Spin-orbit coupling in an ultracold gas of Dysprosium: prospects - PowerPoint PPT Presentation

Spin-orbit coupling in an ultracold gas of Dysprosium: prospects towards topological superfluidity Sylvain Nascimb` ene Laboratoire Kastler Brossel, UPMC, ENS, Coll` ege de France, CNRS October 30 th 2014 Ultracold Dy experiment C. Bouazza, D. Dreon, W. Maineult, L. Sidorenkov, T. Tian, S. N., J. Dalibard October 30th 2014 S. Nascimb` ene S. Nascimb` ene 1 / 26

Outline Artificial spin-orbit coupling with ultracold atoms 1 Ultracold Dysprosium gases 2 Creating and studying a topological superfluid 3 October 30th 2014 S. Nascimb` ene S. Nascimb` ene 2 / 26

Outline Artificial spin-orbit coupling with ultracold atoms 1 Ultracold Dysprosium gases 2 Creating and studying a topological superfluid 3 October 30th 2014 S. Nascimb` ene S. Nascimb` ene 3 / 26

Artificial spin-orbit coupling with ultracold atoms Definition of a spin-orbit coupling An effective spin 1/2 F = 2 example of 87 Rb F = 1 A momentum-dependent spin coupling E � 2 q 2 2 m 1 + � 2 k h ˆ � H = m ˆ q x ˆ σ z + h ˆ σ x q q x 0 2 k October 30th 2014 S. Nascimb` ene S. Nascimb` ene 4 / 26

Spin-orbit coupling from laser coupling Raman transition spin spin E spin spin - k L k L , q + k L q , q - k L -k L 0 k L Coupling between |↓ , q − k L e x � and |↑ , q + k L e x � , with a Rabi frequency h . October 30th 2014 S. Nascimb` ene S. Nascimb` ene 5 / 26

Spin-orbit coupling from laser coupling Raman transition spin spin E spin spin - k L k L , q + k L q , q - k L -k L 0 k L Coupling between |↓ , q − k L e x � and |↑ , q + k L e x � , with a Rabi frequency h . Can be rewritten as � 2 q 2 2 m 1 + � 2 k L ˆ � H = m ˆ q x ˆ σ z + h ˆ σ x q October 30th 2014 S. Nascimb` ene S. Nascimb` ene 5 / 26

Spin-orbit coupled Bose-Einstein condensates 2 degenerate single-particle ground states for strong spin-orbit coupling. weak spin-orbit coupling strong spin-orbit coupling E E q x q x 0 0 October 30th 2014 S. Nascimb` ene S. Nascimb` ene 6 / 26

Spin-orbit coupled Bose-Einstein condensates 2 degenerate single-particle ground states for strong spin-orbit coupling. weak spin-orbit coupling strong spin-orbit coupling E E q x q x 0 0 First realization in the group of I. Spielman (JQI) Y.-J. Lin, K. Jim´ enez-Garc´ ıa, I. B. Spielman, Nature 471 , 83 (2011) Further studies from the groups of S. Chen (UST Shanghai), C. Zhang (Univ. Texas), T. Busch (OIST), Y. Chen (Purdue Univ.) October 30th 2014 S. Nascimb` ene S. Nascimb` ene 6 / 26

Spin-orbit coupling in fermionic alkali atoms Potassium 40 K: Spin-orbit coupled Fermi gas at thermal equilibrium P. Wang, Z.-Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, J. Zhang, Phys. Rev. Lett. 109 , 095301 (2012) Lithium 6 Li: spin-injection spectroscopy L. W. Cheuk, A. T. Sommer, Z. Hadzibabic, T. Yefsah, W. S. Bakr, and M. W. Zwierlein, Phys. Rev. Lett. 109 , 095302 (2012) October 30th 2014 S. Nascimb` ene S. Nascimb` ene 7 / 26

