Microwaveoptical double resonance in a erbium-doped whispering-gallery-mode resonator Li Ma Luke S. Trainor Gavin G. G. King Harald G. L. Schwefel and Jevon J. Longdell

2025-05-02 0 0 4.96MB 8 页 10玖币

侵权投诉

Microwave–optical double resonance in a erbium-doped whispering-gallery-mode

resonator

Li Ma, Luke S. Trainor, Gavin G. G. King, Harald G. L. Schwefel, and Jevon J. Longdell∗

Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and

Department of Physics, University of Otago, Dunedin, New Zealand

(Dated: Wednesday 26th October, 2022; 00:29)

We showcase an erbium-doped whispering-gallery-mode resonator with optical modes that display

intrinsic quality factors better than 108(linewidths less than 2 MHz), and coupling strengths to

collective erbium transitions of up to 2π×1.2 GHz – enough to reach the ensemble strong coupling

regime. Our optical cavity sits inside a microwave resonator, allowing us to probe the spin transition

which is tuned by an external magnetic ﬁeld. We show a modiﬁed optically detected magnetic

resonance measurement that measures population transfer by a change in coupling strength rather

than absorption coeﬃcient. This modiﬁcation was enabled by the strong coupling to our modes, and

allows us to optically probe the spin transition detuned by more than the inhomogeneous linewidth.

We contrast this measurement with electron paramagnetic resonance to experimentally show that

our optical modes are conﬁned in a region of large microwave magnetic ﬁeld and we explore how

such a geometry could be used for coherent microwave–optical transduction.

I. INTRODUCTION

Rare earth ions in solids at low temperatures provide

a unique set of capabilities for coherently manipulating

information. The 4f−4ftransitions have very nar-

row homogeneous [1–3] and inhomogeneous [4,5] optical

linewidths, as well as long lived coherence times for both

nuclear [6] and electron spin transitions [7,8]. Large

optical absorption is possible, despite the weak optical

oscillator strengths, even to the point where negative re-

fractive index could be possible [9]. Furthermore, the use

of erbium dopants gives access to an optical transition at

1.5µm, in the center of the low-loss wavelength region

for optical ﬁbers.

The properties of rare earth ion dopants have enabled

a number of advances in quantum memories [6,10], and

classical signal processing [11,12]. A particular ad-

vantage of using dopants over free space atoms is in-

creased ﬂexibility when coupling the dopants to optical

resonators. The coupling of rare earth ion dopants to

nano-photonic resonators has enabled single site detec-

tion [13] as well as control and readout of single dopants

[14]. Meanwhile, the coupling of ensembles to macro-

scopic resonators has been investigated to improve quan-

tum memories [15], and microwave–optical transduction

[16–18].

Whispering gallery mode (WGM) resonators combine

extremely high quality (Q) factors and moderately small

mode volumes in a convenient monolithic form factor [19].

The guiding of light is provided by total internal reﬂec-

tion from the curved surface of the resonator’s rim. Thus

the resonators can operate over a wide range of wave-

lengths and can be made of any optical material that is

low loss and for which smooth surfaces can be prepared.

For example, recently Q-factors of 109have been demon-

strated [20] for yttrium orthosilicate (YSO) – a popular

∗jevon.longdell@otago.ac.nz

host for cryogenic rare earth ion dopants because of its

low density of spins.

The ﬂexibility in material choice for WGM resonators

has allowed numerous nonlinear optical processes like

second-harmonic generation [21–23], Kerr solitons [24,

25] and optical parametric oscillation [26] in wide fre-

quency ranges. The high Q-factors have enabled ef-

ﬁcient demonstrations of photon pair sources [27] and

allowed squeezing measurements of optical parametric

oscillation operated far above threshold [28]. Interfac-

ing a microwave ﬁeld with the resonators has allowed

for electro-optic demonstrations such as eﬃcient single-

sideband modulation [29] and electro-optic frequency

combs [30,31]. Coupling to ensemble spin states has

previously been achieved through the interaction with

magnon modes of yttrium iron garnet spheres [32].

Cryogenic rare earths in WGM resonators are rela-

tively unexplored, in spite of the promises of very Q-

factors for both the resonators and the ions. It has been

shown that being near to the surface in a WGM resonator

doesn’t adversely eﬀect the ions spectral properties [33].

Optical photons have much higher energies and cou-

ple to matter more strongly than radio-frequency or mi-

crowave photons. This makes optically detected mag-

netic resonance (ODMR) a powerful technique for prob-

ing solid state spins. ODMR works by looking at spin-

state dependent changes in the amount of optical absorp-

tion or ﬂuorescence level, as either property depends on

the population balance [34,35]. ODMR is a more sen-

sitive technique than EPR, not only due to the higher

energy probe photons, but also because thermal noise is

much lower at optical frequencies. The optical detection

signiﬁcantly improves the sensitivity of magnetic reso-

nance spectroscopy and increases the ﬁdelity and spatial

resolution of spin initialization and readout [36–38].

In our resonator we perform ODMR by monitoring

changes in the materials dispersion rather than absorp-

tion. This dispersive measurement is allowed by strong

coupling between an optical resonator mode and an en-

arXiv:2210.13793v1 [quant-ph] 25 Oct 2022

semble mode of the rare-earth ions. Through the change

of a polariton’s frequency we measure the change in cou-

pling due to exciting more ions into the upper spin state.

Large coupling strengths mean we can make this mea-

surement when detuned by more than the inhomogeneous

linewidth of the bare ions. Thereby the amplitude of en-

semble excitation by the optical frequency is reduced.

