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Cooling chromium a dipolar quantum gasCr 3+
Tilman Pfau University of Stuttgart
Outline Lecture 1 Cooling atoms to degeneracy The case of Chromium Laser cooling and its limits Magnetic trapping Good and bad collisions Optical dipole traps and evaporation to BEC Demagnetization cooling
Outline Cooling techniques Uncontrolled dipolar interactions: a pain in the neck Controlled dipolar interaction: Demagnetization cooling Quantum ferro fluid
chromium in technics
chromium in the literature
Cr in periodic table of elements
70Yb
Cr propertiesisotopic distribution Bosons (I=0): 52Cr (83.8%), 50Cr (4.3%), 54Cr (2.4%) Fermion (I=3/2): 53Cr (9.5%) Versatile level scheme new cooling mechanisms 6 unpaired electrons electronic configuration: [Ar]3d54s1 S=3
large magnetic moment: = 6 B
Interacting quantum systems in atomic physicscontact interaction van der Waals dipole dipole interaction Coulomb interaction
U coul (r) =short range isotropic long range anisotropic long range isotropic
q1 q2 40 r
MIT
Innsbruck
The phase transition movie
tof = 5 msec Decreasing T
The route to our Cr BEC
Lab tour
BEC Chamber
HOT Atom Source
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 fieldP. O. Schmidt, et al., J. Opt. Soc. Am. B 20, 5 (2003)
2x108 atoms in the ground state phase space density ~10-7 Evaporation
Magneto-optical Trap52
Cregoli ng 42 & t 5. 6 ra nm ppin g7
7
P4
MOT
S3: 6BN= few 106 atoms T=70 K
A. S. Bell, J. Stuhler, S.Locher, S. Hensler, J. Mlynek, T. Pfau, Europhys. Lett. 45, 156 (1999)
co
Magneto-optical Trap52
Cregoli ng 42 & t 5. 6 ra nm ppin g
7
P4
MOT
1E-9
co
1E-10
7
S3: 6BN ~ 106 atoms T=70 K
1E-11
Rb
Li
Na Sr Element
Cr
A. S. Bell, J. Stuhler, S.Locher, S. Hensler, J. Mlynek, T. Pfau, Europhys. Lett. 45, 156 (1999)
Too bad
Gallagher Pritchard PRL 63, 957 (1989)
Continuous Loading Scheme
Continously Loaded Ioffe-Pritchard (CLIP) TrapJ. Stuhler, et al. Phys. Rev. A 64, 031405 (2001), P.O. Schmidt, et al. Journal of Optics B, 5 (2003)
CLIP Trap(Continously Loaded Ioffe-Pritchard Trap) 2D-MOT + 1D molasses weak axial magnetic curvature field atoms are trapped magnetically Advantages: up to 40x more atoms compared to MOT no need for polarizing the atoms no transfer from MOT to IP
Doppler Cooling in the IP TrapTransfer to ground state Doppler cooling
compress MT
P.O. Schmidt, et al. JOSA B, 20 (2003)
Doppler Cooling - Resultsy ~ 100 ms
z~ 10 ms
Tinitial ~ 1 mK Tzfinal = 124 K = TDoppler Tx,yfinal = 300 K Nfinal = Ninitial PSDfinal / PSDinitial ~ 80
Radial Cooling via Reabsorption
number of reabsorbed photons propto Ilaserx ODr
Experiment & Theory
1/rcool propto Ilaser
1/rcool propto ODrtemperature limited by additional heating effects
Great!
CollisionsmJ = +3 mJ = +3
+gjBB
mJ = +2
elastic Collision GOOD
dipolar Relaxation BAD
Dipolar relaxationdipolar relaxation + spin changing collisions
Very good agreement between theory and experiment no BEC in magnetic trap
atom number
time [sec]
Dipole dipole scatteringExactly solvable in Born approximationS. Hensler, J. Werner, A. Griesmaier, P.O. Schmidt, A. Grlitz, T. Pfau, S. Giovanazzi, K. Rzazewski Appl. Phys. B 77, 765 (2003)
elastic scattering
spin relaxation collisions spin changing collisions
Too bad
Trap atoms in energetically lowest statePumping Optical Dipole trap:the atoms to magnetic ground state:20W fibre Laser @ =1064 nm7P 3
=2B B0
7S 3
1st beam: Pmax=9W w0=30m - Umax~130K
mJ=-3 high field seekerPmax=4.5W w0=50m - Umax~22K
mJ=+3 low field seeker
2nd beam: Dipolar relaxation suppressed
Advantages: operation at any offset field all magnetic substates trapable
Problem Sample still mainly polarized in mJ=+3
Great!
