Spin-orbit coupled degenerate Fermi gas

Jing Zhang

State Key Laboratory of Quantum Optics and

Quantum Optics Devices, Institute of Opto-Electronics,

Shanxi University, Taiyuan 030006, P.R.China

C3QS 2014 14-17 April, Okinawa,

Japan

Shanxi University

Research Research

DivisionsDivisions

State Key Laboratory of Quantum Optics and Quantum Optics Devices

Basic research

and application of

quantum optics

Quantum

measurement and

communication

Generation and

application of

nonclassical

light

Basic research and

application of quantum

optics

Ultracold Bose-

Fermion mixture

Single

molecule and

Ultracold

molecules

Cavity QED

Interaction between

nonclassical light

and atoms

Quantum coherence

effect in atomic ensemble

Qu

an

tum

effe

cts of

inte

ractio

n b

etw

een

ligh

t an

d a

tom

s

All-solid-state

laser technology

Quantum optics

devices

Qu

an

tum

op

tics

dev

ices

Laser workshop Electric workshop Mechanic workshop

Technical platform

Single atoms

manipulation

Motivation: Quantum simulation with

ultracold atoms

Outline

The non-interacting spin-orbit coupled

Fermi gas

The strongly interacting spin-orbit coupled

Fermi gas

• Spin-orbit coupling Feshbach molecules

• Spin-orbit coupling induced coherent production of

Feshbach molecules in a degenerate Fermi gas

Background (SOC)(SOC)

Spin-orbit coupling:

1. From the electron’s point of view, the proton orbits

the electron and produces a magnetic field that

couples with the electron’s spin and alters its orbit;

2. In solids, spin-orbit coupling leads to topological

insulators, quantum spin hall effects, etc….

Phys. Today 63, 33 (2010); Nature 471, 41(2011)

valence band

conduction band

We can control the Hamiltonian of ultracold atoms in a number of ways

Quantum simulation with ultracold atoms

2

interaction

pH V(x) U

2m= + +

Kinetic: Synthetic vector potential Potential: Optical lattice Interaction: Feshbach resonance

Once we could construct such a Hamiltonian for the neutral atoms, we

can simulate the charged particle with neutral atoms!!

For a particle with charge q, moving in a electromagnetic field

2( )

( ) ( )2

pH V r r

m

B A

EA

A

t

q ϕ

ϕ

= + +

= ∇ ×∂= − − ∇∂

−

Vector potential: A

Scalar potential: ( )rϕr z

qA k σ=SOCSOC

Progress in Bose gas (SOC)(SOC)

Y. -J. Lin, et.al., Nature 417, 83 (2011) J.-Y. Zhang, et.al, PRL 109, 115301 (2012)

Collective Dipole Oscillations USTCFirst SOC in BEC

Ch. Qu, et.al, Phys. Rev. A 88, 021604 (2013)

Observation of Zitterbewegung

What will happen

in lattice

or

strong interaction regime?

Landau-Zener transition

A.J.Olson, et.al, arxiv.1310.1818(2013)

SOC in BEC using 1064 nm

Z. Fu, et.al., PRA 84, 043609 (2011)

NIST SXU

WSU Purdue U

New progress in Fermi gas (SOC)(SOC)

P. Wang, et.al., PRL. 109, 095301 (2012); L.W. Cheuk, et.al, PRL.109.095302(2012) R. A. Williams, et.al, PRL.111.095301(2012)

40K 6Li 40K

Review article: Spin-orbit coupling in quantum gases

V. Galitski, I. B. Spielman Nature 494, 49 (2013)

SXU MIT NIST

The non-interacting spin-orbit coupled Fermi gas

Spin-orbit coupled form

Base:

two energy eigenvalues:

two dressed eigenstates:

Theoretical model of two-level system

Translate unitary transformation

(NIST group’s SO Coupling)

R

R

ik x

ik x

e 0U

0 e

−⎛ ⎞= ⎜ ⎟⎝ ⎠

2 2

z x R y R

p δ Ω Ωˆ ˆ ˆ ˆ ˆ ˆH I σ σ cos(2k x) σ sin(2k x)2m 2 2 2

= + + −h

SG

Raman laser

(kR

: Single photon recoil momemtum)

