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

2. 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. 3 Fermi condensates 2004-2005 BEC-BCS crossover Related to, e.g., high temperature superconductivity Tuning Parameter (e.g. B) MoleculesUnitarity regime Cooper pairs Fermi condensate experiments have confirmed that the BCS-BEC evolution is a crossover Groups of: Grimm, Jin, Ketterle, Thomas, Salomon

4. 4 Imbalanced/Polarized Fermi gases Pairing between particles with unequal mass or unequal total number Related to, e.g., high energy physics (colour superconductivity of quarks) Polarization Experiments: 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

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

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

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

8. 8 FFLO (Fulde, Ferrel, Larkin, Ovchinnikov) state FFLO (Fulde, Ferrel, Larkin, Ovchinnikov) state  Finite polazation P and superfluidity simultaneously (also at T=0)  Non-uniform order parameter Observations under debate 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 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. 9 FFLO features for a trapped gas: interface effect c.f. K. Machida, T. Mizushima, M. Ichioka, PRL 2006 P=0.34P=0.88 J. Kinnunen, L.M. Jensen, P. Törmä, PRL 2006 L.M. Jensen, J. Kinnunen, P. Törmä, PRA 2007

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

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

12. 12 Fermi surfaces Free space Lattice

13. 13 T.K. Koponen, T. Paananen, J.-P. Martikainen, M.R. Bakhtiari, P. Törmä, New J. Phys. 2008 VanHove singularities show up in the phase diagrams 3D2D 1D

14. 14 Observation, e.g., by noise correlations 1DBCSFFLO

15. 15 Exact numerical studies of RF-spectroscopy | 1 > | 2 > | f > 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 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 RF-spectroscopy experiments no interactions |1>, |2> (and |3>) interacting 00

16. 16 0.38T F 0.26T F ~ T c 0.18T F 0.10T F T 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. 17 C.H.Schunck, Y.Shin, A.Schirotzek, M.W. Zwierlein, W.Ketterle, Science 2007

18. 18 What is RF-spectroscopy? Coherent rotation (like spin precession in 3 He)? Creation of quasiparticles (like tunneling)? - 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 - 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. 19 Linear response In both cases:

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

21. 21 Quasiparticle creationCoherent 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. 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) M.J. Leskinen, V. Apaja, J. Kajala, P. Törmä, cond-mat/0802.1882 Ground state Time evolution (pulse) ⇒ Spectrum

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

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