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