Cooling of a Bose Einstein Condensate by Spin distillation B. Naylor (PhD), Johnny Huckans O. Gorceix, B. Laburthe-Tolra, E. Maréchal, L. Vernac, P. Pedri (Theory), M. Robert de Saint-Vincent Have left: A.de Paz, A. Chotia, A. Sharma, B. Pasquiou , G. Bismut, M. Efremov, Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborators: Anne Crubellier, Mariusz Gajda, L. Santos (Theory, Hannover), Perola Milman, Rejish Nath
Cooling Mechanisms Lose most energetic atoms, Evaporation : Then system rethermalises Very Efficient up to Very recent result, beat most limitations Olf et al. arXiv:1505.06196 (2015) Demagnetization cooling: Transfer of kinetic energy into magnetic energy Fattori et al. Nature Physics 2 ,765-768(2006) Why do we need new cooling mechanisms? Colder gases?
Quantum magnetism Cold atoms in a lattice Observe magnetic correlation Spin ½ interacting Fermions or Bosons Super-exchange interaction Esslinger: short range anti-correlations I. Bloch, T. Porto, W. Ketterle, R.G. Hulet… Magnetic correlations appear when A condensed atom carries no entropy A gas at a given T has an upper limit to the number of thermal atoms 3 � � T � � Entropy of a saturated cloud: S / N ≈ 3 . 6 k = 3 . 6 k f � � B B th � � T c For a fully saturated gas, the entropy is given by the thermal fraction Removing entropy removing thermal atoms
Chromium Large electronic Spin: S=3 Optical dipole traps equally trap all Zeeman state of a same atom ( ) 2 E m ( ) = m g µ B + α B Linear Zeeman effect S S B 3 2 m = − 1 1 Stern-Gerlach separation: S 0 (magnetic field gradient) m = 0 S -1 -2 m = 1 S -3
Feature introduced by dipolar interactions: Free Magnetization -3 -2 -1 0 1 2 3 � Γ ≈ V dd
Spontaneous magnetization due to BEC T>Tc T<Tc -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Thermal a bi-modal spin population in distribution B=0.9mG Zeeman excited states Cloud spontaneously polarizes ! BEC only in m S =-3 (lowest energy state) Pasquiou et al. PRL 108 , 045307 (2012)
Spin Cooling: Principle of the Experiment Linear Zeeman -1 Step 1: -2 -3
Spin Cooling: Principle of the Experiment Linear Zeeman -1 Step 1: -2 -3 0 Step 2: -1 -2 -3
Spin Cooling: Principle of the Experiment Linear Zeeman -1 Step 1: -2 -3 0 Step 2: -1 -2 -3 Step 3: With RF pulse or Magnetic field gradient
A competition between two mechanisms BEC Thermal m s =-3, -2, -1, … m s =-3 (i) Thermal cloud (ii) BEC melts to re- (iii) Kill spin-excited depolarizes saturate m s =-3 thermal gas states (and cools it)
A competition between two mechanisms BEC Thermal m s =-3, -2, -1, … m s =-3 (i) Thermal cloud (ii) BEC melts to re- (iii) Kill spin-excited depolarizes saturate m s =-3 thermal gas states (and cools it) BEC melts (a little) ? Who Wins ? Losses in thermal cloud due to depolarization
A competition between two mechanisms BEC Thermal m s =-3, -2, -1, … m s =-3 (i) Thermal cloud (ii) BEC melts to re- (iii) Kill spin-excited depolarizes saturate m s =-3 thermal gas states (and cools it) BEC melts (a little) 0.8 ? BEC fraction 0.6 Who Wins final condensate fraction ? 0.4 Losses in 0.2 thermal cloud due to depolarization 0.0 0.2 0.4 0.6 0.8 1.0 1.2
A competition between two mechanisms � � T 1.2 � � � � T c At high T/T c , BEC f melts 1.0 (too few atoms in the BEC to cool the 0.8 thermal gas back to saturation) 0.6 B=1,5mG 0.4 � � T 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 � � � T � c At low T/T c , spin i filtering of excited Theoretical model: rate equation based on the thermal atoms thermodynamics of Bosons with free magnetization. efficiently cools the gas Interactions are included within Bogoliubov approximation
Summary of the experimental results as a function of B Final condensate fraction (large field, no effect)
Theoretical limits for cooling 0.8 � � T � � 0.6 � � T c f 0.4 Process can be repeated 0.2 At each spiling, a factor 2 in entropy is gained 0.0 0.1 0.2 0.3 0.4 0.5 0.6 � � T � � � � T c i There does not seem to be any limit other than practical In principle, cooling is efficient as long as depolarization is efficient
Extension to ultra-low temperatures for non-dipolar gases k T ≈ g µ B In our scheme, limitation around 25 nK, limited by B J B (difficult to control below 100 µG) g µ B = J B 2 . 8 kHz / G Proposal: use Na or Rb at zero magnetization. 1 0 (0 0) (-1 1) Spin dynamics occurs at constant magnetization -1 2 q ≈ 70 Hz / G Olf et al. arXiv:1505.06196 (2015) F=1, m F =-1, 0, 1 We estimate that temperatures in the pK regime may be reached Nota: the spin degrees of freedom may also be used to measure temperature
Shock Cooling Collaboration with M.Gajda et M.Brewczyk Preliminary Results Initial conditions: Thermal Gas at 1 µ K in every spin state m s = -3 -2 -1 0 1 2 3
Shock Cooling Collaboration with M.Gajda et M.Brewczyk Preliminary Results Initial conditions: Thermal Gas at 1 µ K in every spin state m s = -3 -2 -1 0 1 2 3 Then Evaporation while monitoring Spin distribution and momentum distribution What happens? Magnetic Order? Bose order?
Shock Cooling Collaboration with M.Gajda et M.Brewczyk Preliminary Results Initial conditions: Thermal Gas at 1 µ K in every spin state m s = -3 -2 -1 0 1 2 3 Then Evaporation while monitoring Spin distribution and momentum distribution Saturated Thermal Gas Optical Depth -2 -3 BEC forms only in m s =-3 and m s =-2 gas is saturated but never forms a BEC ! BEC position
Shock Cooling Collaboration with M.Gajda et M.Brewczyk Preliminary Results 1.0 Fraction condensée dans m s =-3 0.8 0.6 - Preliminary results suggest good agreement 0.4 0.2 - Simulations give a BEC in m s =-3 and a saturated condensate fraction in ms=-3 thermal gas in m s =-2 with no BEC BEC_theo 0.0 0 200 400 600 800 Time (ms) Interpretation? Favorable fast dynamics (-2 -2) (-3 -1)
Conclusion � � T � � � � T 1.2 c f 1.0 New cooling mechanism to reach very low entropies (in bulk): Use spin to store and remove entropy 0.8 Should be applicable to non-dipolar 0.6 species , with pK regime possible 0.4 � � T � � � � T 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 c i arXiv:1505.05098
Thank you A. de Paz (PhD), A. Sharma, A. Chotia , B. Naylor (PhD) E. Maréchal, L. Vernac,O. Gorceix, B. Laburthe P. Pedri (Theory), L. Santos (Theory, Hannover) Arijit Sharma Aurélie Amodsen De Paz Chotia
Thanks ! – Come and Visit
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