Quantum limits on squeezing

TL;DR

This paper establishes fundamental quantum limits on the amount of steady-state squeezing achievable in bosonic mode networks, based solely on canonical commutation relations and stability, with implications for current experiments.

Contribution

It derives a universal lower bound on squeezing in dissipative schemes and reformulates inseparability criteria for three-mode systems.

Findings

Lower bound on steady-state squeezing approaches 1 in strong coupling.

Adding parametric drives modifies the quantum noise balance, approaching a bound of 1/2.

Two-mode bounds are experimentally approachable at room temperature.

Abstract

In our work, we show how, for a network of bosonic modes, canonical commutation relations constrain the coefficients relating input and internal modes. Based on these constraints, we derive a lower bound on the total steady-state squeezing achievable in reservoir-engineered (dissipative) squeezing schemes, quantified by the sum of mode-optimal quadrature variances normalized to its corresponding input variance. The bound follows solely from canonical commutation relations and stability, and is saturated in the strong-coupling limit at 1. Furthermore, we show that adding independent parametric driving terms for each mode changes the quantum noise-gain balance and yields a distinct optimum bound, approaching 1/2. In addition, we show how these constraints allow us to reformulate the Duan inseparability criterion for a three-mode bosonic system in terms of a single parameter-dependent figure of merit. Our results apply directly to current electromechanical and nanomechanical experiments and indicate that the two-mode bounds can be experimentally approached even at room temperature.