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Cavity cooling of a single atom
James Millen
21/01/09
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]
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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)
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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
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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
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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
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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
A neat example
Cavity cooling of a single atom – Journal club talk 21-01-09
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Cavity cooling of a single atom – Journal club talk 21-01-09
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]
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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]
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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 EK
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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)
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Cavity cooling of a single atom – Journal club talk 21-01-09
The experiment
780.2nm
ΔC = 0
Δa/2π = 35MHz
Finesse = FSR / Bandwidth
F = 4.4x105
Decay κ/2π = 1.4MHz
85Rb( <10cms-1)
• Single photon counter used, QE 32%
• Single atom causes a factor of 100 reduction in transmission
785.3nm
L = 120μm
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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
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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
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
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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
mirror17
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
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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
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Cavity cooling of a single atom – Journal club talk 21-01-09
Direct cooling (1)
• ΔC/2π = 9MHz for 100μsTheory predicts heating [6]
• ΔC = 0 for 500μsAtoms are cooled (PP = 2.25pW)
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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
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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
pro
be
2ms
100μs
• Dipole trap continuously on
• Probe pulsed on for 100μs every 2ms. Probe cools and detects (1.5pW)
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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)
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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
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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)
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