physics with ultracold fermions Selim Jochim Physikalisches Institut Universität Heidelberg The matter we deal with T 40nK 1µK Density n 10 9 10 14 cm 3 Pressures ID: 280440
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Slide1
Few-body
physics
with
ultracold
fermions
Selim
Jochim
Physikalisches Institut
Universität HeidelbergSlide2
The matter we deal with
T
=40nK … 1µKDensity n=10
9
… 10
14cm-3Pressures as low as 10-17mbarkBT ~ 5peVExtremely dilute gases, which can be strongly interacting!
Extreme matter!Slide3
Important
length scales
interparticle separation
size
of the atomsde Broglie wavelength size of the atoms scattering length a , only one length determines
interaction strength
→ Universal
properties
,
independent
of a particular system!
→ We can tune all
the above parameters
in our experiments!
Slide4
Few-body
system
: Tune
the
binding energy of a weakly bound molecule:
Tunability of ultracold systems4
Size (>>
range
of interaction):
Binding energy:
Feshbach resonance: Magnetic-field dependence of s-wave scattering
lengthSlide5
Ultracold Fermi gases
At
ultracold temperatures
, a gas
of
identical fermions is noninteractingIdeal Fermi gas5Slide6
Ultracold Fermi gases
6
Need
mixtures
to
study
interesting
physics
!
Simplest
implementation
:
spin
mixtures
(↑,↓)Slide7
Ultracold Fermi gases
Two
(
distinguishable
)
fermions form a boson ….. … molecules
can form a Bose condensate …
7
→ realize the BEC-BCS crossover!Slide8
Ultracold Fermi gases
Two
(
distinguishable
)
fermions
form a
boson
…..
…
molecules
can
form a Bose
condensate
…
… tune
from strongly
bound molecules to
weakly
bound Cooper pairs
8
From A. Cho, Science 301, 751 (2003)
→ realize the BEC-BCS crossover!Slide9
A
picture
from the
lab …Slide10
What
’s going on in our
lab
Universal
three-body
bound states „Efimov“ trimersT. Lompe et al., Science 330, 940 (2010)
Finite Fermi
systems
with
controlled interactions
A new playground
with control at
the single
atom level!
F. Serwane et al., Science 332, 336 (2011)Slide11
The Efimov
effect
An infinite
number
of
3-body
bound states
exists when
the scattering length diverges: (3 identical
bosons)
At
infinite
scattering
length
:
E
n
=22.7
2
E
n+1 Scattering
length values where
Efimov trimers become
unbound an+1=22.7a
n
1/
a
(
strength
of
attraction
)Slide12
Observing an
Efimov Spectrum?
10nm
(1st
state
)
5.2µm
(3rd
state
)
227nm
(2nd state)
2.7mm(5th state
)0.12mm
(4th state)Slide13
What
is
observed
in experiments?three-body recombination
deeply
bound
moleculeSlide14
Enhanced
recombination
With
an (
Efimov
) trimer at threshold recombination is enhanced:
deeply
bound
molecule
1/
a
(
strength
of
attraction
)Slide15
What
has been
done in experiments?
Observe
and analyze collisional stability in ultracold gasesseminal experiment with ultracold Cs atoms (Innsbruck):
T. Krämer et al., Nature 440, 315 (2006)Slide16
The
6Li atom
16
|1>
|2>
a
12
Need three distinguishable fermions with
(in general) different scattering lengths:
(S=1/2, I=1 -> half-integer total angular
momentum
)Slide17
The
6Li atom
17
|1>
|3>
|2>
a
13
a
12
a
23
Need three distinguishable fermions with
(in general) different scattering lengths:
couple
Zeeman
sublevels
using
Radio-
frequency
B-
fields: „Radio Ultracold“Slide18
2-
and 3-body bound
states ….
Binding
energies
of dimers and trimers:Three different universal dimers with binding energyWhere are trimer
states?
1/
a
(
strength
of
attraction
)Slide19
Where
are the trimer
states?
Observe
crossings
as
inelastic
collisions
T. Ottenstein et al., PRL
101
, 203202 (2008)
T. Lompe et al., PRL
105
, 103201 (2010)
Also:
Penn State:
J. Huckans et al., PRL
102
, 165302 (2009)
J. Williams et al. PRL 103, 130404 (2009)
University of Tokyo:
Nakajima et al., PRL 105, 023201 (2010)
RG based theory: R. Schmidt, S.
Flörchinger et al. Phys. Rev. A 79, 053633 (2009)Phys. Rev. A 79, 042705 (2009)Phys. Rev. A 79, 013603 (2009)Slide20
Can
we
also
measure
binding
energies?Theory
data
from: Braaten et al., PRA
81, 013605 (2010)
RF
field
Attach
a third
atom to a dimer
Measure
binding energies
using RF spectroscopy
|2>
|2>
|2>
|1>
|1>
|3>Slide21
RF-
association
of
trimers
dimer
trimer
T. Lompe
et al.
, Science
330
, 940 (2010)
radio
frequency
radio
frequency
[MHz]Slide22
RF-
association
of
trimers
22
T. Lompe
et al.
, Science
330
, 940 (2010)
T. Lompe
et al.
