Selim Jochim, Universität Heidelberg Ultracold fermions: A bottom-up approach.

Selim Jochim, Universität Heidelberg

Ultracold fermions: A bottom-up approach

A quick advertisement:

4µm

Our 2-D Fermi gas experiment

Momentum Distribution Imaging

P. Murthy et al., PRA 90, 043611 (2014)

in-situ density distribution n(x,y) momentum distribution ñ(kx,ky)

High T

Low T

Tem

pera

ture

Macroscopic occupation of low-momentum states

T/4 = 25ms

x

y

kx

ky

Phase Diagram

Non-Gaussian fraction

normal phase

condensed phase

exp.: Tc/TF

bosonic fermionic

M. Ries et al., PRL 114, 230401 (2015)

see also viewpoint: P. Pieri, Physics 8, 53 (2015)

Investigate the phase coherence of these “condensates”

Phase correlations in 2D

Extract correlation functionfrom momentum distribution

𝑔1 ,trap (𝑟 )=ℱ𝒯 (~𝑛trap(𝒌))( )

Tc/TF = 0.129

consistent with BKT superfluid

BKT:

We are able to extract

η(T, ln(kF a2D))

P. Murthy et al., PRL 115, 010401 (2015)

This talk: Experiments with few particles

Discrete systems: Work at „T=0“

Our approach to prepare few atoms

• superimpose microtrap (~1.8 µm waist)

p0= 0.9999

• 2-component mixture in reservoir

E

n1

Fermi-Dirac dist.

~100µm

F. Serwane et al., Science 332, 336 (2011)

Our approach

• switch off reservoir

p0= 0.9999

+ magnetic field gradient in axial direction


Spilling the atoms ….

•We can control the atom number with exceptional precision

(including spin degree of freedom)

•Note aspect ratio 1:10: 1-D situation

•So far: Interactions tuned to zero …

0 1 2 3 40

102030405060708090

100

2% 2%

coun

ts

fluorescence signal

96%

5 6 7 8 9 100

20

40

60

80

100

120

140

6.5%5%

88.5%

cou

nts

fluorescence signal


Realize multiple wells …

….. with similar fidelity and control?

S. Murmann, A. Bergschneider et al., Phys. Rev. Lett. 114, 080402 (2015)

See also viewpoint: Regal and Kaufman, Physics 8, 16 (2015)

The multiwell setup

Light intensity distribution


A tunable double well

J

• Interactions switched off:

A tunable double well

J

0 25 50 750

1

2

Ato

m n

um

be

r in

we

ll |R

>

Time (ms)

well well

switch off left well before counting atoms

Two interacting atoms

U

J

0 25 50 750

1

2

Ato

m n

umbe

r in

wel

l |R

>

Time (ms)

c)

well well

Interaction leads to entanglement:

Preparing the ground state

• If we ramp on the second well slowly enough, the system will remain in its ground state:

• An isolated singulett


How to scale it up?

• Preparation of ground states in separated double wells

• Combination to larger system

Can this process be done adiabatically ? Can it be extended to larger systems ?

Motivated by: D. Greif et al., Science 340, 1307-1310 (2013) (ETH Zürich)

First steps towards magnetic ordering

Realize a Heisenberg spin chain through strong repulsion

Lots of input from theory: Dörte Blume, Ebrahim Gharashi, N. Zinner, G. Conduit, J. Levinsen, M. Parish, P. Massignan, C. Greene, F. Deuretzbacher

Assume zero range potential in 1D + harmonic confinement Tune with confinement induced resonance near Feshbach resonance:Our system: Lithium-6 atoms with 15kHz transverse confinement

Interacting 6Li atoms in 1D

M. Olshanii, PRL 81, 938941 (1998)

F=3/2

En

erg

y

magnetic field [G]

F=1/2

|>|>

mI= 0

mI= 1

-8 -6 -4 -2 0 2 4 6 8

5/2

3/2

E [ħ

a]

