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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

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 talk 21-01-09


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


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Jaynes-Cummings model (1) [2]

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

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


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


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


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


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A neat example

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


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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 talk 21-01-09


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


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


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


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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

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


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


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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

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


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


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


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


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


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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


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


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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)

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


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


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


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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”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)

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


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