, PRL
105
, 103201 (2010)
With
our
precision
: theoretical prediction
of the
binding energy
confirmed: Need
to include finite
range corrections
for dimer binding
energies
Same results for
two different initial
systems
More recent
results: Nakajima et al., PRL 106,143201 (2011)
Slide23
An ultracold three-component Fermi gas
23
Fermionic
trions
, „Baryons“Slide24
An ultracold three-component Fermi gas
24
Color Superfluid
Starting
grantSlide25
What
’s going on in our
laｂ
Three
component Fermi gasesRF-spectroscopy of Efimov trimers
T. Lompe et al., Science 330, 940 (2010)
Finite Fermi
systems
with controlled
interactionsA new
playground with
control at the
single atom
level!F. Serwane et al., Science
332, 336 (2011)Slide26
Our
motivation
Extreme repeatability and
control
over all degrees of freedom, but limited tunability
Quantum
dots
,
clusters …
Wide
tunability
,
but
no „
identical“ systems
Atoms,
nuclei
…Slide27
Conventional
trap
like
a
soup
plate
!
Shot
glass
type
trap
Creating
a finite gas
of
fermions
Control the number of quantum states in the trap!
…
small
density
of
states
Large density
of states …Slide28
Transfer atoms to a
microtrap …Slide29
Spill most of the atoms:
“laser culling of atoms”: M.
Raizen
et al
.,
Phys. Rev. A 80, 030302(R)
Use a magnetic field gradient to spill:
Lower
trap depth
µ x B
~600
atoms
~2-10
atomsSlide30
Atoms in a
microtrap
Transfer a few
100
atoms
into a tightly focused trap (~1.8µm in size, 1.4kHz axial, 15kHz radial trap
frequencies)
100µm
100µm
Trap potential
is
proportional
to
intensity,
good approximation: harmonic at the centerSlide31
Single
atom detection
CCD
distance
between
2
neighboring
atom
numbers : ~ 6
s1-10 atoms can
be distinguished
with high fidelity > 99%
one
atom
in a MOT1/e-lifetime: 250s
Exposure time 0.5sSlide32
Starting
conditions
Reservoir
temperature
~250nK
Depth of microtrap: ~3µK Expect
Occupation
probability
of
the lowest
energy state: > 0.9999
100µm
100µm
L.
Viverit
et al. PRA 63, 033603 (2001)Slide33
Spill
atoms
in a
controlled
way
Recapture
prepared
atoms
into magneto-optical
trap
Preparation
sequenceSlide34
Spilling
the
atoms ….
We
can control the atom number with exceptional precision!Note aspect ratio 1:10: 1-D situation
1kHz
~400feVSlide35
A
green
laser
pointer trapOutput power:Total output ~70mW
Most of
it
green, 532nm
About 10mW
at 1064nm,
Some pump
light
at 808nm.
At
suitable pump
current
:It
emits
a single
longitudinal mode
(
single
frequency)
Has
very
low
noise: RIN < -110dB/HzSlide36
We
have
decent control over the motional degrees of freedom
! What
about
interactions?Slide37
The
6Li atom
37
|1>
|2>
a
12
(S=1/2, I=1 -> half-integer total angular
momentum
)Slide38
First
few-body interactions …
Interaction-
induced
spilling
!
F. Serwane et al., Science
332
, 336 (2011)Slide39
First
few-body
interactions
What
happens
if we bring the
two
atoms in
the ground state
across the Feshbach
resonanceOne atom
is observed in
n=2
a~0
a>0Slide40
Interactions in 1D
Feshbach
resonance
Confinement
induced resonance
(
for
r
adial
harmonic
confinement
)
M. Olshanii, PRL
81, 938 (1998).
1
D
3D
Trap
has
aspect
ratio 1:10Slide41
Energy
of
2
atoms
in the trapRelative kinetic energy of
two interacting
atoms (
exact
solution!)
x
2
-x
1
(relative
coordinate
)
T. Busch et al., Foundations of Physics
28
, 549 (1998)Slide42
2
distinguishable
vs. 2
identical
fermions
Tunneling time
equal
to
case
of
two
identical
fermions
:
the
system
is
„
fermionized
“
2
distinguishable
fermions
2
identical
fermionsSlide43
Tunneling dynamicsSlide44
Fermionization
relative
wave
function
2
distinguishable fermions
2
identical
fermions
(2-particle limit
of a Tonks-Girardeau gas)
ground
state
Wave
function
square
,
and
energy
are
identical!Slide45
Conclusion
We
detect and
count
single atoms with very high fidelityWe prepare few-fermion systems with unprecedented controlWe control
the interactions in the few-fermion system
A toolbox
for the
study of few-body systemsSlide46
The
future
Investigate interacting
few-body
systems in the ground state: Few-body „quantum simulator“Realize multiple interacting wells
Measure
pairing
in a finite
system
Study
dynamics
of
few-fermion
systems: How
many atoms do we
need to
have
a thermal ensemble?Slide47
Thank
you
very
muchfor your attention!André Wenz
Martin Ries
Gerhard Zürn
Selim Jochim
Thomas Lompe
Johanna Bohn
Friedhelm Serwane