Design of a tabletop interferometer with quantum ampliﬁcation

2025-04-22 0 0 371.8KB 8 页 10玖币

侵权投诉

Jiri Smetana,1, ∗Artemiy Dmitriev,1, †Chunnong Zhao,2Haixing Miao,3, 4, ‡and Denis Martynov1, §

1Institute for Gravitational Wave Astronomy, School of Physics and

Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom

2OzGrav,University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

3State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, China

4Frontier Science Center for Quantum Information, Beijing, China

(Dated: October 11, 2022)

The sensitivity of laser interferometers is fundamentally limited by the quantum nature of light. Recent the-

oretical studies have opened a new avenue to enhance their quantum-limited sensitivity by using active parity-

time-symmetric and phase-insensitive quantum ampliﬁcation. These systems can enhance the signal response

without introducing excess noise in the ideal case. However, such active systems must be causal, stable, and

carefully tuned to be practical and applicable to precision measurements. In this paper, we show that phase-

insensitive ampliﬁcation in laser interferometers can be implemented in a tabletop experiment. The layout

consists of two coupled cavities and an active medium comprised of a silicon nitride membrane and an auxiliary

pump ﬁeld. Our design relies on existing membrane and cryogenic technology and can demonstrate three dis-

tinct features: (i) the self-stabilized dynamics of the optical system, (ii) quantum enhancement of its sensitivity

in the presence of the ampliﬁer, and (iii) optical control of the ampliﬁer gain. These features are needed to

enhance the sensitivity of future interferometric gravitational-wave and axion detectors.

I. INTRODUCTION

Improvements in the performance of gravitational-wave

(GW) detectors continue to stretch the known boundaries of

precision measurement. Ever since the ﬁrst discovery of grav-

itational waves [1], there has been a concerted eﬀort to en-

hance both the sensitivity and bandwidth of these detectors.

These allow us to capture a wider range of astrophysical phe-

nomena whose detection is only possible due to their GW

emission, such as merger events between black holes [1], neu-

tron stars [2], or both [3]. The current pinnacle of sensitivity is

achieved by the Advanced LIGO [4] and Advanced Virgo [5]

detectors and is limited over much of the spectrum by ﬂuctu-

ations brought about by the quantum nature of light [6]. Im-

provements beyond previous quantum-induced limitations in

interferometric systems have been implemented already, rang-

ing from changes to detector conﬁguration (such as the in-

troduction of signal recycling [7,8]) to implementing direct

quantum-noise suppression techniques (such as the squeezed

states of light [9–13]). However, there are reasons for fur-

ther enhancements in the sensitivity and bandwidth of GW

detectors. Continuous improvements in detector sensitivity

will provide us with deeper and better localization [14,15].

Existing performance improvements have led to a faster grow-

ing catalog of GW sources [16–18], which allows us to obtain

population statistics [19]. Further increases in detector band-

width can lead to the observation of high-frequency phenom-

ena, such as remnant collapse, aloowing us to probe neutron

star physics [20–22], and core collapse supernovae [23–25].

There is ample motivation for increasing the sensitivity and

bandwidth without sacriﬁcing either or, ideally, improving

∗gsmetana@star.sr.bham.ac.uk

†admitriev@star.sr.bham.ac.uk

‡haixing@tsinghua.edu.cn

§d.martynov@bham.ac.uk

both. The limits on these two properties are imposed by the

quantum ﬂuctuations of the light ﬁeld itself [26,27], com-

bined with the response of the detector’s optical cavities. It

is diﬃcult to achieve simultaneous improvements in both due

to the constraints imposed by the Mizuno limit [28], which

shows an inverse relationship between the peak sensitivity and

bandwidth of the optical system. One of the key insights into

this limit is the generation of positive dispersion by the op-

tical cavities present in the system. Several proposals have

been made for enhancing the detector performance beyond

the standard quantum-imposed constraint using an optome-

chanical ﬁlter cavity [29–35]. This system has been variously

analysed as a bandwidth-broadening device [30], a white light

cavity [35] and a phase-insensitive ﬁlter [36]. Proposals con-

sider the implementation of the ﬁlter as an auxiliary cavity

attached to existing detectors [30], or as a conversion of the

existing signal-recycling cavity [32]. A mathematically anal-

ogous system has also been proposed that consists of a purely

optical implementation [37]. Many of these proposals con-

sider an unstable system, requiring further active stabilization.

