Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro...
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Transcript of Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro...
![Page 1: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/1.jpg)
Ultracold Fermi gases
University of Trento
BEC Meeting, Trento, 2-3 May 2006
INFM-CNR
Sandro Stringari
![Page 2: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/2.jpg)
Atomic Fermi gases in traps
Ideal realization of non-interacting configuarations
with spin-polarized samples
- Bloch oscillations and sensors (Carusotto et al.),
- Quantum register (Viverit et al)
- Insulating-conducting crossover (Pezze’ et al.)
Role of interactions (superfluidity)
- HD expansion (aspect ratio and pair correlation function)
- collective oscillations and equation of state
- spin polarizability
This talk
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EXPANSION OF FERMI SUPERFLUID
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Hydrodynamics predicts anisotropicexpansion of BEC gas
![Page 5: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/5.jpg)
Evidence for hydrodynamic anisotropic expansion in ultra cold Fermi gas (O’Hara et al, 2003)
HD theoryHydrodynamics predicts anisotropic expansion in Fermi superfluids (Menotti et al,2002)
normal collisionless
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Pair correlations of an expanding superfluid Fermi gas C. Lobo, I. Carusotto, S. Giorgini, A. Recati, S. Stringari, cond-mat/0604282
Recent experiments on Hanbury-Brown Twiss effect with thermal bosons (Aspect, Esslinger, 2005) provide information on
- Pair correlation function measured after expansion - Time dependence calculated in free expansion approximation (no collisions)- Decays from 2 to uncorrelated value 1 (enhancement at short distances due Bose statistics).- For large times decay lengths approach anisotropic law: iiT mRtt /
])1(
2exp[1)(222
22
t
ssg
iT
i
i
![Page 7: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/7.jpg)
Can we describe behaviour of pair correlation function during theexpansion in strongly interacting Fermi gases (eg. at unitarity) ?
- In situ correlation function calculated with MC approach (see Giorgini)
- Time dependence described working in HD approximation (local equilibrium assumption)
QUESTION
![Page 8: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/8.jpg)
unitarity
BEC limit
thermal bosons
4/1akF
Pair spin up-down correlation function
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Pair correlation function in interacting Fermi gas:
- Spin up-down correlation function strongly affected by interactions at short distances. Effect is much larger than for thermal bosons (Hanbury-Brown Twiss)
- In BEC regime ( ) pair correlation function approaches uncorrelated value 1 at distances of the order of scattering length (size of molecule)
- At unitarity pair correlation function approaches value 1 at distances of the order of interparticle distance (no other length scales available at unitarity)
1akF
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Local equilibrium ansatz for expansion
- Dependence on s fixed by equilibrium result (calculated with local value of density)- Time dependence of density determined by HD equations.
Important consequences (cfr results for free expansion of thermal bosons)
- Pair correlation keeps isotropy during expansion- Measurement after expansion ‘measures’ equilibrium correlation function at local density- at unitarity, where correlation function depends on combination , expansion acts like a microscopeskF
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COLLECTIVE OSCILLATIONS AND EQUATION OF STATE
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- Surface modes: unaffected by equation of state - Compression modes sensitive to equation of state.-Theory of superfluids predicts universal values when 1/a=0 :
- In BEC regime one insetad finds
COLLECTIVE OSCILLATIONS IN SUPERFLUID PHASE (T=0)
3/10rad zax 5/12
2rad zax 2/5
Behaviour of equation of state through the crossover canbe inferred through the study of collective frequencies !
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Radial compression mode
3
10
S. Stringari, Europhys. Lett. 65, 749 (2004)
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Experiments on collective oscillations at
- Duke (Thomas et al..)
- Innsbruck (Grimm et al.)
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unitarity
(mean fieldBCS gap eq.)
Duke data agree with value 1.826 predicted at unitarity
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Radial breathing mode at Innsbruck (2006) (unpublished)
MC equation of state
BCS mean field83.13/10
Theory from Astrakharchik et al Phys. Rev. Lett. 95, 030405 (2005)
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Crucial role of temperature:
- Beyond mean field (LHY) effects are easily washed out by thermal fluctuations finite T (Giorgini 2000) Conditions of Duke experiement
- Only lowering the temperature (new Innsbruck exp) one can see LHY effect
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SPIN POLARIZABILITY
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Spin Polarizability of a trapped superfluid Fermi gasA. Recati, I. Carusotto, C. Lobo and S.S., in preparation
Recent experiments and theoretical studies have focused on the consequence of spin polarization ( ) on the superfluid features of interacting Fermi gases
)/()( NNNNP
MIT, 2005
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In situ density profiles for imbalanced configurations at unitarity(Rice, 2005)
Spin-up
Spin-down
difference
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An effective magnetic field can be produced by separating rigidly the trapping potentials confining the two spin species.
])([2
1)( 2222 dxzymrV
For non interacting gas, equilibrium corresponds to rigid displacement of two spin clouds in opposite direction:
)ˆ(2
1)( 0 xdrnrn
This yields spin dipole moment (we assume )
drnrnxrdN
dD ))()((1
)(
2/NNN
![Page 23: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/23.jpg)
We propose a complementary approach where we study the consequence of an effective magnetic field which can be tuned by properly modifying the trapping potentials.
Main motivation: Fermi superfluids cannot be polarized by external magnetic field unless it overcomes a critical value (needed to break pairs).
What happens in a trapped configuration? What happens at unitarity ?
![Page 24: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/24.jpg)
In the superfluid phase atoms like to be paired. and feel the x-symmetric potential
][2
1))()((
2
1)( 22222 dzyxmrVrVrVS
Competition between pairing effects and external potential favouring spin polarization
])([2
1)( 2222 dxzymrV
![Page 25: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/25.jpg)
VV
SV
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SFAt unitarity
Equilibrium between superfluid and spin polarized phases (Chevy 2005)
2/)2)(()(:0
2/)2)(()(:05/3
5/3
rrx
rrx
S
S
44.0
FS
)()(
)()(
0
0
rVr
rVr SS
![Page 27: Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e435503460f94b36146/html5/thumbnails/27.jpg)
Spin dipole moment D(d)/d as a function of separation distance d (in units of radius of the cloud)
44.0
58.0
ideal gas
Deep BEC
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Further projects:
- Collective oscillations of spin polarized superfluid- Rotational effects in spin polarized superfluids