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, $\widehat{a}{\widehat{a}}^{†}$, where $\widehat{a}$ 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 $\mathrm{\mid }\alpha \mathrm{\mid }\gtrsim 0.91$, the $(\hat a^{\dagger})^2$operationservesasamoreefficientamplifiercomparedtothe$\hat a \hat a^\dagger$operationintermsofequivalentinputnoise\mathrm{.}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 ${\widehat{a}}^{†2}\widehat{a}{\widehat{a}}^{†}$, and show that $(\hat a \hat a^\dagger)^2$,$\hat a^{\dagger 2}\hat a \hat a^\dagger$,and$\hat a^{\dagger 4}$exhibitstrongestnoiselesspropertiesfor$|\alpha| \lesssim 0.51$,$0.51 \lesssim |\alpha| \lesssim 1.05 $,and$|\alpha|\gtrsim 1.05 $, respectively. We further show that the $({\widehat{a}}^{†}{)}^2$ 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.