# Quantum-limited directional amplifiers with optomechanics

## TL;DR

This paper proposes optomechanical microwave directional amplifiers that operate at quantum limits, with potential for integrated, noise-suppressed, nonreciprocal signal processing.

## Contribution

It introduces a novel electromechanical setup for phase-preserving and phase-sensitive directional amplification reaching quantum noise limits.

## Key findings

- Both amplifiers reach quantum limits on added noise.
- The phase-sensitive amplifier has an unlimited gain-bandwidth product.
- Strategies for suppressing mechanical noise are discussed.

## Abstract

Directional amplifiers are an important resource in quantum information processing, as they protect sensitive quantum systems from excess noise. Here, we propose an implementation of phase-preserving and phase-sensitive directional amplifiers for microwave signals in an electromechanical setup comprising two microwave cavities and two mechanical resonators. We show that both can reach their respective quantum limits on added noise. In the reverse direction, they emit thermal noise stemming from the mechanical resonators and we discuss how this noise can be suppressed, a crucial aspect for technological applications. The isolation bandwidth in both is of the order of the mechanical linewidth divided by the amplitude gain. We derive the bandwidth and gain-bandwidth product for both and find that the phase-sensitive amplifier has an unlimited gain-bandwidth product. Our study represents an important step toward flexible, on-chip integrated nonreciprocal amplifiers of microwave signals.