Quantum-enhanced metrology with the single-mode coherent states of an optical cavity inside a quantum feedback loop

Abstract

© 2016 American Physical Society. This is an author produced version of a paper published in Physical Review A. Uploaded in accordance with the publisher's self-archiving policy.eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.Quantum-enhanced metrology with the single-mode coherent states of an optical cavity inside a quantum feedback loop In this paper, we use the non-linear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until highly-entangled many-photon states become more readily available.

Quantum-enhanced Metrology without Entanglement based on Optical Cavities with Feedback

“…Combining these two observations, one can design novel quantum-enhanced metrology schemes which require neither entanglement nor a non-linear or interacting Hamiltonian. To illustrate this fact we now review a recent proposal by Clark et al [3] based on a single optical cavity inside a quantum feedback loop for which time is the resource which we want to constrain.…”

“…[3] consists of two main stages, a preparation and a measurement stage. These implement the following tasks: 1) Firstly, the preparation stage prepares the cavity field in a coherent state |α with α being of the form…”

“…However, the operator K 1 in Eq. (14) now needs to be replaced by R(ϕ)K 1 where R(ϕ) is a unitary operator [3], [8], [20]. In other words, all we have to do is to replace the Lindblad operator L by another operator L(ϕ),…”

“…Differing from Ref. [3], this paper does not pay as much attention to the concrete analysis of the proposed scheme. Instead, it focusses its attention on what we believe to be the main mechanisms underlying the observed enhancement.…”

“…In some situations, the length of the measurement process, t, and not the number of incoming photons, N , is the main resource which we want to constrain [3]. If we can write the time t in such cases as t = N ∆t with ∆t being the length of a short time interval, then the standard quantum limit still coincides with Eq.…”