In recent studies [34–36], it has been argued that alternate con-

ﬁgurations of the ﬁlter cavity and the signal read-out scheme

can result in a stable system, which still retains sensitivity en-

hancement beyond the Mizuno limit.

We propose the tabletop layout that can verify the validity

of quantum ampliﬁcation models [32,35,37]. In a scaled-

down system analogous to the analysis in Ref. [35], which

was applied to a contemporary GW detector, we make use of a

coupled-cavity scheme that augments one cavity with a phase-

insensitive ampliﬁer. The ampliﬁer performs a transformation

of its input ﬁeld aaccording to the equation [38]

b=Ga +Kn,(1)

where bis its output mode, nis the ﬁlter noise, Gis the ampli-

ﬁer gain [39], and Kis the noise coupling coeﬃcient related

to Gaccording to the equation |K|2=|G|2−1 in order to make

the transformation unitary.

arXiv:2210.04566v1 [quant-ph] 10 Oct 2022

The eﬀect relies on the ratio between the optomechanical

coupling rate (between the ﬁlter cavity and the mechanical

resonator) and the optical coupling rate (between the two cav-

ities) being close to unity. Since the latter increases as the

main cavity length decreases [21], a straightforward down-

scaling of the kilometer-size design analyzed in [35] to a table-

top experiment is not possible. Such an experiment, however,

is essential for developing deeper understanding of the fun-

damental physics underlying the parity-time-symmetric quan-

tum ﬁltering before it can be applied to GW detectors. Other

technical challenges of the tabletop conﬁguration include ac-

counting for the thermal noise introduced by the mechanical

resonator, stabilizing the resonant frequency (locking) of the

coupled cavity system, and providing eﬀective mode match-

ing between the small beam waist size for the optomechanical

interaction and larger beam size required for the stability of a

meter-scale setup.

We show how the challenges listed above can be overcome

in a tabletop setup with an appropriate choice of parameters.

The proposed interferometer implements an optomechanical

interaction of the signal ﬁeld with a Si3N4membrane, which

can achieve high mechanical quality factors of up to 109[40]

at cryogenic temperatures (10 K). The main goals of the pro-

posed experiment are to (i) demonstrate the stability of the

optical system with the quantum ﬁlter, (ii) measure the prop-

agation of the signal and noise ﬁelds in the system (iii) prove

that phase-insensitive ﬁltering can improve the sensitivity of

quantum-limited interferometric detectors. We outline the

theory of quantum ampliﬁcation in optical interferometers in

Section II and ﬁnd the optomechanical parameters suitable for

tabletop demonstration in Section III. We discuss the quantum

performance of the setup in Section IV.

II. DYNAMICS OF THE PROPOSED SYSTEM

Our design consists of a coupled-cavity interferometer with

a resonant mode, ω0, as shown in Fig. 1. The optimised ex-

perimental parameters are listed in Table I. The signal ﬁeld

at frequencies ω0±ωsis produced inside the high-ﬁnesse

main cavity and is further ampliﬁed inside the ﬁlter cavity.

The ampliﬁcation is achieved by a membrane with a mechan-

ical mode at ωmand an auxiliary pump ﬁeld at frequency

ω0+ωp=ω0+ωm+ωOS, where ωOS is the frequency shift of

the mechanical oscillator due to an optical spring in the ﬁlter

cavity [35].

