SU(2) and SU(1,1) interferometers

Daniel Linnemann

Bernard Yurke, S. L. McCall, John R. Klauder

A Lie-group-theoretical approach to the analysis of interferometers is presented. Conventional interferometers such as the Mach-Zehnder and Fabry-Perot can be characterized by SU(2). We introduce a class of interferometers characterized by SU(1,1). These interferometers employ active elements such as four-wave mixers or degenerate-parametric amplifiers in their construction. Both the SU(2) and SU(1,1) interferometers can in principle achieve a phase sensitivity \ensuremath{\Delta}\ensuremath{\varphi} approaching 1/N, where N is the total number of quanta entering the interferometer, provided that the light entering the input ports is prepared in a suitable quantum state. SU(1,1) interferometers can achieve this sensitivity with fewer optical elements.

Claudio Parmeggiani

Jun Liu, Wenxiao Liu, Shitao Li +3 more

We investigate the sensitivity of the angular rotation measurement with the method of homodyne detection in SU(2) and SU(1,1) interferometers by employing orbital angular momentum (OAM). By combining a coherent beam with a vacuum beam in an SU(2) interferometer, we get the sensitivity of the angular rotation measurement as 12Nl. We can surpass the limit of the angular rotation measurement in an SU(1,1) interferometer by combining a coherent beam with a vacuum beam or a squeezed vacuum beam when the probe beam has OAM. Without injection, the sensitivity can reach 12Nl. In addition, by employing another construction of an SU(1,1) interferometer where the pump beam has OAM, with the same injection of an SU(1,1) interferometer, the sensitivity of the angular rotation measurement can be improved by a factor of 2, reaching 14Nl. The results confirm the potential of this technology for precision measurements in angular rotation measurements.

Wei Du, Jia Kong, Jun Fang Jia +6 more

The use of squeezing and entanglement allows advanced interferometers to detect signals that would otherwise be buried in quantum mechanical noise. High sensitivity instruments including magnetometers and gravitational wave detectors have shown enhanced signal-to-noise ratio (SNR) by injecting single-mode squeezed light into SU(2) interferometers, e.g. the Mach-Zehnder or Michelson topologies. The quantum enhancement in this approach is sensitive to losses, which break the fragile quantum correlations in the squeezed state. In contrast, SU(1,1) interferometers achieve quantum enhancement by noiseless amplification; they noiselessly increase the signal rather than reducing the quantum noise. Prior work on SU(1,1) interferometers has shown quantum-enhanced SNR11 and insensitivity to losses but to date has been limited to low powers and thus low SNR. Here we introduce a new interferometer topology, the SU(2)-in-SU(1,1) nested interferometer, that combines quantum enhancement, the high SNR possible with a SU(2) interferometer, and the loss tolerance of the SU(1,1) approach. We implement this interferometer using four-wave mixing in a hot atomic vapor and demonstrate 2:2(5) dB of quantum SNR enhancement, in a system with a phase variance nearly two orders of magnitude below that of any previous loss-tolerant enhancement scheme. The new interferometer enables new possibilities such as beyond-shot-noise sensing with wavelengths for which efficient detectors are not available.