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Gravity, Bose-Einstein Condensates and Gross-Pitaevskii Equation
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small-amplitude oscillation of BEC is studied by applying variational technique to reduce the Gross-Pitaevskii equation, with gravity included, to the equation of motion of a particle moving in a potential. According to our analysis, if the s-wave scattering length can be tuned to zero using Feshbach resonance for future BEC with occupation numbers as high as ≈1020, there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a 1/r3 gravity at short scales.
Keywords
Bose–Einstein Condensate, Gross–Pitaevskii Equation, Instability, Large Extra Dimension Gravity.
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- Newman, R. D., Berg, E. C. and Boynton, P. E., Tests of the gravitational inverse square law at short ranges. Space Sci. Rev., 2009, 148(1–4), 175–190.
- Arkani-Hamed, N., Dimopoulos, S. and Dvali, G. R., The hierarchy problem and new dimensions at a millimeter. Phys. Lett. B, 1998, 429(3–4), 263–272.
- Antoniadis, I., Arkani-Hamed, N., Dimopoulos, S. and Dvali, G. R., New dimensions at a millimeter to a Fermi and superstrings at a TeV. Phys. Lett. B, 1998, 436(3–4), 257–263.
- Kumar, N., Bose–Einstein condensation: where many become one and so there is plenty of room at the bottom. Curr. Sci., 2005, 89(12), 2093–2100.
- Dalfovo, F., Giorgini, S., Pitaevskii, L. P. and Stringari, S., Theory of Bose–Einstein condensation in trapped gases. Rev. Mod. Phys., 1999, 71(3), 463–512.
- Dimopoulos, S. and Geraci, A. A., Probing submicron forces by interferometry of Bose–Einstein condensed atoms. Phys. Rev. D, 2003, 68(12), 124021-1 to 124021-13.
- Sigurdsson, S., Testing gravity in large extra dimensions using Bose–Einstein condensates. Int. J. Mod. Phys. D, 2002, 11(10), 1541–1544.
- Haddad, L. H. and Carr, L. D., The nonlinear Dirac equation in Bose–Einstein condensates. Physica D, 2009, 238(15), 1413– 1421.
- Das Gupta, P., Raj, S. and Chaudhuri, D., Some exact stationary state solutions of a nonlinear Dirac equation in 2 + 1 dimensions. arXiv:1012.0976[cond-mat.mes-hall].
- Perez-Garcia, V. M., Michinel, H., Cirac, J. I., Lewenstein, M. and Zoller, P., Low energy excitations of a Bose–Einstein condensate: a time-dependent variational analysis. Phys. Rev. Lett., 1996, 77(27), 5320–5323.
- Perez-Garcia, V. M., Michinel, H., Cirac, J. I., Lewenstein, M. and Zoller, P., Dynamics of Bose–Einstein condensates: variational solutions of the Gross–Pitaevskii equations. Phys. Rev. A, 1997, 56(2), 1424–1432.
- Goral, K. and Santos, L., Ground state and elementary excitations of single and binary Bose–Einstein condensates of trapeed dipolar gases. Phys. Rev. A, 2002, 66(2), 023613-1 to 023613-12, and references therein.
- Gerton, J. M., Strekalov, D., Prodan, I. and Hulet, R. G., Direct observation of growth and collapse of a Bose–Einstein condensate with attractive interactions. Nature, 2000, 408(6813), 692–695.
- Tiesinga, E., Verhaar, B. J. and Stoof, H. T. C., Threshold and resonance phenomena in ultracold ground-state collisions. Phys. Rev. A, 1993, 47(5), 4114–4122.
- Inouye, S., Andrews, M. R., Stenger, J., Miesner, H. -J., StamperKurn, D. M. and Ketterle, W., Observation of Feshbach resonances in a Bose–Einstein condensate. Nature, 1998, 392(6672), 151–154.
- Courteille, Ph., Freeland, R. S., Heinzen, D. J., Van Abeelen, F. A. and Verhaar, B. J., Observation of a Feshbach resonance in a cold atom scattering. Phys. Rev. Lett., 1998, 81(1), 69–72.
- Roberts, J. L., Claussen, N. R., Burke Jr, J. P., Greene, C. H., Cornell, E. A. and Wieman, C. E., Resonant magnetic field control of elastic scattering in cold R85b. Phys. Rev. Lett., 1998, 81(23), 5109–5112.
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