BEC in Optical Dipole Trap & Artificial Gauge...
Transcript of BEC in Optical Dipole Trap & Artificial Gauge...
BEC in Optical Dipole Trap & Artificial Gauge Potential
Shuai Chen Department of Modern Physics,
University of Science and Technology of China
Lanzhou, August 1st 2011
Outline
โข Motivation: Quantum simulation with ultracold atoms
โข BEC in Optical dipole trap
โ Optical dipole trap
โ Experiment process to produce BEC in optical dipole trap
โข Artificial gauge potential by Raman coupling
โ How to generate gauge field with Raman coupling
โ Experiment generation of gauge potential
โ Spin Orbit coupling
โ Quantum tunneling in Spin-Orbit coupled BEC
โข Conclusion
Quantum Simulation
โฆnature isnโt classical, dammit, and if you want to make a simulation of nature, youโd better make it quantum mechanical, and by golly itโs a wonderful problem, because it doesnโt look so easy. - Richard P. Feynman, May 1981
published: Int. J. Theo. Phys. (1982)
Quantum Simulation
โข Understand and Design Quantum Materials โ One of the biggest challenges of Quantum Physics in the 21st Century
โข Technological Relevance โ High temperature superconductivity (Power Delivery)
โ Magnetism (Storage, Spintronicsโฆ)
โ Quantum Hall effect (transportationโฆ)
โ Quantum Computing
WHATโS THE PROBLEM? THE CHALLENGE OF QUANTUM MATERIALS
A controllable quantum material is required!
Ultracold Quantum Gas
Open the new era of quantum simulation with ultracold Bose and Fermi Gas!
BEC in 1995 Ultracold Fermi Gas
Superfluid to Mott insulator transition
Greiner et al., Nature 415, 39 (2002)
Mott insulator of Fermions
A. Kastberg et al. PRL 74, 1542 (1995) M. Greiner et al. PRL 87, 160405 (2001)
Brillouin Zones in 2D and the momentum distribution of cold atoms in lattices
Joerdens et al., Nature 455, 204 (2008) U. Schneider et.al., Science 322, 1520 (2008)
Optical lattices
Feshbach resonance
Feshbach resonance of 6Li
BEC-BCS crossover
JILA, MIT, Innsbruckโฆ
K.-K. Ni et.al., Science 322, 231 (2008) K.-K. Ni et.al., Nature 464, 1324 (2010) J. G. Danzl, et.al., Nature Physics 6, 265 (2010)
Formation of ultracold molecule
W. S. Bakr et.al., Nature 462, 75 (2009) J. F. Sherson et.al., Nature 467,69 (2010) Ch. Weitenberg et.al., Nature 471,319 (2011)
Single site resolution and single site addressing
Exchange interaction of spin in super lattice Anderlini et al., Nature 448, 452 (2007) Trotzky et al., Science 319, 295 (2008)
Anderson localization of matter wave Billy et al., Nature 453, 891 (2008) Roati et al., Nature 453, 895 (2008)
Development of quantum simulation
Could ultracold atoms emulate charged particle?
โข To simulate Lorenz Force: ๐น = ๐๐ฃ ร ๐ต
โข To understanding Quantum Hall Effect?
โข To form the topological insulator
โข Large scale Quantum Computing
Nobel Prize 1985 Quantum Hall Effect
Nobel Prize 1998 Fractional Quantum Hall Effect
What is Bose-Einstein Condensate?
de Broglie wavelength
Phase space density
๐๐๐ > 2.612
In 3D free space
Typical road to BEC
Optical dipole trap
Evaporative cooling
Proper for magnetic trap
Good for optical trap
Rb-87 atom
โRb-87 D line dataโ, D. Steck, http://steck.us/alkalidata/
5๐1/2
๐น = 1
๐น = 2
3
2
1 0
2
1
5๐1/2
5๐3/2
coo
ling
rep
um
pin
g
imag
ing
For ground states:
For laser cooling:
+1 0
+1
โ1
+2 โ1 โ2
0 ๐น = 2
๐น = 1
Optical Dipole Trap
Red: ฮ < 0, atoms get attracted to intensity maximum Blue: ฮ > 0, atoms get repelled from intensity maximum
๐dip โ ๐ผ/ฮ
ฮsc โ ๐ผ/ฮ2 Go for large detuning and intensity!
