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The Dark Energy Atom Interferometer Experiment

Jon Coleman, Royal Society Research Fellow

To detect and measure effects of Dark Energy density or any dark contents of the vacuum (DCV)

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• Many thanks to the support of the:– Liverpool Particle Physics Group– Cockcroft Institute– Physics Dept Technical & Workshop Support

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• Looking for a new way to penetrate the mystery of Dark Energy – more generally to penetrate the puzzles

associated with the vacuum. • For a more details:• M. L. Perl and H. Mueller, “Exploring the possibility of detecting Dark Energy in a

terrestrial experiment using atom interferometry” arXiv 1001.4061v1 (2010).• M. L. Perl,” The Possible Detection of Dark Energy on Earth Using Atom

Interferometry”, arXiv 1007.1622v1 (2010).• R. J. Adler, H. Mueller and M. L. Perl, “A terrestrial search for dark contents of the

vacuum, such as Dark Energy, using atom interferometry”, arXiv1101.5626v1 (2011). To be submitted to Physical Review D.; To be published in International Journal of Modern Physics A.

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Present Observations

based telescopes is continuing with more precise measurement using existing and revised instruments and will substantially improve with instruments now under construction.

• Can it only be studied indirectly through observation of the structure and motions of galaxies?

• Dark Energy has been a dominant question in both cosmology and fundamental physics for the past decade.

• The study of Dark Energy using earth and space

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• The average observed Dark Energy density, assuming uniform distribution in the universe, is rDE = 6.3x10-10 J/m3.

• This is the same energy density possessed by a static electric field of 12 V/m, using rEF =e0E2/2.

• Such electric fields easily measured in the lab.

• DE may be small, but non-zero: an area for experiment!

a SQUID in a Undergrad Lab…

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• Unlike an electric field in the laboratory, we cannot turn Dark Energy on and off.

• We do not expect there is a zero Dark Energy field that could be used as an experimental reference.

• Even if the Dark Energy density should have a gradient, we do not know what force it exerts on a material object.

• Although it is easy to sense and measure tiny electromagnetic fields due to the relatively strong electromagnetic coupling.

• Obviously severe experimental problems in detecting Dark Energy or DCV density:

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Atom interferometry - 101 • For a typical atom interferometer. • Cesium atoms vertically drop from

rest in vacuum under the influence of the earth’s gravitational field Fg with the acceleration g=9.8 m/s2.

• In our experiment the drop is about 2 meters. As the Cs atom falls it is excited by laser beams that move the atomic state between the ground state S1/2 and a low lying excited state P3/2.

• The wavelength of this transition is λ=852 nm.

• The S1/2 state has two hyperfine levels, F= 3,4, and the laser beams put an atom in either of these states.

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Atom interferometry - 2• At times 0, T and 2T photon pulses are

applied to the atoms changing state (F=3 or 4) and momentum.

• An atom is placed into superposition of two momentum eigenstates,– by interaction with the photons of counter-

propagating laser beams.• The first component of the matter wave

receives zero momentum transfer while the second is given a downward momentum kick of Dp.

• Both matter wave packets fall freely until time T, whereupon they are given an opposite kick of Dp.

• At 2T the first is given an upward kick of Dp and waves recombine into a modulated single wave packet.

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vacuum envelope

Cs atom source

falling bunch ofCs atoms

upward laserbeams

Cs atom statedetector

1.0 m

Simplified schematic of a singleinterferometer.

Atom interferometry - 3

• The phase f changes as atom falls through changing gravitational potential.

• Probability P of detecting the atom at one output of the interferometer is

Df = Df1 - Df2

Df1, Df2 are phases accumulated by matter waves on the two paths

• The probabilityP = (1 + cosDf) / 2

is measured by laser-driven fluorescence at the detector.

• Wave function of atom has phase factor exp(if)

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Principle of the Experiment• Use two identical, adjacent

interferometers, A and B, assume that Fg is the same everywhere and perpendicular to the earth’s surface. Then ΔφΑ= ΔφΒ and the difference in phase shift is

Δφ = ΔφΑ−ΔφΒ = 0.

