Modelling Magnetic Fields of MicroTrap Arrays for Trapping Ultracold Atoms A. Mouraviev, & W. A. van Wijngaarden Physics Dept., York University www.wvanwijngaarden.info.yorku.ca CUPC 2015
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Modelling Magnetic Fields of MicroTrap
Arrays for Trapping Ultracold Atoms
A. Mouraviev, & W. A. van Wijngaarden
Physics Dept., York University
www.wvanwijngaarden.info.yorku.ca
CUPC 2015
Presenter
Presentation Notes
My work this summer was on modeling magnetic fields of magnetic micro traps for trapping atoms
Ultracold Atoms W.A. van Wijngaarden & B. Lu. Phys. in Can. 60, No. 5 (2004)
Why Study Ultracold Atoms? - Near absolute zero, weird effects such as superfluidity &
superconductivity occur. (D & J Tilley, Superfluidity & Superconductivity, U. Sussex Press, 1986)
How Do You Get Bose Einstein Condensation (BEC)?
- Bosons condense into lowest state at ultralow temperatures (K. Stowe, Intro. Stat. Mech. & Thermo., J. Wiley, Toronto, 1984)
- Macroscopic effects of quantum mechanics evident when de Broglie wavelength λB ~ distance between atoms
h = Planck’s constant M = atom’s mass kB = Boltzmann’s constant
Presenter
Presentation Notes
Some of my supervisor's work is on Ultra Cold atoms and BEC BEC -> Bosons not subject to pauli exclusion principle Macroscopic: Superfluidity – > Zero Viscosity , vortices that never stop rotating ; Superconductivity -> Zero Resistance Debroglie wavelength
t = 6 ms t = 12 t = 10
t = 14 t = 20 t = 18 t = 16
t = 8
Measurement of Ultracold Temperature
Observe expansion of atom cloud after trap turned off.
Presenter
Presentation Notes
Release from trap
How does an Atom Trap Work?
Zeeman Hamiltonian
Zeeman Shift of 87Rb F=2 Hyperfine level
µ = atom’s magnetic moment B = magnetic field
1
-2
0
mF = 2
-1
B 5S1/2 F=2
Atoms in mF = 1, 2 hyperfine levels trapped at minimum magnetic field.
Presenter
Presentation Notes
I – nuclear spin J – electronic angular momentum F = 1 and 2, ground state hyperfine levels \
Double Loop Microtrap B. Jian & WvW, JOSA B 30, No. 2, 238 (2013)
Current I2 = -1.23 I1 Radius R2 = 1.4 R1 B0 = I1/R1
x
z
-y
R1
R2 I2
zm
Presenter
Presentation Notes
Zeeman shift diagram -> put earlier when explaining how atom trap works Explain f and angular momentum. Have an example for Rb -> energy levels
Microtrap Array B. Jian & W. A. van Wijngaarden, J. Phys. B 47, 215301 (2014)
Cu Block Heatsink
2 cm
3 mm
Presenter
Presentation Notes
In the limit of slow atomic motion -bigger
Magnetic Field Calculation using Mathematica
-y S
x
z I
H
Consider loop in yz plane having radius R & current I. I>0 generates field in + x direction.
Presenter
Presentation Notes
Include a single coil
i. Atom Transfer between Microtraps • Atom transferred from double-
loop microtrap A centered at x = 0 to double-loop microtrap B centered at x = R1/2.
• Current IA (IB) linearly decreased (increased) from t = 0 to t = 1.
• Trap profile remains virtually constant throughout transfer.
-3 -2 -1 0 1 2 3 x / R1
2
1.5 1
0.5 0
|B|/B0
t = 0.75
t = 0
t = 1
t = 0.5
t = 0.25
x
z
-y
R1
R2
IA
z
Presenter
Presentation Notes
Trap profile remains virtually constant throughout transfer, important for minimizing atom loss
ii. Addition of Ioffe Coil
2
1.5 1
0.5
0.0
|B| / B0
IIC
x
z
-y
R1
R2 IIC = 9 I1
-1 -0.5 0 0.5 1 x / R1
z / R
1
IIC = 0
z / R
1
1.0
0.8
0.6
0.4
0.2
0.0
Generate trap having nonzero minimum field to prevent spin flips using Ioffe Coil having radius RIC = R1/8 centered at (1.4, 0, 0.15) R1.
-1 -0.5 0 0.5 1 x / R1
1.0
0.8
0.6
0.4
0.2
0.0
1.5 1
0.5
0.0 0 0.5 1 1.5 z / R1
-1 -0.5 0 0.5 1 x / R1
3 2 1 0
Bmin = 0.104 Bo at (0.48, 0, 0.47) R1
-1 -0.5 0 0.5 1 x / R1
z / R
1
1.0
0.8
0.6
0.4
0.2
0.0
2
1.5 1
0.5
0.0
|B|/B0
Trap Potential due to Ioffe Coil
Trap depth = 0.48 B0
Bias Field Effect on Trap Position & Depth
x
z
-y
R1
R2 xC
Bzbias
0
0.1
0.2
0.3
0.4
0.5
0
0.2
0.4
0.6
0.8
1
-0.75 -0.5 -0.25 0 0.25 0.5 0.75
Trap
Dep
th /
Bo
Mic
rotr
ap z
Pos
iton
/ R1
Bzbias / Bo
Presenter
Presentation Notes
-reduce number of ticks in y axis
Conclusions • Microtraps use much smaller currents than macroscopic traps
• Double-loop microtraps useful to create one or two dimensional arrays of ultracold atoms. Current can be adjusted or bias field varied to modify trap position & depth – useful for surface studies.
• Modelled how to transfer atoms between two adjacent double loop microtraps. Trap profile remains constant during transfer minimizing atom loss.
• Trap having nonzero magnetic field minimum generated by adding small Ioffe coil, partially embedded in atom chip, useful to prevent atom loss due to spin flips.
Applications: Precision Measurements, Frequency Standards, Surface Sensing, Atom Interferometry, Quantum Information Processing etc.
Additional Information: www.wvanwijngaarden.info.yorku.ca
Laser Cooling H. Metcalf & P. v. d. Straten, Laser Cooling & Trapping (Springer,1999)
Analogous to stopping transport truck on highway (atom) by bouncing beam of ping pong balls (photons) off it.
10-2
10-6
10-4
100
102
104
Kel
vins
Mass M
Velocity v h / λPhoton Momentum
h = Planck’s constant
# photons to stop thermal 87Rb atom = M v / (h / λ) = 50,000 photons
Stopping Time T = 50,000 x τ excited state lifetime = 1.4 msec
Stopping Distance = v τ / 2 = 20 cm
Laser Power to stop 109 atoms/sec = 109 x 50,000 h ν / T ≈ 10 mW
Doppler cooling limit = h Γ transition linewidth /2 k ≈ 100 µK
Analogous to stopping transport truck on highway (atom) by bouncing beam of ping pong balls (photons) off it.
10-2
10-6
10-4
100
102
104
Kel
vins
10-2
10-6
10-4
100
102
104
Kel
vins
Mass M
Velocity v h / λPhoton Momentum
h = Planck’s constant
# photons to stop thermal 87Rb atom = M v / (h / λ) = 50,000 photons
Stopping Time T = 50,000 x τ excited state lifetime = 1.4 msec
Stopping Distance = v τ / 2 = 20 cm
Laser Power to stop 109 atoms/sec = 109 x 50,000 h ν / T ≈ 10 mW
Doppler cooling limit = h Γ transition linewidth /2 k ≈ 100 µK
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