Novel Probes for Fermionic GasesNovel Probes for Fermionic Gases

J. Meineke, T. Müller, B. Zimmermann, D. Stadler

J.-P. Brantut, H. Moritz, T. Esslinger

ETH Zürich

J. Meineke, T. Müller, B. Zimmermann, D. Stadler

J.-P. Brantut, H. Moritz, T. Esslinger

ETH Zürich

Experimental setup

6Li atomsMicroscopeobjectives

Microscope setup

Microscope setup

High-resolution imaging system:

• resolution: 660nm (FWHM) for =671nm

• NA = 0.53, magnification factor: 54

Microscopic manipulation

flexible micro-tweezers

Atoms in micro-traps

a=2.5 m 6.9 m

Square lattice Ring lattice

B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, H. Moritz, New Journal of Physics 13, 043007 (2011)

Imaging through the microscope

500m

“standard” imaging

20μm

high resolution imaging

Information on• correlations, quantum statistics?• temperature, susceptibilities?• entanglement?

Microscopic probing …

… of in-situ density fluctuations

Quantum statistics and fluctuations

Suppressed density fluctuations in a degenerate Fermi gasdue to Pauli principle!

...

2

11

3

23 V

N NN 2

thermal higher order quantum correction

thermal quantum degenerate

probe volume

For 1D Bose gases: J. Esteve et al., PRL 96,130403 (2006) & J. Armijo et al., PRL 105, 230402 (2010)For 2D Bose gases: C.-L. Hung, X. Zhang, Na. Gemelke, C. Chin, Nature 470, 236 (2011)

Measurement of density fluctuations

• Account for photon shot noise and imaging effects

• Calculate mean and variance over many realizations

different realizations absorption imaging

Fluctuation in gas on a pixel

Effect of imaging resolution

Manifestation of antibunching

Our work at ETH Zürich:PRL 105, 040401 (2010)

Indication for the level oflocal quantum degeneracy

Similar work at MIT in TOF:PRL 105, 040402 (2010)

Thermodynamic properties

Fluctuation-dissipation theorem:2N

NTkB

densityfluctuations

model independent measurement of temperature

Compressibility κ

local density approximation

1)(

rr

rN

Q. Zhou and T. L. Ho, arXiv: 0908.3015, to appear in PRL; κ in SF-MI: N. Gemelke, X. Zhang, C.-L. Hung, C. Chin, Nature 460, 995 (2009).

20

0

NN

UU

TkB

Fluctuation-based thermometry

Temperature: Conventional Fluctuation-based

degenerate 20530 nK 14531 nK

thermal 1,6 0.2 K 1,1 0.06 K

N

UU

TkN B

00

2

T. Müller , B. Zimmermann, J. Meineke, J.-P. Brantut, T. Esslinger, H. Moritz, Phys. Rev. Lett. 105, 040401 (2010)

Local Spin-FluctuationsLocal Spin-Fluctuations

hm2i = h(n1 ¡ n2)2i = hn21i +hn2

2i ¡ 2hn1n2i

hn1n2i = hª y"ª "ª

y#ª #i

Two-component quantum gas

Atom-Light InterfaceAtom-Light Interface

Hammerer et al., Rev. Mod. Phys. 82, 1041 (2010)

X̂ out = X̂ in + ·p2M̂z

Light

Atoms

Atom-Light InterfaceAtom-Light Interface

Bruun et al., PRL 102, 030401 (2009)

hX̂ 2outi = 1

2 + ·2hM̂

2z i

Measuring Spin-PolarizationMeasuring Spin-Polarization

Measuring Spin-PolarizationMeasuring Spin-Polarization

Á / (n1 ¡ n2)| {z }m

Spin-polarization

Speckle: Sanner et al., PRL 106, 010402 (2011)

Phase

The InterferometerThe Interferometer

The InterferometerThe Interferometer

PerformancePerformance

Single component: Phase-shift proportional to atomic density

PerformancePerformance

Photon shot-noise limited

ResultsResults

Distribution of Spin-PolarizationDistribution of Spin-Polarization

Weakly interacting gas

Distribution of Spin-PolarizationDistribution of Spin-Polarization

Weakly interacting gas

Distribution of Spin-PolarizationDistribution of Spin-Polarization

Weakly interacting gas

Distribution of Spin-PolarizationDistribution of Spin-Polarization

Strong repulsive interactions

Suppression of Spin-FluctuationsSuppression of Spin-Fluctuations

±m2

±m2thermal

• Relative suppression

• Agrees with theory for noninteracting Fermions

• Analogous to suppression of density-fluctutations due to

antibunching

9.2dB

Spin-SusceptibilitySpin-Susceptibility

kBTÂ=±M 2 ) kBTÂcol =A±m2

spin-susceptibility  = @(n1¡ n2)@(¹ 1¡ ¹ 2)

Measurements of spin-susceptibility: Salomon, Zwierlein, Ketterle

Spin-SusceptibilitySpin-Susceptibility

kBTÂ=±M 2 ) kBTÂcol =A±m2

spin-susceptibility  = @(n1¡ n2)@(¹ 1¡ ¹ 2)

EntanglementEntanglement

EntanglementEntanglement

~J =P

~¾i

¢ J 2z

hN i ¸ 23 ) A±m2

ncol¸ 2

3Wiesniak et al., NJP 7, 258 (2005); Toth et al., PRA 79, 042334 (2009)

EntanglementEntanglement

~J =P

~¾i

¢ J 2z

hN i ¸ 23 ) A±m2

ncol¸ 2

3

ncol (¹m¡ 2)

Am

2 (

μm

-2)

Wiesniak et al., NJP 7, 258 (2005); Toth et al., PRA 79, 042334 (2009)

fluctuationscorrelationsfluctuationscorrelations

Novel ProbesNovel Probes

thermodynamicproperties

thermodynamicproperties

mesoscopicsystems

mesoscopicsystems

Microscopic access

TeamworkTeamwork

DavidStadler

TorbenMüller

SebastianKrinner

Jean-PhilippeBrantut

Henning Moritz

Tilman Esslinger

JakobMeineke

Data ProcessingData Processing

Novel Probes for Fermionic GasesNovel Probes for Fermionic Gases

J. Meineke, T. Müller, B. Zimmermann, D. Stadler

J.-P. Brantut, H. Moritz, T. Esslinger

ETH Zürich

J. Meineke, T. Müller, B. Zimmermann, D. Stadler

J.-P. Brantut, H. Moritz, T. Esslinger

ETH Zürich