Evaporative cooling in a crossed optical trapTotal evaporation time ~30s incl. RF evaporation in MT Evaporation in ODT is very efficient: Maximum PSD gain of 3 orders of magnitude per Order of magnitude loss in number of atoms Max >90. 000 atoms in condensate phase
http://www.colorado.edu/physics/2000/applets/bec.html
The route to our Cr BEC
Condensate fractionideal gasT=1.1K
corr. for finite size and weak interaction*
x=581 Hz y=406 Hz z=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)
Dipolar relaxationdipolar relaxation + spin changing collisions
Very good agreement between theory and experiment no BEC in magnetic trap
atom number
time [sec]
Demagnetization of chromium is a pain! BUT1915: Einstein - de Haas for a quantum gas?
could it be useful?
Coupling spin and motion
Coherent Einstein - de Haas effect for
B F40F 43S 41D
42P623.704
laser frequency with respect to 5 P 3/2 -level (Thz)
n=39,l>F 39F 42S 40D
453
41D
n=40
41 D5/2
623.700
Dn (MHz) 0 10 electrical field (V/cm) 20
226
41 D3/2
41P
623.696
0
0
5 electrical field (V/cm)
10
electrical field (V/cm)
experimental resultscomparison theory - experiment623.704 453
laser frequency with respect to 5 P 3/2 -level (Thz)
41D
n=40
41 D5/2
623.700
Dn (MHz) [MHz]
laser frequency and electric field varied Stark map excellent agreement theory experiment
226
41 D3/2
623.696
0
10 electrical field (V/cm)
20
0
0
5 electrical field (V/cm)
10
levels split up, according to |mJ| in electric field, states mix excitable from 5P3/2A.Grabowski, R. Heidemann, R. Lw, J. Stuhler and T. Pfau arXiv:quant-ph/0508082
623.7047
laser frequency with respect to 5 P 3/2 -level (THz)
623.704
laser frequency with respect to 5 P 3/2-level (Thz)
623.7046 623.7045 623.7044 623.7043 623.7042 0
623.702
623.700
623.698 0 10 electrical field (V/cm) 20
5 electrical field (V/cm)
10
Reminder: Stark map of Rubidiumlaser frequency with respect to 5 P 3/2-level (THz)140
relative Frequenz (MHz)
n=40,l>F 40F 43S 41D
BEC exp.
120 100 80 60 40 20 0
43S1/2
0
42P n=39,l>F 39F 42S 40D
1 2 3 elektrisches Feld (V/cm)
4
41P
electrical field (V/cm)
Separation of ions from Rydberg atoms
Red shift: ions Blue shift: van der Waals
Rydberg Rydberg interactionblockade condition
C6 ablock6
Max(, )
ryd
ablock 5 m3 nBEC ablock
104
MOT work: Storrs, Paris, Michigan, Freiburg,3 nMOT ablock < 10
ablock 5 m
Collective states super atomsE
G
1 E = { ryd , g , g ,..., g + g , ryd , g ,..., g + ... + g , g , g..., ryd N G = g , g , g ..., g
}
= N 0
Collective coherent time scale
Coherent collective scaling
N 0
collective and coherent !
Rn
0.49 0.06 g,0
1.1 0.1 0
ng,0 0
Change 0
ng,0 = 7.2 1013 cm-3
Fit:
N ryd (t ) = N (1 esat ryd
sat Rt / N ryd
)
Blockade time scale:
R 0 ng
ng,0 = 2.9 1012 cm-3
Rydberg excitation of a BECBEC survives Rydberg excitation BEC
thermal cloud
Rydberg excitation of a BEC
T