Transcript Towards Bose-Einstein Condensation of Chromium

towards
Ultracold Chromium
a dipolar quantum gas
Tilman Pfau
University of Stuttgart
History of BEC
Rb 1995
11
Na 1995
3
Li
1997
1
H
1998
1
10
1
3
5
2
1
1
1
1
1
2
1
2001
1
1
Cs 2002
1
Yb 2003
Yb
2003
Cr 2004
Cr 2004
1
1
He* 2001
K
3
1
Stuttgart, 25.Nov12004
1
1
1
Chromium
• No HFS
• High magnetic moment 6mB
70
Yb
Why bother?
Contact and Long Range Interaction in
Quantum gases
Contact interaction
• isotropic
• short range
Dipolar interaction
• anisotropic
• long range
z

r
nonlinear matter wave optics
strong correlations:
Bose-Hubbard...
stability and ground state of BEC
magnetism: Heisenberg, Ising,
frustrated lattices...
Dipolar coupling in fluids
Ferrofluids
~ 2-20 nm
Application:
rotary seals in disk drives
dampers for audio speakers
Dipolar coupling in gases?
k BTc  VDD
1
~ 3 ~n
r
solid
n ~1023/cm3
Tc~ 1K (Texc ~ 100-1000K)
air
n ~1019/cm3
Tc~ 0.1 mK
ultracold gas
n ~1014/cm3
Tc~ 1 nK
 12 
n  

2
 m 0m M 
2
Weak interaction:
3
magnetic dipoles
n <<1021/cm3
electric dipoles
n <<109/cm3
How strong is the dipolar
interaction?
dipole strength (tunable)
compare to
contact interaction:
scattering length (tunable)
atoms
m
Cr
Rb
Na
edd=0.15
edd=0.007
edd=0.003
magnetic dipoles
heteronuclear molecules
Rydberg atoms
d
e.g.: CaH, NH3, CrRb
edd~100
e.g.: Rb (n=40)
edd~108
electric dipoles
How to tame Chromium
4 stable isotopes:
Bosons
Fermion
52Cr
50Cr
54Cr
53Cr
83.8%
4.3%
2.4%
9.5%
Preparation of an ultracold Cr sample:
• Continously loaded Ioffe Pritchard trap
(CLIP-trap)
J. Stuhler, et al., Phys. Rev. A 64, 031405 (2001)
P. O. Schmidt, et al., J. Opt. B 5, S170 (2003)
• Compress IP-trap
• Doppler cooling in the IP-trap at high
offset field
P. O. Schmidt, et al., J. Opt. Soc. Am. B 20, 5 (2003)
2x108 atoms in the ground state
phase space density r~10-7
• Temperature is adjusted by evaporation
Evaporation in crossed trap
BEC
r~0.5
Cr BEC
T>Tc
T<Tc
tof 0…13msec
T<Tc
T<Tc
time of flight
Phase transition
tof = 5 msec
Decreasing T
Critical behaviour
Condensate fraction
ideal gas
corr. for finite size
and weak interaction
exp.
Tc~700 nK
nx=581 Hz
ny=406 Hz
nz=138 Hz
Lifetime and condensate formation
t~ 6 sec
n0i= 2 1014 cm-3
t~400msec
n0i= 2 1015 cm-3
Rb F=2, mF=2
L3 = 1.8 10−29 cm6 s−1
J. Söding et al. APB, 69, 257 (1999)
Cr S=3, mS=-3
L3 < 1 10−29 cm6 s−1
Dipolar interaction as perturbation
• isotropic harmonic trap
BEC without dipoles
perturbation by dipole interaction:
• Thomas –Fermi limit
 parabolic density profile
nTF(r)
2 RTF
Fdd(r)
Dipolar interaction and the aspect ratio
cf. anisotropic trap
+ contact interaction
no dipoles
Isotropic trap:
+ contact interaction
+ dipolar interaction
in trap
time of flight
S. Giovanazzi, A. Görlitz, T.P.
J. Opt. B 5, 208 (2003)
no inversion !
Preliminary data
on dipolar expansion
31 measurements
aspect ratio ry/rz
Theory with
no free
parameters
S. Giovanazzi
L. Santos
P. Pedri
y
z
nx=942 Hz
ny=712 Hz
nz=128 Hz
time of flight [ms]
equations
Tuning the dipolar interaction
Br
spinning polarization
z

z
Bz


rr
L  spinning  trap
[-1/2, 1]

Magic angle spinning
in solid state NMR
Random example:
Solid sample
Broadening by dipolar coupling
Stability diagram
TF i.e. N  
eDD = 4
Br (t)
cigar
Bz
r
z

trap shape
pancake
S. Giovanazzi, A. Görlitz, T.P.
Phys. Rev. Lett. 89, 130401 (2002)
magic angle 54.7°
K. Góral, K. Rzazewski, T.P.;
PRA, 61, 051601 (R) (2000)
L. Santos, et al.; PRL 85, 1791(2000)
How to tune a
closed
channel
coupling
open channel
Feshbach resonances I
Quantum numbers - notation
atomic
electrons
s,l
molecular
electrons
S,L
closed
channel
coupling
molecular
nuclei
open channel
Feshbach resonances II
Ab initio potentials
S=2 S=4
model potentials
S=6
Cr2 from:
Z. Pavlovic, B. O. Roos, R. Côté, and H. R. Sadeghpour
Phys. Rev. A 69, 030701 (2004)
Variational parameters:
C6, C8, a
Sensitive to last bound states
Feshbach resonances III
model potentials
Variational parameters:
C6, C8, a
Sensitive to last bound states
plus centrifugal potentials (e.g. = 4 )
closed
channel
Selection rules
Possible couplings:
2nd order
coupling
open channel
Spin - Orbit
Spin - Spin
Selection rules:
first order
not allowed!
second order
Momentum conservation:
S=6
MS
-2
-3
-4
-5
-6
g - wave
=4
d - wave
-4
-5
-6
=2
X
s - wave
=0
S=2
S=4
X
MS
MS
0
-1
-2
-2
-3
-4
-2
-3
-4
m  M S = 0
-4
-5
-6
initial state
(open channel)
first order
second order
3 resonances
8 resonances
Our resonances (observed by losses)
=2
=4
=4
individual calibration by RF
=4
Comparison exp vs. theory
Theory:
A. Simoni
E. Tiesinga
NIST
Deviation
exp-theo
0.6 G
What do we now about Chromium know?
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.
Outlook for a dipolar BEC
Play the dipolar game
 expansion of a dipolar gas

Collective excitations
 stability of a dipolar condensate
L. Santos et al., PRL 85(9):1791, 2000
 dipolar order
H. Pu et al., PRL, 87:140405, 2001
 macroscopic spin tunneling
H. Pu et al., PRL 89:0904001,2002

roton in the dispersion relation
L. Santos et al., Phys. Rev. Lett. 90, 250403 (2003)
Further outlook
Trap fermion
Lithography:
I. Averbukh
controlled single atom deposition?
cw atom laser ?
The dragon tamers
S. Hensler
A.Griesmaier
T. Koch
M. Fattori
Former members:
J. Werner
P.O.Schmidt
A. Görlitz
J. Stuhler
phD students and postdocs wanted!
Theory:
K. Rzazewski
S. Giovanazzi
A. Simoni
E. Tiesinga
P. Pedri
L. Santos