Collective excitations in a dipolar Bose-Einstein Condensate Laboratoire de Physique des Lasers...
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Transcript of Collective excitations in a dipolar Bose-Einstein Condensate Laboratoire de Physique des Lasers...
Collective excitations in a dipolar Bose-Einstein Collective excitations in a dipolar Bose-Einstein CondensateCondensate
Laboratoire de Physique des LasersUniversité Paris NordVilletaneuse - France
Former PhD students and post-docs: Q. Beaufils, T. Zanon, R. Chicireanu, A. Pouderous
Former members of the group: J. C. Keller, R. Barbé
B. Pasquiou
O. Gorceix P. Pedri
B. Laburthe
L. Vernac
E. Maréchal
G. Bismut
Why are dipolar gases interesting?
Strongly anisotropic Magnetic Dipole-DipoleInteractions (MDDI)
repulsive interactions attractive interactions
3
2220 )(cos31
4 RgSV BJdd
Angle between dipoles
Long range radial dependence
Great interest in ultracold gazes of dipolar molecules
What’s so special about Chromium?
6 valence electrons (S=3): strong magnetic dipole of
•Dimensionless quantity: strength of MDDI relative to s-wave scattering
gdmdd 3/20
B6
Large dipole-dipole interactions: 36 times larger than for alcali atoms.
Magnetic dipole of Cr52
maS /4 2
Only two groups have a Chromium BEC: in Stuttgart and Villetaneuse
How to make a Chromium BEC in 14s and one slide ?How to make a Chromium BEC in 14s and one slide ?
425 nm
427 nm
650 nm
7S3
5S,D
7P3
7P4
An atom: 52Cr
N = 4.106
T=120 μK
750700650600550500
600
550
500
450
(1) (2)
Z
An oven
A small MOT
A dipole trap
A crossed dipole trap
All optical evaporation
A BEC
(Rb=109 or 10)
(Rb=780 nm)
Oven at 1350 °C(Rb 150 °C)
A Zeeman slower
Q. Beaufils et al., PRA 77, 061601 (2008)
Outline
I) Hydrodynamics of a Dipolar BEC
II) Experimental results for collective excitations
III) How to measure the systematic effects
Similar results in Stuttgart
PRL 95, 150406 (2005)
I) 1 - One first effect of dipole dipole interactions: Modification of the BEC aspect ratio
Thomas Fermi profileStriction of BEC(non local effect)
Parabolic ansatz is still a good ansatz
B
B
The magnetic field is turned of 90°
Shift of the aspect ratio σ
))2/()0(/())2/()0((2
x
y
z
y
z
x
I) 2 - Dynamic properties of interactions in a BEC
•2 quadrupole modesLowest modes
•1 monopole modeHighest mode
Out of equilibrium: 3 collective modes
I) 2 - Dynamic properties of interactions in a BEC
•2 quadrupole modesLowest modes
•1 monopole modeHighest mode
Out of equilibrium: 3 collective modes
I) 2 - Dynamic properties of interactions in a BEC
•2 quadrupole modesLowest modes
•1 monopole modeHighest mode
Out of equilibrium: 3 collective modes
Theory: Superfluid hydrodynamics of a BEC in the Thomas-Fermi regime
Continuity equation
Euler Equation
)v.(nt
n
)( 2ddext gnVmv
t
vm
I) 3 - Introducing a dipolar mean field
Theory: Non local mean-field
The frequencies of the collective modes depend on the orientation of the magnetic field relative to the trap axis.
)r(n)rr(Vrd)r(dd
3
dd
dependent on the orientation of the magnetic dipoles
B
B
)0(Qfrequency )2/(Qfrequency
))2/()0(/())2/()0((2
exp
QQQQ
B
We measure a relative shift
•Frequency shift proportional to dd
II) 1 - How to excite one collective mode of the BEC
15ms modulation of the IR power with a 20% amplitude at a frequency ω close to the intermediate collective mode resonance.
