Quantum functionalities via feedback amplification

Abstract

Feedback amplification is a key technique for synthesizing various important functionalities, especially in electronic circuits involving op-amps. This paper presents a quantum version of this methodology, where the general phase-preserving quantum amplifier and coherent (i.e., measurement-free) feedback are employed to construct systems that produce several useful functionalities; quantum versions of differentiator, integrator, self-oscillator, and active filters. The class of active filters includes the Butterworth filter, which can be used to enhance the capacity of an optical quantum communication channel, and the non-reciprocal amplifier, which enables back-action-free measurement of a superconducting qubit. A particularly detailed investigation is performed on the unstable active filter for realizing a broadband gravitational-wave detector; that is, the feedback amplification method is used to construct an active filter that compensates the phase delay of the signal and eventually recovers the sensitivity in the high frequency regime.

Broadband sensitivity improvement via coherent quantum feedback with PT symmetry

“…5, in magenta and purple curves; aside from quantum noise, we have only included ĉ-oscillator thermal noise. This significant potential for improvement motivates further studies into this direction [45,46]. Application to microwave axion detectors.-For an axion detector consisting of a stationary magnetic field B 0 and a single mode of a microwave resonator, the interaction Hamiltonian can be written as Vaxion = α axion (Ψ 1 â1 + Ψ 2 â2 ) where â1,2 are the mode quadratures, and Ψ 1,2 are two quadratures of the oscillations of the axion field A(t) = Ψ(t)e −iω 0 t + Ψ * (t)e iω 0 t with…”

Feasibility study of a coherent feedback squeezer

“…In this paper, we investigate a coherent feedback squeezer (CFS) [Fig. 1(a)], which is an alternative implementation based on a quantum coherent feedback (measurement-free) control [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. CFS consists of a high-gain DOPO and a negative coherent feedback loop with a beamsplitter whose reflectivity determines the strength of the squeezing operation as in MFS.…”

“…Thus, we need to carefully consider the feasibility of whether the feedback loop causes oscillation or not. Quantum coherent feedback system have been eagerly investigated in terms of the application and the stability [19][20][21][22]24]. However, previous studies do not fully cover the stability analysis involving certain actual properties such as wavelength dispersion, phase-matching bandwidth, and periodic resonances of the feedback loop.…”

“…Recently, Shimazu and Yamamoto reported useful applications of negative coherent feedback systems including quantum versions of the differentiator, integrator, self-oscillator, and active filters [22]. Negative coherent feedback makes a system robust and broadband as an electrical circuit using well-known op-amps [19].…”

Direct approach to realising quantum filters for high-precision measurements

“…Illustrative example: an unstable filter -To demonstrate the power of this approach, we will go beyond passive optical cavities by considering a non-trivial active filter for beating the universal gain-bandwidth product limit in resonant detection schemes [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55], specifically, the so-called unstable filter [47] which has a broadband anomalous dispersion. The filter is unusual because it seemingly violates the Kramers-Kronig relations which imply that a stable anomalous-dispersion filter without absorption violates causality, however since this system is dynamically unstable this restriction does not apply [56][57][58][59].…”