Comparison of Laser Interferometry and Atom Interferometry for Gravitational Wave Observations in Space Peter L. Bender JILA, University of Colorado Boulder Boulder, CO Focus Meeting 14: The Gravitational Wave Symphony of Structure Formation International Astronomical Union General Assembly Honolulu, Hawaii: August 3–14, 2015

A 2013 paper by P. W. Graham, J. M. Hogan, M. A. Kasevich and S. Rajendran [Phys. Rev. Lett. 110, (2013)] proposed GW measurements using an atom interferometer at each end of a single baseline. a.The suggested approach makes use of extremely narrow single photon transitions, such as the 698 nm clock transition in 87 Sr. b.The main case discussed has a L=1,000 km baseline between spacecraft, N=300 large momentum transfer beamsplitter pulse sequences, 2T=100 s observation time, and a suggested GW sensitivity of 1 × √(Hz) c.The authors point out that many error sources such as laser frequency noise cancel out because they are essentially the same for both atom interferometers. d.However, there appear to be a large number of issues for discussion concerning the requirements for meeting the suggested GW sensitivity for the main case considered in the paper.

A space-time diagram of the proposed configuration for differential gravitational wave measurements between two atom interferometers. FIGURE 2 FROM PAPER BY GRAHAM ET AL.:

The required laser beam power appears to be a major constraint on the achievable sensitivity. An example given has a Rabi frequency of 1 kHz. However, even with 1 meter diameter transmitted laser beams, the transmitted laser beam power to achieve this Rabi frequency a distance L=1,000 km away is extremely high. Even for a 80 Hz Rabi frequency, the required laser power is about 30W. If a Rabi frequency of 80 Hz is assumed, an atom cloud temperature of about 0.04 pK is needed in order to allow 50% of the atoms to contribute to the signal. a.Achieving the survival of 1200 velocity state transitions by the two parts of the wave function that is required with N=300 LMT beam splitters is challenging, since the best success rate reported so far appears to be about 50% for less than 200 transitions

The main case discussed by Graham et al. apparently requires very large sun shields. a.After a N = 300 beamsplitter pulse sequence, the wave function velocity difference will be 600 times 6.7 mm/s, or 4 m/s. b.Before additional pulses are applied 50 seconds later, the atoms would travel 200 m. Small jitter in the offsets from the suggested values of the experimental parameters for a space mission would lead to the amplitudes of the two parts of the wave function in the two interferometers being significantly different. a.Thus it probably will be necessary to measure both the amplitude difference and the phase difference for the two parts of the wave function for each atom cloud separately.

If isotopes with nuclear moments are used, magnetic field shifts have to be corrected for. a.As an example, for 87 Sr, the optical frequency dependence for the m F = 1/2 to 1/2 hyperfine component is Hz/G. Thus even an 8x10 -8 G magnetic field would give a 1x frequency shift. b.From ACE spacecraft measurements, magnetic field fluctuations over roughly 10 s periods are ~ G. A paper that compares these requirements with those for laser interferometry was published in 2014: a.P. L. Bender, “Comparison of Atom Interferometry with Laser Interferometry for Gravitational Wave Observations in Space,” Phys. Rev. D, 89, (2014).

More recently, an additional paper was posted on arXiv by J. M. Hogan and M. A. Kasevich: “Atom Interferometric Gravitational Wave Detection using Heterodyne Laser Links,” arXiv: , 27 January In this paper, much longer baselines between the two spacecraft were discussed. The characteristics assumed for the more sensitive of the two mission designs discussed were as follows: a.Two spacecraft separated by a distance L=6 × 10 8 m. b.Separate master lasers M1 and M2 on the two spacecraft. c.Local oscillator lasers L1 and L2 on the two spacecraft, each phase locked to the master laser beam from the other spacecraft. d.The phase locking doesn’t require much received power so the separation distance L could be made quite large.

Schematic diagram of the proposed differential atom interferometer mission with a long baseline L and heterodyne laser links. FIGURE 1 FROM PAPER BY HOGAN AND KASEVICH:

The target sensitivity is a factor 10 higher than that of the LISA mission for frequencies above a few millihertz. This is the sensitivity that LISA would have if the telescopes for sending laser beams between spacecraft were 1 meter in diameter rather than 30 cm. a.Because of the large increase in L, the number of units of the photon recoil momentum transferred to the atom clouds for the beam splitter and mirror laser pulse sequences could be reduced from 300 to 12. b.This reduced the path lengths required for the atom clouds to 6 meters, which simplified the problem of shielding the paths from sunlight. c.The required path length is based on the total observation times of 150, 138, 118, and 106 seconds for different atom cloud pairs that were assumed. d.120 concurrently operating interferometers are assumed, or about one atom cloud launch per second.

A space-time diagram of the proposed LMT beam splitter with N=3. FIGURE 1 FROM PAPER BY GRAHAM ET AL.:

In addition to these requirements, it is assumed that the atom shot noise for each atom cloud would be reduced from 10 −3 rad to rad by increasing the number of atoms per cloud. a.This increase in measurement accuracy and the larger value of L appear to make the requirement on measuring the differential fluctuations in the magnetic field between the spacecraft more severe. b.It appears that determining the fringe amplitude and phase on each atom cloud will be necessary. This can be done using methods such as those demonstrated by Sugarbaker et al. (2013), but with some loss in efficiency. c.With the assumed parameters, each cloud will have roughly 5,000 off-resonance laser pulses act on it, so the pulse frequencies will need to be quite far off resonance. Thus, it is difficult to see how 120 interferometers can be operated concurrently over the same optical path.

Conclusion: The required apparatus for the proposed type of mission is extremely complex. a.If 87 Sr is used in the atom interferometers, it seems necessary to cool the atoms to a temperature of about 2 pK and launch the atom clouds with little jitter in the mean velocities. b.Including the capability to determine the fringe amplitutde and phase on each atom cloud, and reducing the atoms shot noise limit to rad/√Hz is likely to increase the number of atoms needed per cloud to more than c.Showing that these requirements can be met over the lifetime of the mission appears to be a major challenge. d.With the many requirements on the launching systems for the atom clouds, the cloud temperatures, the wavefront aberrations, the complete laser beam transmission system, the sun shields, etc., the overall spacecraft design would be much more difficult than for a laser interferometer mission that would give equal gravitational wave sensitivity.