Broadband sensitivity improvement via coherent quantum feedback with PT symmetry

Abstract

A conventional resonant detector is often subject to a trade-off between bandwidth and peak sensitivity that can be traced back to quantum Cramer-Rao Bound. Anomalous dispersion has been shown to improve it by signal amplification and is thus more robust against decoherence, while it leads to instabilities. We propose a stable quantum amplifier applicable to linear systems operating at the fundamental detection limits, enabled by two-mode non-degenerate parametric amplification. At threshold, one mode of the amplifier forms a PTsymmetric system of original detector mode. Sensitivity improvements are shown for laser-interferometric gravitational-wave detectors and microwave cavity axion detectors. Introduction.-Oscillators are often used to measure weak classical forces. In the early days of gravitational-wave (GW) detection, excitations of mechanical oscillators (resonant bars) were read out by inductive, capacitive [1] or parametric [2] transducers and via a superconducting quantum interference device (SQUID) amplifer [1-3]. A more sensitive technique is to read out the phase fluctuations in a light beam (Michelson and Fabry-Perot type interferometers) [4-6] using photodetection. Signal recycling [7] and Resonant Sideband Extraction (RSE) [8] techniques were designed optimize GW sensitivity by tailoring the optical frequency response. In this process, Mizuno noticed a trade off between bandwidth and peak sensitivity [9] -analogous to the gain-bandwidth product in electronic amplifiers [10]. Braginsky et al. [11,12] showed 1 , using the energy-phase uncertainty relation, that the power spectral density of equivalent spacetime strain noise is S h (Ω) ≥ 4 2 /S E (Ω) where S E is the spectral density of energy in the cavity, andThis integral embodies a bandwidth-sensitivity trade-off. This was also obtained by Tsang, et al. using Quantum Fisher Information [13], and further elaborated in Refs. [14][15][16][17]. For coherent states, ∆E 2 = ω 0 E, and in this case Eq. ( 1) is also referred to as the Energetic Quantum Limit (EQL) for GW detection 2 . The EQL trade-off applies to all quantum metrology experiments that use oscillators at coherent states.Detectors.-In this paper, we consider two types of detectors. GW detectors (of the laser interferometer type [6]) use optical resonators to increase the interaction between the spacetime

Designing optimal linear detectors -- a bottom-up approach

“…In this section we will consider the non-minimal realisation of the general first-order system, showing that the Heisenberg limit can be saturated with the addition of hidden internal modes that internally amplify the signal. We will first show that the minimal realization of a first-order system without squeezing is constrained by the Mizuno limit [33], and use the recent discovery that an infinite DC signal response can be achieved by adding a pair of modes that do not manifest in the input-output dynamics [20] and thus do not add any additional noise. We will show how this is the simplest case of a general class of such non-minimal realisations, and that a quantum-mechanics-free subspace is formed allowing for arbitrary modification of the system dynamics.…”

“…We now consider adding two auxiliary modes b and ĉ as shown in Fig. 2 and discussed in [20], without modifying the input-output dynamics. In Appendix.…”

“…The terms with coupling rates g b and g c are coupled to â via a beamsplitter, and the terms with coupling rates g b † and g c † via a non-linear crystal (or equivalently an optomechanical interaction with optomechanical coupling frequency g, as discussed in [12,20]). Each auxiliary mode has just one degree of freedom, and thus the transfer matrices are given by,…”

“…for low frequency signals). The later is motivated by the parity-time (PT) symmetric system explored in [20,21]. In both cases, we use the systematic realisation framework developed in [22] to realise the simplest single degree-of-freedom system with squeezing, which can be extended to arbitrarily many degrees-of-freedom using this framework.…”

Enhancing the sensitivity of interferometers with stable phase-insensitive quantum filters

“…In practice, whitelight cavities require the development of external stabilization controllers that were not found yet. The next step was made in [46,47], where a stable phase-insensitive amplification based on a PT-symmetric [48] optomechanical interaction has been proposed. In this Letter, we present causal and stable quantum amplifiers that increase the quantum-limited sensitivity without compromising bandwidth or stability of the interferometer.…”