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DFT Study of Exotic Pairing Phases in Imbalanced Fermi Condensates J. Pei (UTK/ORNL) With: W. Nazarewicz, J. Dukelsky UNEDF workshop, Lansing, June 22, 2010 Expected exotic FFLO pairing In imbalanced Fermi systems, pairing with none-zero momentum can happen: Flude-Ferrell-Larkin-Ovchinnikov (FFLO) Oscillation pairing gap is expected; Modulated densities (crystallized). It exists in many theoretical calculations, but difficult to find. Some signatures in heavy fermions systems. Radovan, et al. Nature 425, 51, 2003. r r r iqn x ( x ) 0 Cn e n UNEDF workshop, Lansing, June 22, 2010 Some experiments Advantages of using cold atoms: interaction is controllable; clear physics; High Tc; implications for other Fermi systems Unitary limit: two body s-wave scattering length diverges: as→±∞ 834 G System is strongly correlated and its properties do not dependent on the value of scattering length as Trapped by optical and magnetic potential w02 2 r 2 / w2 ( z ) 1 2 2 U (r , z ) mB z U 0 [1 2 e ], w( z ) w0[1 ( z / z0 ) 2 ] 2 w ( z) approximate HO potential: Aspect ratio: η=wr/wz U (r , z ) U (1 exp( 1 ( w2 r 2 w2 z 2 ) / U )) 0 r z 0 2 highly elongate trap is of great interests! (good for looking FFLO pairing) UNEDF workshop, Lansing, June 22, 2010 Experiments(Rice) Phase Separation Superfluid Core is deformed from the trap shape and such deformation effects disappear at high temperatures Trap aspect ratio~50: highly elongate Particle numbers~105 G.B.Partridge, et al, PRL97,190407,2006 G.B.Partridge, et al, Science,311,503,2006 UNEDF workshop, Lansing, June 22, 2010 Experiments(MIT) Phase separation However, no superfluid core deformation Y.Shin, et al, PRL 97,03401,2006 Clogston-Chandrasekhar limit of superfluidity Trap aspect ratio=5, particles=106 UNEDF workshop, Lansing, June 22, 2010 Experiments-others • French group: 105 particles, aspect ratio=23 (agree with MIT) No core deformation Question??? 1. different experimental conditions 2. or theory is not precise C. Salomon, et al, PRL103, 18 (2009) 170402 UNEDF workshop, Lansing, June 22, 2010 Finite-size effect Finite-size effect of trap deformations and particle numbers small deformation trap doesn't violate LDA solutions M.Ku, PRL 102, 255301, 2009 Sensarma, et al. arxiv: 07061741 Tezuka, et al. arxiv: 0811.1650 Non-equilibrium state observed in Rice experiment Parish, et al. PRA 063305(2009) Surface tension is important at large deformations T.N. De Silva, et al, PRL 97, 070402(2006) UNEDF workshop, Lansing, June 22, 2010 Theoretics Quantum Monte Carlo: QMC is very precise but limited to small systems Bogoliubov de-Genes equation: Mean Field approximation FFLO normal PS BP TK Koponen, PRL 99,120403 Plenty of calculations, no Hartree potential, and not quantitatively accurate A contest of computation: Tokyo U:30000 particles; Rice U: 105 particles DFT: at the unitary limit, the physical properties only depends on the density. It is good for DFT descriptions. Superfluid Local Density Approximation (SLDA) is very precise. UNEDF workshop, Lansing, June 22, 2010 Coexistence of difference phase? SDLA calculations with different initials sin(qz)exp(-(z-zc)/a), why sensitive? J.P, W. Nazarewicz, J. Dukelsky, arxiv:1005:3239 UNEDF workshop, Lansing, June 22, 2010 Quasi-continuum back ground discussions Is that Quantum fluctuations can be considered by a generator-coordinate DFT FFLO is a superposition of different wavepackets UNEDF workshop, Lansing, June 22, 2010 SLDA and ASLDA difference Very different Hartree potentials in ASLDA Related to different effective mass Deformed core solution is washed out in ASLDA. Because of their different Hartree potentials BdG calculations are similar to SLDA calculations. UNEDF workshop, Lansing, June 22, 2010 Propose to access LO states Pairing oscillations become remarkable as trap aspect ratio increase The oscillations are perpendicular to the long axis Oscillation periods are almost the same. Periods are related to the qLO Numerical: evolve the trap from a ground-state solution at a moderately elongated trap to reach an excited state Experiments: can be accessible by elongate the trap adiabatically. UNEDF workshop, Lansing, June 22, 2010 Conclusions Phase separation is demonstrated in trapped system both by SLDA and ASLDA Energy structures of coexistent phases are shown. Superfluid Core deformation is not shown in ASLDA. The FFLO is predicted in highly elongated trap, both by SLDA and ASLDA. However, It has a higher energy than LDA solution. Could be access by experiments, need very low temperature. Thanks: A. Bulgac, M.M. Forbes UNEDF workshop, Lansing, June 22, 2010