Cascading amplifiers can create exponentially large coherence

A standard laser beam has photon degeneracy, or coherence, $\mathfrak{C}$, of at most $8\mu^2$, where $\mu$ is the number of photons in the laser itself. Even quantum-engineered lasers, if required to produce a beam with the standard statistical properties, have limited coherence, scaling as $\mu^4$. Moreover, such lasers (still unrealised) require very unconventional gain and output-coupling mechanisms. Here, we propose a different path to increasing $\mathfrak{C}$: cascaded linear amplifiers, with conventional couplings. By dropping the requirement on the beam's properties, this approach can, in theory, achieve $\mathfrak{C}$ scaling exponentially in $\mu$. Here $\mu$ is the total source excitation number, across all the amplifiers. Two amplifiers suffice to surpass the standard $\mu^2$ scaling.