• But suppose, there is an additional force on the atoms caused by dark energy, FDE in the vicinity of interferometer A but not in the vicinity of interferometer B.

• ThenΔφ = ΔDE

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Based upon two assumptions: • First, that dark energy possesses some

space inhomogeneity in density.– If the cosmological constant explanation of dark

energy is correct, this experiment will give a null signal.

• Second that it exerts a sufficiently strong non-gravitational force on matter.

• If we find such a noise signal, we can and must show it is not Instrumental noise.

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NATURE OF THE SOUGHT SIGNAL

• We do not record Δφ which will average to zero, we record the root mean square Δφ rms. We can then determine the dark energy equivalent acceleration, gDE.

• We expect to be able to detect the dark energy equivalent acceleration, gDE with a precision of 10-15 m/s2.

• Apparatus sampling rate is of the order of Hertz.

• Hence the dark energy signal is a noise signal.

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Experimental Configuration

To cancel systematic effects:• Incorporate the two

interferometers in one vacuum envelope,

– reduce problems from common mode noises such as vibrations.

– drop sources for simplicity. • Sources are staggered

vertically,– total phase change for each

atom is measured during the same velocity period.

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Beginning Summer 2010

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University of Liverpool, November 2011

Progress

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The next 12 Months

• Prototype Interferometer.– Put in one arm, including a source, a beam splitter

using Raman pulses, and a detector. – Take advantage of communications industry

revolution (i.e. low cost, high quality), and use commercial laser, fibre, optical components, etc…

• Beyond 2012– Refine design & Improve accuracy for

• Benchmark measurement of g @ 10-9

– Build double arm system – Explore Parameter space

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Improving Sensitivity• A crucial factor in the sensitivity of the

experiment depends upon having a large phase shift f where

f = constant (gT2)

• Here g is the acceleration of gravity and T is the time it takes for the atom cloud to fall from the source at the top to the detector at the bottom of the interferometer.

• In the apparatus under construction the fall height, h, is 1 m and f is about 107 radians.

• Since T2 is proportional to h, f is proportional to h. if h = 10 m would give 10 times the present f, in principle the higher the better.

• The Daresbury tower, is approx. 100 meters high, it would seem that the benefits of exploiting this structure are obvious.

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Summary

• An experimental direct-detection effort is underway.

• Using the principals of atom physics to investigate cosmological questions.

• Even if this experiment fails to detect a signal on the laboratory scale, it will, in and of itself, be an extremely important constraint on the nature of Dark Energy and more generally on the Dark Content of the Vacuum.

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CASCADE – SC cavity for HSP

• Searching for hidden sector photons with superconducting cavities brings the benefit of cavity quality factors ~109 – NC cavities only ~106

• Cryogenic temperatures improve S/N – near elimination of thermal noise

• Address theoretically interesting region of 1’s – 100’s meV

• ILC crab cavities pre-existing shielded cryostat

• Receiver under test

Expected limits:

Peter Williams et al

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• The leading order phase difference between the paths due to gravity is given by

Df = nkgT2drop

• where n is the number of photon momenta transferred to the atom in each beam splitter, k is the laser wave number, and g is the local gravitational acceleration in the laboratory. The sensitivity f of the interferometer depends quadratically on the drop time, Tdrop.

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Magnitude of dark energy density:

• Counting mass as energy via E=Mc2,the average density of all energy is the critical energy

• ρcrit=9 x10-10J/m3

• ρmass≈0.3 x ρcrit= 2.7 x10-10J/m3

• ρdark energy≈0.7 x ρcrit= 6.3 x10-10J/m3

• Use ρDE to denote ρdark energy

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• ρDE ≈ 6.3 x10-10J/m3 is a very small energy density but as shown in the next section we work with smaller electric field densities in the laboratory

• ρDE is taken to be at least approximately uniformly distributed in space