The Heisenberg limit for laser coherence

TL;DR

This paper establishes a new quantum limit for laser coherence, showing it can scale up to the Heisenberg limit of order μ^4, surpassing the previous standard quantum limit of μ^2, with potential realization in circuit QED.

Contribution

The authors derive an upper bound on laser coherence scaling and demonstrate a model achieving this limit, revealing the ultimate quantum limit for laser coherence.

Findings

Derived an upper bound of O(μ^4) for laser coherence.

Constructed a model reaching the Heisenberg limit.

Proposed potential implementation using circuit QED.

Abstract

To quantify quantum optical coherence requires both the particle- and wave-natures of light. For an ideal laser beam [1,2,3], it can be thought of roughly as the number of photons emitted consecutively into the beam with the same phase. This number, $\mathfrak{C}$, can be much larger than $\mu$, the number of photons in the laser itself. The limit on $\mathfrak{C}$ for an ideal laser was thought to be of order $\mu^2$ [4,5]. Here, assuming nothing about the laser operation, only that it produces a beam with certain properties close to those of an ideal laser beam, and that it does not have external sources of coherence, we derive an upper bound: $\mathfrak{C} = O(\mu^4)$. Moreover, using the matrix product states (MPSs) method [6,7,8,9], we find a model that achieves this scaling, and show that it could in principle be realised using circuit quantum electrodynamics (QED) [10]. Thus $\mathfrak{C} = O(\mu^2)$ is only a standard quantum limit (SQL); the ultimate quantum limit, or Heisenberg limit, is quadratically better.