Optical dipole potential:
Photon scattering Rate: โ๐
ฮ
ฮ = โ๐ โ โ๐0
|๐
|๐
โ๐0
0
๐ธ
ฮ
Optical Dipole Trap
Experimental setup
Setup for BEC in Optical trap
Setups for Lasers (cooling, repumping & probe )
Vacuum system
2D MOT chamber
Science Chamber: 3D MOT & Dipole trap
Differential pump stage
Ion pump
Ti: sublimation pump
Ion pump
Science Chamber: 10โ11 mbar
2D MOT chamber: 10โ9 mbar
MOT loading to Dark Molasses
Dark MOT Atom number: ~ 3 ร 109 Density: ๐~1 ร 1012/cm3 Temperature: ๐~200ฮผK
Dark molasses Atom number: ~ 2 ร 109 Density: ๐~5 ร 1011/cm3 Temperature: ๐~40ฮผK
Optical Dipole Trap loading
Beam waist: ~80ฮผm Crossing angle: 75ยฐ Initial trap depth: ~500ฮผK
Atom number: ~ 1.4 ร 107 density: ~1 ร 1012/cm3 Temperature: ~100ฮผK
Dipole trap laser: Yb doped fiber laser, 1070nm, 50W
Time of flight: 2ms
Evaporative cooling and Imaging of BEC
Time of Flight Image: CCD pixel cize: 16ฮผm Magnification: 1: 1 N/A: 0.18 Resolution: 16ฮผm
10 ms Time of flight image
~100ฮผK 1.4 ร 107 atoms
~20ฮผK 6.0 ร 106 atoms
~5ฮผK 2.5 ร 106 atoms
Formation of BEC
๐ > ๐๐ Thermal atoms
๐ = ๐๐ BEC appears
๐ < ๐๐ Bi-mode distribution
๐ โช ๐๐ Pure BEC
Critical temperature๏ผ ๐๐~100nK Atom number: ๐ = 2.5 ร 105 Density of atoms: ๐ > 1013/cm3 Trapping frequency: *50, 50, 80+Hz Effective temperature: 10nK
Image for BEC: CCD pixel cize: 16ฮผm Magnification: 4: 1 N/A: 0.18 Resolution: ~4.0ฮผm
Could ultracold atoms emulate charged particle?
โข To simulate Lorenz Force: ๐น = ๐๐ฃ ร ๐ต
โข To understanding Quantum Hall Effect?
โข To form the topological insulator
โข Large scale Quantum Computing
Nobel Prize 1985 Quantum Hall Effect
Nobel Prize 1998 Fractional Quantum Hall Effect
For a particle moving in the potential ๐(๐), the Hamitonian:
Magnetic field: ๐ต = ๐ป ร ๐ด
Electric field: ๐ธ = โ๐๐ด
๐๐กโ ๐ป๐
Once we could construct such a Hamitonian for the neutron atoms, we can simulate the charged particle with neutron atoms!!
Yes! If we can construct the gauge potential
๐ป ๐, ๐ =๐2
2๐+ ๐(๐)
Vector potential: ๐ด Scalar potential: ๐(๐)
For a particle with charge ๐, moving in a electromagnetic field,
the form or Hamitonian can be expressed as:
๐ปโฒ(๐, ๐) =๐ โ ๐๐ด 2
2๐+ ๐ ๐ + ๐(๐)
Possible schemes
โข BEC in a rotating trap
โ Coriolis force-> Lorentz force
โ Only modest effective fields
โ limited to rotational symmetric setups and does not allow to study transport phenomena
โข Light-induced gauge field (geometric phase)
โ Need a spatially varying basis of internal states
BvFLorentz vFcoriolis
ยท Dark state and Bright state ยท Spin Hall Effect
G. Juzeliunas, et.al., PRA 73, 025602 (2006) K. J. Guenter, et.al., PRA 79, 011604 (2009) I. B. Spielman, PRA 79, 063613 (2009)
S.-L. Zhu et.al., PRL 97, 240401 (2006)
Laser coupling with spatial gradients
Add an effective electric field
Gauge field generation โข based on EIT configuration โข retained in the dark state
โข Easy to adjust parameters in experiment โข Verify the effective gauge field by measuring the momentum distribution
I. B. Spielman, PRA 79, 063613 (2009)
Hamitonian:
0~
min k
Atom detuning with spatial gradients
Some Experiment Progress
Y.-J. Lin, et.al., PRL 102, 130401 (2009)
Y.-J. Lin, et.al., Nature 462, 628 (2009)
Synthetic magnetic fields for BEC: ๐ต = ๐ป ร ๐ด
Vortices are formed in condensates
the Hamitonian of the dressed state:
Y.-J. Lin, et.al., arXiv: 1008.4864 (2010)
Electric field generation: ๐ธ = โ๐๐ด/๐๐ก
Vector Potential generation:
Spin-Orbit coupling
Y. -J. Lin, et.al., Nature 417, 83 (2011)
Phase transition due to the interaction of atoms for different โspinโ in BEC
Proved the SO coupling in 1D
Still many open questions!
