Efficient noiseless linear amplification for light fields with larger amplitudes

Abstract

We suggest and investigate a scheme for non-deterministic noiseless linear amplification of coherent states using successive photon addition, $({\hat{a}}^{†}{)}^2$, where ${\hat{a}}^{†}$ is the photon creation operator. We compare it with a previous proposal using the photon addition-then-subtraction, $\hat{a}{\hat{a}}^{†}$, where $\hat{a}$ is the photon annihilation operator, that works as an appropriate amplifier only for weak light fields. We show that when the amplitude of a coherent state is $|\alpha |\gtrsim 0.91$, the $({\hat{a}}^{†}{)}^2$ operation serves as a more efficient amplifier compared to the $\hat{a}{\hat{a}}^{†}$ operation in terms of equivalent input noise. Using $\hat{a}{\hat{a}}^{†}$ and $({\hat{a}}^{†}{)}^2$ as basic building blocks, we compare combinatorial amplifications of coherent states using $(\hat{a}{\hat{a}}^{†}{)}^2$, ${\hat{a}}^{†4}$, $\hat{a}{\hat{a}}^{†}{\hat{a}}^{†2}$, and ${\hat{a}}^{†2}\hat{a}{\hat{a}}^{†}$, and show that $(\hat{a}{\hat{a}}^{†}{)}^2$, ${\hat{a}}^{†2}\hat{a}{\hat{a}}^{†}$, and ${\hat{a}}^{†4}$ exhibit strongest noiseless properties for $|\alpha |\lesssim 0.51$, $0.51\lesssim |\alpha |\lesssim 1.05$, and $|\alpha |\gtrsim 1.05$, respectively. We further show that the $({\hat{a}}^{†}{)}^2$ operation can be used for amplifying superpositions of the coherent states. In contrast to previous studies, our work provides efficient schemes to implement a noiseless amplifier for light fields with medium and large amplitudes.

16 pages, 5 figures, to be published in Optics Express