Efficient noiseless linear amplification for light fields with larger amplitudes

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 $(hat a hat a^dagger)^2$, $hat a^{dagger 4}$, $hat a hat a^daggerhat a^{dagger 2}$, 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.