Different from the magnetic dipolar atoms, polar molecules have additional rotational degree
of freedom, which can have widely tunable eigenstate energies by detuning the external DC
or AC electric field. Here we follow the earlier work of P. Zoller’s scheme to calculate
the effective potential energy between two identical (bosonic or fermionic) polar molecules,
taking into account their rotational states under various external fields. Our results show a
dramatic change of dipolar interaction, and hence lead to various new kinds of many-body
effects. Besides, we also give further calculation of condensation profile of possible rotating
DBEC and investigate possible directions to find new phenomena such as stabilized supersolid
phase with applying appropriate external fields.

[1] A. Micheli, G. Pupillo, H. P. B‥uchler, and P. Zoller, Phys. Rev. A 76, 043604 (2007).
[2] Masatoshi Kajita, Phys. Rev. A 74, 032710 (2006)
[3] L. Fallani and M. Inguscio, Science 322, 1520 (2008)
[4] S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. Buchler and P. Zoller, Nature Physics 4,
878 (2008).
[5] L. Mathey and A. Polkovnikov, arXiv:0904.2881v1 (2009)
[6] J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995)
[7] P. Rabl, D. DeMille, J. M. Doyle, M. D. Lukin, R. J. Schoelkopf,4, and P. Zoller, Phys.
Rev. Lett. 97, 033003 (2006)
[8] B. Sun, W. X. Zhang, S. Yi, M. S. Chapman, and L. You, Phys. Rev. Lett 97, 123201
(2006).
[9] E. A. L. Henn, J. A. Seman, G. Roati, K. M. F. Magalh˜aes, and V. S. Bagnato,
arXiv:0904.2564v1 (2009).
[10] M. Iskin and C. A. R. S’a de Melo, Phys. Rev. Lett. 99, 110402 (2007).
[11] K. Kanjilal, John L. Bohn, and D. Blume, Phys. Rev. A 75, 052705 (2007).
[12] D. Blume and Chris H. Greene, Phys. Rev. A 65, 043613 (2003).
[13] Ryan M. Wilson, Shai Ronen, John L. Bohn, Han Pu, Phys. Rev. Lett. 100, 245302 (2008).
[14] Shai Ronen, C. E. Bortolotti, John L. Bohn, Phys. Rev. A 74, 013623 (2006).
[15] K.-K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Pe’er, B. Neyenhuis, J. J. Zirbe, S.
Kotochigova, P. S. Julienne, D. S. Jin, J. Ye, Science 322, 231 (2008).
[16] Stefano Giovanazzi, Axel G‥orlitz, and Tilman Pfau, Phys. Rev. Lett. 89, 130401 (2002).
[17] A.V. Gorshkov, P. Rabl, G. Pupillo, A. Micheli, P. Zoller, M. D. Lukin, and H. P. B‥uchler,
Phys. Rev. Lett. 101, 073201 (2008).