Peter Wolf1,2, Pierre Lemonde1, Astrid Lambrecht3, Sébastien Bize1,Arnaud Landragin1, André Clairon1

1- SYRTE , Observatoire de Paris2-Bureau International des Poids et Mesures

3-LKB, Université Pierre et Marie Curie (Paris 6)

Les Houches, June 2005

Measuring Forces in the Casimir Regime Using Cold Atoms in an Optical Lattice

Measuring Forces in the Casimir Regime Using Cold Atoms in an Optical Lattice

ContentsContentsContentsContents

- 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

Sr optical lattice clockSr optical lattice clockSr optical lattice clockSr optical lattice clock

Katori, Proc. 6th Symp. Freq. Standards and Metrology (2002).Pal’chikov, 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 andfree fall neutral atoms optical standards

3P01

461 nm

689 nm

698 nm(87Sr: 1 mHz)

1S0

1P1

3S1

688 nm

679 nm

trap

trap

Potential accuracy ≤ mHz (f / f ≈ 10-17-10-18) ?

Using gravity: Wannier-Stark ladderUsing gravity: Wannier-Stark ladder Using gravity: Wannier-Stark ladderUsing gravity: Wannier-Stark ladder

- 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).

P. Lemonde, P. Wolf, arXiv:physics/0504080

Non-resonant tunneling localization

For Sr: g = m g /2 ~ 900 Hz

g

Resonant tunneling delocalization

406 nm

2 w = 180 m

The Sr clockThe Sr clockThe Sr clockThe Sr clock

Ti : Saph Laser @ 813 nm

650 mW available

Probe beam @ 698 nm

Climbing up or down the W-S ladderClimbing up or down the W-S ladder Climbing up or down the W-S ladderClimbing up or down the W-S ladder

|g>

|e>

g

ixik

i WeW ˆ0

- W-S localised in a given well with small rebounds in neighbouring wells.-Probe laser couples |g> to |e> in the same well, but also to neighbouring wells when detuned by g.-At a few Er the coupling strengths 0 ≈ 1. g ≈ 900 Hz is well resolved by laser Very efficient control of the external states using the frequency of the probe laser.

Climbing up Climbing up andand down: the interferometer down: the interferometer Climbing up Climbing up andand down: the interferometer down: the interferometer

|g>

|e>

- Coherent superposition of internal states by /2 pulse on resonance.- Spatially separate and recombine atoms by a series of pulses detuned by 0, g.

- Cumulated phase difference determines final internal state (interference fringes).- Sensitivity: with = 10-4 rad (after integration), T = 0.1 s, E / 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 trap).

- How do you populate only one well initially ??

mirror

203 nm

Atom – surface QED interactionAtom – surface QED interaction Atom – surface QED interactionAtom – surface QED interaction

- Atom – surface interaction dominated by QED potential (VdW, C–P, …).- Orders of magnitude (for Sr in 813 nm trap):

Well no. 1 2 3 4 5 25Distance / nm 203 610 1016 1423 1829 10366C-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 |e>.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).

Controlling the Atom – surface QED interactionControlling the Atom – surface QED interaction Controlling the Atom – surface QED interactionControlling the Atom – surface QED interaction

- Searching for new interactions requires control of the QED potential, ideally at or below the 10-4 Hz level:

1. Calculate and correct (possible at about the % level).2. Place the atoms sufficiently far from the surface (QED < 10-2 Hz).3. Transparent (at the dominant atomic frequencies) source mass at

variable distance.4. Differential measurement between several isotopes.5. Mirror with narrow band reflectivity.6. 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 ≈ 10 m) .• In a second step 1. + 4. + 5. (explore ≈ 0.2 to 10 m).

mirror

Other perturbationsOther perturbations Other perturbationsOther 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 ( ≈ 1012 at/cm3):- bosonic isotopes (Sr, Yb).- fermionic isotopes polarise (87Sr, 171Yb, 173Yb).- use hyperfine states (Cs, Rb).

Vibrations: Isolation g/g 10-8 @ 0.1 s O.K. even for large separations (10 m).Knowledge of mg/h: 10-8 O.K.Knowledge of atom – surface separation:

- trapping laser trap/ trap << 10-7.- wave fronts 10-4 trap (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 ???

ConclusionConclusion ConclusionConclusion

QED measurement: - probably limited by knowledge of atom-surface separation. - 10-4 measurement seems feasible. - test dependence on distance and state (1S0, 3P0, HF, …).

1.+ 2.1.+ 4.+ 5

New interactions:- assuming Sr with trap = 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, trap, , 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).