LISA optimal sensitivity

The multiple Doppler readouts available on the Laser Interferometer Space Antenna (LISA) permit simultaneous formation of several interferometric observables. All these observables are independent of laser frequency fluctuations and have different couplings to gravitational waves and to the various LISA instrumental noises. Within the functional space of interferometric combinations LISA will be able to synthesize, we have identified a triplet of interferometric combinations that show optimally combined sensitivity. As an application of the method, we computed the sensitivity improvement for sinusoidal sources in the nominal, equal-arm LISA configuration. In the part of the Fourier band where the period of the wave is longer than the typical light travel-time across LISA, the sensitivity gain over a single Michelson interferometer is equal to root2. In the mid-band region, where the LISA Michelson combination has its best sensitivity, the improvement over the Michelson sensitivity is slightly better than root2, and the frequency band of best sensitivity is broadened. For frequencies greater than the reciprocal of the light travel-time, the sensitivity improvement is oscillatory and similar toroot3>, but can be greater than root3 near frequencies that are integer multiples of the inverse of the one-way light travel-time in the LISA arm.