bec in optical dipole trap & artificial gauge...
TRANSCRIPT
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
• Motivation: Quantum simulation with ultracold atoms
• BEC in Optical dipole trap
– Optical dipole trap
– Experiment process to produce BEC in optical dipole trap
• Artificial gauge potential by Raman coupling
– How to generate gauge field with Raman coupling
– Experiment generation of gauge potential
– Spin Orbit coupling
– Quantum tunneling in Spin-Orbit coupled BEC
• Conclusion
Quantum Simulation
…nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy. - Richard P. Feynman, May 1981
published: Int. J. Theo. Phys. (1982)
Quantum Simulation
• Understand and Design Quantum Materials – One of the biggest challenges of Quantum Physics in the 21st Century
• Technological Relevance – High temperature superconductivity (Power Delivery)
– Magnetism (Storage, Spintronics…)
– Quantum Hall effect (transportation…)
– Quantum Computing
WHAT’S 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, Innsbruck…
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?
• To simulate Lorenz Force: 𝐹 = 𝑞𝑣 × 𝐵
• To understanding Quantum Hall Effect?
• To form the topological insulator
• 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
𝜌𝑝𝑠 > 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
“Rb-87 D line data”, D. Steck, http://steck.us/alkalidata/
5𝑆1/2
𝐹 = 1
𝐹 = 2
3
2
1 0
2
1
5𝑆1/2
5𝑃3/2
coo
ling
rep
um
pin
g
imag
ing
For ground states:
For laser cooling:
+1 0
+1
−1
+2 −1 −2
0 𝐹 = 2
𝐹 = 1
Optical Dipole Trap
Red: Δ < 0, atoms get attracted to intensity maximum Blue: Δ > 0, atoms get repelled from intensity maximum
𝑈dip ∝ 𝐼/Δ
Γsc ∝ 𝐼/Δ2 Go for large detuning and intensity!
Optical dipole potential:
Photon scattering Rate: ℏ𝜔
Δ
Δ = ℏ𝜔 − ℏ𝜔0
|𝑒
|𝑔
ℏ𝜔0
0
𝐸
Γ
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: 10−11 mbar
2D MOT chamber: 10−9 mbar
MOT loading to Dark Molasses
Dark MOT Atom number: ~ 3 × 109 Density: 𝑛~1 × 1012/cm3 Temperature: 𝑇~200μK
Dark molasses Atom number: ~ 2 × 109 Density: 𝑛~5 × 1011/cm3 Temperature: 𝑇~40μK
Optical Dipole Trap loading
Beam waist: ~80μm Crossing angle: 75° Initial trap depth: ~500μK
Atom number: ~ 1.4 × 107 density: ~1 × 1012/cm3 Temperature: ~100μK
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: 16μm Magnification: 1: 1 N/A: 0.18 Resolution: 16μm
10 ms Time of flight image
~100μK 1.4 × 107 atoms
~20μK 6.0 × 106 atoms
~5μK 2.5 × 106 atoms
Formation of BEC
𝑇 > 𝑇𝑐 Thermal atoms
𝑇 = 𝑇𝑐 BEC appears
𝑇 < 𝑇𝑐 Bi-mode distribution
𝑇 ≪ 𝑇𝑐 Pure BEC
Critical temperature: 𝑇𝑐~100nK Atom number: 𝑁 = 2.5 × 105 Density of atoms: 𝑛 > 1013/cm3 Trapping frequency: *50, 50, 80+Hz Effective temperature: 10nK
Image for BEC: CCD pixel cize: 16μm Magnification: 4: 1 N/A: 0.18 Resolution: ~4.0μm
Could ultracold atoms emulate charged particle?
• To simulate Lorenz Force: 𝐹 = 𝑞𝑣 × 𝐵
• To understanding Quantum Hall Effect?
• To form the topological insulator
• Large scale Quantum Computing
Nobel Prize 1985 Quantum Hall Effect
Nobel Prize 1998 Fractional Quantum Hall Effect
For a particle moving in the potential 𝑉(𝑟), the Hamitonian:
Magnetic field: 𝐵 = 𝛻 × 𝐴
Electric field: 𝐸 = −𝜕𝐴
𝜕𝑡− 𝛻𝜑
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
𝐻 𝑝, 𝑟 =𝑝2
2𝑚+ 𝑉(𝑟)
Vector potential: 𝐴 Scalar potential: 𝜑(𝑟)
For a particle with charge 𝑞, moving in a electromagnetic field,
the form or Hamitonian can be expressed as:
𝐻′(𝑝, 𝑟) =𝑝 − 𝑞𝐴 2
2𝑚+ 𝑉 𝑟 + 𝜑(𝑟)
Possible schemes
• BEC in a rotating trap
– Coriolis force-> Lorentz force
– Only modest effective fields
– limited to rotational symmetric setups and does not allow to study transport phenomena
• Light-induced gauge field (geometric phase)
– Need a spatially varying basis of internal states
BvFLorentz vFcoriolis
· Dark state and Bright state · 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 • based on EIT configuration • retained in the dark state
• Easy to adjust parameters in experiment • 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: 𝐵 = 𝛻 × 𝐴
Vortices are formed in condensates
the Hamitonian of the dressed state:
Y.-J. Lin, et.al., arXiv: 1008.4864 (2010)
Electric field generation: 𝐸 = −𝜕𝐴/𝜕𝑡
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 “spin” in BEC
Proved the SO coupling in 1D
Still many open questions!
