experiments on few fermion systems of ultracold atoms · • quantum control in a many-body system...
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Experiments on few fermion systems
of ultracold atoms
…and the crossover to many-body systems
Workshop
Resonances and Non-Hermitian Quantum
Mechanics in Nuclear and Atomic Physics
Trento, June 2014
Gerhard Zürn
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Realize a well-controlled and tunable quantum system using ultracold atoms
A tunable few-body system
Few-fermion systems in nature:
• atoms, nuclei
well defined quantum state
limited tunability of interaction
How can one study few body effects?
interaction
Artificial Quantum system:- quantum dots
- atomic clusters
Wide tunability,
but no „identical“ systems
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• Quantum control in a many-body system is becoming possible!
W. Bakr et al., Science 329, 547, 2010 C. Weitenberg et al., Nature 471, 319-324, 2011
Control at the single particle level
We aim for bottom up approach:
Start with few-fermion system and then increase towards a many-body system
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Outline
• Preparation and control of few-fermion systems
• Pairing in a few-fermion system with attractive interactions
• From few to many: Building a Fermi sea from single
particles
• (Two fermions in a double well)
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Outline
• Preparation and control of few-fermion systems
• Pairing in a few-fermion system with attractive interactions
• From few to many: Building a Fermi sea from single
particles
• (Two fermions in a double well)
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High Fidelity Preparation
• 2-component mixture in reservoir T=250nK
• superimpose microtrapscattering thermalisation
• switch off reservoir
p0= 0.9999
+ magnetic field gradient in
axial direction
expected degeneracy: T/TF= 0.1
count
F. Serwane, G. Zürn, T. Lompe, T. Ottenstein, A. Wenz and S. Jochim, Science 332, 336 (2011)
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Single atom detection
CCD
1-10 atoms can be distiguished
with high fidelity (> 99% )
1/e-lifetime: 250s
Exposure time 0.5s
F. Serwane, G. Zürn, T. Lompe, T. Ottenstein, A. Wenz and S. Jochim, Science 332, 336 (2011)
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fluorescence normalized to atom number
2 atoms 8 atoms
F. Serwane, G. Zürn, T. Lompe, T. Ottenstein, A. Wenz and S. Jochim, Science 332, 336 (2011)
Lifetime in ground state ~ 60s
count the
atoms
High Fidelity Preparation
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750 800 850 900
-20
-10
0
10
20
a3
D [
10
3 a
0]
magnetic field [G]
3D
-1
0
1
g1
D [
10
ap
erp ħ
p
erp]
750 800 850 900
-20
-10
0
10
20
a3
D [
10
3 a
0]
magnetic field [G]
1D
M. Olshanii, PRL 81, 938 (1998)
2
31D 2
3
2 1g =
1 /
D
D
a
ma Ca a
radially strongly confined
aspect ratio: II / perp 1:10 1D
Z. Idziaszek and T. Calarco, PRA 74, 022712 (2006)
Interaction in 1D
PRL 110, 135301 (2013) PRL 110, 203202 (2013)
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Studying few-body physics
control of the particle number
tunability of the interpart. interactionshaping the trapping potential
-3 -2 -1 0 1 2 3
-2
0
2
E [hll]
-1/g
[allh
ll]-1
imbalanced
balanced
T. Busch et al., Found. Phys. 28, 549 (1998)
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Outline
• Preparation and control of few-fermion systems
• Pairing in a few-fermion system with attractive interactions
• From few to many: Building a Fermi sea from single
particles
• (Two fermions in a double well)
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Probing the system
Observe tunneling dynamics:
•Tilt the trap such that the highest-lying states have an experimentally
accessible tunneling time of about 10-1000ms.
From the observed tunneling time scale we can then infer the total
energy of the system
G. Zürn, F. Serwane, T. Lompe, A. Wenz, M. Ries, J. Bohn and S. Jochim, PRL 108, 075303 (2012)
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Attractive interactions
• Use this to determine the pairing energy
• Problem: tunneling of the two particles is correlated
G. Zürn, A. Wenz , S. Murmann, A. Bergschneider, T. Lompe, and S. Jochim, PRL 111, 175302 (2013)
0 250 500 750 10000.0
0.5
1.0
1.5
2.0
569 G g
= 0.01 [aref
ħref
]
N
Hold time [ms]0 250 500 750 1000
0.0
0.5
1.0
1.5
2.0
569 G g
= 0.01 [aref
ħref
]
350 G g
= - 0.64
N
Hold time [ms]0 250 500 750 1000
0.0
0.5
1.0
1.5
2.0
569 G g
= 0.01 [aref
ħref
]
350 G g
= - 0.64
1202 G g
= - 1.42
N
Hold time [ms]
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Correlated tunneling
• Set up rate equation for tunneling
G. Zürn, A. Wenz , S. Murmann, A. Bergschneider, T. Lompe, and S. Jochim, PRL 111, 175302 (2013)
• extract single particle separation energy
• Fit rate coefficients to the data (consistent with subsequent single particle tunneling)
0 100 200 300 400 500
0.0
0.2
0.4
0.6
0.8
1.0
P2 fit
Pi
Hold time [ms]
0 100 200 300 400 500
0.0
0.2
0.4
0.6
0.8
1.0
P2 fit
P1 fit
g
= - 0.64
Pi
Hold time [ms]
2.0 1.5 1.0 0.5 0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
g
[aref
ħref
]
g
= 0.01
g
= - 0.44
g
= - 0.64
g
= - 1.42
g
= - 1.76
P1
N
-0.3
-0.2
-0.1
0.0
0 0 -1 -2
E
[ħ
ref ]
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1 2 3 4 5 6
-0.3
-0.2
-0.1
0.0
0.1
E21
E11
E20
E00
E10
E22
Ese
p [
ħ
ref ]
Particle number
Odd-even effect with ultracold fermions
• How does the energy of the system evolve for larger systems?
