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Ultracold Chromium
a dipolar quantum gas
Quantum Optyks VI, Krynica 16.6.05
Tilman Pfau
University of Stuttgart
Interacting quantum systems in atomic physics
contact interaction
van der Waals
dipole dipole interaction Coulomb interaction
U coul (r) 
short range
isotropic
long range
anisotropic
this talk
long range
isotropic
q1 q2
4πε0 r
Dipolar systems
magnetic
dipoles
electric dipoles
Chromium
Hetero-nuclear molecules
[Ar]3d54s1  S=3
Light induced dipoles
Erbium, Europium …
R. Löw, R. Gati, J. Stuhler and T. Pfau
EPL, in press
Rydberg atoms in E-field
see poster
d
Cr in periodic table of elements
70Yb
Cr - element properties

isotopic distribution

3 Bosons (I=0): 52Cr (83.8%), 50Cr (4.3%),
(2.4%)

1 Fermion (I=3/2): 53Cr (9.5%)

versatile level scheme

electronic configuration


54Cr
[Ar]3d54s1  S=3
large magnetic moment
6 µB!
dipole-dipole interaction!
Cr BEC phase transition
tof = 5 msec
Decreasing T
The Dragontamers
S. Hensler
A.Griesmaier
T. Koch
M. Fattori
Former members:
J. Werner
P.O.Schmidt
A. Görlitz
J. Stuhler
Theory:
K. Rzazewski
S. Giovanazzi
A. Simoni
E. Tiesinga
P. Pedri
L. Santos
Was it worth
all the trouble?
Dipole dipole scattering
Exactly solvable in Born approximation
S. Hensler, J. Werner, A. Griesmaier, P.O. Schmidt, A. Görlitz, T. Pfau, S. Giovanazzi, K. Rzazewski
Appl. Phys. B 77, 765 (2003)
elastic scattering
spin relaxation collisions
spin changing collisions
Dipolar relaxation
atom number
dipolar relaxation
+ spin changing collisions
• Very good agreement between
theory and experiment
• no BEC in magnetic trap
time [sec]
Demagnetization
is a pain!
BUT
could it be useful?
1915:
Einstein - de Haas
for a quantum gas?
Adiabatic demagnetization cooling of a solid
e.g. S=3
Einstein‘s model of a solid
L
<<
kBT
Spin reservoir (large S)
Cv~NkB
D
<<
Phonon reservoir
Cv<<NkB
coupling
Adiabatic demagnetization cooling of a trapped gas?
e.g. S=3
L
>>
kB T
Spin reservoir (large S)
>>
trap
Phonon reservoir
Demagnetising
collisions
Cv<<NkB
Cv~NkB
Single demagnetization step (kBT>>hntrap)
Continuous recycling
Would it work in ODT?
S. Hensler, A. Greiner, J. Stuhler, T. Pfau,
submitted
Example:
ntrap = 500 Hz
Includes:
3 body losses
heat rate due to pump photons
BUT no reabsorption …
Elastic dipole dipole interaction?
elastic scattering only!
7S
3
mJ=+3
mJ=-3
„high field seeker“
optical dipole trap
Strength of elastic dipole-dipole interaction
dipole interaction
compare to
contact interaction:
tunable!
contact interaction
atoms
d
m
Rb
Na
Cr
tuning Rydberg atoms
het.-nucl. molecules
edd=0.007
edd=0.003
edd=0.15
magnetic dipoles
Feshbach
resonance
e.g.: CaH, NH3,
CrRb
eJ.ddWerner
~100
et al.
PRL 94, 183201 (2005)
electric dipoles
spinning
polarization
e.g.: Rb (n=40)*
edd~108
S. Giovanazzi, A. Görlitz, T.P.
PRL 89, 130401 (2002)
Evaporative cooling – phase space density gain
expansion
T>Tc
T<Tc
T<Tc
lifetime of the condensate
t~400msec
n0i= 2×1015 cm-3
t~6 sec
n0i= 2×1014 cm-3
Cr S=3, mS=-3
L3  10−29 cm6 s−1 (upper limit)
Rb F=2, mF=2
L3 = 1.8 × 10−29 cm6 s−1
J. Söding et al. APB, 69, 257 (1999)
Condensate fraction
ideal gas
T=1.1μK
corr. for finite size
and weak interaction*
nx=581 Hz
ny=406 Hz
nz=138 Hz
Tc~700 nK
T=625nK
exp.
A. Griesmaier,
et al.
PRL 94,
