Ground state cooling via Sideband cooling
Fabian Flassig TUM June 26th, 2013 Motivation
• Gain ultimate control over all relevant degrees of freedom • Necessary for constant atomic transition frequencies • Do many fancy experiments!!!
Entangled states of trapped atomic ions, R. Blatt, D. Wineland, Nature 453 (2008) State manipulation of single atoms in an optical cavity, M. Uphoff Context
• Sideband cooling • Raman sideband cooling • Temperature • Lamb-Dicke regime • Ion vs. Atom trapping • Cooling of single 87Rb atom to ground state • Outlook Sideband cooling Free atom in space Captured in a trap Cooling the atom Quantized states of motion
| ⟩ For every excitation level
| ⟩
| ⟩
| ⟩ Resonant optical excitation
| ⟩
| ⟩
| ⟩ Detuned optical excitation
Resonance freqency | ⟩
Resolved-sideband| cooling⟩ of a micromechanical oscillator, A. Schliesser et al., Nature Physics 4, 415 - 419 (2008) Red shifted optical excitation
| ⟩
| ⟩
| ⟩ Rabi oscillations
• Oscillation between ground and excited state • Without pumping no cooling effect
Quantum computing with trapped ions, H. Häffner et al., Physics Reports 469, 4 (2008) Pump to fast-decaying higher level
| ⟩
| ⟩
| ⟩ In sum
| ⟩ = | ⟩
| ⟩ | ⟩
| ⟩ | ⟩ Raman sideband cooling Raman process
• Transition between two states via virtual excited state using two laser beams
http://en.wikipedia.org/wiki/Raman_cooling Why use Raman process?
• Raman allows sub-natural line width resolution of sidebands (due to long-lasting ground states) => Allows addressing sidebands individually
Resolved-sideband cooling of a micromechanical oscillator, A. Schliesser et al., Nature Physics 4, 415 - 419 (2008) Raman sideband cooling
| ⟩
| ⟩ | ⟩ Transfer atom via Raman
| ⟩
| ⟩ | ⟩ Pump atom back
| ⟩
| ⟩ | ⟩ Temperature Heating effects
• Cooling rate limited by Lamb-Dicke factor • Heating caused by: – Trap laser phase instabilities – Raman lasers causing excitations
• Lowest temperature: heating rate = cooling rate How to determine temperature?
• -1) is given by:
( Ω) • is decay rate of= stateΓ • is Lamb-Dicke factor2( Ω) + Γ • Γ is Rabi frequency • Mean occupation state is: Ω
= Quantum dynamics of single− trapped ions, Leibfried, D., et al., Reviews of Modern Physics 75.1, 281 (2003) How to determine temperature?
• = −P • Extreme cases: < – → → = 0 = 0 – = 0 → → = = ∞ = ∞ Resolved-sideband cooling of a micromechanical oscillator, A. Schliesser et al., Nature Physics 4, 415 - 419 (2008) Lamb-Dicke regime Lamb-Dicke regime
• Lamb-Dicke factor gives probability of photon recoil energy leading to an increase in state of motion • with being recoil frequency
= • Confinement of atom to ≤ 15nm to achieve
≤ 0.1 Low Lamb-Dicke factor High Lamb-Dicke factor Ion vs. Atom trapping Trap
• For ions: Traps providing a quadratic potential, e.g. Paul trap • For atoms: dipole traps and MOTs are used Ion vs. Atom
• Basically no difference for cooling process • To reach Lamb-Dicke regime for atoms high laser power is necessary • Plus high stability for trap Cooling of single 87Rb atom to ground state
Ground-state cooling of a single atom at the center of an optical cavity Andreas Reiserer, Christian Nölleke, Stephan Ritter, and Gerhard Rempe Phys. Rev. Lett. 110, 223003 (2013) Aim of experiment
• Cool a single 87Rb atom to ground state of motion – Using a dipole trap and Raman sideband cooling Preprocedure
• Capture 87Rb atoms in MOT • Transfer them to a dipole trap • Precool via laser cooling • Via imaging select a single atom and bring it to the center of the trap • Bring atom to F=1 state • Do the actual cooling process 87Rb 87Rb Cooling process
• Apply Raman beams for 5ms for all three sideband frequencies (corresponding to dimensions of trap) • Apply repump pulse for 10ns every 200ns to repump atom to F=1 state – Needs to be pulsed due to Rabi oscillations
Quantum computing with trapped ions, H. Häffner et al., Physics Reports 469, 4 (2008) Experiments with atoms
= • (89±2)% of atoms in 3D ground− state of motion Outlook Schrödinger Cat state Ion lattices and quantum gates
Entangled states of trapped atomic ions, R. Blatt, D. Wineland, Nature 453 (2008) Some bigger stuff
• For single atoms, successful sideband cooling is relatively new • Cool whole mechanical parts?
Sideband cooling of micromechanical motion to the quantum ground state, J. D. Teufel et al., Nature 475 (2011) Thank you
• Especially to M. Uphoff! • And to you for your attention!