The issue of spontaneous emission for alkali atoms The electric dipole operator is inefficient for flipping the electron/nuclear spin. Residual coupling coming from the P state L · S coupling. Scalar dipole potentials: Γ scattering / Ω dipole ≃ Γ / ∆. Raman coupling: the P 1 / 2 and P 3 / 2 lines tend to cancel each other � 1 1 � Γ scattering / Ω Raman ≃ Γ − . ∆ 1 / 2 ∆ 3 / 2 P 3/2 10 6 D FS W Raman / G sc scalar dipole trap P 1/2 10 5 10 4 Raman coupling 1000 770 nm 767 nm 100 750 760 770 780 790 l (nm) S 1/2 For an optimized detuning: Ω Raman = 1 E r ↔ Heating rate of 700 nK/s. October 30th 2014 S. Nascimb` ene S. Nascimb` ene 8 / 26

Outline Artificial spin-orbit coupling with ultracold atoms 1 Ultracold Dysprosium gases 2 Creating and studying a topological superfluid 3 October 30th 2014 S. Nascimb` ene S. Nascimb` ene 9 / 26

The Dysprosium atom 2 fermions, 3 bosons J = 8 ground state, electronic config. 4 f 10 ( 5 I 8 ) 6 s 2 ( 1 S 0 ) Quantum degeneracy for bosons and fermions in the group of B. Lev M. Lu, N. Q. Burdick, S. H. Youn, B. L. Lev, Phys. Rev. Lett. 107 , 190401 (2011) M. Lu, N. Q. Burdick, B. L. Lev, Phys. Rev. Lett. 108 , 215301 (2012) October 30th 2014 S. Nascimb` ene S. Nascimb` ene 10 / 26

Optical transitions 333 G /2 p = 32 MHz 421 nm (slowing and imaging transition) 6s 6p ( 1 P 1 ) 400 Wavelength (nm) 500 6s 6p ( 3 P 1 ) 667 1000 626 nm (MOT transition) G /2 p = 135 kHz 2000 6s 2 ( 1 S 0 ) 8 11 7 9 10 12 J value The 4 f 10 core electrons play no role in these optical transitions. October 30th 2014 S. Nascimb` ene S. Nascimb` ene 11 / 26

Atomic beam and Zeeman slower ZS laser transverse cooling of the atomic beam Zeeman slower in-vacuum atomic beam mirror effusion cell oven shutter @ 1350 °C 1250 °C 1350 °C 10 g of Dy October 30th 2014 S. Nascimb` ene S. Nascimb` ene 12 / 26

Magneto-optical trap MOT beams @ 626 nm 10 8 atoms at 50 µ K, still under characterization T. Maier, H. Kadau, M. Schmitt, A. Griesmaier, T. Pfau , Opt. Lett. 39 , 3138 (2014) October 30th 2014 S. Nascimb` ene S. Nascimb` ene 13 / 26

Optical trapping and transport dipole trap @ 1070 nm for transport dipole trap for evaporation In the science cell: forced evaporation to reach quantum degeneracy October 30th 2014 S. Nascimb` ene S. Nascimb` ene 14 / 26

Raman coupling close to a narrow optical transition The 6 s 2 → 6 s 6 p ( 1 P 1 ) transition at λ b ∼ 400 nm is spin-independent. Narrow J → J ′ transitions efficiently couple Zeeman levels. Spin-independent light shift V scalar ∼ α (Γ b / ∆ b + Γ / ∆) I Spin-dependent light shift V vector ∼ � Ω Raman ∼ α (Γ / ∆) I Γ 2 b / ∆ 2 b + Γ 2 / ∆ 2 � � Spontaneous emission Γ scattering ∼ α I / � l b = 420 nm G b = 2 p 30 MHz 4 10 6 W Raman / G sc 3 10 6 D b J ‘= 9 l = 626 nm 2 10 6 G = 2 p 135 kHz D 1 10 6 0 622 624 626 628 630 l (nm) J = 8 For the detuning ∆ = (Γ / Γ b )∆ b ∼ 1 nm one gets Ω Raman / Γ scattering ∼ ∆ b / Γ b ∼ 10 7 : negligible heating October 30th 2014 S. Nascimb` ene S. Nascimb` ene 15 / 26

