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 30th 2014 Ultracold Dy experiment

• C. Bouazza, D. Dreon, W. Maineult, L. Sidorenkov, T. Tian,
• S. N., J. Dalibard
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Outline

1

Artificial spin-orbit coupling with ultracold atoms

2

Ultracold Dysprosium gases

3

Creating and studying a topological superfluid

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Outline

1

Artificial spin-orbit coupling with ultracold atoms

2

Ultracold Dysprosium gases

3

Creating and studying a topological superfluid

• S. Nascimb`

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Artificial spin-orbit coupling with ultracold atoms

Definition of a spin-orbit coupling An effective spin 1/2 F = 2 F = 1 example of 87Rb A momentum-dependent spin coupling ˆ H =

• q

2q2 2m 1 + 2k m ˆ qx ˆ σz + hˆ σx

qx

E

2k h

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Spin-orbit coupling from laser coupling

q

E

spin spin spin spin

, q - kL , q + kL

• kL

kL

Raman transition kL

• kL

Coupling between |↓, q − kLex and |↑, q + kLex, with a Rabi frequency h.

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Spin-orbit coupling from laser coupling

q

E

spin spin spin spin

, q - kL , q + kL

• kL

kL

Raman transition kL

• kL

Coupling between |↓, q − kLex and |↑, q + kLex, with a Rabi frequency h. Can be rewritten as ˆ H =

• q

2q2 2m 1 + 2kL m ˆ qx ˆ σz + hˆ σx

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Spin-orbit coupled Bose-Einstein condensates

2 degenerate single-particle ground states for strong spin-orbit coupling.

qx E qx E

weak spin-orbit coupling strong spin-orbit coupling

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Spin-orbit coupled Bose-Einstein condensates

2 degenerate single-particle ground states for strong spin-orbit coupling.

qx E qx E

weak spin-orbit coupling strong spin-orbit coupling

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.)

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Spin-orbit coupling in fermionic alkali atoms

Potassium 40K: 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 6Li: 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)
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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: Γscattering/Ωdipole ≃ Γ/∆. Raman coupling: the P1/2 and P3/2 lines tend to cancel each other Γscattering/ΩRaman ≃ Γ

• 1

∆1/2 − 1 ∆3/2

• .

750 760 770 780 790 100 1000 104 105 106

l (nm) WRaman / Gsc

scalar dipole trap Raman coupling S1/2 P1/2 P3/2 770 nm 767 nm DFS

For an optimized detuning: ΩRaman = 1 Er ↔ Heating rate of 700 nK/s.

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Outline

1

Artificial spin-orbit coupling with ultracold atoms

2

Ultracold Dysprosium gases

3

Creating and studying a topological superfluid

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The Dysprosium atom

2 fermions, 3 bosons J = 8 ground state, electronic config. 4f 10(5I8) 6s2(1S0) 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)
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Optical transitions

7 8 9 10 11 12 2000 1000 667 500 400 Wavelength (nm) 333 J value 421 nm (slowing and imaging transition) 626 nm (MOT transition) G/2p = 135 kHz G/2p = 32 MHz 6s 6p (3P1) 6s 6p (1P1) 6s2 (1S0)

The 4f 10 core electrons play no role in these optical transitions.

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Atomic beam and Zeeman slower

effusion cell oven @ 1350 °C 10 g of Dy 1250 °C 1350 °C atomic beam shutter Zeeman slower ZS laser in-vacuum mirror transverse cooling

• f the atomic beam
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Magneto-optical trap

MOT beams @ 626 nm

108 atoms at 50 µK, still under characterization

• T. Maier, H. Kadau, M. Schmitt, A. Griesmaier, T. Pfau , Opt. Lett. 39, 3138 (2014)
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Optical trapping and transport

dipole trap @ 1070 nm for transport dipole trap for evaporation

In the science cell: forced evaporation to reach quantum degeneracy

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Raman coupling close to a narrow optical transition

