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Cavity cooling of a single atom

Cavity cooling of a single atom. James Millen 21/01/09. Outline. Introduction to Cavity Quantum Electrodynamics (QED) - The Jaynes-Cummings model - Examples of the behaviour of an atom in a cavity Cavity cooling of a single atom [1]. 2.

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Cavity cooling of a single atom

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  1. Cavity cooling of a single atom James Millen 21/01/09

  2. Outline • Introduction to Cavity Quantum Electrodynamics (QED)- The Jaynes-Cummings model- Examples of the behaviour of an atom in a cavity • Cavity cooling of a single atom [1] 2 Cavity cooling of a single atom – Journal club talk 21-01-09

  3. Why cavity QED? • Why study the behaviour of an atom in a cavity? • It is a very simple system in which to study the interaction of light and matter • It is a rich testing ground for elementary QM issues, e.g. EPR paradox, Schrödinger’s cat • Decoherence rates can be made very small • Novel experiments: single atom laser (Kimble), trapping a single atom with a single photon (Rempe) 3 Cavity cooling of a single atom – Journal club talk 21-01-09

  4. Jaynes-Cummings model (1) [2] • Consider an atom interacting with an electromagnetic field in free space 4 Cavity cooling of a single atom – Journal club talk 21-01-09

  5. Jaynes-Cummings model (2) [2] • Consider a pair of mirrors forming a cavity of a set separation 5 Cavity cooling of a single atom – Journal club talk 21-01-09

  6. Dynamical Stark effect (1) • This Hamiltonian has an analytic solution • N.B. This is for light on resonance with the atomic transition 6 Cavity cooling of a single atom – Journal club talk 21-01-09

  7. Dynamical Stark effect (2) • This yields eigenfrequencies: Splitting non-zero in presence of coupling g, even if n = 0! (Vacuum splitting observed, i.e. Haroche [3]) 7 Cavity cooling of a single atom – Journal club talk 21-01-09

  8. A neat example 2 2 2 1 1 1 8 Cavity cooling of a single atom – Journal club talk 21-01-09

  9. Cavity Cooling of a Single Atom P. Maunz, T. Puppe, I. Scuster, N. Syassen, P.W.H. Pinkse & G. Rempe Max-Planck-Institut für Quantenoptik Nature 428 (2004) [1] 9 Cavity cooling of a single atom – Journal club talk 21-01-09

  10. Motivation • Conventional laser cooling schemes rely on repeated cycles of optical pumping and spontaneous emission • Spontaneous emission provides dissipation, removing entropy • In the scheme presented here dissipation is provided by photons leaving the cavity. This is cooling without excitation • This allows cooling of systems such as molecules or BECs [4],or the non-destructive cooling of qubits [5] 10 Cavity cooling of a single atom – Journal club talk 21-01-09

  11. Principle • Light blue shifted from resonance • At node the atom does not interact with the field • If the atom moves towards an anti-node it does interact • The frequency of the light is blue-shifted, it has gained energy • The intensity rapidly drops in the cavity, the atom has lost EK 11 Cavity cooling of a single atom – Journal club talk 21-01-09

  12. A problem? • Can an atom gain energy by moving from an anti-node to a node? • No, because for an atom initially at an anti-node the intra-cavity intensity is very low • Excitations are heavily suppressed:- at the node there are no interactions- at the anti-node the cavity field is very low→ Lowest temperature not limited by linewidth dd(Doppler limit) 12 Cavity cooling of a single atom – Journal club talk 21-01-09

  13. The experiment L = 120μm 780.2nm ΔC = 0 Δa/2π = 35MHz 785.3nm 85Rb( <10cms-1) Finesse = FSR / Bandwidth F = 4.4x105 Decay κ/2π = 1.4MHz • Single photon counter used, QE 32% • Single atom causes a factor of 100 reduction in transmission 13 Cavity cooling of a single atom – Journal club talk 21-01-09

  14. Trapping • Nodes and antinodes of dipole trap and probe coincide at centre • Atoms trapped away from centre are neither cooled nor detected by the probe • Initially the trap is 400μK deep, when atom detected it’s deepened to 1.5mK. 95% of detected atoms are trapped 14 Cavity cooling of a single atom – Journal club talk 21-01-09

  15. The experiments • Trap lifetime: The lifetime of the dipole trap is measured and found to depend upon the frequency stability of the laser • Trap lifetime with cooling: The introduction of very low intensity cooling light increases the trap lifetime • Direct cooling: The cooling rate is calculated for an atom allowed to cool for a period of time • Cooling in a trap: An atom in a trap is periodically cooled, and an increase in trap lifetime is observed 15 Cavity cooling of a single atom – Journal club talk 21-01-09