Our layout is similar to a contemporary GW detector with

the auxiliary signal recycling cavity tuned to broaden the an-

tenna response at the expense of the gain at DC: the carrier

ﬁeld at the frequency ω0is resonant in the arm cavity but

anti-resonant in the signal recycling cavity. Our main cav-

ity and ﬁlter cavity can be identiﬁed with the arm cavity and

signal recycling cavity of the canonical GW detector, respec-

tively. The distinguishing feature of our layout is the sili-

con nitride (Si3N4) membrane embedded in the ﬁlter cavity.

Among a vast diversity of optomechanical oscillators [41], we

choose the membrane because it can support relatively large

beam sizes (∼1 mm) and can exhibit high mechanical fre-

TABLE I. Experimental parameters.

Parameter Symbol Value

Main cavity length L04.1 m

Main cavity input coupler transmissivity T030 ppm

Main cavity loss 010 ppm

Filter cavity length Lf2 m

Filter cavity bandwidth γf/2π30 kHz

Filter cavity input coupler transmissivity Tf0.5 %

Filter cavity loss f2000 ppm

Membrane eigenmode ωm/2π300 kHz

Motional mass M 40 ng

Membrane thickness h 50 nm

Membrane transmissivity Tm0.8

Membrane temperature T10 K

Input pump power Pin 70 mW

Filter cavity power Pf3.4 W

Pump frequency oﬀset ωp/2π303 kHz

quencies (∼300 kHz) with a suﬃciently high intrinsic ten-

sion. These properties make the technology readily applicable

to the km-scale Advanced LIGO detectors without changing

the g-factors of their signal recycling cavities.

In [35], the mechanical resonator was coupled to the ﬁlter

cavity as a reﬂective component. However, the reﬂectivity of

silicon nitride membranes is typically low (≈0.2). This fact

makes their use as a reﬂective component in the ﬁlter cavity

impractical due to the high added optical loss. In this sec-

tion, we show how a pumped membrane dispersively coupled

to the coupled-cavity system (i.e. using the membrane-in-the-

middle technique [42]) leads to the phase-insensitive ampliﬁ-

cation of the signal ﬁeld. In the analysis, we consider standard

equations for ﬁeld propagation and interaction at an optical

component. The quantum ampliﬁcation occurs when an opti-

cal ﬁeld interacts with the membrane which is driven by the

radiation pressure force from the beat of the pump and signal

ﬁelds. The optical ﬁelds are deﬁned in Fig. 1.

Interference on the input test mass in the main cavity is

given by the equations

a1(t)=r0a2(t−τ/2) +t0χaf3(t−τf/2)

af(t)=−r0χaf3(t−τf/2) +t0a2(t−τ/2),(2)

where τand τfare the round-trip times in the main and ﬁlter

cavities, r0and t0are the ﬁeld reﬂectivity and transmissivity

of the input mirror of the main cavity, and χ=eiθ, where θis

the relative carrier phase delay across the ﬁlter cavity, tuned to

π/2 to achieve the signal recycling. We keep χas a parameter

in the following analysis to maintain generality and cover the

detuned signal recycling case in future studies.

Microscopic motion of the main cavity causes a small frac-

tion of the static ﬁeld, A, in the main cavity to convert to

a time-dependent ﬁeld near the end mirror according to the

equation

a2(t)=a1(t−τ/2) −2iA ω0

cx(t),(3)

where xis the displacement of the end mirror and cis the

speed of light. The ﬁeld returning to the membrane from the

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

DesignofatabletopinterferometerwithquantumamplicationJiriSmetana,1,ArtemiyDmitriev,1,yChunnongZhao,2HaixingMiao,3,4,zandDenisMartynov1,x1InstituteforGravitationalWaveAstronomy,SchoolofPhysicsandAstronomy,UniversityofBirmingham,BirminghamB152TT,UnitedKingdom2OzGrav,UniversityofWesternAustralia,35St...

展开>> 收起<<

Design of a tabletop interferometer with quantum ampliﬁcation.pdf

共8页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Design of a tabletop interferometer with quantum ampliﬁcation

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: