  We present experimental and theoretical results on a new interferometer
topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson
interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder
interferometer with parametric amplifiers in place of beam splitters. This
SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves high
signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit
(SQL) and tolerance to photon losses external to the interferometer, e.g., in
detectors. We implement a SISNI using parametric amplification by four-wave
mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We
observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels
(and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant
interferometers. We find experimentally the optimal FWM gains and find
agreement with a minimal quantum noise model for the FWM process. The results
suggest ways to boost the in-practice sensitivity of high-power
interferometers, e.g., gravitational wave interferometers, and may enable
high-sensitivity, quantum-enhanced interferometry at wavelengths for which
efficient detectors are not available.
