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Peter Wolf 1,2 , Pierre Lemonde 1 , Astrid Lambrecht 3 , Sébastien Bize 1 ,

Measuring Forces in the Casimir Regime Using Cold Atoms in an Optical Lattice. Peter Wolf 1,2 , Pierre Lemonde 1 , Astrid Lambrecht 3 , Sébastien Bize 1 , Arnaud Landragin 1 , André Clairon 1 1- SYRTE , Observatoire de Paris 2-Bureau International des Poids et Mesures

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Peter Wolf 1,2 , Pierre Lemonde 1 , Astrid Lambrecht 3 , Sébastien Bize 1 ,

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  1. 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

  2. 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

  3. 3S 1 1P1 688 nm ltrap 461 nm 679 nm ltrap 1 689 nm 0 3P 698 nm (87Sr: 1 mHz) 1S0 Sr 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 and free fall neutral atoms optical standards Potential accuracy ≤ mHz (df / f≈ 10-17-10-18) ?

  4. 2 w = 180 mm 406 nm Resonant tunneling  delocalization g Non-resonant tunneling  localization For Sr: Dg = m gl/2 ~ 900 Hz Using gravity: Wannier-Stark ladder P. Lemonde, P. Wolf, arXiv:physics/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).

  5. The Sr clock Ti : Saph Laser @ 813 nm 650 mW available Probebeam @ 698 nm

  6. |e> Dg |g> Climbing up or down the W-S ladder • 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 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.

  7. mirror 203 nm Climbing up and down: the interferometer |e> |g> • 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 ??

  8. Atom – 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 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 |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).

  9. mirror 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 < 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).

  10. 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 @ 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 << 10-7. - wave fronts   10-4ltrap (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 ???

  11. 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.

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