Atom interferometry test of short range gravity : recent progress in the ForCa-G experiment

Transcription

1 Atom interferometry test of short range gravity : recent progress in the ForCa-G experiment Experiment : Matthias Lopez, Obs Cyrille Solaro, Obs Franck Pereira, Obs Theory : Astrid Lambrecht, LKB Axel Maury, LKB Gabriel Dufour, LKB Marie-Christine Angonin, Obs Peter Wolf, Obs 1

2 Outline Introduction Inertial sensors with cold atoms, Why gravity needs testing State of the art in our lab Vertical lattice, Wannier Stark ladder, Bloch frequency & local gravimetry. Experimental Setup. The next step Casimir-Polder potential probing, Mirrors in vacuum, Manipulation of atoms in the surface vicinity 2

3 Inertial sensors with cold SYRTE, in the IACI group. Gyrometer (Remi Geiger) Gradiometer (Franck Pereira & Sebastien Merlet) Gyrometer on chip (Carlos Guerrida) Trapped atomic clock on chip (P. Rosenbusch) MIGA (GW) (Geiger and LP2N, LBB and more) Gravimeter (Franck Pereira & Sebastien Merlet) σ g g = s 3

4 Gravitation, why does it need testing? Two powerful theories : Standard Model : Electromagnetic, weak and strong & General Relativity: Gravitation. These two theories are fundamentally incompatible. Unifying models with higher dimensionality predict that gravitational force should differ at short range. (Adelberg, Ann. Rev. Part. Sci 53, 77, 2003) They predict neither range, nor magnitude merely constraints. 4

5 Constraints Klein-Gordon equation μ μ + m2 c 2 ħ 2 U = 0 Yukawa type potential: U(r) = C r e mc ħ r This formalism is used to parameterize the deviation, it yields no physical content but range λ and amplitude α U Newton = GMm r 1 + αe r λ 5

6 Gravitation, measurements at different scales Long range (10 3 to m): Telemetry (satellite or lunar) (Ciufolini, Science 279, 2100 (1998)) Planetary Orbitography (Kolosnitsyn, Gen. Rel. Grav. 36, 1619 (2004)) Pulsars (Will, Astrophysics and Space Science 63, 731 (2004)) Medium range ( ~ meters): Free fall tower (Eckhart, Phys. Rev. Lett., 60, 2567 (1988)) Short range ( < meter): Torsion pendulum (Hoskins, Phys. Rev. D., 32, 3084 (1985)) Optical interferometry (Smullin, Phys. Rev. D 72, (2005)) Casimir effect (Decca, Phys. Rev. Lett. 78, 5(1997)) 6

7 log 10 a Some visual insight on constraints Large Scale Small Scale Lab Satellite log 10 l (m) LLR Orbitometry E. Fischbach, R. Hellings, & al. (2003) A. Geraci et al., Phys Rev D 78, (2008) 7

8 Principle of the experiment, Hamiltonian. A vertical trapped atomic interferometer close to a surface Mirror Energy g λ l /2 = 266 nm B l l / 2 Site m Rb Atoms 2 P Ulattice H 1 cos 2k latticez ma gz 2m 2 a Kinetic energy Trapping potential Gravity z Bloch Frequency : hν B = mag λ l 2 = h Hz 8

9 Principle of the experiment, solutions. Eigenstates : Wannier Stark states m, φ m > = Eigenvalues E m, With the following property : E m E m+ m = m hν B Wannier-Stark ladder Knowledge of ν B yields knowledge on the local field (gravitationnal and more )! 9

10 Principle of the experiment, interferometry. Two counter-propagating Raman beams couple : Internal degrees of freedom : Rb hyperfine structure External degrees of freedom : position on lattice π/2 π/2 RamseyTime T t ν HFS Δm ν B MIRROR MIRROR MIRROR m m+δm g m+δm We then measure populations in both hyperfine states P e P e + Pg = C cos Δϕ m m where Δϕ = U m+δm U m ħ T Which yields the Bloch frequency ν B! 10

11 Current experimental setup 1. Cold atoms in a 3D Magneto Optical Trap 3D 10 7 atoms in 2μK (Bonus step : Evaporative cooling) vacuum nm 7W Laser, 800 μm waist chamber k Provides the vertical lattice nm 500mW Laser, 200 μm waist k 2 k 1 Provides transverse confinement lattice 4. 2 counter-propagating Raman beams Allows for coherent superposition of wave packets, suitable for interferometry MOT 3D π/2 π/2 MOT 3D MixTrap Detection time up to 3 s

12 Measuring the Bloch Frequency ν B Coherent superposition of states on site m and m+δm Verified with Rabi oscillations. Tramsey U = 100ms 1.8 Er 1 fringe Δm every = +610Hz Interferometric fringes within an enveloppe. We locate the central fringe. ν CF = Δm ν B Today : σ g g = σ ν B ν B = s Corresponds to 0.1 mhz in 100 seconds Integration time! 12

