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Bulletin of the American Physical Society

Phase estimation in an SU(1,1) interferometer with displaced squeezed states

Sushovit Adhikari, Narayan Bhusal, Chenglong You, Hwang Lee, Jonathan P. Dowling

Published Mar 5, 2019• 0 citations
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Abstract

In this paper, we study the phase sensitivity of an SU(1,1) interferometer with coherent and displaced-squeezed-vacuum (DSV) states as inputs, and parity and on-off as detection strategies. Our scheme with parity is sub-shotnoise limited and approaches the Heisenberg limit with increasing squeezing strength of the optical parametric amplifier (OPA). Also, for the on-off detection scheme, we show that sub-shotnoise sensitivity is possible by increasing the squeezing strength of the OPA.

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In this paper, we study the phase sensitivity of an SU(1,1) interferometer with coherent and displaced-squeezed-vacuum (DSV) states as inputs, and parity and on-off as detection strategies. Our scheme with parity is sub-shotnoise limited and approaches the Heisenberg limit with increasing squeezing strength of the optical parametric amplifier (OPA). Also, for the on-off detection scheme, we show that sub-shotnoise sensitivity is possible by increasing the squeezing strength of the OPA.
We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of phase estimation approaches the Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cram\'er-Rao bound of the SU(1,1) interferometer.
We study the phase sensitivity of an SU(1,1) interferometer from two aspects, i.e., the phase estimation determined by the error propagation formula and that by the quantum Cramér-Rao bound (QCRB). The results show that the phase sensitivity by using the intensity detection reaches the sub-shot-noise limit with a coherent state and an m-photon-added squeezed vacuum state (m-PA-SVS) as inputs. The phase sensitivity gradually approaches the Heisenberg limit for increasing m, and the ultimate phase precision improves with the increase of m. In addition, the QCRB can be saturated by the intensity detection with inputting the m-PA-SVS.
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a coherent state in one input port and a squeezed-vacuum state in the other input port using the method of homodyne detection. In this interferometer, beam splitting and recombination are generated by the parametric amplifiers instead of the beam splitters. Compared with the traditional Mach–Zehnder interferometer, the phase sensitivity of this interferometer can be improved due to the amplification process of the parametric amplifiers. Combined with the squeezed state input, the sensitivity can be improved further due to the noise reduction. The phase sensitivity of our scheme can approach the Heisenberg limit and the associated optimal condition is analyzed. The scheme can be implemented with current experimental technology.
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a thermal state and a squeezed vacuum state as inputs and parity detection as the measurement. We find that the phase sensitivity can beat the shot-noise limit and approaches the Heisenberg limit, with increasing input photon number, in an ideal situation. We also consider the effect of various noises, including photon loss, dark counts, and thermal photon noise. Our results show that the phase sensitivity is below the shot-noise limit with photon loss and dark counts, but cannot beat the shot-noise limit in the presence of thermal noise.
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a thermal state and a squeezed vacuum state as inputs and parity detection as the measurement. We find that the phase sensitivity can beat the shot-noise limit and approaches the Heisenberg limit, with increasing input photon number, in an ideal situation. We also consider the e ect of various noises, including photon loss, dark counts, and thermal photon noise. Our results show that the phase sensitivity is below the shot-noise limit with photon loss and dark counts, but cannot beat the shot-noise limit in the presence of thermal noise.