Gravity tests by atom interferometry: Gravity tests by atom - PowerPoint PPT Presentation

Gravity tests by atom interferometry: Gravity tests by atom interferometry: Gravity tests by atom interferometry: Measurement of G Measurement of G Measurement of G and test of Newtonian law at micrometric distances and test of Newtonian law at micrometric distances and test of Newtonian law at micrometric distances Guglielmo M. Tino Guglielmo M. Tino Università degli Studi di Firenze - Dipartimento di Fisica, LENS Istituto Nazionale di Fisica Nucleare - Sezione di Firenze G. M. Tino, GGI Workshop, Firenze 29/9/2006

Outline • Atom interferometry • Applications to gravity measurements • Measuring G with atoms • Precision gravity measurement at µ m scale with laser-cooled Sr atoms in an optical lattice • Prospects G. M. Tino, GGI Workshop, Firenze 29/9/2006

G. M. Tino, GGI Workshop, Firenze 29/9/2006 atom laser Atom optics laser laser laser atom atom Atomic beam Oven interferometers beam-splitters mirrors lenses

Light shifts and optical traps optical lattices 1D optical lattice ⇒ array of 2D disk-like trapping potentials 2 D optical lattice ⇒ array of 1D potential tubes 3 D optical lattice ⇒ 3D simple cubic array of h.o. potentials Review: I. Bloch, 2005 First exp. demonstration: S. Chu et al., 1986 G. M. Tino, GGI Workshop, Firenze 29/9/2006

Microfabricated atom optics O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, Phys. Rev. Lett. 67, 3231 (1991) D. W. Keith, C. R. Ekstrom, Q. A. Turchette, D. E. Pritchard, Phys. Rev. Lett. 66, 2693 (1991) G. M. Tino, GGI Workshop, Firenze 29/9/2006

G. M. Tino, GGI Workshop, Firenze 29/9/2006 F. Shimizu et al., Phys. Rev. A 46, R17 (1992) Double slit interference with cold atoms

Quantum interference path I amplitude A I Initial state Final state | ψ i 〉 | ψ f 〉 path II amplitude A II Interference of transition amplitudes P ( | ψ i 〉⇒ | ψ f 〉 ) = | A I + A II | 2 = | A I | 2 + | A II | 2 + 2 Re ( A I A II * ) G. M. Tino, GGI Workshop, Firenze 29/9/2006

∆ϕ effects • Accelerations • Rotations • Laser frequency detuning • Laser phase • Photon recoil • Electric/magnetic fields • Interactions with atoms and molecules G. M. Tino, GGI Workshop, Firenze 29/9/2006

Matter wave sensors ∆Φ = ⋅ 2 k T a accelerations: acc drift 2 ⎛ ⎞ ∆ ϕ c a ⎜ ⎟ ≈ − 11 17 mat ~ 10 10 ⎜ ⎟ ∆ ϕ ⎝ ⎠ v ph at 2 m rotations: ∆Φ = π ⋅ Ω at 2 A rot h Ω ∆ ϕ ⋅ λ ⋅ m c ≈ ⋅ 10 mat at ~ 5 10 ∆ ϕ h ph G. M. Tino, GGI Workshop, Firenze 29/9/2006

Raman interferometry in an atomic fountain z(t) π π π 2 2 � � � Phase difference between the paths: k k k R2 R2 R2 ∆Φ = k e [z(0)-2z(T)+z(2T)]+ Φ e k e = k 1 - k 2 , ω e = c k e with z(t) = -g t 2 /2 + v 0 t + z 0 & Φ e = 0 ⇒ ∆Φ = k e gT 2 g = ∆Φ / k e T 2 T T � � � k k k R1 R1 R1 t Final population: N a = N/2 (1+cos[ ∆Φ ]) Interference fringes – Firenze 2006 T = 150 ms ⇒ 2 π = 10 -6 g ⇒ Sensitivity 10 -9 g/shot S/N = 1000 M. Kasevich, S. Chu, Appl. Phys. B 54, 321 (1992) A. Peters, K.Y. Chung and S. Chu, Nature 400, 849 (1999) G. M. Tino, GGI Workshop, Firenze 29/9/2006

Stanford atom gravimeter Resolution: 3x10 -9 g after 1 minute Absolute accuracy: ∆ g/g<3x10 -9 A. Peters, K.Y. Chung and S. Chu, Nature 400, 849 (1999) G. M. Tino, GGI Workshop, Firenze 29/9/2006

Stanford/Yale gravity gradiometer from M.A. Kasevich M.J. Snadden et al., Phys. Rev. Lett. 81, 971 (1998) G. M. Tino, GGI Workshop, Firenze 29/9/2006

Stanford/Yale gyroscope T.L. Gustavson, A. Landragin and M.A. Kasevich, Class. Quantum Grav. 17, 2385 (2000) G. M. Tino, GGI Workshop, Firenze 29/9/2006

SYRTE cold atom gyroscope One pair of Raman 30 cm lasers switched on Ω 3 times 50 cm Detections Launching velocity: 2.4 m.s -1 Maximum interaction time : 90 ms 3 rotation axes 2 acceleration axes Cycling frequency 2Hz Expected sensitivity (10 6 at): • gyroscope : 4 10 -8 rad.s -1 .Hz -1/2 • accelerometer : 3 10 -8 m.s -2 .Hz -1/2 Magneto-Optical Traps G. M. Tino, GGI Workshop, Firenze 29/9/2006

