Atom-interferometry limits on dark energy Jun Geena Kim P. Hamilton, D. Schlippe, and H. Mueller University of California, Berkeley Paul Hamilton Müller group University of California at Berkeley

1.Screened scalar fields as dark energy 2.Atom interferometry search for dark energy P. Hamilton, M. Jaffe, P. Haslinger, Q. Simmons, H. Müller, J. Khoury arXiv: Future reach with atom interferometry Eliminate theories with coupling up to Planck mass Outline

Evidence ESA/Planck SDSS SCP + + =

Known unknowns Dark energy density ~1 hydrogen atom / m 3 or an energy scale of 2.4 meV ESA/Planck

Dark energy sources Cosmological constant New energy scale = new field? Scalar fields advantages Can explain why cosmic acceleration started now Allow for equations of state with w ≠ -1

Scalar dark energy Simple scalar models lead to equivalence principle violations in conflict with solar system tests and fifth force searches. What if scalar field effects are somehow reduced in normal matter? Only two ingredients needed for screening 1)Scalar field self-potential 2)Coupling to local matter density

Chameleon fields Khoury, Weltman Phys. Rev. D 69, The “chameleon” as a model screened scalar field Self-potential Coupling to local density

Chameleon fields Khoury, Weltman Phys. Rev. D 69, Normal matterIn vacuum Coupling to local density Self-potential

Chameleon screening Unscreened Screened Only a thin shell contributes in macroscopic objects 1 cm 10 nm Chameleon field acts as a potential for objects

Screened force Unscreened force can be much stronger than gravity

Public outreach Burrage, Copeland, Hinds arXiv: Realization: Single atom’s small size makes it ideal test mass which evades screening Semi-famous internet meme

Screened force Unscreened force can be much stronger than gravity

Atom interferometry Time 0 T 2T Height

Detection Optically push one state to side before imaging Fluorescence detection of two output states Sphere moved in and out with translation stage 3 mm

Cavity interferometer 4 lasers, 2 optical cavities 7 frequency and phase locks Upper Mirror Lower Mirror 3D MOT 2D MOT For more information:

Gravimetry fringes Height Time

Reversed interferometers Time Height Alternate momentum kick directions to reduce systematics

Results Red = sphere near Blue = sphere far Difference between sphere near/far

Systematics Differential measurement How else can the sphere affect our measurement? Changes in interferometry laser Check power dependence Magnetic fields Increase bias field x10 Electric fields Negligible due to small polarizability

Constraints on parameters Neutrons n=1 n=5 screened unscreened Atom interferometry

Dark energy limits

Photon coupling comparison Limits including experiments using an additional coupling to the photon CAST- arxiv: Atom interferometry Atom interferometry does not need photon coupling

The future 3-4 orders of magnitude improvement reaches Planck Mass couplings

The future ModelDescription ChameleonMass couples to matter density SymmetronCoupling depends on matter density f(R) gravity Preferred scaleMaps to chameleon theory Varying dilatonTime varying equivalence principle violation Topological DMAnomalous forces K-mouflage Pressuron Galileon Atom interferometry can help constrain many scalar dark energy theories

“Force-Free Gravitational Redshift: Proposed Gravitational Aharonov-Bohm Experiment” M. Hohensee, B. Estey, P. Hamilton, A. Zeilinger, H. Müller, PRL 108, (2012) x [m] Optical lattice Field mass Gravitational Aharonov-Bohm Effect See poster by Matt Jaffe

Dark energy / optical cavity interferometer Paul Hamilton Philipp Haslinger Matt Jaffe Justin Khoury Quinn Simmons Antihydrogen interferometer Paul Hamilton Philipp Haslinger ALPHA collaborators Andrey Zhmoginov Joel Fajans Jonathan Wurtele XUV atom interferometer Paul Hamilton Collaborators Birgitta Whaley Ali Belkacem PI : Holger Müller Lithium atom interferometer Kayleigh Cassell Eric Copenhaver Paul Hamilton Talk tomorrow Poster Other projects:

Systematics - Magnetic

Systematics – AC Stark

Systematics - All

F=3 atoms F=4 atoms Recent Mach-Zehnder data F=4 / (F=3 + F=4)

Chameleon mass

Atom screening

Mass screening

Exclusion plot regions

Strong coupling

Lorentz invariance requires Holds exactly in all of QM and QFT Phase of a quantum state [de Broglie, 1924, Ph.D thesis (!)] An atom interferometer measures the phase difference: (for Mach – Zehnder) Compton frequency Time dilationRedshift

0 T 2T Time Height Light pulse atom interferometer Beamsplitter Interferometer Demonstrated sensitivity of atom interferometers Accelerations: ~ppb ! Rotations: <nrad/s !

Upper Mirror Lower Mirror 3D MOT 2D MOT Magnetic Shields Cavity parameters: L = cm, waist~600 μm, finesse~200 Cavity interferometer apparatus Cavity mirror Δp=2n ℏ k Cavity lock laser Interferometry laser

2D magneto-optical source 3D magneto-optical trap Molasses cooling Optical lattice load Adiabatic release Optical pumping State and spatial selection Velocity selection Interferometer sequence Fluorescence detection Experimental sequence Which requires stable operation of: 4 lasers, 2 optical cavities 7 frequency and phase locks