Quantum-limited detection of arrival time and carrier frequency of time-dependent signals

TL;DR

This paper establishes fundamental quantum limits for joint measurement of light pulse arrival time and frequency, and demonstrates an optimal detection scheme approaching these limits using a quantum pulse gate.

Contribution

It derives and experimentally verifies quantum uncertainty bounds for joint time-frequency measurements and introduces an optimal detection scheme that saturates these limits.

Findings

Quantum uncertainty bounds for joint time-frequency measurements are derived and verified.

Detection restricted to finite windows is described by a quantum rotor, invalidating the Heisenberg relation.

The proposed scheme approaches the ultimate quantum limit in experiments.

Abstract

Precise measurements of both the arrival time and carrier frequency of light pulses are essential for time-frequency-encoded quantum technologies. Quantum mechanics, however, imposes fundamental limits on the simultaneous determination of these quantities. In this work, we derive and experimentally verify the quantum uncertainty bounds governing joint time-frequency measurements. We show that when detection is restricted to finite time windows, the problem is naturally described by a quantum rotor, rendering the commonly used Heisenberg uncertainty relation inapplicable. We further propose an optimal detection scheme that saturates these fundamental limits. By sampling the Q-function, we demonstrate the reconstruction of the Wigner function beyond the harmonic oscillator. Using an experimental implementation based on a quantum pulse gate, we confirm that the proposed scheme approaches the ultimate quantum limit for simultaneous time-frequency measurements. These results provide a new framework for joint time-frequency detection with direct implications for precision measurements and quantum information processing.