  16. Trap lifetime (1) • Dipole trap and probe on, atom detected • Probe turned off for Δt • Probe turned back on, presence of atom checked 16 Cavity cooling of a single atom – Journal club talk 21-01-09

  17. Trap lifetime (2) • Lifetime found to be 18ms • Light scattering arguments give a limit of 85s, cavity QED a limit of 200ms [6] • Low lifetime due to heating through frequency fluctuations • Note: Heating proportional to trap frequency axial trap frequency ≈ 100 radial trap frequency→ most atoms escape antinode and hit a mirror 17 Cavity cooling of a single atom – Journal club talk 21-01-09

  18. Trap lifetime with cooling (1) • Dipole trap and probe on, atom detected • Probe reduced in power for Δt • Probe turned back on, presence of atom checked 18 Cavity cooling of a single atom – Journal club talk 21-01-09

  19. Trap lifetime with cooling (2) • A probe power of only 0.11pW doubles the storage time(0.11pW corresponds to only 0.0015 photons in the cavity!) Pre-frequency stabilization improvement Post-frequency stabilization improvement • At higher probe powers the storage time is decreased • The probe power must be high enough to compensate for axial heating from the dipole trap, and low enough to prevent radial loss • Monte Carlo simulations confirm that at low probe powers axial loss dominates, at high probe powers radial loss dominates 19 Cavity cooling of a single atom – Journal club talk 21-01-09

  20. Direct cooling (1) • ΔC/2π = 9MHz for 100μsTheory predicts heating [6] • ΔC = 0 for 500μsAtoms are cooled (PP = 2.25pW) 20 Cavity cooling of a single atom – Journal club talk 21-01-09

  21. Direct cooling (2) • For the first ~100μs the atom is cooled • After this the atom is localised at an antinode • From the time taken for this localisation to happen, a friction coefficient β can be extracted, and hence a cooling rate • For the same levels of excitation in free space this is 5x faster than Sisyphus cooling, and 14x faster than Doppler cooling 21 Cavity cooling of a single atom – Journal club talk 21-01-09

  22. Cooling in a dipole trap (1) 100μs on probe off 2ms If artificially introducing heating isn’t to your taste… • Dipole trap continuously on • Probe pulsed on for 100μs every 2ms. Probe cools and detects (1.5pW) 22 Cavity cooling of a single atom – Journal club talk 21-01-09

  23. Cooling in a dipole trap (2) • The lifetime of the atoms in the dipole trap without cooling is 31ms • With the short cooling bursts the lifetime is increased to 47ms • 100μs corresponds to a duty cycle of only 5%, yet the storage time is increased by ~50% • It takes longer to heat the atom out of the trap in the presence of the probe, hence the probe is decreasing the kinetic energy (cooling) 23 Cavity cooling of a single atom – Journal club talk 21-01-09

  24. Summary • An atom can be cooled in a cavity by exploiting the excitation of the cavity part of a coupled atom-cavity system • Storage times for an atom in an intra-cavity dipole trap can be doubled by application of an exceedingly weak almost resonant probe beam • Cooling rates are considerably faster than more conventional laser cooling methods, relying on repeated cycles of excitation and spontaneous emission 24 Cavity cooling of a single atom – Journal club talk 21-01-09

  25. References [1] P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse and G. Rempe “Cavity cooling of a single atom”Nature428, 50-52 (4 March 2004) [2] E.T. Jaynes and F. W. Cummings“Comparison of quantum and semiclassical radiation theories with application to the beam maser” Proc. IEEE51, 89 (1963) [3] F. Bernardot, P. Nussenzveig, M. Brune, J. M. Raimond and S. Haroche “Vacuum Rabi Splitting Observed on a Microscopic Atomic Sample in a Microwave Cavity”Europhys. Lett.17 33-38 (1992) [4] P. Horak and H. Ritsch “Dissipative dynamics of Bose condensates in optical cavities”Phys. Rev. A 63, 023603 (2001) [5] A. Griessner, D. Jaksch and P. Zoller“Cavity assisted nondestructive laser cooling of atomic qubits” arXiv quant-ph/0311054 [6] P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher and H. Ritsch“Cavity-induced atom cooling in the strong coupling regime”Phys. Rev. Lett. 79 (1997) 25 Cavity cooling of a single atom – Journal club talk 21-01-09

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