This work was motivated by the challenge of transfer-

ring quantum states from microwave to optical frequen-

cies [39,40]. Superconducting qubits operate at frequen-

cies of about 10 GHz and hence must operate at temper-

atures of tens of millikelvins in order to not be swamped

by thermal photons. Interconnecting qubits in diﬀerent

cryostats is therefore diﬃcult as a direct link would need

to operate at a similar temperature [41]. The suggested

alternative is coherently transducing the microwave pho-

tons to optical frequencies where they can propagate

through room temperature links with minimal thermal

background. By controlling the spin-state energy split-

ting with an external magnetic ﬁeld, we can engineer a

three-level system with appropriate energy levels for the

transduction. This modiﬁed ODMR helps us with system

characterisation as the optical probe naturally measures

only those ions within the optical mode volume.

II. EXPERIMENTAL SETUP

Our WGM resonator is made from YSO doped with

isotopically enriched erbium-170 at 50 ppm. The res-

onator is a disk of major radius R= 2.1 mm and thick-

ness of 0.5 mm, with its curved sidewall surface ﬁnely

polished by diamond slurry [42]. The crystal D2axis is

normal to the disk plane. It is well known that YSO

has yttrium ions sitting in two diﬀerent crystallographic

sites each with two diﬀerent orientations [43]. Here we

address the erbium ions at site 1 with the optical transi-

tion around ν0= 195 116.7 GHz.

The optical pump couples into the WGM resonator

by a right-isosceles gadolinium gallium garnet prism via

evanescent coupling. The crystal’s baxis points from the

disk center to the coupling prism. The prism is moved

by a linear piezo stage to accurately tune the extrinsic

optical coupling rate in situ. Such a prism conveniently

allows for coupling with a straight-through geometry in

the cryostat. We label WGMs with their electric ﬁeld

parallel to the D2axis as the transverse electric (TE)

polarization; those polarized in plane are transverse mag-

netic (TM). TM modes have lower coupling contrast than

TE modes due to their diﬀerent local refractive indices

at the coupling point.

The WGM resonator sits inside a microwave

resonator—see Fig. 1(a)—which uses two metal rings,

above and below the optical WGM resonator, to conﬁne

the microwave mode near the optical mode volume. The

resonator is based on previous designs [44]; one modiﬁ-

cation here is that to allow a greater tuning range, the

whole ﬂoor of the resonator was movable rather than just

(a) Microwave and optical apparatus

Optical Pump

& Signal

Microwave In

Er:YSO WGM

& Prism

(b) Energy-level diagram

1536 nm

4I15/2

4I13/2

νμ

𝐷2

𝐷1𝑏

Crystal-field levels Zeeman splittingCrystal Orientation

FIG. 1. (a) A schematic of the ODMR apparatus. The mi-

crowave resonator (orange) is a shielded copper cavity with

the top and bottom rings that clamp onto the WGM res-

onator. Two coaxial pins (gold) are used for coupling mi-

crowave in and out the cavity. The WGM resonator (light

blue disc) is placed between the copper rings, with a prism

(dark blue) that couples the optical pump (red) to the WGM

resonator via evanescent coupling. (b) Energy-level diagram

of the erbium ions. With an external magnetic ﬁeld, the crys-

tal levels of 4I13/2and 4I15/2have Zeeman split. νµshows

the microwave transition that interacts with our microwave

resonator; also shown are the four optical transitions that in-

teract with the optical resonator in ascending order of energy.

a tuning pin. Another modiﬁcation is that the top ring

has an asymmetric slot, designed to break the near two-

fold rotational symmetry of the microwave magnetic ﬁeld

and relax the phase matching requirements for future up-

conversion experiments. A layer of indium is used be-

tween the metal rings and WGM resonator to reduce the

gap between the two and better clamp the resonator.

The combined optical and microwave resonators were

mounted in a home-built cryostat. The base temperature

is 4 K, which can be temporarily reduced to 2.9 K by a

helium evaporation system. A 3D vector magnet applies

a tunable external magnetic ﬁeld along the D2axis. The

magnetic ﬁeld causes Zeeman splitting of the 4I13/2and

4I15/2transition which we examine here, see Fig. 1(b).

A tunable ﬁber laser around 1536 nm is focused by

lenses outside the cryostat onto the prism–resonator in-

terface for evanescent coupling, and the reﬂected light

is collected on a photodiode. An electro-optic phase

modulator (EOM) and second photodiode are used for

generation of a Pound–Drever–Hall (PDH) error signal.

The EOM also allows for accurate relative frequency cal-

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：

Microwave{opticaldoubleresonanceinaerbium-dopedwhispering-gallery-moderesonatorLiMa,LukeS.Trainor,GavinG.G.King,HaraldG.L.Schwefel,andJevonJ.LongdellDodd-WallsCentreforPhotonicandQuantumTechnologies,NewZealandandDepartmentofPhysics,UniversityofOtago,Dunedin,NewZealand(Dated:Wednesday26thOctober,202...

展开>> 收起<<

Microwaveoptical double resonance in a erbium-doped whispering-gallery-mode resonator Li Ma Luke S. Trainor Gavin G. G. King Harald G. L. Schwefel and Jevon J. Longdell.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！

Microwaveoptical double resonance in a erbium-doped whispering-gallery-mode resonator Li Ma Luke S. Trainor Gavin G. G. King Harald G. L. Schwefel and Jevon J. Longdell

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: