Efficient noiseless linear amplification for light fields with larger amplitudes

TL;DR

This paper proposes and compares new schemes for noiseless linear amplification of light fields, especially effective for medium to large amplitudes, using photon addition operations to improve amplification efficiency and noise performance.

Contribution

It introduces a scheme using successive photon addition $( ext{a}^ ext{dagger})^2$ for better amplification of larger amplitude coherent states, surpassing previous methods for medium and large light fields.

Findings

$( ext{a}^ ext{dagger})^2$ outperforms $ ext{a} ext{a}^ ext{dagger}$ for $| ext{alpha}| ext{gtrsim} 0.91$

Different amplification schemes exhibit optimal noiseless properties at specific amplitude ranges

$( ext{a}^ ext{dagger})^2$ can amplify superpositions of coherent states effectively.

Abstract

We suggest and investigate a scheme for non-deterministic noiseless linear amplification of coherent states using successive photon addition, $(\hat a^{\dagger})^2$, where $\hat a^\dagger$ is the photon creation operator. We compare it with a previous proposal using the photon addition-then-subtraction, $\hat a \hat a^\dagger$, 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 $(\hat a^{\dagger})^2$ operation serves as a more efficient amplifier compared to the $\hat a \hat a^\dagger$ operation in terms of equivalent input noise. Using $\hat a \hat a^\dagger$ and $(\hat a^{\dagger})^2$ as basic building blocks, we compare combinatorial amplifications of coherent states using $(\hat a \hat a^\dagger)^2$, $\hat a^{\dagger 4}$, $\hat a \hat a^\dagger\hat a^{\dagger 2}$, and $\hat a^{\dagger 2}\hat a \hat a^\dagger$, and show that $(\hat a \hat a^\dagger)^2$, $\hat a^{\dagger 2}\hat a \hat a^\dagger$, and $\hat a^{\dagger 4}$ 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 $(\hat a^{\dagger})^2$ 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.