The 6s2 → 6s6p(1P1) transition at λb ∼ 400 nm is spin-independent. Narrow J → J′ transitions efficiently couple Zeeman levels. Spin-independent light shift Vscalar ∼ α (Γb/∆b + Γ/∆) I Spin-dependent light shift Vvector ∼ ΩRaman ∼ α (Γ/∆) I Spontaneous emission Γscattering ∼ α

• Γ2

b/∆2 b + Γ2/∆2

I/

D

J ‘= 9 l = 626 nm G = 2p 135 kHz J = 8

lb = 420 nm Gb = 2p 30 MHz

622 624 626 628 630 1 106 2 106 3 106 4 106

l (nm) WRaman / Gsc

Db

For the detuning ∆ = (Γ/Γb)∆b ∼ 1 nm one gets ΩRaman/Γscattering ∼ ∆b/Γb ∼ 107 : negligible heating

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Outline

1

Artificial spin-orbit coupling with ultracold atoms

2

Ultracold Dysprosium gases

3

Creating and studying a topological superfluid

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s-wave superfluidity in ultracold Fermi gases

Without spin-orbit coupling: s-wave superfluidity in spin-1/2 Fermi systems

qx E

2-fold degeneracy

m 4 Fermi points

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s-wave superfluidity in ultracold Fermi gases

Without spin-orbit coupling: s-wave superfluidity in spin-1/2 Fermi systems

qx E

2-fold degeneracy

m

s-wave interactions g

• k,k′,q

ˆ c†

k+q,↑ˆ

c†

k′−q,↓ˆ

ck′,↓ˆ ck,↑. ⇒ s-wave gap ∆

• k

ˆ c†

k,↑ˆ

c†

−k,↓ + h.c.

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Spin-orbit coupled Fermi gases

qx E qx E m m 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

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Spin-orbit coupled Fermi gases

qx E qx E m m 4 Fermi points 2 Fermi points

In the ‘spinless’ situation, let us project interactions on the single occupied branch.

• k,k′,q

g(k, k′, q)ˆ c†

k+qˆ

c†

k′−qˆ

ck′ˆ ck Dressed s-wave interactions have an odd symmetry g(k, k′, −q) = −g(k, k′, q). ⇒ p-wave gap

• k

∆(k)ˆ c†

kˆ

c†

−k + h.c.,

with ∆(−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)
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Phase diagram

Topological superfluidity when the Fermi surface is effectively ‘spinless’: −h < µ < h In local density approximation: µ(x) = µ0 − 1

2mω2 xx2.

trivial superfluid trivial superfluid topological superfluid

density position

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Phase diagram

Topological superfluidity when the Fermi surface is effectively ‘spinless’: −h < µ < h In local density approximation: µ(x) = µ0 − 1

2mω2 xx2.

Majorana fermions trivial superfluid trivial superfluid topological superfluid

density position

2 Majorana fermions are located at the phase separation points.

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Properties of Majorana fermions

1

Their energy is locked at the Fermi level δE/∆ < max

• e−L/ξ, e−∆/kBT, e−∆/Vperturbation

holes particles

• D/2

D/2 E

Majoranas gi

dE

→ Topologically protected qubits

2

Non-abelian quantum statistics

topological superconductor Majorana quasi-particle braiding

Braiding operations do not commute.

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Observing the Majorana fermions using quasi-particle spectroscopy

We send a radio frequency to couple |↑ states to a third Zeeman state initially empty. Resonance condition: ωRF = δZeeman + Equasiparticle Already used for s-wave superfluids.

• J. T. Stewart, J. P. Gaebler & D. S. Jin, Nature 454, 744 (2008)

excitation energy transfer probability m m+D

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Conclusions

Dysprosium is suited for simulating spin-orbit coupling Spin-orbit coupling + s-wave interactions ⇒ p-wave superfluidity Majorana fermions located at the edges of a topological superfluid Alternative route: using an s-wave superfluid as a Cooper pair reservoir + spin-orbit coupling

• S. Nascimbene, J. Phys. B: At. Mol. Opt. Phys. 46, 134005 (2013)
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Thanks for your attention

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