G. Zürn, A. Wenz , S. Murmann, A. Bergschneider, T. Lompe, and S. Jochim, PRL 111, 175302 (2013)
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Theory: M. Rontani et. al, arXiv:1404.7762
Theory:
- Study non-perturbative regime
- Pairing in higher dimensions (2D, 3D)
- larger systems, superfluidity
Prospects:
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Outline
• Preparation and control of few-fermion systems
• Pairing in a few-fermion system with attractive interactions
• From few to many: Building a Fermi sea from single
particles
• (Two fermions in a double well)
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N=2 N=5…N=1
From few to many-body physics
How many is many?
Observable: Interaction energy vs. particle number and interaction strength
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RF-Spectroscopy
EintEHFS
-0.2 0.0 0.2 0.4 0.60.0
0.2
0.4
0.6
Tra
nsfe
rred
fra
ction
free-free
Frequency [kHz]
EHFS + Eint
-0.2 0.0 0.2 0.4 0.60.0
0.2
0.4
0.6
Tra
nsfe
rred
fra
ction
free-free
N=1, g1D
= - 0.27 allħ
ll
Frequency [kHz]
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Measure the interaction energy
A. N. Wenz, G. Zürn, S. Murmann, I. Brouzos, T. Lompe and S. Jochim, Science 342, 457 (2013)
A single impurity repulsively interacting
with an increasing number of majority particles
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Natural scales of the system
The interaction energy diverges for Nmaj∞. Therefore rescale Eint onto natural
scale of a Fermi gas EF to obtain a dimensionless quantity:
Eint Eint/EF
The interaction strength is rescaled with the Fermi momentum kF (~1/interparticle
spacing) to obtain a dimensionless quantity:
g1D g1D/kF
g1D/kF ~ γ the Lieb-Liniger parameter
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N=1
N=2
N=3N=4
N=5
Measure the interaction energy
Analytic solution of the two particle problem
T.Busch et al., Found. Phys. 28, 549 (1998)
Analytic solution for an infinite number of majority particles
J. McGuire, J. Math. Phys. 6,432 (1965)
Adapted from homogeneous to trapped case by local density approximation
non interacting strongly repulsive
A. N. Wenz, G. Zürn, S. Murmann, I. Brouzos, T. Lompe and S. Jochim, Science 342, 457 (2013)
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Measure the interaction energy
2 particles
N particles
3 particles
non interacting strongly repulsive
S.E. Gharashi et al.,
PRA 86, 042702 (2012)
Four is Many!
A. N. Wenz, G. Zürn, S. Murmann, I. Brouzos, T. Lompe and S. Jochim, Science 342, 457 (2013)
see also:
Astrakharchik,
Conduit, T.-L. Ho,
Lewenstein, Rontani,
Santos, Zinner …
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Outline
• Preparation and control of few-fermion systems
• Pairing in a few-fermion system with attractive interactions
• From few to many: Building a Fermi sea from single
particles
• Realize a tunable potential
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Creating a tunable potential
Acousto-
optic
deflector
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Tunneling in a double-well
JPreparation Detection scheme
U = 0
• Single-part. tunneling
• Calibration of J
~1/2𝐽
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• Correlated tunneling
• Calibration of U
U ≠ 0
9
JPreparation Detection scheme
Tunneling in a double-well
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Measuring Energies in a DW
Conditional
single-particle tunnelingResonant pair tunneling
Measure amplitudes of
single-particle and pair
tunneling as a function of
tilt
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Preparation of the ground state
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The eigenstates
Spectrum of eigenenergies
for the balanced case:
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Number statistics for the balanced case depending on the interaction strength:
Single occupancy
Double occupancy
12
Occupation statistics
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Single occupancy
Double occupancy
12
Number statistics for the balanced case depending on the interaction
strength:
Occupation statistics
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Summary
• We can prepare and control few-fermion systems
• Observed Crossover from few- to many-body regime
• Next: Fermi-Hubbard physics
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How to prepare systems which are
not balanced in spin ?
• Go to 27G, where magnetic moment
of state | 2 vanisches
• Gradient only affects atoms in state | 2
• Further changes between hyperfine
states with RF transfer
Breit-Rabi Formula
Creating imbalanced systems
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Feshbach resonances in 6Li
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The ground state of the double well
Two non-interacting particles:
One particle:
• basis
• Ground state
• Ground state at U=0
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11
Eigenenergies in the Hubbard Model
How to measure energy differences between eigenstates?
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