Probing macroscopic quantum states with a sub-Heisenberg accuracy

TL;DR

This paper introduces an optimal time-domain variational measurement protocol for probing macroscopic quantum states with sub-Heisenberg accuracy, enabling quantum tomography and entanglement verification in gravitational-wave detectors.

Contribution

It proposes a novel measurement scheme that surpasses Heisenberg limits for macroscopic quantum state characterization, applicable to gravitational-wave detection and gravity decoherence tests.

Findings

Achieves quantum state characterization below the Heisenberg Uncertainty.

Identifies readout loss as the main limitation in measurement accuracy.

Demonstrates potential for EPR entanglement verification in GW detectors.

Abstract

Significant achievements in the reduction of classical-noise floor will allow macroscopic systems to prepare nearly Heisenberg-Limited quantum states through a continuous measurement, i.e. conditioning. In order to probe the conditional quantum state and confirm quantum dynamics, we propose use of an optimal time-domain variational measurement, in which the homodyne detection phase varies in time. This protocol allows us to characterize the macroscopic quantum state below the Heisenberg Uncertainty -- i.e. Quantum Tomography -- and the only limitation comes from readout loss which enters in a similar manner as the frequency-domain variational scheme proposed by Kimble et al.. In the case of no readout loss, it is identical to the back-action-evading scheme invented by Vyatchanin et al. for detecting gravitational-wave (GW) signal with known arrival time. As a special example and to motivate Macroscopic Quantum Mechanics (MQM) experiments with future GW detectors, we mostly focus on the free-mass limit -- the characteristic measurement frequency is much higher than the oscillator frequency -- and further assume the classical noises are Markovian, which captures the main feature of a broadband GW detector. Besides, we consider verifications of Einstein-Podolsky-Rosen (EPR) type entanglements between macroscopic test masses in GW detectors, which enables to test one particular version of Gravity Decoherence conjectured by Diosi and Penrose.