Quantum Double Lock-in Amplifier

TL;DR

This paper introduces a quantum double lock-in amplifier protocol that enables complete extraction of an unknown phase, amplitude, and frequency of a signal within noisy environments using quantum mixers and orthogonal pulse sequences.

Contribution

It presents a novel quantum double lock-in amplifier protocol utilizing two quantum mixers and orthogonal pulse sequences, extending classical lock-in techniques to quantum systems.

Findings

The protocol can extract full signal characteristics even with unknown initial phase.

Numerical simulations show robustness against pulse imperfections and stochastic noise.

Implementation demonstrated using a five-level double-Λ system with $^{87}$Rb atoms.

Abstract

Quantum lock-in amplifier aims to extract an alternating signal within strong noise background by using quantum strategy. However, as the target signal usually has an unknown initial phase, we can't obtain the complete information of its amplitude, frequency and phase in a single lock-in measurement. Here, to overcome this challenge, we give a general protocol for achieving a quantum double lock-in amplifier and illustrate its realization. In analog to a classical double lock-in amplifier, our protocol is accomplished via two quantum mixers under orthogonal pulse sequences. The two orthogonal pulse sequences act the roles of two orthogonal reference signals in a classical double lock-in amplifier. Combining the output signals, the complete characteristics of the target signal can be obtained. As an example, we illustrate the realization of our quantum double lock-in amplifier via a five-level double-$\Lambda$ coherent population trapping system with $^{87}$Rb atoms, in which each $\Lambda$ structure acts as a quantum mixer and the two applied dynamical decoupling sequences take the roles of two orthogonal reference signals. Our numerical calculations show that the quantum double lock-in amplifier is robust against experimental imperfections, such as finite pulse length and stochastic noise. Our study opens an avenue for extracting complete characteristics of an alternating signal within strong noise background, which is beneficial for developing practical quantum sensing technologies.