13 Phenomenology in the vicinity of a conducting surface U tot = U grav + U CP + U Yukawa Gravitationnal Potential g We have an interferometer that measures g locally Casimir, surf-surf Casimir-Polder, surf-dipole Casimir-Polder Interaction U C = A ħcπ2 240L 3 Surface L Atom U CP = 3ħcα 0 8πL 4 L Deviation (the quest ) By precisely calculating and measuring those 2 effects : New constraints on range λ and amplitude α 13

14 MIRROR, M Consequence of CP on energy levels in the vicinity of a mirror. Energy e> g> ν B ν B +ν CP Position 14

15 Δν CP (x 3.77 khz) Numerical Calculations of the Casimir Polder potential Pelisson,PRA 86, (2012) Energy Shift due to Casimir-Polder Interaction Real C-P Potential Naïve C-P Potential z atom distance from mirror (in site units) ΔE = ~2 Hz! 4 orders of magnitude higher than our 15

16 A quick break! What we have : A trapped interferometer capable of measuring local potentials, with enough resolution to probe with great accuracy the CP potential. The vertical lattice reflection mirror, which is currently outside the vacuum chamber needs to be placed inside! What we need : The means to transport atoms close to the surface, in a well controlled manner. 16

17 Mirror inside (coming soon ) At the moment, we have one ultra low pressure vacuum chamber (10-10 mbar) MIRROR The mirror is outside We will in the next months add another science chamber on top. 4 mirrors (1/2 inch) on translation stage Large optical access Electric field control Independant vacuum 532 nm The naked vacuum cell 17

18 Moving the atoms from one vacuum cell to the other, the idea. Atom elevator (aka Bloch lift) By controlling the frequency difference between 2 laser beams, we effectively create a moving lattice, accelerating and decelerating the Rb Atoms. Parameters : 40 GHz detuning 100 mw/beam U = 100 Er a = 120 g 18

19 Moving the atoms from one vacuum Ben Dahan, PRL 76, 4508 (1996) Cadoret, PRL 101, (2008) cell to the other. Test on atoms from an optical molasse Efficiency limited by Size of beam < size molasse Temperature of atoms Spontaneous emission 19

20 Is loading the MixTrap from a Magneto-Optical Trap enough? The Problem: atoms populate 4000 sites 15 atoms per site, covering a length of 1mm. 2 μk temperature, which implies low efficiency of the Bloch Elevator (3 atoms per site once lifted) The requirements: Lots of atoms too maintain decent signal at the detection Populate smaller span of sites More atoms per site Reduce temperature We need to load the MixTrap from a cooler, smaller and denser sample The solution: 20

21 Reaching our goal through evaporative cooling f1=300mm mm f=150mm 196µm mm f2=100mm 35.5µm 100 W 1064nm laser 2 AOM to control beam power f=150mm -1 order 300 mm f=150mm 300 mm f=150mm +1 order AOM AOM Create a cigar shaped trapping dipolar potential: Width ~ 30 um Length ~ 150 um Vacuum chamber 150mm 150mm 172x48.5µm 110 mm EVAPORATIVE COOLING 21

22 Benefits of evaporative cooling Within a few seconds, we increase phase-space density by : Lower temperature Better space density Fewer states populated in transverse confinement Better contrast at longer Ramsey time Better resolution on the Bloch Frequency ν B We now have atoms/cm 3 More atoms per site, less sites are populated atoms in σ = 4 sites (1 um) We can expect better site adressability close to the surface. Loading from Molasse Loading from Dipolar Trap Number of atoms Sites populated Atoms per site Preparation time 500 ms to 1s 3 seconds 22

23 The unsuspected benefit of higher densities. What we would expect : Different collisional shifts in different sites should kill the contrast at long times, due to spin dephasing. (ν coll = 0,4Hz for at/cm 3 ) What we see for Δm = 0 : Identical Spin Rotation Effect Deutsch, PRL 105, (2010) Collision induced spin rephasing : 23

24 Numerically: Discerning CP from a possible deviation to Newton s law By properly modelling the Casimir Polder potential induced by the di-electric mirror on the atomic dipole. Main Challenge : Mirror is not a perfect conductor, its complex permittivity needs to be well characterized. A. Lambrecht and collegues (LKB) Calculated CP potential is then substracted from measurement deviation(?) Experimentally: It s easy to work with alternatively with 2 Rubidium isotopes : 87 Rb & 85 Rb They have the same atomic polarizability α 0. However their masses differ, m 87 /m 85 87/85 Same experiment with 87 Rb & 85 Rb, then «What we have left should behave like gravitational force» We have 4 mirrors slots : we have control over the test masses! 24

25 At the end of the day By inserting a mirror inside and properly controlling our site populations close to this mirror we can conservatively expect : Explore the λ 10 μm range Where CP < 10-2 Hz Explore the λ 0,2-1 μm range With differential measurements 25

26 Conclusion and perspectives We expect our ultra-cold Rb atoms to provide us with a great tool to probe short range forces with great accuracy. A unique tool to probe Casimir forces The means to discern a possible 5th force or at least set new constraints. Short term prospects: Insert mirror in vacuum Transport atoms close to the mirror surface Perform interferometric potential measurement at short ranges 26

27 Thank you for your attention! Franck Pereira Cyrille Solaro Peter Wolf Astrid Lambrecht The Atomic Interferometry and Inertial SYRTE, Paris Observatory 27