* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Atom Interferometry and Precision Tests in Gravitational Physics
Bohr–Einstein debates wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Geiger–Marsden experiment wikipedia , lookup
Renormalization group wikipedia , lookup
Quantum teleportation wikipedia , lookup
Wheeler's delayed choice experiment wikipedia , lookup
Path integral formulation wikipedia , lookup
Atomic orbital wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Electron configuration wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Wave–particle duality wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Chemical bond wikipedia , lookup
Hydrogen atom wikipedia , lookup
Double-slit experiment wikipedia , lookup
Matter wave wikipedia , lookup
Tight binding wikipedia , lookup
Atom Interferometry and Precision Tests in Gravitational Physics Lecture II Calculation of the phase difference between the two arms of an atom interferometer • Examples • Experiments • Main references - A. D. Cronin, J. Schmiedmayer, D. E. Pritchard, Optics and interferometry with atoms and molecules, Rev. Mod. Phys. 81, 1051 (2009). - C. Cohen-Tannoudji, D. Guery-Odelin, Advances in Atomic Physics: An Overview, World Scientific (2011) - J. Schmiedmayer, Interferometry with atoms, Lectures at the E. Fermi School on Atom Interferometry, Varenna (2013). - G. M. Tino, M. A. Kasevich (eds). Atom Interferometry. Proc. International School of Physics ‘Enrico Fermi’, Course CLXXXVIII, Varenna 2013, SIF and IOS (2014). G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 In two-slit interference is it possible to determine which slit the atom passes through? Discussion between Bohr and Einstein, Fifth Solvay International Conference on Electrons and Photons, 1927 Einstein: The recoil of the slits’ support B is δp if the particle passes in the upper slit and -δp if the particle passes in the lower slit. The path of the particle can be determined by measuring the momentum of the slits’ support. Bohr: The slits’ support momentum should be known with an uncertainty much smaller than δp. Because of the uncertainty principle, the spread δx in the position of the support would then be larger than the separation between the slits so that the interference pattern is washed out. (Question called “which-path information” or “welcher weg”. See also discussion in terms of entanglement of particle and apparatus) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Recoiling Beam Splitter how to build a “light“ beam splitter Emitting one Photon one Photon and a mirror Bragg scattering from a standing light wave two classical fields mirror The emitted photon has full information about the path Information about the path is erased by the mirror Diffraction at a standing light wave = diffraction at a grating (λ/2) The photon is the ultimate light weight beam splitter, the path of the atom can be inferred from the recoil The photon acts as a beamsplitter The recoil is taken up by the mirror The scattered photon is hidden in the classical light field and has no information about the path. from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Emission of a single photon: The ultimate light weight beam splitter Single spontaneous photon generates coherence between matterwaves J. Tomkovic, et al., Single spontaneous photon as a coherent beamsplitter for an atomic matter-wave, Nature Physics, 7, 379–382 (2011) from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (1) Reference: Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994) REVIEW OF CLASSICAL LAGRANGIAN DYNAMICS Lagrangian for a particle of mass M in a potential V(z) Canonical momentum Hamiltonian Action Principle of least action. The actual path Γcl taken by a classical particle is the one for which the action is extremal. Alternative expression for the classical action G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (2) THE QUANTUM PROPAGATOR Evolution operator U Quantum propagator Amplitude for the particle to arrive at point zbtb starting from point zata. Feynman's expression for the quantum propagator Feynman (1948) Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (3) THE QUANTUM PROPAGATOR FOR QUADRATIC LAGRANGIANS Quadratic Lagrangian Free particle Examples: Particle in a gravitational field Particle in a rotating reference frame Simplified expression for the propagator => In the case of a plane wave incident => ∝ To calculate the final wavefunction at a particular position we consider the trajectory of a classical particle whose initial momentum is po and which passes through that final point. The phase of the final wavefunction is determined by the action along this classical path and the phase of the wavefunction at the trajectory's initial point. P. Storey and C. Cohen-Tannoudji, J. Phys. II France 4, 1999 (1994) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (4) EFFECT OF A PERTURBATION ON THE LAGRANGIAN Perturbation on the Lagrangian => To first order in ϵ, the phase shift δφ introduced into the final wavefunction by the perturbation is determined simply by the integral of the perturbation along the unperturbed path. APPLICATION TO INTERFEROMETRY Total phase shift between the two arms => introduced by the perturbation The phase shift introduced by a perturbation on the Lagrangian is determined simply by the integral of the perturbation around the closed unperturbed path comprising the two arms of the interferometer. Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (5) EXAMPLES IN INTERFEROMETRY (I): FREE PARTICLE Lagrangian Classical action Quantum propagator Wavefunction at the initial point ( ) => Wavefunction at the final point Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (6) EXAMPLES IN INTERFEROMETRY (II): 2-LEVEL ATOM CROSSING A TRAVELLING LASER WAVE The effect of the laser interaction is to change the atomic wavefunction by one of the four multiplying factors: Uij is defined as the transition amplitude from the jth to the ith internal atomic state, calculated by taking the coordinate origin to be z1 t1 and the phase φ to be zero. Ch. J. Bordé, Atomic Interferometry and Laser Spectroscopy, in Laser Spectroscopy X, World Scientific (1991) Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (7) EXAMPLES IN INTERFEROMETRY (III): PARTICLE IN A GRAVITATIONAL FIELD Lagrangian From Lagrange equations => => => Classical action Momentum Hamiltonian Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (8) EXAMPLES IN INTERFEROMETRY (IV): ATOM INTERFEROMETRY GRAVIMETER =0 Raman pulse interferometer M. Kasevich, S. Chu (1991) =0 : Path ACB Path ADB => => P. Storey and C. Cohen-Tannoudji, J. Phys. II France 4, 1999 (1994) ω is swept continuously to compensate for Doppler effect. G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Stanford atom gravimeter Resolution: 3x10-9 g after 1 minute Absolute accuracy: Δg/g<3x10-9 A. Peters, K.Y. Chung and S. Chu, Nature 400, 849 (1999) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (8) EXAMPLES IN INTERFEROMETRY (V): PARTICLE IN A ROTATING FRAME Lagrangian for a free particle, in terms of the coordinates of the Galilean frame R' => => Rotation considered as a perturbation => => => Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Comparison with Sagnac effect in an optical interferometer => Sagnac phase shift (considering the same area A) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Gyroscope F. Riehle, Th. Kisters, A. Witte, J. Helmcke, Ch. J. Bordé, Phys. Rev. Lett. 67, 177 (1991) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Stanford/Yale gyroscope T.L. Gustavson, A. Landragin and M.A. Kasevich, Class. Quantum Grav. 17, 2385 (2000) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 SYRTE cold atom gyroscope 50 cm 30 cm One pair of Raman lasers switched on 3 times Detections Ω Launching velocity: 2.4 m.s-1 Maximum interaction time : 90 ms 3 rotation axes 2 acceleration axes Cycling frequency 2Hz Expected sensitivity (106 at): • gyroscope : 4 10-8 rad.s-1.Hz-1/2 • accelerometer : 3 10-8 m.s-2.Hz-1/2 Magneto-Optical Traps B. Canuel et al., Six-Axis Inertial Sensor Using Cold-Atom Interferometry, PRL 97, 010402 (2006) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 compact From M. Kasevich, Stanford University Talk at the International Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Firenze, September 2006 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Calculation of the phase difference between the two arms of an atom interferometer (9) EXAMPLES IN INTERFEROMETRY (VI): AHARONOV-BOHM EFFECTS Lagrangian for a charged particle in an electromagnetic field => The scalar Aharonov-Bohm effect Phase shift introduced between the two wavepackets by an electric potential U applied for a time T The vector Aharonov-Bohm effect Phase shift introduced between the two wavepackets by the vector potential A The important features of both the scalar and vector Aharonov-Bohm effects are: the absence of force on the particle, the topological nature of the effect, and the fact that the phase shift is global and non-dispersive. Pippa Storey and Claude Cohen-Tannoudji, The Feynman path integral approach to atomic interferometry. A tutorial, J. Phys. II France 4, 1999-2027 (1994) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Experiments on topological phases with neutral atom interferometers EXAMPLES IN INTERFEROMETRY (VII): TOPOLOGICAL PHASES topological phase in a matter wave interferometer operated with a particle carrying a magnetic dipole if the interferometer arms encircle a line of electric charges producing a field E. Aharonov-Casher topological phase He-McKellar-Wilkens topological phase topological phase when a particle with an electric dipole d propagates in a magnetic field B S. Lepoutre, A. Gauguet, G. Trénec, M. Buchner, and J. Vigué, He-McKellar-Wilkens Topological Phase in Atom Interferometry, PRL 109, 120404 (2012) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Beam splitters Alexander D. Cronin, Jörg Schmiedmayer, David E. Pritchard, Optics and interferometry with atoms and molecules, Rev. Mod. Phys. 81, 1051 (2009). G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Multi-photon Bragg diffraction In multiphoton Bragg diffraction, the atom coherently scatters 2n photons from a pair of antiparallel laser beams with frequencies ω1 and ω2. The atom emerges in its original internal quantum state moving with a momentum 2nℏk. Atom kinetic energy Match with the energy nℏk(ω1-ω2) lost by the laser field, determines the resonance condition for the Bragg diffraction order n. Holger Mueller, Sheng-wey Chiow, Quan Long, Sven Herrmann, Steven Chu, Atom Interferometry with up to 24-Photon-Momentum-Transfer Beam Splitters, PRL 100, 180405 (2008) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Precision gravity measurement at µm scale with Bloch oscillations of Sr atoms in an optical lattice ν = m g λ /2 h G. Ferrari, N. Poli, F. Sorrentino, G. M. Tino, Long-Lived Bloch Oscillations with Bosonic Sr Atoms and Application to Gravity Measurement at the Micrometer Scale, Phys. Rev. Lett. 97, 060402 (2006) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Particle in a periodic potential:Bloch oscillations periodic potential Bloch’s theorem λ/2 with a constant external force F quasimomentum q [2π/λ] Bloch oscillations Quantum theory for electrons in crystal lattices: F. Bloch, Z. Phys. 52, 555 (1929) Never observed in natural crystals (evidence in artificial superlattices) Direct observation with Cs atoms: M.Ben Dahan, E.Peik, J.Reichel, Y.Castin, C.Salomon, PRL 76, 4508 (1996) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Bloch oscillations in a vertical optical lattice Gravity force makes the momentum oscillate !"# !$# −kL 0 +kL G. Ferrari, N. Poli, F. Sorrentino, G. M. Tino, Long-Lived Bloch Oscillations with Bosonic Sr Atoms and Application to Gravity Measurement at the Micrometer Scale, Phys. Rev. Lett. 97, 060402 (2006) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 N. Poli, F.Y. Wang, M.G. Tarallo, A. Alberti, M. Prevedelli, G.M. Tino, Phys. Rev. Lett. 106, 038501 (2011) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Large momentum beam-splitters G.M. Tino, School on Ultracold Atoms Precision Les Houches, September 2014 G.M. Tino, “E. and Fermi” SchoolMeasurements, on Atom Interferometry, Varenna, July 2013 Lecture by Pierre Cladé G.M. Tino, School on Ultracold Atoms Precision Les Houches, September 2014 G.M. Tino, “E. and Fermi” SchoolMeasurements, on Atom Interferometry, Varenna, July 2013 Precision measurement of h/M and α Stanford: X ≡ Cs σα/α ~ 7 ppb A.Wicht, J. M. Hensley, E. Sarajlic, S. Chu, Phys. Scr. 102, 82 (2002). Berkeley: X ≡ Cs σα/α ~ 2 ppb S.-Y. Lan, P.-C. Kuan, B. Estey, D. English, J. M. Brown, M. A. Hohensee, H. Muller, Science 339, 554 (2013). Paris: X ≡ Rb σα/α ~ 0.6 ppb R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, F. Biraben, Phys. Rev. Lett. 106, 080801 (2011). σα/α < 0.1 ppb ? G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Search for physics beyond the SM G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Atom IFM Experiments Atomic and Molecular Physics Electric Polarizability Ekstrom et al. PRA 51, 3883 (1995) Insert an interaction region in the interferometer which allows to ally a constant electric field to one arm of the interferometer Applying an electric field E to one arm creates a phase shift from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Coherence Length Experiment Ekstrom et al. PRA 51, 3883 (1995) Coherence length Na: λdB = 17 pm lcoh = 160 pm Experiment: • shift the matter wave in one arm of the interferometer by a potential • Observe the contrast of the interference pattern In the experiment with Na2 molecules or in the experiment with C-60 the coherence length is smaller than the object ! from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Refractive Index In Analogy to Light Refractive index for matter waves Refractive index for a Potential V(r): Refractive index from (forward-) scattering : Refractive index: light in matter matter waves in light matter waves in matter Example: Neutrons in a solid: Na (v=1000 m/s) in 1 mtorr Ne: atoms in light from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Atom IFM Experiments Atomic and Molecular Physics Schmiedmayer et al. PRL 74, 1043 (1995) Refractive index for Na matter waves What can we measure best from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Search for electron-proton charge inequality • Electrostatic, ferromagnetic, diamagnetic levitation Millikan (1935), Morpurgo (1966-1984), Braginsky (1970), Stover (1967), Rank (1968), LaRue (1979) • Gas flow Piccard and Kessler (1925), Hillas & Cranshaw (1960), King (1960) • Acoustic cavity Dylla and King (1973) • Atomic and molecular beams Hughes (1957), Chamberlain & Hughes (1963), Fraser (1965), Shapiro (1957), Shull (1967) Present limit δep< 1x10-21 e (From G. Carugno and G. Ruoso, 2005) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Proposals to Test Atom Neutrality with Atom Interferometry δep ~ 10-21 e C. Champenois, M. Büchner, R. Delhuille, R. Mathevet, C. Robilliard, C. Rizzo, J. Vigué, Matter Neutrality Test Using a Mach-Zehnder