MAGIA • Measure g by atom interferometry • Add source masses a M • Measure change of g g � Precision measurement of G � Precision measurement of G Precision measurement of G � Test of Newtonian law at micrometric distances � Test of Newtonian law at micrometric distances Test of Newtonian law at micrometric distances http://www.fi.infn.it/sezione/esperimenti/MAGIA/home.html G. M. Tino, GGI Workshop, Firenze 29/9/2006

Why atoms? • Extremely small size • Well known and reproducible properties • Quantum systems • Precision gravity measurement by atom interferometry • Potential immunity from stray fields effects • Different states, isotopes,… G. M. Tino, GGI Workshop, Firenze 29/9/2006

Measurement of the Newtonian gravitational constant G by atom interferometry G. M. Tino, GGI Workshop, Firenze 29/9/2006

Measurements of the Newtonian gravitational constant G Cavendish 1798 G = 6.673 (10) × 10 -11 m 3 kg -1 s -2 [1.5×10 -3 ] Quinn G = 6.6742 (10) × 10 -11 m 3 kg -1 s -2 2001 [1.5×10 -4 ] G. M. Tino, GGI Workshop, Firenze 29/9/2006

MAGIA: Experimental procedure • trap, cool and launch 2 clouds of Rb atoms I II • apply Raman light pulses masses in position 1 • detect atoms state selectively • repeat several times z 1 • plot N a /N and fit the differential phase shift ∆Φ g between the clouds 1 1 • move masses to position 2 repeat all procedure z 2 • subtract the differential phase shifts for 2 2 the two mass positions φ − φ = φ + φ + φ I I ( z ) ( z , t ) 1 2 g 1 SM Sys 1 I ( ) − φ − φ + φ ( ) ( , ) z z t g 2 SM Sys 2 I φ − φ = φ − φ + φ II II ( z ) ( z , t ) 1 2 g 1 SM Sys 1 II ( ) − φ + φ + φ ( z ) ( z , t ) g 2 SM Sys 2 II ⇒ φ − φ − φ − φ I I II II ( ) ( ) 1 2 1 2 = φ + φ ∆ ∆ 4 ( z , t ) SM Sys G. M. Tino, GGI Workshop, Firenze 29/9/2006

Atom gravity gradiometer apparatus Source masses and support Laser and optical system L. Cacciapuoti, M.de Angelis, M. Fattori, G. Lamporesi, T. Petelski, M.Prevedelli, J. Stuhler, G.M. Tino, Analog+digital phase and frequency detector for phase locking of diode lasers, Rev. Scient. Instr. 76, 053111 (2005) G. M. Tino, GGI Workshop, Firenze 29/9/2006

G. M. Tino, GGI Workshop, Firenze 29/9/2006 Atom interference fringes 35 cm GRADIOMETER

G: first result G = 6.64 (6) × 10 -11 m 3 kg -1 s -2 A. Bertoldi, G. Lamporesi , L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, G. M. Tino, Eur. Phys. J D, 2006 (available online as Highlight Paper) - arXiv:physics/0606126 G. M. Tino, GGI Workshop, Firenze 29/9/2006

SOURCE MASSES Arrangement : 2x12 cylinders in a hexagonal arrangement Material : INTERMET 180K (95.3% W, 3,2% Ni, 1,5% Cu) produced by PLANSEE 100 µ m hole seen Properties : with a microscope Density = 18 g cm -3 Resistivity = 12x10 -8 Wm Non magnetic radius 5 cm HIP treatment Thermal expansion = 5x10 -6 K -1 height 15 cm Surface roughness = 3 µ m mass 20 kg Characterization Possible holes in the center of big blocks can change the average density of max 10 -4 (Simulations show maximum shift of G of less than 10 -4 ) •Hot Isostatic Pressing of cylinders at 1200 ° C and 1500 atm to reduce holes •Ultrasonic and destructive test Ultrasonic tests on a simply •Density comparison at different points in sintered cylinder (above) and cooperation with INRIM in Torino (relative 15 samples obtained on an also HIPed one (below) measurement will reveal differences smaller than from one cylinder for density comparison 0.002 g/cm -3 ) G. M. Tino, GGI Workshop, Firenze 29/9/2006

atoms Appropriate trajectories L E Masses separation in the two configurations and atomic clouds A initial position have been chosen in order to minimize the D dependence on atomic initial parameters and reach the accuracy on G of 10 -4 . • the interferometer is realized T around an acceleration max/min • the Earth’s gravity gradient U must be over-compensated • only high density material can N be used G S T E N G. M. Tino, GGI Workshop, Firenze 29/9/2006

MAGIA – Relevant numbers • time separation between pulses T=150 ms • 10 6 atoms • shot noise limited detection • launch accuracy: 1 mm e ∆ v ~ 5 mm/s • knowledge of the masses dimensions and relative positions: 10 µ m • 10000 measurements G. M. Tino, GGI Workshop, Firenze 29/9/2006

Experiments on gravity at small spatial scale G. M. Tino, GGI Workshop, Firenze 29/9/2006