The cloud then oscillates freely for a variable time
Imaging process with TOF of 5ms
Aλ/2 plate controls the trap geometry : angle Φ
Parametric excitations:Modulation of the « stiffness » of the trap
by modulating its depth
II) 2- Oscillations of the aspect ratio of the BEC after parametric excitations
•Trap geometry close to cylindrical symmetry•Very low (3%) noise on the TF radii
•High damping due to the large anharmonicity of the trap
Change between two directions of the magnetic
field
We measure exp
27 OOHzQ 7 %5,2exp
II) 3 - Trap geometry dependence of the measured frequency shift
Large sensitivity of the collective mode to trap geometry at the vicinity of spherical symmetry, unlike the striction of the BEC
Good agreementWith theoretical
predictions
•Related to the trap anisotropy
Relative shift of the quadrupole
mode frequency
Relative shift of the aspect ratio
II 1 - Influence of the BEC atom number
smaller number of atoms
Gaussian anzatz in order to take the quantum kinetic energy into account.
In our experiment, it is not negligible compared to the mean-field due to MDDI.
Hz25mR/2
TF
2
Large number of atoms (>10000)
Thomas Fermi Regime
Parabolic density profile
No more in the Thomas Fermi Regime
Parabolic anzatz is not valid
Results of simulations with the Gaussian anzatz:It takes three times more atoms for the frequency shift of the collective
mode to reach the TF predictions than for the striction of the BEC
Simulations with Gaussian anzatz
Blue and Red
Two different trap geometries
III) 1 - Measurement of the trap frequencies
parametric oscillations of the trap depth
+Potential gradient
Excitation of center of mass motion
Center of mass motion only depends on external
potential
Direct measurement of the trap frequencies
A good way of measuring systematic shifts of trap frequencies
III) 2 - Origins of the systematic shifts on the trap frequencies
In a Gaussian trap: magnetic gradient induced frequency shift
=> Trap geometry dependent Shift
Light shift of Cr is slightly dependent on the laser polarization orientation with respect to the static magnetic field.Relative associated shift independent of the trap geometry.
422
3
wm
g
Acceleration due to magnetic potential gradient
Waist of the trap along the gradient
III) 3 - Experimental results for the systematic shifts of the trap frequencies
)2(cos/ 4 ba
Fit byExcitation of
center of mass motion
Measurement of the trap frequencies
The magnetic field is turned of
90°
Measurement of relative systematic
shiftD
Summary Characterization of the effect of MDDI on a collective mode
of a Cr BEC. Good agreement with TF predictions for a large enough
number of Atoms.
Large sensitivity to trap geometry.
Useful tool to characterize a BEC beyond the TF regime, for lower numbers of atoms.
First measurement of the tensorial light shift of Chromium.
Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu
Collaboration: Anne Crubellier (Laboratoire Aimé Cotton)
B. Pas
quio
u
O. G
orce
ix
Q. B
eauf
ils
Paolo
Ped
ri
B. Lab
urth
e
L. V
erna
c
J. C
. Kel
ler
E. Mar
écha
l
G. B
ismut
Trap geometry (aspect ratio) dependent shifts
Theoretical results with a parabolic anzatz
Eberlein, PRL 92, 250401 (2004)with assumed cylindrical symmetryof the trap
See also:Pfau, PRA 75, 015604 (2007)for non axis-symmetric traps
Collective excitations of a BEC
Collisionless hydrodynamics of a BEC in the Thomas-Fermi regime
Continuity equation
Euler Equation
Time evolution of the BEC
Scaling law
Superfluid velocity
)v.(nt
n
)gnVmv(t
vm
ext
2
)t(R
z
)t(R
y
)t(R
x1
)t(R)t(R)t(R8
N15)t,r(n 2
z
2
2
y
2
2
x
2
zyx
2
z
2
y
2
xz)t(y)t(x)t(
2
1)t,r(v
with)t(R
)t(R)t(
j
j
j
Equation of Motion
From the s-wave pseudopotential with a being the s-wave scattering lenght.
Three solution for the linearized equation:
Two « quadrupole » modesIn our case the two lowest modes
One « monopole » modeIn our case the highest mode
)t(R),t(R),t(Ru)t(Rzyxjj
with shouuu
and
zyx2
2
sRRR
naN15
u