Gravity measurements with atom interferometry Fiodor Sorrentino, 28/10/2010 Dipartimento di Fisica e Astronomia, Università di Firenze & INFN, Polo Scientifico di Sesto Fiorentino,via Sansone 1-50019 Sesto Fiorentino (FI) Istituto di Cibernetica CNR, via Campi Flegrei 34, 80078 Pozzuoli (NA), Italy.
Matter-wave interferometry Quantum interference path I Initial state ψ i amplitude A I path II Final state ψ f amplitude A II Interference of transition amplitudes P ( ψ i ψ f )= A I + A II 2 = A I 2 + A II 2 +2Re(A I A II ) de Broglie wave λ db = h/mv with electrons since 1953 with neutrons since 1974 with atoms since 1991
Atom interferometry Flux Δϕ atom optics different internal states/isotopes phase difference may depend on: accelerations rotations photon recoil laser phase laser frequency detuning electric/magnetic fields interactions with atoms/molecules atomic flux at exit port 1 at exit port 2
Matter-wave vs optical inertial sensors Accelerations a Φ acc = ktdrift 2 ( a φ mat φ ph c v at ) 2 10 11 10 17 Rotations Ω Φ rot =2π 2m at φ mat φ ph h A Ω m atλc h 5 10 11
Raman interferometry Final population: N a = N/2(1 + cos [ Φ]) with Φ = k e gt 2 T = 150 ms 2π = 10 6 g S/N=1000 Sensitivity 10 9 g/launch
Raman interferometry Final population: N a = N/2(1 + cos [ Φ]) with Φ = k e gt 2 T = 150 ms 2π = 10 6 g S/N=1000 Sensitivity 10 9 g/launch
AI Gradiometer T=5 ms resol. = 2.3 10 5 g/shot T=50 ms resol. = 1.0 10 6 g/shot Φ = ke gt F. Sorrentino, 28/10/10 T=150 ms resol. = 3.2 10 8 g/shot 2 G. T. Foster et al., Opt. Lett 27, 951 (2002) Gravity measurements...
AI gravimeters
Comparison with other techniques
Comparison with other techniques
Comparison with other techniques
Comparison with other techniques
Applications of absolute gravimeters Mineral exploration Environmental monitoring Water table monitoring in deep and/or multiple acquifers Monitoring of mining effect Slope and earth fill dam stability Global sea level studies for earth warming assessment On site inspection of sites for nuclear test or else Geophysical research Detection of vertical crustal motion in seismogenic areas Post glacial rebound studies Monitoring of magma migration in active volcanic areas Calibrating measurement needed by other techniques (height measurements, relative gravimeter)
Applications of accurate gradiometers Airborne gravity measurement for oil and mineral exploration hazard investigation Satellite gravity measurement GOCE Project GRACE Project MICROSCOPE Project Gravity gradiometry gives higher resolution in Monitoring of anomalies (A.J. Romaides JPD, R. Bell Sci. Am). Data processing (M. Fedi...) Joint gravimetric-seismological data inversion (...) Gradiometer based on absolute Gravimeter combines complementary range of sensitivity for different mass/distance source Tensorometer
Stanford atom gravimeter resolution: 8 10 9 g in 1 second accuracy: g/g 3 10 9 limited by tidal models A. Peters, K.Y. Chung and S. Chu, Nature 400, 849 (1999) H. Müller et al., Phys. Rev. Lett 100, 031101 (2008)
Sanford/Yale gravity gradiometer limited by QPN J. M. McGuirk et al., Phys. Rev. A 65, 033608 (2002)
Stanford/Yale gyroscope sensitivity: 6 10 10 rad s 1 Hz scale factor stability < 5 ppm bias stability < 70 µdeg/h T.L. Gustavson, A. Landragin and M.A. Kasevich, Class. Quantum Grav. 17, 2385 (2000) D. S. Durfee, Y. K. Shaham, M.A. Kasevich, Phys. Rev. Lett. 97, 240801 (2006)
Other AI sensors SYRTE absolute gravimeter gyroscope six-axis inertial sensor IQO gyroscope JPL gradiometer MAGIA F. Sorrentino, 28/10/10 Gravity measurements...