-1/g1D

1/2

Energy of 2 atoms in a harmonic trap

Relative energy of two contact-interacting atoms:

T. Busch et al., Foundations of Physics 28, 549 (1998)

𝑉 (𝑥 )=12𝜇𝜔2𝑥2+𝑔1 𝐷𝛿(𝑥)

repulsive attractive

B-field

-8 -6 -4 -2 0 2 4 6 8

5/2

3/2

E [ħ

a]

-1/g1D

1/2





B-field

𝑉 (𝑥 )=12𝜇𝜔2𝑥2+𝑔1 𝐷𝛿(𝑥)

-8 -6 -4 -2 0 2 4 6 8

5/2

3/2

E [ħ

a]

-1/g1D

1/2



G. Zürn et al., PRL 108, 075303 (2012)



B-field

fermionization

𝑉 (𝑥 )=12𝜇𝜔2𝑥2+𝑔1 𝐷𝛿(𝑥)

-8 -6 -4 -2 0 2 4 6 8

5/2

3/2

E

[ħ a]

-1/g1D

1/2

Energy of more than two atoms?


B-field

Energy of more than two atoms

Fermionization

Energy¿

−1 /𝑔1𝐷 ¿¿

Non-interacting

Gharashi, Blume, PRL 111, 045302 (2013)Lindgren et al., New J. Phys. 16 063003 (2014)

Bugnion, Conduit, PRA 87, 060502 (2013)

S=1/2

Realization of a spin chain

Energy¿

−1 /𝑔1𝐷 ¿¿

Non-interacting

Fermionization



S=1/2

S=3/2

S=1/2

Realization of a spin chain

Distinguish states by:• Spin densities• Level occupation

Energy¿

−1 /𝑔1𝐷 ¿¿

Non-interacting Antiferromagnet

Ferromagnet

Fermionization



S=1

S=3/2

S=1/2

Measurement of spin orientation

Non-interacting systemEnergy¿

−1 /𝑔1𝐷 ¿¿

Ramp on interaction strongth

Spin chain


Non-interacting system

Spill of one atom

Ramp on interaction strength

„Minority tunneling“

Energy¿

−1 /𝑔1𝐷 ¿¿

„Majority tunneling“

Remove minority atom

N = 2 N = 1

Spin chain


At resonance: Spin orientation of rightmost particle allows identification of state

Theory by Frank Deuretzbacher et al.

Measurement of occupation probabilities

Spill technique to measure occupation numbers

8

Remove majority component

with resonant light

We can prepare an AFM spin chain!

9

Can we scale it up??

Approach 2:

• Can we induce suitable correlations by spilling atoms?

𝐽𝑇𝑢𝑛𝑛𝑒𝑙

𝐽𝑆𝑝𝑖𝑙𝑙

?

Summary

• We studied the phase diagram and coherence properties of a 2-D Fermi gas and

• prepare and manipulate isolated mesoscopic systems with extremely good fidelity in flexible trapping geometries

• We prepared antiferromagnetic spin chains in 1D tubes

J 0 25 50 750

1

2

Ato

m n

umbe

r in

wel

l |R

>

Time (ms)

PRL 114, 080402 (2015)

PRL 114, 230401 (2015)PRL 115, 010401 (2015)

PRL 108, 075303 (2012)S. Murmann et al., arxiv:1507.01117

Outlook

• Can we scale up our systems?

• or

𝐽𝑇𝑢𝑛𝑛𝑒𝑙

𝐽𝑆𝑝𝑖𝑙𝑙

?

See Andrea Bergschneider‘s poster

Vincent Klinkhamer

Andrea Bergschneider

Gerhard Zürn

Thank you for your attention!

Funding:

AndreWenz

Thomas Lompe(-> MIT)

Dhruv Kedar

Martin Ries

Mathias Neidig

Puneet Murthy

Simon Murmann

Michael Bakircioglu Justin

Niedermeyer

Luca Bayha

Selim Jochim, Universität Heidelberg Ultracold fermions: A bottom-up approach.

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