How to do it? โ Dispersion relations
(๐ โ ๐๐ด)2
2๐
๐2
2๐
๐ธ
momentum p
Where ๐ด is the vector potential In general, โ๐ดโ could be a number (abel gauge potential) โ๐ดโ could also be a matrix (non-abelian gauge potential)
๐๐ด
Raman coupling: Basic concepts
Resonant Raman Rabi Frequency:
ฮฉ =ฮฉ1ฮฉ2
4ฮ ฮฉ1 ฮฉ2
ฮ
๐ฟ
|๐
|๐1
|๐2
โ๐1 โ๐2
ฮ : Single photon detuning ๐ฟ : Raman detuning ฮฉ1, ฮฉ2: Rabi frequency
๐2 ๐1
atoms
๐
For ๐1 โ ๐2, ๐1 = ๐2 = ๐
Recoil momentum: โ๐๐ = โ๐ sin๐
2
Recoil Energy: ๐ธ๐ =โ2๐๐
2
2๐
ฮsc โ ฮฉ/ฮ2
Take care: Spontaneous photon scattering
๐ ๐ฅ
๐ธ
๐ฟ = 0 ๐ฟ โ 0
How to realize such a vector potential? Two level atoms with counter propagate Raman coupling
๐ป = โ
โ
2๐(๐ ๐ฅ + ๐๐)
2 โ ๐ฟ/2 /2
/2โ
2๐(๐ ๐ฅ โ ๐๐)
2 + ๐ฟ/2
โ๐ ๐ฅ: quasi-momentum in ๐ฅ direction โ๐๐: recoil momentum of single laser
|โ1 : ๐๐ฅ = ๐ ๐ฅ + ๐๐
|0 : ๐๐ฅ = ๐ ๐ฅ โ ๐๐
for real momentum during probe:
๐๐ด
๐ฃ๐ =๐๐ธ
๐๐ ๐ฅ= 0
๐ฟ/2 |โ1
๐ฟ/2
: Raman Rabi frequency ๐ฟ: Raman detuning
|0
Three level case For Rb87 ๐น = 1 hyperfine state:
๐ป =
(๐ ๐ฅ + 2๐๐)2โ๐ฟโฒ ฮฉ/2 0
ฮฉ/2 ๐ ๐ฅ2โ ๐ ฮฉ/2
0 ฮฉ/2 (๐ ๐ฅ โ 2๐๐)2+๐ฟโฒ
real momentum during TOF detection:
๐ฟโฒ
๐ฟโฒ
๐
๐: quadratic Zeeman shift
๐ฟโฒ: Raman detuning
|โ1
|0
|+1
|โ1 : ๐๐ฅ = ๐ ๐ฅ + 2๐๐
|0 : ๐๐ฅ = ๐ ๐ฅ
|+1 : ๐๐ฅ = ๐ ๐ฅ โ 2๐๐
๐ ๐ฅ
๐ธ
๐๐ด
Spin-Orbit Coupling Two level atoms with counter propagate Raman coupling ๐ป = โ
โ
2๐(๐ ๐ฅ + ๐๐)
2 โ ๐ฟ/2 /2
/2โ
2๐(๐ ๐ฅ โ ๐๐)
2 + ๐ฟ/2
|โ โฒ |โ โฒ
๐ ๐ฅ
If ฮฉ โช 4๐ธ๐
|โ โฒ = |โ1 + ฮต|0 , |โ โฒ = |0 + ฮต|โ1
๐ป =โ2๐2
2๐I +
2๐๐ฅ โ
ฮด
2๐๐ง + 2ฮฑ๐ ๐ฅ๐๐ง
Spin-Orbit coupling!
We can mark spin |โ = |โ1 , |โ = |0
๐ป =๐ โ ๐๐ด 2
2๐
โ๐๐ดโ is not a number, but a matrix! Non-abelian gauge potential!