MAGIA Misura Accurata di G mediante Interferometria Atomica Measure g by atom interferometry Add source masses Measure change of g a M g http://www.fi.infn.it/sezione/esperimenti/magia/home.html
Atom gradiometer + source masses Sensitivity 10 9 g/shot one shot G/G 10 2 500 Kg tungsten mass Peak mass acceleration a g 10 7 g 10000 shots G/G 10 4
MAGIA sensitivity Present sensitivity to differential acceleration: 1.4*10-8 g @ 1 s
MAGIA results corresponding to a statistical uncertainty of 400 ppm on G F. Sorrentino, Y.H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, G.M. Tino, arxiv:1002.3549
Future of AI inertial sensors Compact and transportable system without performance degradation ground applications (geophysic) space applications (satellite geodesy, inertial navigation, tests of fundamental physics): Novel schemes to improve sensitivity/accuracy high-momentum beam spitters coherent/squeezed atomic states to surpass QPN detection large size AI and ultracold atoms (nk temperature) New applications GW, quantum gravity, etc. φ = kgt 2
Compact AI sensors
Compact AI sensors
Conclusions New atomic quantum devices can be developped with unprecedented sensitivity using ultracold atoms and atom optics Applications: Fundamental physics, Earth science, Space research Well developped laboratory prototypes Work in progress for transportable/space-compatible systems need for input from geophysics community (i.e. applications of simultaneous absolute gravity acceleration/gradient measurement)
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Space-based geodesy 100 m 100 km Accelerometers 300 km Earth Accelerometer sensitivity: 10-13 g/hz 1/2 _ Long free-fall times in orbit Measurement baseline _ 100 m (Space station) _ 100 km (Satellite constellation) GOCE mission, 4x10-3 E Sensitivity: _ 10-4 E/Hz 1/2 (Space Station) _ 10-7 E/Hz 1/2 (Satellite constellation) (1 E = 10-9 s -2 ) Earthquake prediction; Water table monitoring http://www.esa.int/export/esalp/goce.html from M. Kasevich, Talk at the International Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Firenze, September 2006
Other possible applications of AI Earth observations ground airborne satellite Fundamental physics testing equivalence principle atom neutrality GW detection quantum gravity Metrology definition of mass unit through Watt balance
Raman interferometry in a 87 Rb atomic fountain z(t) 2 R2kr R2kr R2kr T T 2 R1kr R1kr R1kr Phase difference between the paths: Φ = k c [z(0)]2z(t )] + Φ e k e = k 1 k 2 with z(t) = gt 2 /2+v 0 t + z 0 & Φ e =0 Φ = k e gt 2 t Final population: N a = N/2(1 + cos[ Φ]) T = 150 ms 2π = 10 6 g S/N=1000 Sensitivity 10 9 g/shot A. Peters et al., Nature 400, 849 (1999)
Present limitations of AI shot-noise limit to sensitivity ~ atomic flux ~ 10 18 s -1 with H (~ 10 11 s -1 with alkali) in a 100 mw laser the photon flux is > 10 18 s -1 much lower path difference than in optical interferometers better beam splitters, optical cavities nevertheless AI inertial sensors are already competitive long term stability (bias & scale factor) and accuracy future developments to improve sensitivity high momentum beam splitters high flux atomic sources sub-shot noise detection (quantum degenerate gases, etc.) large size AI, µ-gravity, ultracold atoms 1/ Ṅ
Possible applications of AI Already achieved: inertial sensing (accelerations, gravity gradients, rotations) measuring fundamental constants ( α, G) Proposed: tests of GR (equiv. principle, limits on PPN parameters, Lense- Thirring, etc. ) GW detection atom neutrality testing Newton s 1/r 2 law at short distance realization of mass unit (Watt balance)
Launching two clouds: juggling Goal: Prepare 2 clouds with same velocity at distance of 35 cm ~100 ms between two launches F. Sorrentino, 28/10/10 Gravity measurements...