short lattice pulse on BEC in the Kapitza-Dirac (or Raman-Nath) regime, which, in the classical picture, corresponds to phase modulation imprinted on matter wave. A short pulse of optical lattice is illuminated on a Bose-Einstein condensate (BEC) working in the regime of Kapitza-Dirac (or Raman-Nath) scattering[18,19,20,21,22] In this process, the lattice potential imprints a phase modulation on matter wave in position space. Predicted by Kapitza and Dirac for electrons[27], it was first demonstrated with an atomic beam[18], later with cold atoms[28]
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