Ultracold fermions:
A bottom-up approach
Selim Jochim, Universität Heidelberg
A quick advertisement:
4µm
Our 2-D Fermi gas experiment
Momentum Distribution Imaging
Temperature
High T
ky
y
kx
x
T/4 = 25ms
Macroscopic
occupation of
low-momentum
states
Low T
in-situ density distribution n(x,y)
P. Murthy et al., PRA 90, 043611 (2014)
momentum distribution ñ(kx,ky)
Phase Diagram
Non-Gaussian
fraction
normal phase
exp.: Tc/TF
condensed phase
bosonic
M. Ries et al., PRL 114, 230401 (2015)
see also viewpoint: P. Pieri, Physics 8, 53 (2015)
fermionic
Investigate the phase coherence of
these “condensates”
Phase correlations in 2D
Extract correlation function
from momentum distribution
𝑔1,trap (𝑟) = ℱ𝒯 𝑛trap (𝒌)
= ℱ𝒯(
)
Tc/TF = 0.129
BKT: 𝑔1 𝑟 ∼ 1 𝑟 𝜂
consistent with BKT superfluid
 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
Fermi-Dirac dist.
E
~100µm
1
n
p0= 0.9999
• 2-component mixture in reservoir
• superimpose microtrap (~1.8 µm waist)
F. Serwane et al., Science 332, 336 (2011)
Our approach
• switch off reservoir
p0= 0.9999
+ magnetic field gradient in
axial direction
F. Serwane et al., Science 332, 336 (2011)
counts
Spilling the atoms ….
140
100
90
120
80
100
70
60
80
50
60
40
40
30
20
20
10
0
96%88.5%
• We can control the atom number
with exceptional precision
(including spin degree of freedom)
2%
5
0
61
5%
7
2% 6.5%
2 8
39
fluorescence signal
10
4
• Note aspect ratio 1:10: 1-D
situation
• So far: Interactions tuned to
zero …
F. Serwane et al., Science 332, 336 (2011)
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
S. Murmann, A. Bergschneider et al., Phys. Rev. Lett. 114, 080402 (2015)
A tunable double well
J
A tunable double well
Interactions switched off:
well |𝐿⟩
well |𝑅⟩
J
switch off left
well before
counting
atoms
Atom number in well |R>
•
2
1
0
0
25
Time (ms)
50
75
Two interacting atoms
Interaction leads to entanglement:
well |𝑅⟩
J
U
Atom number in well |R>
well |𝐿⟩
2
c)
1
0
0
25 Time (ms)
50
75
Preparing the ground state
•
If we ramp on the second well slowly enough, the system will remain in its
ground state:
•
An isolated singulett
S. Murmann, A. Bergschneider et al., Phys. Rev. Lett. 114, 080402 (2015)
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
Interacting 6Li atoms in 1D
Assume zero range potential in 1D + harmonic confinement
𝑉 𝑥1 − 𝑥2 = 𝑔1𝐷 𝛿 𝑥1 − 𝑥2
Tune 𝑔1𝐷 with confinement induced resonance near Feshbach resonance:
𝜔
Our system: Lithium-6 atoms with 2𝜋 ~15kHz transverse confinement
Energy
F=3/2
F=1/2
|> mI= 0
|> mI= 1
magnetic field [G]
M. Olshanii, PRL 81, 938941 (1998)
Energy of 2 atoms in a harmonic trap
Relative energy of two contact-interacting atoms:
1 2 2
𝑉 𝑥 = 𝜇𝜔 𝑥 + 𝑔1𝐷 𝛿(𝑥)
2
E [ħa]
5/2
3/2
repulsive
1/2
attractive
B-field
-8
-6
-4
-2
2
0
-1/g1D
4
T. Busch et al., Foundations of Physics 28, 549 (1998)
6
8
Energy of 2 atoms in a harmonic trap
Relative energy of two contact-interacting atoms:
1 2 2
𝑉 𝑥 = 𝜇𝜔 𝑥 + 𝑔1𝐷 𝛿(𝑥)
2
E [ħa]
5/2
3/2
repulsive
1/2
attractive
B-field
-8
-6
-4
-2
2
0
-1/g1D
4
T. Busch et al., Foundations of Physics 28, 549 (1998)
6
8
Energy of 2 atoms in a harmonic trap
Relative energy of two contact-interacting atoms:
1 2 2
𝑉 𝑥 = 𝜇𝜔 𝑥 + 𝑔1𝐷 𝛿(𝑥)
2
E [ħa]
5/2
3/2
fermionization
repulsive
1/2
attractive
B-field
-8
-6
-4
-2
G. Zürn et al., PRL 108, 075303 (2012)
2
0
-1/g1D
4
T. Busch et al., Foundations of Physics 28, 549 (1998)
6
8
Energy of more than two atoms?
E [ħa]
5/2
3/2
repulsive attractive
1/2
B-field
-8
-6
-4
-2
0
2
-1/g1D
4
6
8
Energy of more than two atoms
Fermionization
Non-interacting
S=1/2
− 1 𝑔1𝐷 𝑎|| ℏ𝜔||
Gharashi, Blume, PRL 111, 045302 (2013)
Lindgren et al., New J. Phys. 16 063003 (2014)
−1
Bugnion, Conduit, PRA 87, 060502 (2013)
Realization of a spin chain
Fermionization
Noninteracting
S=3/2
S=1/2
S=1/2
− 1 𝑔1𝐷 𝑎|| ℏ𝜔||
Gharashi, Blume, PRL 111, 045302 (2013)
Lindgren et al., New J. Phys. 16 063003 (2014)
−1
Bugnion, Conduit, PRA 87, 060502 (2013)
Realization of a spin chain
Fermionization
Non-interacting
Antiferromagnet
S=3/2
Ferromagnet
S=1
S=1/2
− 1 𝑔1𝐷 𝑎|| ℏ𝜔||
Gharashi, Blume, PRL 111, 045302 (2013)
Lindgren et al., New J. Phys. 16 063003 (2014)
−1
Bugnion, Conduit, PRA 87, 060502 (2013)
Distinguish states by:
• Spin densities
• Level occupation
Measurement of spin orientation
Ramp on interaction strongth
Non-interacting system
− 1 𝑔1𝐷 𝑎|| ℏ𝜔||
−1
Measurement of spin orientation
Ramp on interaction strength
Spill of one atom
Non-interacting system
„Minority tunneling“
„Majority tunneling“
Remove minority atom
− 1 𝑔1𝐷 𝑎|| ℏ𝜔||
−1
N=2
N=1
Measurement of spin orientation
At resonance: Spin orientation of rightmost particle allows identification of state
Theory by Frank Deuretzbacher et al.
Measurement of occupation probabilities
Remove majority
component
with resonant light
Spill technique to measure
occupation numbers
8
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
PRL 114, 230401 (2015)
PRL 115, 010401 (2015)
prepare and manipulate isolated mesoscopic systems with
extremely good fidelity in flexible trapping geometries
J
•
Atom number in well |R>
•
2
PRL 114, 080402 (2015)
1
0
0
25
Time (ms)
50
75
We prepared antiferromagnetic spin chains in 1D tubes
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
Thomas Lompe
(-> MIT)
Thank you for your attention!
Mathias Neidig Simon Murmann
Andrea Bergschneider
Dhruv
Kedar
Luca Bayha
Martin Ries
Vincent Klinkhamer
Andre Gerhard Zürn
Wenz
Justin
Niedermeyer
Puneet Murthy
Funding:
Michael
Bakircioglu