How to do it? – Dispersion relations
(𝑝 − 𝑞𝐴)2
2𝑚
𝑝2
2𝑚
𝐸
momentum p
Where 𝐴 is the vector potential In general, “𝐴” could be a number (abel gauge potential) “𝐴” could also be a matrix (non-abelian gauge potential)
𝑞𝐴
Raman coupling: Basic concepts
Resonant Raman Rabi Frequency:
Ω =Ω1Ω2
4Δ Ω1 Ω2
Δ
𝛿
|𝑒
|𝑔1
|𝑔2
ℏ𝜔1 ℏ𝜔2
Δ : Single photon detuning 𝛿 : Raman detuning Ω1, Ω2: Rabi frequency
𝑘2 𝑘1
atoms
𝜃
For 𝜔1 ≈ 𝜔2, 𝑘1 = 𝑘2 = 𝑘
Recoil momentum: ℏ𝑘𝑟 = ℏ𝑘 sin𝜃
2
Recoil Energy: 𝐸𝑟 =ℏ2𝑘𝑟
2
2𝑚
Γsc ∝ Ω/Δ2
Take care: Spontaneous photon scattering
𝑘 𝑥
𝐸
𝛿 = 0 𝛿 ≠ 0
How to realize such a vector potential? Two level atoms with counter propagate Raman coupling
𝐻 = ℏ
ℏ
2𝑚(𝑘 𝑥 + 𝑘𝑟)
2 − 𝛿/2 /2
/2ℏ
2𝑚(𝑘 𝑥 − 𝑘𝑟)
2 + 𝛿/2
ℏ𝑘 𝑥: quasi-momentum in 𝑥 direction ℏ𝑘𝑟: recoil momentum of single laser
|−1 : 𝑘𝑥 = 𝑘 𝑥 + 𝑘𝑟
|0 : 𝑘𝑥 = 𝑘 𝑥 − 𝑘𝑟
for real momentum during probe:
𝑞𝐴
𝑣𝑔 =𝜕𝐸
𝜕𝑘 𝑥= 0
𝛿/2 |−1
𝛿/2
: Raman Rabi frequency 𝛿: Raman detuning
|0
Three level case For Rb87 𝐹 = 1 hyperfine state:
𝐻 =
(𝑘 𝑥 + 2𝑘𝑟)2−𝛿′ Ω/2 0
Ω/2 𝑘 𝑥2− 𝜖 Ω/2
0 Ω/2 (𝑘 𝑥 − 2𝑘𝑟)2+𝛿′
real momentum during TOF detection:
𝛿′
𝛿′
𝜖
𝜖: quadratic Zeeman shift
𝛿′: Raman detuning
|−1
|0
|+1
|−1 : 𝑘𝑥 = 𝑘 𝑥 + 2𝑘𝑟
|0 : 𝑘𝑥 = 𝑘 𝑥
|+1 : 𝑘𝑥 = 𝑘 𝑥 − 2𝑘𝑟
𝑘 𝑥
𝐸
𝑞𝐴
Spin-Orbit Coupling Two level atoms with counter propagate Raman coupling 𝐻 = ℏ
ℏ
2𝑚(𝑘 𝑥 + 𝑘𝑟)
2 − 𝛿/2 /2
/2ℏ
2𝑚(𝑘 𝑥 − 𝑘𝑟)
2 + 𝛿/2
|↑ ′ |↓ ′
𝑘 𝑥
If Ω ≪ 4𝐸𝑟
|↑ ′ = |−1 + ε|0 , |↓ ′ = |0 + ε|−1
𝐻 =ℏ2𝑘2
2𝑚I +
2𝜎𝑥 −
δ
2𝜎𝑧 + 2α𝑘 𝑥𝜎𝑧
Spin-Orbit coupling!
We can mark spin |↑ = |−1 , |↓ = |0
𝐻 =𝑝 − 𝑞𝐴 2
2𝑚
“𝑞𝐴” is not a number, but a matrix! Non-abelian gauge potential!
