Diapositive 1

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Measuring Forces in the Casimir Regime Using Cold
Atoms in an Optical Lattice
Peter Wolf1,2, Pierre Lemonde1, Astrid
Lambrecht3, Sébastien Bize1, Arnaud Landragin1,
André Clairon1 1- SYRTE , Observatoire de
Paris 2-Bureau International des Poids et
Mesures 3-LKB, Université Pierre et Marie Curie
(Paris 6) Les Houches, June 2005
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Contents

• A clock using neutral Sr atoms trapped in a
  periodic potential (optical lattice).
• Using gravity Wannier-Stark ladder and states.
• The Sr clock.
• An atomic interferometer in a Wannier-Stark
  ladder.
• Measuring the atom-surface interaction
  potential.
• The QED interaction (VdW, Casimir-Polder, ).
• Search for new interactions.
• Controlling the QED interaction.
• Perturbations.
• Conclusion

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Sr optical lattice clock
Katori, Proc. 6th Symp. Freq. Standards and
Metrology (2002). Palchikov, et al., J. Opt. B.
5 (2003) S131. Katori et al. PRL 91, 173005
(2003). Courtillot et al., PRA 68, 030501(R),
(2003). Takamoto et al., Nature 435, 321, (2005).
Clock transition 1S0-3P0 transition
Combine advantages of single trapped ion and free
fall neutral atoms optical standards
Potential accuracy mHz (df / f 10-17-10-18)
?
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Using gravity Wannier-Stark ladder
P. Lemonde, P. Wolf, arXivphysics/0504080

• Lattice clocks use a 1D periodic potential, with
  confinement in transverse direction by the
  Gaussian profile of the laser.
• Energy bands ? frequency shifts and line
  broadening
• ? requires high laser intensity ( 100
  Er).
• Resonance broken by gravity Wannier-Stark (W-S)
  ladder of localised metastable states (1010 s
  lifetime).
• Required clock performance reached at low
  intensities (? 5 Er).

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The Sr clock
Ti Saph Laser _at_ 813 nm 650 mW available
Probe beam _at_ 698 nm
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Climbing up or down the W-S ladder

• W-S localised in a given well with small
  rebounds in neighbouring wells.
• Probe laser couples ggt to egt in the same well,
  but also to neighbouring wells when detuned by
  ?Dg.
• At a few Er the coupling strengths W0 W?1.
• Dg 900 Hz is well resolved by laser
• ? Very efficient control of the external states
  using the frequency of the probe laser.

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Climbing up and down the interferometer
egt
ggt

• Coherent superposition of internal states by p/2
  pulse on resonance.
• Spatially separate and recombine atoms by a
  series of p pulses detuned by 0, ?Dg.
• Cumulated phase difference determines final
  internal state (interference fringes).
• Sensitivity with Df 10-4 rad (after
  integration), T 0.1 s, ? DE / h 10-4 Hz.
• Measurement of g and m/h at the 10-8 10-9
  level (separating by 10 100 wells).
• Superposition close to a mirror of the cavity
  allows a sensitive measurement of the potential
  difference between the two wells (QED, new
  interactions).
• Accurate measurement of the potential (rather
  than mechanical force).
• Accurate knowledge of the distance (determined
  by ltrap).
• How do you populate only one well initially ??

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Atom surface QED interaction

• Atom surface interaction dominated by QED
  potential (VdW, CP, ).
• Orders of magnitude (for Sr in 813 nm trap)
• Well no. 1 2 3 4 5 25
• Distance / nm 203 610 1016 1423 1829 10366
• C-P / Hz (105) 103 100 40 10 10-2
• Effect of trapping laser is negligible (A.
  Lambrecht).
• More accurate calculations of QED interaction
  under way.
• Use it to select atoms in a particular well
  close to the surface
• 1. Pulse detuned by QED potential ? transfer
  only one well to egt.
• 2. Pusher laser beam to eliminate all other
  atoms.
• Works with all other field gradients that induce
  a spatial variation of the W-S ladder.
• 10-4 Hz uncertainty ? potentially a 10-7 QED
  measurement (but distance at 10-7 ??).
• Allows some variation of the distance (choice of
  well).

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Controlling the Atom surface QED interaction

• - Searching for new interactions requires
  control of the QED potential, ideally at or below
  the 10-4 Hz level
• Calculate and correct (possible at about the
  level).
• Place the atoms sufficiently far from the surface
  (QED lt 10-2 Hz).
• Transparent (at the dominant atomic frequencies)
  source mass at variable distance.
• Differential measurement between several
  isotopes.
• Mirror with narrow band reflectivity.
• Casimir shield source masses of variable
  density.
• 1. 2. is easiest (experimentally) and fairly
  efficient.
• 3. reduces QED by 10-2 and allows a continuous
  variation of the atom-surface distance.
• 4. reduces the signal by 10-2 but potential
  reduction of QED
• by 10-5 to 10-6.
• Probably 1. 2. at first (explore l 10 mm) .
• In a second step 1. 4. 5. (explore l 0.2 to
  10 mm).

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Other perturbations
Phase coherence of the probe laser (10-4 rad) -
Raman pulses using hyperfine states (Rb, Cs). -
2nd atomic cloud far from the surface (Sr,
Yb). - Bragg pulses (study in progress.). Light
shifts (5 Er) - magic wavelength (Sr, Yb). -
control intensity to 10-4 (Rb, Cs). Collisions (r
1012 at/cm3) - bosonic isotopes (Sr, Yb). -
fermionic isotopes ? polarise (87Sr, 171Yb,
173Yb). - use hyperfine states (Cs,
Rb). Vibrations Isolation ? dg/g ? 10-8 _at_ 0.1 s
? O.K. even for large separations (10
mm). Knowledge of mg/h ? 10-8 ? O.K. Knowledge
of atom surface separation - trapping laser ?
dltrap / ltrap ltlt 10-7. - wave fronts ? ? 10-4
ltrap (limiting for QED, O.K. for new
interactions). - interferometer ? nm. - surface
roughness etc. ? ??? note - less
problematic at large separation (10 nm).
- cancellation between isotopes. Others ???
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Conclusion
QED measurement - probably limited by
knowledge of atom-surface separation. -
10-4 measurement seems feasible. - test
dependence on distance and state (1S0, 3P0, HF,
).

• New interactions
• - assuming Sr with ltrap 813 nm.
• 4 to 5 orders of magnitude improvement.
• 2 stage experiment.
• General
• no perfect atom. Yb and Rb most promising.
• original and radically different from all
  previous experiments in this field.
• other interferometer configurations are
  possible.
• many knobs to turn (Ptrap, ltrap, r, d, ).
• well supported by existing technology and
  know-how in atomic physics and metrology.
• very recent idea (see also Dimopoulos, PRD 68,
  124021) ? might still have a catch.
• ambitious project (cf. Sr clock ? 4 yrs).

1. 4. 5
1. 2.