Experimental realization of spin-orbit coupling in degenerate Fermi gas

766.7 nm

770.1 nm

B

Raman laser 1

773 nm

Raman laser 2

773 nmRaman laser 1

773 nm

Raman laser 2

773 nm

0 200 400 600 800-2

-1

0

1

2

B@GD

Energy@G

HzD

9/2,9/2

9/2,-9/2

9/2,7/2∼10.4 MHz

773 nm

|9/2,7/2>

|9/2,9/2>

|9/2,7/2> → |9/2,5/2>

δ ∼ 170 KHz∼30 GT=0.3 Tf

SO Coupled Fermi Gases: Raman Rabi Oscillation

First prepare fermion in

9/2, and then turn on

Raman coupling with

square envelop pulse

t

P. Wang, Z. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, and J. Zhang, arXiv:1204.1887

appear in Phys. Rev. Lett.P. Wang, Z. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, and J. Zhang, arXiv:1204.1887

Phys. Rev. Lett. 109, 095301 (2012);

<< trapping frequency

9/2,9/2

9/2,7/2

SO Coupled Fermi Gases: Equilibrium Momentum distribution

Break spatial reflectional symmetry:

Preserve reversal symmetry:

Time of flight measurement with Stern-Gerlach effect

SO Coupled Fermi Gases: Momentum distribution in helical bases

(A) Double peak structure in lower branch

(B) Small population in higher branch

(A) Double peak structure gradually disappears

(B) Significant population in higher branch

T=0.6-0.7 Tf

Momentum-resolved RF spectroscopy of non-interacting SO

coupling Fermi gas

Ez : the energy split of the two Zeeman states

: energy-momentum dispersion of the initial state

: energy-momentum dispersion of the final state (empty state)

-4 -2 0 2 4

-4 -2 0 2 4

|9/2,5/2>

Angle resolved

photoemission

spectroscopy ARPES)

Momentum-resolved RF spectroscopy of non-interacting SO

coupling Fermi gas

When we know:

Then:

δ=0 Ω=1.5Er

Momentum-resolved RF spectroscopy of non-interacting SO

coupling Fermi gas

Adiabatically change the trap frequency

-4 -2 0 2 4

-4 -2 0 2 4

RFν

When we know:

Then:

Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi GasL. W. Cheuk, A. T. Sommer, Z. Hadzibabic, T. Yefsah, W. S. Bakr, M. W. Zwierlein, arXiv:1205.3483,

Phys. Rev. Lett. 109, 095302 (2012)

:SO coupling

The strongly interacting spin-orbit coupled Fermi gas

Cooper pairs

weak coupling α<0

molecules

α>0

localized pairs Nonlocalized pairs

Crossover

Feshbach

resonance

9/2,-9/2

9/2,-7/2

9/2,-9/2 9/2,-7/2+

S-wave B0= 202.2 G

RF spectroscopy of strongly interacting ultracold Fermi gas

RF

mixer

23Zω

BEC – BCS Crossover

Cooper pairs

weak coupling α<0

molecules

α>0

localized pairs Nonlocalized pairs

Crossover

Feshbach

resonance

RF spectroscopy of strongly interacting ultracold Fermi gas

C. A. Regal and D. S. Jin, PRL (2003); J. T. Stewart, et al. Nature (2008)

Raman

coupling

The influence of spin-orbit coupling on Feshbach bound

molecules

Ramp magnetic field to create

Feshbach molecules, then open

Raman coupling with zero detuning

for |9/2,-9/2> and |9/2,-7/2>.

Z. Fu, L. Huang, Z. Meng, P. Wang, X.-J. Liu, H. Pu, H. Hu, J. Zhang, Phys. Rev. A 87,

053619 (2013)

Spin mixture

Spin-orbit coupling Feshbach molecules

characteristic blue and red shifts in the atomic and

molecular responses, respectively.

No one-photon effect

Large δ

RF spectrum of weakly bound molecules in spin-orbit

coupled atomic Fermi gases

H. Hu, H. Pu, J. Zhang, S.-G. Peng, and X.-J. Liu, Phys. Rev. A 86, 053627 (2012); S.-G.

Peng, X.-J. Liu, H. Hu, K. Jiang, arXiv:1210.2160

Free atoms

Bound molecues

Ω

Spin-Orbit Coupling Induced Coherent Production of

Feshbach Molecules in a Degenerate Fermi gas

Case 1: without SO coupling

Case 2: with SO coupling

triplet state

remain in triplet state without S-wave interaction

without SO coupling

With SOC

h(p)

ˆ

pn

h(q)

ˆ

qn

↓ ↓

Without SOC

h(p)

ˆ

pn

h(q)

