the anisotropic excitation spectrum of a chromium bose-einstein condensate laboratoire de physique...
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The anisotropic excitation spectrum of a chromium Bose-Einstein Condensate
Laboratoire de Physique des LasersUniversité Sorbonne Paris Cité
Villetaneuse - France
Olivier GORCEIX
44th EGASGöteborg – July 11, 2012
Interactions within a BECVan der Waals / contact interactions :
isotropic and short ranged
Effective potentiel proportionnal to aS (R), with aS = scattering length, aS adjustable thanks to Feshbach resonances
Dipole-dipole interactions: anisotropic and long-ranged highly magnetic atoms Cr, Er, Dy, dipolar molecules; Rydberg atoms
Chromium atoms carry a permanent magnetic dipole of 6µB
MDDI are 36 times bigger than in alkali BECs but still
dd (Cr)=0.159 while dd (Rb)=0.0044
where dd quantifies the ratio dipolar / contact interactions
Dipole-dipole interaction potential
22 203
11 3cos ( )
4dd J BV S gR
Anisotropy
Chrome (S=3): both contact AND dipolar interactions
R
Mean field becomes non local and anisotropic
Spin and rotation are coupled
is equal to 0.16
Pfau et al,PRL 95, 150406 (2005)
First reported effects of DDIs on BECs with Cr BECs
Eberlein et al, PRL 92, 250401 (2004)
Striction of the BEC(non local effect)
Vdd adds a non localanisotropic mean-field
B
Anisotropy in theBEC expansion
Bismut et al., PRL 105, 040404 (2010)
0.16dd
The effects of DDIsare experimentallyevidenced bydifferentialmeasurements,for two orthogonalorientations of the B field
DDIs change inthe few % rangethe physics ofa ground state BEC
DDIs
1st PART
COLLECTIVE OSCILLATIONS
Impact of the dipolar interactions on their frequencies
A small correction induced by dipolar interactions
repulsion attraction
Collective excitations of a dipolar BEC
We repeat the experiment for two orthogonal orientations
of B
1.2
1.0
0.8
0.6
2015105
Asp
ect
rati
o
Parametric excitation
MDDI are anisotropic, they impact on the q-pole excitation eigenfrequencies of a trapped BEC
In this mode, oscillations along y and z are in opposition
( )t ms
15 000 atoms
Trap geometry dependence of the measured frequency shift
Trap anisotropy
Shift of the quadrupole
mode frequency (%)
Shift of the aspect ratio
(%)
Theory PRL 92, 250401 (2004)
Good agreement with Thomas-Fermi predictions
BEC always stretches along B
While the sign of the quadrupole shift depends on the trap geometry
0.16dd
This exp:Bismut et al., PRL 105, 040404 (2010)
2nd PART
RAMAN-BRAGG SPECTROSCOPY OF A DIPOLAR BEC
Sound velocity anisotropy induced by dipolar interactions
A more pronounced dipolar effect
Rev. Mod. Phys. 77, 187 (2005)
c is the sound velocity
c is also the critical velocity
for superfluidity in the Landau model
healing length
0( 2 )k k k cE E n g Bogoliubov spectrum
1k
m
kEk 2
22 /12 0 kgnE ck
Quasi-particles, phonons kck 1k free particles
kk E
when
where gc= 4ħ2a /m
Excitation spectrum of a BEC with pure contact interactions
224
( ) (3cos 1)3 k
dV k
A 20% effect expected on the speed of sound !Much larger than the (~3%) effects for striction and collective excitations
Excitation spectrum of the BEC with DDIs
kB
1cos312 20 kddckkk gnEE
if , and if ,0k //cc 2/ k cc
0( 2 )k k k cE E n g becomes:
2.11
21///
dd
ddcc
0.16dd
k
or B┴
frequencies and Angular separation
absorption image after TOF of 5 ms
Profile at resonance ie when ħ (q)
Raman-Bragg spectroscopy of a BEC
k
Ene
rgy
1 2
0.8k
Moving lattice upon the BEC
Lattice beams crossing with an angle and a detunedcauses resonant momentum exchange when
2 sin( / 2)Lk k
From the excitation spectrum we infer the speed of sound
=14° Phonon regime
Anisotropic speed of sound
0.15
0.10
0.05
0.00
3000200010000
Frequency difference (Hz)
Fra
ctio
n of
exc
ited
atom
s
Width of resonance curve: finite size effects (inhomogeneous broadening)
Speed of sound depends on the relative angle between spin and excitation wavevector
c┴ ≠ c
Anisotropic speed of sound
Theo Exp
Parallel 3.6 mm/s 3.4 mm/s
Perpendicular 3 mm/s 2.8 mm/s
Good agreement between theory and experiment:
Bismut el al, arXiv :1205.6305
At ultralow T ≈ 300nK and B ≈ 40 nT the chemical potential becomes greater than the Zeeman splitting -> NEW PHYSICS
-3-2-1 0
2 1
3
Magnetism and thermodynamics - spinor physics
Above and Below threshold
TOF + Stern-Gerlach
Spin 3 phase diagramSpontaneous demagnetization
Pasquiou et al, PRL 106, 255303 and 108, 045307
Conclusion
Dipolar interactions induce anisotropy in the BEC excitation spectra - collective modes;- phonon dispersion law : sound velocity
Magnetism and thermodynamics of a spin 3 BEC with free magnetisation
Perspectives
Extension of our work on magnetism to strongly correlated states in 3D optical lattticesEinstein-de-Haas effect: spin-rotation couplingImproved spatial resolution for in situ imaging of magnetization domains
Extension to a Fermi sea of 53Cr atoms
E.Maréchal, OG, P. Pedri, Q. Beaufils (PhD), B. Laburthe, L. Vernac, B. Pasquiou (PhD), G. Bismut (PhD)
The chromium BEC crewThe chromium BEC crewwww-lpl.univ-paris13.fr:8082
Thank you for your attention
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