Interferometer, in The Hydrogen Atom, Lecture Notes in Physics Vol. 570, Springer (2001) +/- V δep ~ 10-25 e G. Ferrari, G. M. Tino, Measuring the electric charge of neutral atoms by atom interferometry, INFN Internal Report (2006) δep ~ 10-28-10-30 e A. Arvanitaki, S. Dimopoulos, A. A. Geraci, J. Hogan, M. Kasevich, How to Test Atom and Neutron Neutrality with Atom Interferometry, Phys. Rev. Lett. 100, 120407 (2008) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Interferometry with trapped atoms from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 Atom Chip Review: R. FolmanSchool et al. Adv.At.Mol.Opt.Phys. 2002 Varenna-Summer July 2013 J. Schmiedmayer: Lecture 2: Atom IFM @ Chips ATOM CHIP components for atom manipulation Magnetic interaction U mag ! ! = "µ ! B current carrying wires: very versatile, tight confining micro magnets: strong quiet fields, tighte confinement + = Electric interaction additional degree of freedom to manipulate atom potentials together with magnetic traps: state dependent optical elements Adiabatic Potentials Couple internal states by RF, MW, optical fields additional degree of freedom to structure potentials state dependent guides and traps, Integration with other techniques optical lattices (addressable 2-d lattice) cavity QED nano-optics, nano electronics many more ... from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 I. Bloch G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 neutral-atom manipulation using integrated micro-devices combining the best of two worlds: •cold neutral atoms - a well controllable quantum system • technologies of nano-fabrication, micro-electronics, micro-optics ATOM CHIP Take the tools of quantum optics and atomic physics and make them robust and applicable by miniaturizing and integrating them using the techniques of nano-fabrication, micro-electronics and micro-optics. • create a tool box for building quantum devices from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Beam splitter splitting the trapped wave function in a double well Generic double well potential: U(x,t) = a(t) x2 + b x4 from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 U. Hohenester et al. PRA 75, 023602 (2007) J. Ground et al. PRA 79, 021603(R) (2009) G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 RF and MW induced adiabatic potentials create adiabatic dressed state potentials by coupling electronic ground states of an atom – coupling between stable states allows to create conservative potentials even with on resonant radiation – shaping the potential: • detuning the states with an external magnetic field • spatial dependent coupling strength (RF field) -> allows strong field seeker traps – coupling is magnetic: the amplitude and the relative orientation of the RF field and the detuning field are important – – – – first experiment: dressed neutrons:! E. Muskat et al., PRL 58, 2047 (1987). first proposal of a MW trap (detuned)! C. Agosta, et al. PRL. 62, 2361 (1989). MW experiment (Cs, detuned)! R. Spreeuw, et al. PRL 72, 3162 (1994). RF dressed state traps ! ! O. Zobay, B. M. Garraway, PRL 86, 1195 (2001). (with magnetic field detuning but neglecting polarization) – RF potentials for thermal Rb atoms:! Y. Colombe, et al. Europhys. Lett. 67, 593 (2004). – Full implementation ! ! T. Schumm et al Nature Physics 1, 57 (2005) from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Mach-Zehnder Interferometer for trapped BEC T. Berrada, et al., Nat. Comm. 4, 2077 (2013) from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Interferometer signal trapped MZ interferometer T. Berrada, et al., Nat. Comm. 4, 2077 (2013) Interferometer signal stays with full contrast even though thermal coherence length lth << system size! Physics: the emerging pre-thermalized length scale >> system size M. Gring, et al., Science 337, 1318 (2012) -> 1d de-phasing is irrelevant M. Kuhnert et al. PRL 110, 090405 (2013) from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Phase diffusion T. Berrada, et al., Nat. Comm. 4, 2077 (2013) Phase diffusion Uniform distributions Peaked distributions Number squeezing reduces phase diffusion Castin & Dalibard, PRA 55, 4330 (1997) Javanainen & Wilkens, PRL 78, 4675 (1997) from J. Schmiedmayer, E. Fermi School on “Atom Interferometry”, Varenna 2013 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 Cavity-assisted spin squeezing Coherent spin state Spin squeezed state Exploit QND cavity/probe interactions to create spin-squeezed input state for atom interferometry. Possible >100x gain in sensor sensitivity. Squeezing via QND optical probe from M. Kasevich - ICAP 2014 Implementation Homogeneous atom/cavity coupling allows for free space read-out. Lee, et al. Opt. Lett. 2014 from M. Kasevich - ICAP 2014 Squeezed state atom detection noise π/2 – cavity homodyne readout/squeezing – cavity homodyne readout 17 dB reduction in variance from M. Kasevich - ICAP 2014 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014 G.M. Tino, School on Ultracold Atoms and Precision Measurements, Les Houches, September 2014