Download 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]
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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, 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]
• 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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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 blueshifted, 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
ΔC = 0
Δa/2π = 35MHz
785.3nm
85Rb(
• Single photon counter used,
QE 32%
• Single atom causes a factor of
100 reduction in transmission
<10cms-1)
Finesse = FSR / Bandwidth
F = 4.4x105
Decay κ/2π = 1.4MHz
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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 it’s
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 Δt
• 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 Δt
• Probe turned back on, presence
of atom checked
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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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Direct cooling (1)
• ΔC/2π = 9MHz for 100μs
Theory predicts heating [6]
• ΔC = 0 for 500μs
Atoms 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 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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Cooling in a dipole trap (1)
If artificially introducing heating isn’t to your taste…
probe
• Dipole trap
continuously on
100μs
on
off
2ms
• 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. 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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