Cavity cooling of a single atom

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

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Cavity cooling of a single atom Journal club
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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, Schrödingers 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

• Consider an atom interacting with an
  electromagnetic field in free space

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Jaynes-Cummings model (2) 2

• Consider a pair of mirrors forming a cavity of a
  set separation

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Dynamical Stark effect (1)

• 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)

• This yields eigenfrequencies

Splitting non-zero in presence of coupling g,
even if n 0! (Vacuum splitting observed, i.e.
Haroche 3)
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A neat example
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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
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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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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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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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The experiment
L 120µm
780.2nm ?C 0 ?a/2p 35MHz
785.3nm
85Rb( lt10cms-1)
Finesse FSR / Bandwidth F 4.4x105 Decay ?/2p
1.4MHz

• Single photon counter used, QE 32
• Single atom causes a factor of 100 reduction in
  transmission

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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 its deepened to 1.5mK. 95 of detected
  atoms are trapped

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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

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Trap lifetime (1)

• Dipole trap and probe on, atom detected

• Probe turned off for ?t

• Probe turned back on, presence of atom checked

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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

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Trap lifetime with cooling (1)

• Dipole trap and probe on, atom detected

• Probe reduced in power for ?t

• Probe turned back on, presence of atom checked

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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

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Direct cooling (1)

• ?C/2p 9MHz for 100µsTheory predicts heating 6

• ?C 0 for 500µsAtoms are cooled (PP 2.25pW)

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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 ß 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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Cooling in a dipole trap (1)
If artificially introducing heating isnt to your
taste

• Dipole trap continuously on

• Probe pulsed on for 100µs every 2ms. Probe cools
  and detects (1.5pW)

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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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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
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. CummingsComparison
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.
ZollerCavity assisted nondestructive laser
cooling of atomic qubits arXiv quant-ph/0311054
6 P. Horak, G. Hechenblaikner, K.M. Gheri, H.
Stecher and H. RitschCavity-induced atom
cooling in the strong coupling regime Phys. Rev.
Lett. 79 (1997)
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Cavity cooling of a single atom Journal club
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