We systematically investigate the interaction effects during time-of-flight(TOF) expansion of a pure condensate released from an optical lattice potential. By simulating the expansion process both in the spatial and momentum space, we find that the condensate fraction keeps decreasing due to the inter-particle interaction, showing a universal power-law dependent of the expansion time and interaction. Our results imply that the so-called ”condensate fraction” measured in the standard TOF experiment can be very different from the true condensate fraction inside the optical lattice due to such dynamical
depletion. We further propose a theoretical scheme to estimate the condensate fraction based on the existing TOF experimental results, including both the finite time and finite interaction effects.

[1] Anderson, M. H., J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198(1995); Bradley, C. C., C. A. Sackett, J. J. Tollett, and R. G. Hulet, Phys. Rev. Lett. 75, 1687(1995); Davis, K. B., M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969(1995).
[2] Andrews, M. R., C. G. Townsend, H. J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275, 637(1997).
[3] Matthews, M. R., B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 83, 2498(1999); Madison, K. W., F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84, 806(2000); Abo-Shaeer, J. R., C. Raman, J. M. Vogels, and W. Ketterle, Science 292, 476(2001).
[4] Courteille, P., R. Freeland, D. Heinzen, F. van Abeelen, and B. Verhaar, Phys. Rev. Lett. 81, 69(1998); Inouye, S., M. Andrews, J. Stenger, H. J. Miesner, S. Stamper-Kurn, and W. Ketterle, Nature 392, 151(1998).
[5] Greiner, M., M. O. Mandel, T. Esslinger, T. Hnsch, and I. Bloch, Nature 415, 39(2002).
[6] Jaksch, D., C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108(1998).
[7] D. F.Walls and G. J. Milburn, Quantum Optics (Springer-Verlag Berlin Heidelberg New York, 1994); Marlan O. Scully and M. Suhail Zubairy, Quantum Optics(Cambridge University Press, 1997); Stephen M. Barnett and Paul M. Radmore, Methods in Theoretical Quantum Optics(Clarendon Press Oxford, 1997)
[8] A. Polkovnikov, Phys. Rev. A, 68, 033609 (2003); Phys. Rev. A, 68, 053604 (2003).
[9] A. Polkovnikov and D.-W. Wang, Phys. Rev. Lett. 93, 070401 (2004).
[10] M. J. Steel et al., Phys. Rev. A 58, 4824 (1998); A. Sinatra et al., J. Mod. Opt. 47,
2629 (2000); Phys. Rev. Lett. 87, 210404 (2001); J. Phys. B: At. Mol. Opt. Phys. 35,
3599 (2002).
[11] Sadhan K Adhikari and Paulsamy Muruganandam, J. Phys. B: At. Mol. Opt. Phys. 35(2002)2831-2843; J. Phys. B: At. Mol. Opt. Phys. 36(2003)2501-2513.
[12] Lloyd N. Trefethen, Spectral Methods in MATLAB( Society for Industrial and Applied Mathematics, 2000)
[13] William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing(Cambridge University Press, 2007).
[14] M. Olshanii, Phys. Rev. Lett. 81, 938 (1998).
[15] C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases(Cambridge University Press, 2002); James F. Annett Superconductivity, Superfluids and Condensates(Oxford University Press, 2004)