𝛿/2 |−1
𝛿/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
−1
+2
−1 −2
0 𝐹 = 2
𝐹 = 1
Rb-87 Ground states
First experiment: produce gauge potential
Counter propagate Raman lasers
Raman lasers: Wavelength: 790.07nm Beam waist: 180μm Recoil energy: 𝐸𝑟 = 3.68kHz
Calibration of Raman coupling strength
Raman Rabi Oscillation
Counter propagation
Resonant Raman Rabi Frequency:
Ω =Ω1Ω2
4Δ
0 /2 3/2 2
|1, −1
|2,0
Bias magnetic field: 𝐵 = 3.2 Gauss Quadratic Zeeman shift: 𝜖 = 0.4𝐸𝑟 Coupling Strength: Ω = 4.25𝐸𝑟
𝛿 = −1.5𝐸𝑟 𝛿 = +1.5𝐸𝑟 𝛿 = 0
𝑞𝐴 = 0 𝑞𝐴 > 0 𝑞𝐴 < 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 |−1 |−1 |−1 |−1
|↑ ′ |↓ ′
|↑ ′ = |−1 + ε|0
|↓ ′ = |0 + ε|−1
Raman laser configuration changed
Raman laser: Wavelength: 803.3nm Beam waist: 180μm Cross angle: 105 Recoil energy: 2.24kHz
𝑘𝜋 𝑘𝜎
2𝑘𝑟
|−1
|0
𝑡 = 0 240ms 60ms 120ms 180ms
Tunneling in momentum space Raman coupling: Ω = 2.2𝐸𝑟 Detuning: 𝛿 = −0.22𝐸𝑟 Bias field: 𝐵 = 7.2 Gauss Quadratic Zeeman shift: 𝜖 = 3.328𝐸𝑟
𝑘 𝑥
|↓ = |0 + ϵ|−1
tunneling
|↑ = |−1 + ϵ|0
|−1 : 𝑘𝑥 = 𝑘 𝑥 + 𝑘𝑟
|0 : 𝑘𝑥 = 𝑘 𝑥 − 𝑘𝑟 Real momentum of atom state during probe:
Josephson effect theory
Make 𝑠 stands for the difference between the population of the two parts, and the 𝜃 stands for the phase difference between the coefficients:
The total wave funtion:
𝑠 = |𝑏|2 − |𝑎|2 𝜃 = 𝜃𝑏 − 𝜃𝑎
𝜓 = 𝑎 𝜓𝑎 + 𝑏|𝜓𝑏
In the Coordinate Space
𝐻 𝑥 = −ℏ2
2𝑚
𝜕2
𝜕𝑥2+ 𝑉(𝑥)
The 1D Hamitonian:
Solve the Schrödinger Equation:
The Schrödinger Equation:
Lead to Josephson oscillation.
|𝜓𝑎 |𝜓𝑏
• In the Momentum Space The 1D Spin-Orbit coupling Hamitonian:
Josephson effect theory
The 𝜌 and the 𝜃 has the samilar definition as in the coordinate space
𝜌 = |𝜉2|2 − |𝜉1|
2 𝜑 = 𝜑2 − 𝜑1
the Schödinger equation:
the similar dynamic process as in the coordinate space
Josephson oscillation in momentum space!
The total wave funtion:
𝜓 = 𝜉1 𝜓1 + 𝜉2|𝜓2
𝜉1 = 𝜉1 𝑒𝑖𝜑1 , 𝜉2 = 𝜉2 𝑒𝑖𝜑2
In harmonic trap,
𝑉𝑒𝑥𝑡 =1
2𝑚𝜔2𝑥2 = −
𝑚ℏ2𝜔2
2
𝜕2
𝜕𝑝2
|𝜓1 |𝜓2
𝐻 = −𝑚ℏ2𝜔2
2
𝜕2
𝜕𝑝2+ 𝐸(𝑝)
Tunneling in momentum space
𝜹 = 0.15𝐸𝑟 𝜹 = 0.5𝐸𝑟 𝜹 = 0.05𝐸𝑟
Raman coupling: Ω = 2.2𝐸𝑟 Bias field: 𝐵 = 7.2 Gauss Quadratic Zeeman shift: 𝜖 = 3.328𝐸𝑟
Conclusion
• Rb-87 BEC in optical dipole trap is produced
• Artificial gauge potential is generated with Raman coupled BEC
• Generation of Spin-Orbit coupled BEC with Raman coupling
• Quantum tunneling and Josephson Effect in momentum space is observed
Future plan
利用BEC和空间多维Raman激光耦合产生非阿贝尔等效规范
场,观测中性超冷原子在非阿贝尔规范场中的行为, 模拟带电
粒子的自旋轨道耦合导致的相变问题。
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 • Group Leader: Jian-Wei Pan
• Experiment
– Jinyi Zhang, Zhidong Du, Sicong Ji, Yingzhu and SC
• Theory
– Long Zhang, Ran Wei, YJD
• Cooperation
– Hui Zhai
• Former member
– Bo Yan, Mingfei Han
Supported by: