Number operator-annihilation operator uncertainty as an alternative of the number-phase uncertainty relation

TL;DR

This paper proposes an alternative uncertainty relation based on number and annihilation operators, which depends on the expectation value of particle number and can be experimentally tested, offering a new perspective on quantum uncertainties.

Contribution

It introduces a new uncertainty relation between number and annihilation operators that depends on particle number expectation, avoiding phase operator issues.

Findings

Bound on uncertainties depends on particle number expectation

Number-phase intelligent states approximately saturate the relation

Proposes experimental setups for verification

Abstract

We consider a number operator-annihilation operator uncertainty as a well behaved alternative to the number-phase uncertainty relation, and examine its properties. We find a formulation in which the bound on the product of uncertainties depends on the expectation value of the particle number. Thus, while the bound is not a constant, it is a quantity that can easily be controlled in many systems. The uncertainty relation is approximately saturated by number-phase intelligent states. This allows us to define amplitude squeezing, connecting coherent states to Fock states, without a reference to a phase operator. We propose several setups for an experimental verification.