Comparison of LISA and Atom Interferometry for Gravitational Wave Astronomy in Space Peter L. Bender JILA, University of Colorado and NIST 46 th RENCONTRES DE MORIOND Gravitational Waves and Experimental Gravity March 20 – 27, 2011, La Thuile, Valle d’Aosta, Italy

REFERENCES Atomic gravitational wave interferometric sensor Savas Dimopoulos, 1,* Peter W. Graham, 2,† Jason M. Hogan, 1,‡ Mark A. Kasevich, 1,§ and Surjeet Rajendran PHYSICAL REVIEW D 78, (2008) Comment on “Atomic gravitational wave interferometric sensor” Peter L. Bender PHYSICAL REVIEW D, accepted for publication An Atomic Gravitational Wave Interferometric Sensor in Low Earth Orbit (AGIS-LEO) Jason M. Hogan, David M. S. Johnson, Susannah Dickerson, et al. arXiv: v1, 14 Sep 2010

FIG. 11. The proposed setup for the AGIS-Sat. 3 experiment. Two satellites S1 and S2 house the lasers and atom sources. The atoms are brought a distance d ~ 30 m or 130 m from the satellites at the start of the interferometer sequence. The dashed lines represent the 100 m paths traveled by the atoms during the interferometer sequence. Continuous Laser Beam Pulsed Laser Beam

Parameters for Proposed AGIS- Satellite 2 GW Sensor S. Dimopoulos et al., Phys. Rev. D 78, (2008) Parameters:Satellite separation:L = 1 × 10 3 km Atom cloud path length:I L = 200 m Atom cloud temperature:θ = 100 pK Atom thermal velocity:V = 1 × m/s Separation of Raman pulses:T = 100 s Repetition rate:1/s Sensitivity, to 0.5 Hz:h = 2 × /√Hz Est. Parameters:Atom cloud radius:b = 5 mm Laser beam radius:a = 500 mm

Assumed AGIS-Sat. 2 Mission Design The mission characteristics given in Table III of Dimopoulos et al. (2008) are assumed, where they differ from those given in the text. Confocal laser beams are transmitted between the telescopes, as recommended in the AGIS-LEO paper. The beams have to be apodized to reduce Fresnel ripples. Successive stimulated Raman transitions based on many added  pulses are used to produce 400 photon momentum splittings. This approach is discussed by McGuirk, Snadden and Kasevich in PRL 85, 4498 (2000):

Overlooked Error Sources in the AGIS-Sat. 2 and 3 Proposals The laser beam from one end will be on continuously and serve as a phase reference. However, there will be some fluctuations in its wavefront aberrations over the 100 s intervals between the  /2, , and  /2 pulses from the other laser. These aberration fluctuations will have more effect on the laser phase seen by the near atom clouds than those for the far atom clouds because of the small atom cloud radius, the long laser path, and diffraction. The laser wavefront aberration fluctuations would have to be attenuated to a level of 2×10 -8 wavelengths in order to achieve the quoted gravitational wave sensitivity for the Sat. 2 proposal, and 10 times better for Sat. 3. Because of the 100 s time between pulses for the Sat. 2 and 3 proposals, the atom cloud temperature would have to be stable to less than 2 pK from cloud to cloud.

Specific Problems with the AGIS-Sat. 2 Proposal The authors say the paper gives “The details of our proposal for an atomic gravitational wave interferometric sensor (AGIS).” However, no sketch or description of what the satellites might look like has been given. There is no mention in the 2008 paper of needing mode-cleaner cavities after the lasers, even though large mode-cleaner cavities are included in discussions of ground-based laser gravitational wave detectors. A possible rough design for the mode-cleaner cavities is needed in order to permit consideration of the impact on the satellite design. A requirement on the temperature fluctuation between atom clouds is not given. It is stated that telescopes with about 1 meter diameter and 1 Watt of laser power would permit operation over 1,000 km baselines. However, such operation with 200 atom clouds in the interferometer at the same time, as specified, does not seem possible.

COMPLEXITY Even without much tighter requirements on wavefront aberration noise mitigation and cloud temperature fluctuations: The proposed AGIS-Sat. 2 mission is far more complex than LISA! The statement that, compared with LISA, the proposed AGIS missions would be able to reach the suggested sensitivities “with reduced engineering requirements” is not supported by anything in the published paper. With the much tighter requirements: It seems unlikely that the suggested sensitivity could be achieved in an affordable mission.

Parameters for Proposed AGIS-LEO GW Sensor J. Hogan et al., arXiv: v1, 14 Sept Parameters:Satellite separation:L = 30 km Atom cloud path length:I L = 15 m Separation of Raman pulses:T = 4 s Repetition rate:20/s Satellite altitude:1000 km Sensitivity, 0.07 to 10 Hz:h = 3 × /√Hz Est. Parameters:Atom cloud radius:b = 5 mm Laser beam radius:a = 150 mm

Issues Concerning the AGIS-LEO Proposal The laser wavefront aberration fluctuations would have to be attenuated to a level of 2×10 -8 wavelengths in order to achieve the quoted gravitational wave sensitivity. None of the gravitational wave sources shown in the sensitivity figure for AGIS-LEO have a reasonable probability of being observable during a mission lifetime. Operation at 1000 km altitude in Earth orbit appears to complicate the mission operations seriously. At 1000 km altitude, it does not appear possible to obtain any new information about time-variations in the Earth’s mass distribution. Possible operation only when in Earth shadow is suggested to avoid the need for large sunshields over the atom interferometers, but would substantially interfere with the scientific objectives.

Does the AGIS-LEO Proposal Discussion of Wavefront Aberration Noise Mitigation Help the AGIS-Sat. 2 Proposal? The need for “A high-finesse mode-scrubbing optical cavity” after the laser to reduce the laser wavefront aberration noise is recognized. However, no estimate of the amplitude of this noise is given, and the required performance level of the mode-cleaner cavities is not discussed. Use of an “extra propagation segment” to reduce wavefront aberration noise does not seem practical. Effects due to atom spatial distribution variations and atom velocity variations also are discussed. They are much less for AGIS-LEO than for AGIS-Sat. 2 because the pulse separation time T is 4 s rather than 100 s. But the suggested use of spatially resolved detection of the atoms in the cloud does not appear to help.

Summary The following two issues need to be addressed: – The wavefront aberration noise level from lasers with adequate output power levels – The design and performance level of mode-cleaner cavities that can handle the required laser power levels. A modified version of the AGIS-Sat. 2 proposal with a reduced time T between pulses seems more realistic to pursue. However, it still would be much more complex than LISA. Studies of an AGIS-LEO mission appear to be considerably less attractive than studies of a modified AGIS-Sat. 2 mission. This is partly because the design problems for operation in Earth orbit are more severe, and partly because the science justification given so far appear to be very weak.