cupc oct 14, 2015
TRANSCRIPT
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
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
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.
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.
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
Microtrap Array B. Jian & W. A. van Wijngaarden, J. Phys. B 47, 215301 (2014)
Cu Block Heatsink
2 cm
3 mm
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.
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
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
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