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Recent developments in density imbalanced Fermi gases

Päivi Törmä. Recent developments in density imbalanced Fermi gases. Helsinki University of Technology. Symposium on Quantum Phenomena and Devices at Low Temperatures Espoo, March 30th 2008. Motivation.

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Recent developments in density imbalanced Fermi gases

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  1. Päivi Törmä Recent developments in density imbalanced Fermi gases Helsinki University of Technology Symposium on Quantum Phenomena and Devices at Low Temperatures Espoo, March 30th 2008

  2. Motivation • Recent experiments on density imbalanced Fermi gases: phase separation; non-Fermi liquid normal states??? • Imbalanced Fermi gases and FFLO state in optical lattices • Non-BCS pairing with non-equal mass/number/chemical potential??? • Of interest in high energy, nuclear, and solid state physics • FFLO (spatially varying order parameter); no unambiguous observation yet • Exact numerical studies of RF-spectroscopy • RF spectroscopy: important method for probing quantum states of ultracold gases • Deeper theoretical understanding needed, only linear response applied so far

  3. Fermi condensates 2004-2005 Fermi condensate experiments have confirmed that the BCS-BEC evolution is a crossover Groups of: Grimm, Jin, Ketterle, Thomas, Salomon Molecules Unitarity regime Cooper pairs Tuning Parameter (e.g. B) BEC-BCS crossover Related to, e.g., high temperature superconductivity

  4. Imbalanced/Polarized Fermi gases Polarization Pairing between particles with unequal mass or unequal total number Related to, e.g., high energy physics (colour superconductivity of quarks) M.W.Zwierlein, A.Schirotzek, C.H.Schunck, W.Ketterle, Science 2006 G.B.Partridge, W.Li,R.I.Kamar, Y.Liao, R.G.Hulet, Science 2006 G.B.Partridge, W.Li,Y.Liao, R.G.Hulet, M.Haque, H.Stoof, PRL 2006 M.W.Zwierlein, C.H.Schunck, A.Schirotzek, W.Ketterle, Nature 2006 C.H.Schunck, Y.Shin, A.Schirotzek, M.W. Zwierlein, W.Ketterle, Science 2007 Y.Shin, C.H.Schunck, A.Schirotzek, W.Ketterle, Nature 2008 Experiments:

  5. P=0 P=1 M.W.Zwierlein, A.Schirotzek, C.H.Schunck, W.Ketterle, Science 2006

  6. Established: Phase separation in a harmonic trap: superfluid in the middle, normal state at the edges of trap 3D reconstruction Partridge, Li, Liao, Hulet, Haque, Stoof, PRL 2006 Shin, Zwierlein, Schunck, Schirotzek, Ketterle, PRL 2006

  7. - Value of the critical polarization? - Nature of the normal state? C.H.Schunck, Y.Shin, A.Schirotzek, M.W. Zwierlein, W.Ketterle, Science 2007

  8. FFLO (Fulde, Ferrel, Larkin, Ovchinnikov) state Finite polazation P and superfluidity simultaneously (also at T=0) Non-uniform order parameter Observations under debate H.A. Radovan, N.A. Fortune, T.P. Murphy, S.T. Hannahs, E.C. Palm, S.W. Tozer, D. Hall, Nature 2003 A. Bianchi, R. Movshovich, C. Capan, P.G. Pagliuso, J.L. Sarrao, PRL 2003 K. Kakuyanagi, M. Saitoh, K. Kumagai, S. Takashima, M. Nohara, H. Takagi, Y. Matsuda, PRL 2005 V.F. Correa, T.P. Murphy, C. Martin, K.M. Purcell, E.C. Palm, G.M. Schmiedeshoff, J.C. Cooley, S.W. Tozer, PRL 2007 The parameter window for existence of this phase is exceedingly small for particles in free space, in 3D See e.g. D.E. Sheehy, L. Radzihovsky, PRL 2006 COULD ONE OBSERVE THE FFLO STATE IN ULTRACOLD GASES?

