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

2. Outline Cavity cooling of a single atom – Journal club talk 21-01-09 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

3. Why cavity QED? Cavity cooling of a single atom – Journal club talk 21-01-09 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

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

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

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

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

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

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

10. Cavity cooling of a single atom – Journal club talk 21-01-09 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

11. Cavity cooling of a single atom – Journal club talk 21-01-09 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 E K 11

12. Cavity cooling of a single atom – Journal club talk 21-01-09 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

13. Cavity cooling of a single atom – Journal club talk 21-01-09 The experiment 780.2nm Δ C = 0 Δ a /2π = 35MHz Finesse = FSR / Bandwidth F = 4.4x10 5 Decay κ/2π = 1.4MHz 85 Rb( <10cms -1 ) Single photon counter used, QE 32% Single atom causes a factor of 100 reduction in transmission 785.3nm L = 120μm 13

14. Cavity cooling of a single atom – Journal club talk 21-01-09 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

15. Cavity cooling of a single atom – Journal club talk 21-01-09 The experiments 1.Trap lifetime: The lifetime of the dipole trap is measured and found to depend upon the frequency stability of the laser 2.Trap lifetime with cooling: The introduction of very low intensity cooling light increases the trap lifetime 3.Direct cooling: The cooling rate is calculated for an atom allowed to cool for a period of time 4.Cooling in a trap: An atom in a trap is periodically cooled, and an increase in trap lifetime is observed 15

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

17. Cavity cooling of a single atom – Journal club talk 21-01-09 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

18. Cavity cooling of a single atom – Journal club talk 21-01-09 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

19. Cavity cooling of a single atom – Journal club talk 21-01-09 Trap lifetime with cooling (2) Pre-frequency stabilization improvement Post-frequency stabilization improvement A probe power of only 0.11pW doubles the storage time (0.11pW corresponds to only 0.0015 photons in the cavity!) 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

20. Cavity cooling of a single atom – Journal club talk 21-01-09 Direct cooling (1) Δ C /2π = 9MHz for 100μs Theory predicts heating [6] Δ C = 0 for 500μs Atoms are cooled (P P = 2.25pW) 20

21. Cavity cooling of a single atom – Journal club talk 21-01-09 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

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

23. Cavity cooling of a single atom – Journal club talk 21-01-09 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

24. Cavity cooling of a single atom – Journal club talk 21-01-09 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

25. References Cavity cooling of a single atom – Journal club talk 21-01-09 [1] P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse and G. Rempe “Cavity cooling of a single atom” Nature 428, 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. IEEE 51, 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