๐ฟ/2 |โ1
๐ฟ/2
: Raman Rabi frequency
|0
2-level Raman coupling
3-level Raman coupling
State selection for atoms
With relative large Bias field (large quadratic Zeeman shift) quasi-2-level Raman coupling
+1 0
+1
โ1
+2
โ1 โ2
0 ๐น = 2
๐น = 1
Rb-87 Ground states
First experiment: produce gauge potential
Counter propagate Raman lasers
Raman lasers: Wavelength: 790.07nm Beam waist: 180ฮผm Recoil energy: ๐ธ๐ = 3.68kHz
Calibration of Raman coupling strength
Raman Rabi Oscillation
Counter propagation
Resonant Raman Rabi Frequency:
ฮฉ =ฮฉ1ฮฉ2
4ฮ
0 /2 3/2 2
|1, โ1
|2,0
Bias magnetic field: ๐ต = 3.2 Gauss Quadratic Zeeman shift: ๐ = 0.4๐ธ๐ Coupling Strength: ฮฉ = 4.25๐ธ๐
๐ฟ = โ1.5๐ธ๐ ๐ฟ = +1.5๐ธ๐ ๐ฟ = 0
๐๐ด = 0 ๐๐ด > 0 ๐๐ด < 0
Formation of the uniform Gauge potential
Spin-Orbit coupling
Stage 1 Stage 2 Stage 3
Increase the strength of counter propagate Raman coupling
Time of Flight Image after Stage 2
|0
kx
|0 |0 |0 |โ1 |โ1 |โ1 |โ1
|โ โฒ |โ โฒ
|โ โฒ = |โ1 + ฮต|0
|โ โฒ = |0 + ฮต|โ1
Raman laser configuration changed
Raman laser: Wavelength: 803.3nm Beam waist: 180ฮผm Cross angle: 105 Recoil energy: 2.24kHz
๐๐ ๐๐
2๐๐
|โ1
|0
๐ก = 0 240ms 60ms 120ms 180ms
Tunneling in momentum space Raman coupling: ฮฉ = 2.2๐ธ๐ Detuning: ๐ฟ = โ0.22๐ธ๐ Bias field: ๐ต = 7.2 Gauss Quadratic Zeeman shift: ๐ = 3.328๐ธ๐
๐ ๐ฅ
|โ = |0 + ฯต|โ1
tunneling
|โ = |โ1 + ฯต|0
|โ1 : ๐๐ฅ = ๐ ๐ฅ + ๐๐
|0 : ๐๐ฅ = ๐ ๐ฅ โ ๐๐ Real momentum of atom state during probe:
Josephson effect theory
Make ๐ stands for the difference between the population of the two parts, and the ๐ stands for the phase difference between the coefficients:
The total wave funtion:
๐ = |๐|2 โ |๐|2 ๐ = ๐๐ โ ๐๐
๐ = ๐ ๐๐ + ๐|๐๐
In the Coordinate Space
๐ป ๐ฅ = โโ2
2๐
๐2
๐๐ฅ2+ ๐(๐ฅ)
The 1D Hamitonian:
Solve the Schrรถdinger Equation:
The Schrรถdinger Equation:
Lead to Josephson oscillation.
|๐๐ |๐๐
โข In the Momentum Space The 1D Spin-Orbit coupling Hamitonian:
Josephson effect theory
The ๐ and the ๐ has the samilar definition as in the coordinate space
๐ = |๐2|2 โ |๐1|
2 ๐ = ๐2 โ ๐1
the Schรถdinger equation:
the similar dynamic process as in the coordinate space
Josephson oscillation in momentum space!
The total wave funtion:
๐ = ๐1 ๐1 + ๐2|๐2
๐1 = ๐1 ๐๐๐1 , ๐2 = ๐2 ๐๐๐2
In harmonic trap,
๐๐๐ฅ๐ก =1
2๐๐2๐ฅ2 = โ
๐โ2๐2
2
๐2
๐๐2
|๐1 |๐2
๐ป = โ๐โ2๐2
2
๐2
๐๐2+ ๐ธ(๐)
Tunneling in momentum space
๐น = 0.15๐ธ๐ ๐น = 0.5๐ธ๐ ๐น = 0.05๐ธ๐
Raman coupling: ฮฉ = 2.2๐ธ๐ Bias field: ๐ต = 7.2 Gauss Quadratic Zeeman shift: ๐ = 3.328๐ธ๐
Conclusion
โข Rb-87 BEC in optical dipole trap is produced
โข Artificial gauge potential is generated with Raman coupled BEC
โข Generation of Spin-Orbit coupled BEC with Raman coupling
โข Quantum tunneling and Josephson Effect in momentum space is observed
Future plan
ๅฉ็จBECๅ็ฉบ้ดๅค็ปดRamanๆฟๅ ่ฆๅไบง็้้ฟ่ดๅฐ็ญๆ่ง่
ๅบ๏ผ่งๆตไธญๆง่ถ ๅทๅๅญๅจ้้ฟ่ดๅฐ่ง่ๅบไธญ็่กไธบ๏ผ ๆจกๆๅธฆ็ต
็ฒๅญ็่ชๆ่ฝจ้่ฆๅๅฏผ่ด็็ธๅ้ฎ้ขใ
Focus on Spin-Orbit coupled BEC
Study the phase transition of the Spin-Orbit coupled BEC
Stripe phase of Spin-Orbit coupled BEC
Chunji Wang et.al., PRL 105, 160403 (2010)
Boson pairing and fractional vortices phase of Spin-Orbit coupled BEC
C. -M. Jian & H. Zhai, arXiv: 1105.5700
Acknowledgement โข Group Leader: Jian-Wei Pan
โข Experiment
โ Jinyi Zhang, Zhidong Du, Sicong Ji, Yingzhu and SC
โข Theory
โ Long Zhang, Ran Wei, YJD
โข Cooperation
โ Hui Zhai
โข Former member
โ Bo Yan, Mingfei Han
Supported by: