CUPC Oct 14, 2015
- 1. 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
- 2. 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
- 3. t = 6 ms t = 12t = 10 t = 14 t = 20t = 18t = 16 t = 8 Measurement of Ultracold Temperature Observe expansion of atom cloud after trap turned off.
- 4. 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 B5S1/2 F=2 Atoms in mF = 1, 2 hyperfine levels trapped at minimum magnetic field.
- 5. 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/R1x z -y R1 R2 I2 zm
- 6. Microtrap Array B. Jian & W. A. van Wijngaarden, J. Phys. B 47, 215301 (2014) Cu Block Heatsink 2 cm 3 mm
- 7. 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.
- 8. 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
- 9. 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/R1 IIC = 0 z/R1 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
- 10. 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/R1 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
- 11. 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 TrapDepth/Bo MicrotrapzPositon/R1 Bzbias / Bo
- 12. 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
- 13. 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 Kelvins Mass M Velocity v h / λ Photon 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 Kelvins 10-2 10-6 10-4 100 102 104 Kelvins Mass M Velocity v h / λ Photon 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