ˆ

qn↓ ↓

triplet state singlet state

SO coupling can coherently produce s-wave Feshbach molecules from a fully

polarized Fermi gas

Translate unitary transformation

Raman coupling with

transferred momentum

Spin-orbit coupling

Fu, L. Huang, Z. Meng, P. Wang, L. Zhang, S. Zhang, H. Zhai, P. Zhang, J. Zhang, arXiv:1306.4568

Nature Phys. 10, 110 (2014)

Analyze by the original Raman-coupling Hamiltonian

Single particle Hamiltonian:

Two-atom Hamiltonian

Symmetric

Symmetric

Anti-symmetric

Anti-symmetric

It is also the same for inhomogeneous Ω!

= 0

G. K. Campbell et al., “Probing interactions between ultracold fermions”, Science (2009)

+V(x)

Small

Spin-orbit coupling

One photon momentum

M. D. Swallows et al., “Suppression of Collisional Shifts in a Strongly Interacting Lattice

Clock”, Science (2011)

+V(x)

Small

Large

“Strong confinement effect”

Energy penalty effect

Large

a fully polarized Fermi gas

Even with homogeneous Ω, there still is s-wave interaction due to spin orbit coupling

Spin-Orbit Coupling Induced Coherent Production of

Feshbach Molecules in a Degenerate Fermi gas

Two-photon Raman detuning:

The population of Feshbach molecules detected by the rf

pulse as a function of duration time of the Raman pulse

Raman

Z. Fu, L. Huang, Z. Meng, P. Wang, L. Zhang, S. Zhang, H. Zhai, P. Zhang, J. Zhang, arXiv:1306.4568

Nature Phys. 10, 110 (2014)

30 kHz

The population of Feshbach molecules and scattering atoms in |9/2;-7/2> state

as a function of two-photon detuning of the Raman pulse

The population of Feshbach molecules and scattering atoms

Ω=1.3Er

15 ms

Dependence on the Raman coupling strength and temperature for

Rabi oscillation between Feshbach molecular state and a fully

polarized Fermi gas

Direct evidence for the coherent nature of molecular production

= 0

SO coupling provides

finite matrix element

between a singlet state (s-

wave) and a triplet state

(p-wave), and therefore,

implies the bound pairs of

a system with SO coupling

have triplet p-wave

component, which can

become topological

superfluid.

Demonstrate experimentally:Ω=2.8Er

Ω=1.95Er

Ω=1.3Er

Ω=0.65Er

0.3Tf ~0.9Tf

Creation of Feshbach molecules for different magnetic fields

Detection: dissociated by a magnetic sweep over the Feshbach resonance

Atom-molecule transition amplitude depends on the overlap between the wave-

function of Feshbach molecule and the one of two free atoms (Franck-Condon factor)

R. A. Williams, M. C. Beeler, L. J. LeBlanc, K. Jimenez-Garcia, I. B. Spielman, arXiv:1306.1965;

Phys. Rev. Lett. 111, 095301 (2013)

A Raman-induced Feshbach resonance in an single-component

Fermi gas

Conclusion The non-interacting spin-orbit coupled Fermi gas

The strongly interacting spin-orbit coupled

Fermi gas

Related works:Raman spectroscopy

Optical control of a magnetic Feshbach resonance

P. Wang, Z. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai,

and J. Zhang, Phys. Rev. Lett. 109, 095301 (2012);

Z. Fu, L. Huang, Z. Meng, P. Wang, X.-J. Liu, H. Pu, H. Hu, J.

Zhang, Phys. Rev. A 87, 053619 (2013)

Z. Fu, L. Huang, Z. Meng, P. Wang, L. Zhang, S. Zhang, H. Zhai, P.

Zhang, J. Zhang, arXiv:1306.4568; Nature Phys. 10, 110 (2014)

Phys. Rev. A 85, 053626 (2012); Phys. Rev. A 86, 033607 (2012).

Phys. Rev. A 88, 041601(R) (2013)

RF control of a magnetic Feshbach resonance

poster, in prepare

Acknowledgement

Experiment:

Pengjun Wang

Zhengkun Fu

Lianghui Huang

Zengming Meng

Peng Peng

Cooperation (Theory) :

Tsinghua University

Hui Zhai

Rice University

Han Pu

Swinburne University of Technology

Hui Hu, Xiaji Liu

Renmin University of China

Peng Zhang

University of Hong Kong

Shizhong Zhang