160401 (2005)
* S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. A 54, R4633 (1996)
Expansion driven by interaction
T<Tc
Cr
edd=0.15
time of flight
Dipolar interaction as perturbation
BEC without dipoles in an
isotropic harmonic trap
in Thomas –Fermi limit
2 RTF
nTF(r)
perturbation by dipole interaction:
 parabolic density profile
B
Fdd(r)
dipole-dipole interaction & aspect ratio
y
B
z
B
z
aspect ratio
time of flight
r y/rz<1
smaller
aspect
ratio !
r y/rz>1
Magnetostriction!
larger
aspect
ratio !
dipolar expansion - magnetostriction
31 measurements
nx=942 Hz
ny=712 Hz
nz=128 Hz
J. Stuhler, A. Griemaier, T.
Koch, M. Fattori, S.
Giovanazzi, P. Pedri
L. Santos, T. Pfau
submitted
Theory – No free parameters!
S. Giovanazzi, A. Görlitz, and T. Pfau, J. Opt. B: Quantum Semiclass. Opt. 5, S208 (2003).
dipolar coupling in fluids
Ferrofluids
~ 2-20 nm
Strength of elastic dipole-dipole interaction
dipole interaction
compare to
contact interaction:
tunable!
contact interaction
tuning
atoms
m
Rb
Na
Cr
edd=0.007
edd=0.003
edd=0.15
magnetic dipoles
Feshbach
resonance
spinning
polarization
FRs: centrifugal terms & notation
Skip Feshbach
Quantum numbers - notation
atomic
electrons
s,l
molecular
electrons
S,L
S=2 S=4
S=6
centrifugal potentials (e.g.
4)
molecular
nuclei
Cr2 ab initio potentials: Z. Pavlovic et al., PRA 69, 030701 (2004)
FRs: couplings & selection rules
Possible couplings:
2nd order
Spin-Orbit
Spin - Spin
Selection rules:
first order
not allowed!
second order
angular momentum conservation:
expected FRs in Cr
S=6
MS
-2
-3
-4
-5
-6
g - wave
4
d - wave
-4
-5
-6
2
X
MS
S=2
-2
-3
-4
-2
-3
-4
X
-4
-5
-6
initial state
(open channel)
MS
0
-1
-2
m  M S  0
first order
3 resonances
second order 8 resonances
s - wave
0
S=4
} 11
How to see the FR resonance
B
Feshbach resonances in 52Cr
• expectation for collisions of ultracold, fully polarized Cr:
11 resonances (3 first order, 8 second order)
• results (assignment by A. Simoni, E. Tiesinga):
increasing B-field
2
S=6
4
S=4
4
S=2
4
not yet ass.
exp. vs. theory
/Br ~ 210-4
/Br ≈ 0.003
av. agreement of resonance
despite 6 valence e-, Cr is
positions better than 0.6 G incl. not too complicated
• no hyperfine interaction (I=0)
only spin-spin interaction!
J. Werner et al. PRL 94, 183201 (2005)
• dipole-dipole interaction is
dominant coupling mechanism
What do we know about Chromium now?
S=2 S=4
S=6
a6= 112(14) a0
a4= 58(6) a0
a2= -7(20) a0
C6=733(70) a.u.
C8=75(+90/-75) a.u.
summary

Cr-BEC with 105 atoms
new twist: dipole-dipole interaction
dipolar effects visible in Cr

Feshbach resonances




all 11 FR up to 2nd order dipole- dipole
interactions detected (+3)
theo. & exp. fit  a6,a4,a2,C6,C8
outlook


experimental set up
 tuning of contact interaction
 tuning of dipole-dipole interaction
 field compensation
play the dipolar game !
 excitations
 stability and ground state
of condensate
 Roton-Maxon dispersion
Supersolid
relation
 new quantum phase
transitions ...
unstable
stable
pancake
Checkerboard
Further outlook
Demagnetization cooling
Trap fermion (see Poster Villetaneuse)
Lithography:
controlled single atom deposition?
Cr3+:Al203 Cr3+:LiSAF Cr3+:LiNb03
Cr:GaN
cw atom laser ?
More projects….
postdocs &
phd students
welcome !!!
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