Outline Artificial spin-orbit coupling with ultracold atoms 1 Ultracold Dysprosium gases 2 Creating and studying a topological superfluid 3 October 30th 2014 S. Nascimb` ene S. Nascimb` ene 16 / 26

s -wave superfluidity in ultracold Fermi gases Without spin-orbit coupling: s -wave superfluidity in spin-1/2 Fermi systems E 2-fold degeneracy m q x 0 4 Fermi points October 30th 2014 S. Nascimb` ene S. Nascimb` ene 17 / 26

s -wave superfluidity in ultracold Fermi gases Without spin-orbit coupling: s -wave superfluidity in spin-1/2 Fermi systems E 2-fold degeneracy m q x 0 � c † c † s -wave interactions g ˆ k + q , ↑ ˆ k ′ − q , ↓ ˆ c k ′ , ↓ ˆ c k , ↑ . k , k ′ , q � c † c † ⇒ s -wave gap ∆ ˆ k , ↑ ˆ − k , ↓ + h . c . k October 30th 2014 S. Nascimb` ene S. Nascimb` ene 17 / 26

Spin-orbit coupled Fermi gases E E m m q x q x 0 0 4 Fermi points 2 Fermi points 4 Fermi points: looks like a spin-1/2 Fermi gas 2 Fermi points: looks like a spinless Fermi gas October 30th 2014 S. Nascimb` ene S. Nascimb` ene 18 / 26

Spin-orbit coupled Fermi gases E E m m q x q x 0 0 4 Fermi points 2 Fermi points In the ‘spinless’ situation, let us project interactions on the single occupied branch. � g ( k , k ′ , q )ˆ c † c † k + q ˆ k ′ − q ˆ c k ′ ˆ c k k , k ′ , q Dressed s -wave interactions have an odd symmetry g ( k , k ′ , − q ) = − g ( k , k ′ , q ). � c † c † ⇒ p -wave gap ∆( k )ˆ k ˆ − k + h . c ., with ∆( − k ) = − ∆( k ) . k C. Zhang, S. Tewari, R. M. Lutchyn, S. Das Sarma, Phys. Rev. Lett. 101 , 160401 (2008) R. A. Williams et al, Science 335 , 314 (2012) October 30th 2014 S. Nascimb` ene S. Nascimb` ene 18 / 26

Phase diagram Topological superfluidity when the Fermi surface is effectively ‘spinless’: − h < µ < h In local density approximation: µ ( x ) = µ 0 − 1 2 m ω 2 x x 2 . trivial trivial topological superfluid superfluid superfluid density position October 30th 2014 S. Nascimb` ene S. Nascimb` ene 19 / 26

Phase diagram Topological superfluidity when the Fermi surface is effectively ‘spinless’: − h < µ < h In local density approximation: µ ( x ) = µ 0 − 1 2 m ω 2 x x 2 . Majorana fermions trivial trivial topological superfluid superfluid superfluid density position 2 Majorana fermions are located at the phase separation points. October 30th 2014 S. Nascimb` ene S. Nascimb` ene 19 / 26

Properties of Majorana fermions Their energy is locked at the Fermi level 1 � e − L /ξ , e − ∆ / k B T , e − ∆ / V perturbation � δ E / ∆ < max E D /2 particles d E Majoranas g i 0 -D /2 holes → Topologically protected qubits Non-abelian quantum statistics 2 topological superconductor Majorana quasi-particle braiding Braiding operations do not commute. October 30th 2014 S. Nascimb` ene S. Nascimb` ene 20 / 26