Recent developments in density Recent developments in density imbalanced Fermi gasesimbalanced Fermi gases

Päivi TörmäPäivi Törmä

Symposium on Quantum Phenomena and Devices at Low Temperatures

Espoo, March 30th 2008

Helsinki University of Technology

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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

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Fermi condensates 2004-2005

BEC-BCS crossoverRelated to, e.g., high temperature superconductivity

TuningParameter (e.g. B)

Molecules Unitarity regime Cooper pairs

Fermi condensate experiments have confirmed that the BCS-BEC evolution is a crossover

Groups of: Grimm, Jin, Ketterle, Thomas, Salomon

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Imbalanced/Polarized Fermi gases

Pairing between particles with unequal mass or unequal total number

Related to, e.g., high energy physics (colour superconductivityof 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

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P=0P=1

M.W.Zwierlein, A.Schirotzek, C.H.Schunck, W.Ketterle, Science 2006

6Shin, Zwierlein, Schunck, Schirotzek, Ketterle, PRL 2006Shin, Zwierlein, Schunck, Schirotzek, Ketterle, PRL 2006

3D reconstruction

Partridge, Li, Liao, Hulet, Haque, Stoof, Partridge, Li, Liao, Hulet, Haque, Stoof, PRL 2006PRL 2006

Established: Phase separationin a harmonic trap: superfluid in the middle,normal state at the edges of trap

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

- Value of the critical polarization?- Nature of the normal state?

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FFLO (Fulde, Ferrel, Larkin, Ovchinnikov) stateFFLO (Fulde, Ferrel, Larkin, Ovchinnikov) state Finite polazation P and superfluidity simultaneously Finite polazation P and superfluidity simultaneously

(also at T=0)(also at T=0) Non-uniform order parameterNon-uniform order parameter

Observations under debateObservations under debate H.A. Radovan, N.A. Fortune, T.P. Murphy, S.T. Hannahs, E.C. Palm, S.W. H.A. Radovan, N.A. Fortune, T.P. Murphy, S.T. Hannahs, E.C. Palm, S.W.

Tozer, D. Hall, Nature 2003Tozer, D. Hall, Nature 2003 A. Bianchi, R. Movshovich, C. Capan, P.G. Pagliuso, J.L. Sarrao, PRL 2003A. 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, K. Kakuyanagi, M. Saitoh, K. Kumagai, S. Takashima, M. Nohara, H. Takagi,

Y. Matsuda, PRL 2005Y. Matsuda, PRL 2005 V.F. Correa, T.P. Murphy, C. Martin, K.M. Purcell, E.C. Palm, G.M. V.F. Correa, T.P. Murphy, C. Martin, K.M. Purcell, E.C. Palm, G.M.

Schmiedeshoff, J.C. Cooley, S.W. Tozer, PRL 2007Schmiedeshoff, J.C. Cooley, S.W. Tozer, PRL 2007

The parameter window for existence of this phase is The parameter window for existence of this phase is exceedingly small for particles in free space, in 3Dexceedingly small for particles in free space, in 3D

See e.g. D.E. Sheehy, L. Radzihovsky, PRL 2006See e.g. D.E. Sheehy, L. Radzihovsky, PRL 2006

COULD ONE OBSERVE THE FFLO STATEIN ULTRACOLD GASES?

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FFLO featuresfor a trapped gas:interfaceeffect

c.f. K. Machida, T. Mizushima, M. Ichioka, PRL 2006

P=0.34 P=0.88

J. Kinnunen, L.M. Jensen, P. Törmä, PRL 2006L.M. Jensen, J. Kinnunen, P. Törmä, PRA 2007

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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, 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 T. Koponen, T. Paananen, J.-P. Martikainen, P. Törmä, PRL 2007

Order parameter (gap) Quasiparticle energy

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

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Fermi surfaces

Freespace

Lattice

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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

3D 2D

1D

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Observation, e.g., by noise correlations

1D BCS FFLO

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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

N FN F

|1>, |2> (and |3>) interacting

0 0

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0.0

0.4

(d)

(c)

(a)

0.0

0.4

-20 0 20 400.0

0.4

frac

tiona

l los

s in

|2>

RF frequency offset (kHz)

0.0

0.4(b)

0.38TF

0.26TF ~ Tc

0.18TF

0.10TF

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

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

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What is RF-spectroscopy?

Coherent rotation (like spin precession in 3He)?

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

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Linear response

In both cases:

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Linear response

Discussion: M.J. Leskinen, V. Apaja, J. Kajala, P. Törmä, cond-mat/0802.1882

Fermi Golden ruleSum rules:

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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

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Exact solution (no mean field, fully coherent time evolution, no linear response), in 1D, using Matrix Product State (relatedto DMRG) methods (G. Vidal, PRL 2003, 2004)

M.J. Leskinen, V. Apaja, J. Kajala, P. Törmä, cond-mat/0802.1882

Ground stateTime evolution (pulse) ⇒ Spectrum

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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

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Summary

Density imbalanced Fermi gases: superfluidity, phase Density imbalanced Fermi gases: superfluidity, phase separation, nature of the strongly interacting normal state, separation, nature of the strongly interacting normal state, exotic pairing and superfluidityexotic 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 Nonlinear effects considerably suppress the pairing

signal in RF-spectroscopy (exact calculations in 1D, signal in RF-spectroscopy (exact calculations in 1D, coherent rotation)coherent rotation)