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Kluwer Academic Publishers eBooks

Optimal Signal-to-Quantum Noise Ratio in Squeezed Displaced Number States

Yinqi Feng, A. I. Solomon

Published Dec 19, 2005• 1 citation
Publisher

Abstract

For an arbitary quantum state of radiation with frequency the optimum signal-to-quantum noise ratio for fixed energy (or power per unit frequency) h ω N 3 has the value 4 N 3 ( N 3 +1), attainable by the squeezed coherent vacuum. The question arises as to what ρ is attainable when the vacuum is imperfect, and there are n photons present. We show that in such a situation the attainable signal-to-quantum noise ratio ρ is reduced by a factor (2 n +1) 2 . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47097-7_15

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For an arbitary quantum state of radiation with frequency the optimum signal-to-quantum noise ratio for fixed energy (or power per unit frequency) h ω N 3 has the value 4 N 3 ( N 3 +1), attainable by the squeezed coherent vacuum. The question arises as to what ρ is attainable when the vacuum is imperfect, and there are n photons present. We show that in such a situation the attainable signal-to-quantum noise ratio ρ is reduced by a factor (2 n +1) 2 . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum noise in a model of a singly resonant frequency doubler including phase mismatch and a driving in the harmonic mode is analyzed. The squeezing spectra calculated inside the linear approximation are given. For squeezing in the fundamental mode, the optimum working point corresponds to turning points of dispersive bistability induced by cascading of the second order nonlinear response. In the case of the harmonic mode phase mismatch as well as a finite driving in the harmonic allows for surpass the 1/9 limit of the standard SHG scheme. The squeezing improvement when the driving is included is substantial for parameter values corresponding to reported experiments. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy that attains the quantum Fisher information, whereas the customarily used homodyne detection becomes useless in the limit of small displacements, due to the same effect that gives Rayleigh's curse in optical superresolution. There is a quantum advantage: a squeezed or a Fock state with N average photons allow to asymptotically estimate the parameter with a sqrt[N] better precision than classical states with same energy.
We experimentally demonstrate a new scheme for generating amplitude squeezed solitons in an asymmetric fiber Sagnac loop. We measure by direct detection a 5.7±0.1 dB (73%) and, with corrections for linear losses 6.2±0.1 dB (76%), reduction in the photon number fluctuations below the shot noise level. The same scheme is also shown to generate a significant classical noise reduction and is limited by Raman effects in fiber. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We present the optimal estimation of an unknown squeezing transformation of the radiation field. The optimal estimation is unbiased and is obtained by properly considering the degeneracy of the squeezing operator. For coherent input states, the root-mean square of the estimation scales as ${(2\sqrt{\overline{n}})}^{\ensuremath{-}1}$ versus the average photon number n‾\overline{n}n, while it can be improved to ${(2\overline{n})}^{\ensuremath{-}1}$ by using displaced squeezed states.