  9. FFLO features for a trapped gas: interface effect J. Kinnunen, L.M. Jensen, P. Törmä, PRL 2006 L.M. Jensen, J. Kinnunen, P. Törmä, PRA2007 P=0.34 P=0.88 c.f. K. Machida, T. Mizushima, M. Ichioka, PRL 2006

  10. Imbalanced gases in optical lattices Order parameter (gap) Quasiparticle energy Phase separation Minimize T. Koponen, T. Paananen, J.-P. Martikainen, P. Törmä, PRL 2007 T. Koponen, J. Kinnunen, J.-P. Martikainen, L.M. Jensen, P. Törmä, New J. Phys. 2006

  11. FFLO area is much bigger than in other systems (due to nesting of Fermi surfaces)

  12. Fermi surfaces Free space Lattice

  13. VanHove singularities show up in the phase diagrams 3D 2D 1D T.K. Koponen, T. Paananen, J.-P. Martikainen, M.R. Bakhtiari, P. Törmä, New J. Phys. 2008

  14. Observation, e.g., by noise correlations 1D BCS FFLO

  15. Exact numerical studies of RF-spectroscopy |1>, |2> (and |3>) interacting | f > no interactions | 2 > | 1 > 0 0 RF-spectroscopy experiments Pairing - C. Chin, M. Bartenstein, A. Altmayer, S. Riedl, S. Jochim, J.H. Denschlag, R. Grimm, Science 2004 - T. Stöferle, H. Moritz, K. Gunter, M. Köhl, T. Esslinger, PRL 2006 - C.H. Schunck, Y. Shin, A. Schirotzek, W. Ketterle, Science 2007 - And more by Grimm, Ketterle groups Hartree mean fields - C. Regal and D. Jin, PRL 2003 - S. Gupta, Z. Hadzibabic, M.W. Zwierlein, C.A. Stan, K. Dieckmann, C.H. Schunck, E.G.M. van Kempen, B.J. Verhaar, W. Ketterle, Science 2003

  16. T 0.4 (a) 0.38T F 0.0 (b) 0.4 0.26T ~ T F c fractional loss in |2> 0.0 (c) 0.4 0.18T F 0.0 (d) 0.4 0.10T F 0.0 -20 0 20 40 RF frequency offset (kHz) C. Chin, M. Bartenstein, A. Altmayer, S. Riedl, S. Jochim, J.H. Denschlag, and R. Grimm, Science 305, 1128, 2004 J. Kinnunen, M. Rodriguez, P. Törmä, Science 305, 1131, 2004

  17. C.H.Schunck, Y.Shin, A.Schirotzek, M.W. Zwierlein, W.Ketterle, Science 2007

  18. - P. Törmä, P. Zoller,PRL 2000 - J. Kinnunen, M. Rodriguez, P. Törmä, Science 2004 - Y. He, Q. Chen, K. Levin,PRA 2005 - Y. Ohashi, A. Griffin, PRA 2005 - A. Perali, P. Pieri, G.C. Strinati, PRL 2008 - S. Basu, E. Mueller, arXiv:0712.1007 - P. Massignan, G.M. Bruun, H. Stoof PRA 2008 - M. Veillette, E.G. Moon, A. Lamarcraft, L. Radzihovsky, S. Sachdev, D.E. Sheehy, arXiv:0803.251 - And more by Törmä, Levin, Griffin, Mueller What is RF-spectroscopy? Creation of quasiparticles (like tunneling)? Coherent rotation (like spin precession in 3He)? - M.W. Zwierlein, Z. Hadzibabic, S. Gupta,W. Ketterle, PRL 2003 - Z.Yu, G. Baym,PRA 2006 - M.Punk, W.Zwerger, PRL 2007 - G.Baym, C.J.Pethick, Z.Yu, M.W.Zwierlein, PRL 2007

  19. In both cases: Linear response

  20. Linear response Sum rules: Fermi Golden rule Discussion: M.J. Leskinen, V. Apaja, J. Kajala, P. Törmä, cond-mat/0802.1882

  21. Quasiparticle creation Coherent rotation Likely to happen when - Decoherence (“projection measurement”) - Coupling to continuum - Coherent time evolution (“projection measurement” only after the pulse) - Coupling to a similar final state Linear response

  22. Exact solution (no mean field, fully coherent time evolution, no linear response), in 1D, using Matrix Product State (related to DMRG) methods (G. Vidal, PRL 2003, 2004) Ground state Time evolution (pulse) ⇒ Spectrum M.J. Leskinen, V. Apaja, J. Kajala, P. Törmä, cond-mat/0802.1882

  23. ● 1% of |2> transferred * 5% △ 50% ▇ Quasiparticle picture Linear response sum rule result M.J. Leskinen, V. Apaja, J. Kajala, P. Törmä, cond-mat/0802.1882

  24. Summary • Density imbalanced Fermi gases: superfluidity, phase separation, nature of the strongly interacting normal state, exotic pairing and superfluidity • FFLO state stable in optical lattices (flat Fermi surfaces) • Nonlinear effects considerably suppress the pairing signal in RF-spectroscopy (exact calculations in 1D, coherent rotation)

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