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The European Physical Journal Plus

Quantum enhancement of phase sensitivity for SU(1,1) interferometer via low-noise boost of phase sensing photons using non-Gaussianity

Dezheng Guo, Xin Wang, Junren Cheng, Wen-Jia Rao, Jun Xin

Published Mar 11, 2024• 0 citations
Publisher
DOI
10.1140/epjp/s13360-024-05034-0

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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.

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SU(1,1) interferometry via four-wave mixing in Rb

Travis Horrom, Brian E. Anderson, Prasoon Gupta +1 more

Quantum-enhanced precision measurements have emerged as one of the most useful applications of quantum optics. Exploiting quantum states of light and quantum processes, classical measurement limits can be surpassed, leading to improvements in areas including clocks, spectroscopy, magnetometry, and imaging. One measurement where straightforward quantum enhancements are possible is phase sensing with an interferometer. One can inject squeezed vacuum states into the dark port of the beamsplitter in a traditional interferometer to reduce the quantum noise and reach phase sensitivities beyond the shot noise limit. An alternate approach is to replace the beamsplitters of an interferometer with nonlinear parametric amplifiers, which produce nonclassical states of light that can be used to surpass classical performance. This so called SU(1,1) interferometer can theoretically approach sensitivities that scale as 1/n, the Heisenberg limit where n is the interior phase sensing photon number, compared to the shot noise limit of 1/ √ n for a traditional interferometer [1]. I will present our group’s experimental progress in testing a Mach-Zender SU(1,1) interferometer using four-wave mixers (4WMs) in hot Rb atoms as the parametric beamsplitters. The 4WM process generates entangled twin beams which serve as the two arms of the interferometer, and are then recombined in a second 4WM cell, resulting in a phase-sensitive output. We will extend the work done on this interferometer [2, 3] by performing a detailed analysis of the output signal to noise through homodyne measurements, and will attempt to observe the better-than-shot-noise scaling of the sensitivity. We will also consider the various difficulties of this optical interferometer such as the susceptibility to loss and imperfect mode-matching within the interferometer. Our group is also considering an analogous SU(1,1) interferometer in a cold atom system. Collisions in a spinor Bose-Einstein condensate of sodium atoms give rise to a 4WM process that produces spin states of the atoms which are entangled in atom number. These interactions can be controlled to set up an SU(1,1) atom interferometer, where the relevant measurements are now atomic population differences rather than photon intensities. These enhancements can lead to drastic improvements in atomic spin interferometry [3, 4].

•Jan 1, 2015•3 citations
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.
Encoding is an indispensable procedure in general phase measurement, and it is usually performed with a deterministic unitary transformation between the initial probe state and the final state. In order to improve the measurement precision, many studies focus on the optimization of the initial probe state. In this paper, we propose a scheme of subtracting one photon from the output state of an SU(1,1) interferometer. In addition to improving the output state, we find that this scheme can be used to optimize the encoding procedure. The performance of this type of optimization is only strong when the phase-sensitive negativity is induced in the Wigner function of the equivalent probe state. If a nearly perfect single-photon detector is used for the single-photon subtraction operation, the phase sensitivity within a narrow phase range can surpass $1/(\sqrt{\ensuremath{\nu}}N)$, where NNN is the mean number of photons inside the SU(1,1) interferometer, and $\ensuremath{\nu}$ is the number of copies of the Gaussian probe state.
Quantum-enhanced precision measurements have emerged as one of the most useful applications of quantum optics. Exploiting quantum states of light and quantum processes, classical measurement limits can be surpassed, leading to improvements in areas including clocks, spectroscopy, magnetometry, and imaging. One measurement where straightforward quantum enhancements are possible is phase sensing with an interferometer. One can inject squeezed vacuum states into the dark port of the beamsplitter in a traditional interferometer to reduce the quantum noise and reach phase sensitivities beyond the shot noise limit. An alternate approach is to replace the beamsplitters of an interferometer with nonlinear parametric amplifiers, which produce nonclassical states of light that can be used to surpass classical performance. This so called SU(1,1) interferometer can theoretically approach sensitivities that scale as 1/n, the Heisenberg limit where n is the interior phase sensing photon number, compared to the shot noise limit of 1/ √ n for a traditional interferometer [1]. I will present our group’s experimental progress in testing a Mach-Zender SU(1,1) interferometer using four-wave mixers (4WMs) in hot Rb atoms as the parametric beamsplitters. The 4WM process generates entangled twin beams which serve as the two arms of the interferometer, and are then recombined in a second 4WM cell, resulting in a phase-sensitive output. We will extend the work done on this interferometer [2, 3] by performing a detailed analysis of the output signal to noise through homodyne measurements, and will attempt to observe the better-than-shot-noise scaling of the sensitivity. We will also consider the various difficulties of this optical interferometer such as the susceptibility to loss and imperfect mode-matching within the interferometer. Our group is also considering an analogous SU(1,1) interferometer in a cold atom system. Collisions in a spinor Bose-Einstein condensate of sodium atoms give rise to a 4WM process that produces spin states of the atoms which are entangled in atom number. These interactions can be controlled to set up an SU(1,1) atom interferometer, where the relevant measurements are now atomic population differences rather than photon intensities. These enhancements can lead to drastic improvements in atomic spin interferometry [3, 4].