Measuring the gravitational force of a miniature source

Measuring the gravitational force of a miniature source mass on an atom Holger Müller

Contents 1. Introduction 2. Dark matter through the fine structure constant 3. Dark energy through screenedboson mediated forces 4. Outlook: galileons, symmetrons, and the next few orders of magnitude

The standard model is incomplete Image: CDMS Reconstructed Observed matter mass distribution (Chandra x-ray (lensing) observations)

LIGO as a dark matter detector E. D. Hall, Th. Callister, V. V. Frolov, H. Müller, M. Pospelov, and R. X. Adhikari v Dark asteroids, 0. 1 -1013 kg One event every 10 years assuming only gravity Fgravity Multiple events/year with Yukawa coupling ar. Xiv: 1605. 01103

Moore’s law in atomic physics

Light pulse atom interferometer Each data point is from a single launch, determines g to 1. 3 ng =>11 ng/sqrt(Hz) HM et al. , PRL 100, 031101 (2008); PRD 80, 016002 (2009)

Fine Structure Constant α Select Alpha Measurements Muonium (1999) Neutron ħ/m (1995) Quantum Hall (1997) Cesium ħ/m (2002) g-2 (Washington, 1987) Rubidium ħ/m (2010) 0. 66 ppb (ħ/m. Rb) g-2 (Harvard, 2008) 0. 24 ppb (g 2) Rev. Mod. Phys. 84, 1527 (2012)

Measuring Alpha to Test QED Ramsey-Bordé Interferometer Kinetic Energy x t

kg h/m g-2 R∞ α me/m. At • All experiments and all theories have ppb accuracy • Substantial parts of the Standard Model have to be right to yield α and g-2 at that level

Anomalous Phases 1 ppb July ‘ 16 August ‘ 16

Common-mode Bloch Oscillations • Increases total phase of interferometer • Increases frequency splitting of last two pulse • >107 rad matter-wave phase difference Bloch Oscillations Now 2 x 125 BOs = >500 ħk

Electron/Muon coupling strength Dark photons, hadrophobic * Be High energy limits assume 100% decay into e+ e- and become weaker if this is not the case. Mass

Electron/Muon coupling strength Dark photons Be Mass

Wikipedia Paul Hamilton, Philipp Haslinger, Matt Jaffe, Brian Estey, Justin Khoury H. M. Dark energy

The standard model is incomplete Saul Perlmutter

Dark Energy density Λ ≈10 -52/m 2 ≈1/(present size of universe)2 Energy density corresponding to that is more intuitive • 7 Hydrogen rest masses/m 3 • E=14 V/m • One photon of λ≈100 μm per λ 3 λ ħω ħω λ

1831 Faraday's law and Maxwell's equations 1861 -65 1886 -89 Planck

Dark Energy: Models? Vacuum fluctuations ~ Λuv 4 (Pauli, circa 1920) 123 orders of magnitude off Cancellations cutting Λuv 4 and Λuv 2 m 4 log(Λuv/m) still 33 orders off Þ New physics needed • Typically new bosons • To solve problem, must couple to normal matter • ~Gravitational strength • Must be compatible with existing experiments

Testing gravity

Chameleon screening Screened 1 nm Unscreened Only a thin shell contributes in macroscopic objects 1 cm

The idea Probing Dark Energy with Atom Interferometry C. Burrage, E. J. Copeland, E. A. Hinds JCAP 1503 (2015) 03, 042 Realization: Single atom’s small size in ultra high vacuum makes it ideal test mass which evades screening

Unscreened force for atoms Unscreened force can be much stronger than gravity

Cavity-based atom interferometer Features • Intensity enhancement • Well-defined optical mode • High accuracy and resolution • Goal: Δp=100ħk Cavity mirror Cavity mode Δp=2 nℏk Well-defined beam waist Cavity mirror P. Hamilton et al. , PRL (2015)

Setup 3 mm

Results Red = sphere near Blue = sphere far Difference between sphere near/far P. Hamilton, M. Jaffe, P. Haslinger, Q. Simmons, H. Müller, J. Khoury ar. Xiv: 1502. 03888

Dark energy limits T. Jenke et al. PRL 112, 151105 (2014) H. Lemmel et al. Phys. Lett. B 743 (2015) 310 -314 βM=MPl/M Amol Upadhye Phys. Rev. D 86, 102003 (2012) K. Li et al. ar. Xiv: 1601. 06897 (2016) P. Hamilton, M. Jaffe, P. Haslinger, Q. Simmons, H. Müller, J. Khoury Science 349, 849 (2015).

Photon coupling comparison CAST- arxiv: 1503. 04561 Gamme. V collaboration J. Steffen et al. PRL 105, 261803 (2010) Limits including experiments using an additional coupling to the photon Atom interferometry does not need photon coupling

Outlook

IMPROVED SETUP Colder atoms • Raman sideband cooling • 100 s of n. K Vibration isolation • dominant noise source • 2 nd stack Launch • Longer T • signal proportional T 2 Tungsten test mass • Slotted for systematics control • Gravity 70 nm/s 2

Now measuring 35 nm/s 2 Seeing gravity of sphere

Systematics (incomplete) Tilt AC Stark Shifts • Large variations within cavity and across atom cloud

General dark energy models Kinetic term • Long-ranged screening • “Vainshtein” mechanism • P(X) • Gallileon Potential • Local screening • Chameleons, • Peebles-Ratra Coupling • Similar to chameleon • Symmetrons • Damour-Polyakov Joyce, Jain, Khoury and Trodden, ar. Xiv: 1407. 0059

Symmetrons, Damour-Polyakov Kinetic term Potential Coupling λ=1, μ=10 -5 e. V, M=1 Te. V. Atom interferometer A. Upadhye, private comm.

Galileons Kinetic term Potential Coupling Modulated screening LLR c 4 Moons orbit modulated by suscreening Modulated screening on ISS c 3 Direct detection of force by atom interferometer Joyce, Jain, Khoury and Trodden, ar. Xiv: 1407. 0059

Preliminary improved limits

Summary

Thanks Justin Khoury (U Penn) Philipp Haslinger, HM, Matt Jaffe, Paul Hamilton