Harnessing Brillouin Interaction in Rare-earth Aluminosilicate Glass Microwires for Optoelectromechanic Quantum Transduction Mrittunjoy Guha Majumdar1and C. M. Chandrashekar1 2 3y

2025-04-29 0 0 935.77KB 7 页 10玖币

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Harnessing Brillouin Interaction in Rare-earth Aluminosilicate Glass Microwires for

Optoelectromechanic Quantum Transduction

Mrittunjoy Guha Majumdar1, ∗and C. M. Chandrashekar1, 2, 3, †

1Quantum Optics & Quantum Information, Department of Instrumentation and Applied Physics,

Indian Institute of Science, Bengaluru 560012, India

2The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India

3Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India

Quantum transduction, the process of converting quantum signals from one form of energy to an-

other is a key step in harnessing diﬀerent physical platforms and the associated qubits for quantum

information processing. Optoelectromechanics has been one of the eﬀective approaches to undertake

transduction from optical-to-microwave signals, among others such as those using atomic ensembles,

collective magnetostatic spin excitations, piezoelectricity and electro-optomechanical resonator using

Silicon nitride membrane. One of the key areas of loss of photon conversion rate in optoelectrome-

chanical method using Silicon nitride nanomembranes has been those in the electro-optic conversion.

To address this, we propose the use of Brillouin interactions in a ﬁber mode that is allowed to be

passed through a ﬁber taper in rare-earth Aluminium glass microwires. It suggests that we can

eﬃciently convert a 195.57 THz optical signal to a 325.08 MHz microwave signal with the help of

Brillouin interactions, with a whispering stimulated Brillouin scattering mode yielding a conversion

eﬃciency of ∼45%.

I. INTRODUCTION

Integrated quantum information processing with lo-

calised quantum computing systems and distributed

quantum communication architecture requires the abil-

ity to transduce eﬃciently between the relevant plat-

forms [1–4]. Functionally, that often means a paramet-

ric conversion between distinct regimes in which the

systems are operating. For instance, if we utilise su-

perconducting qubits for quantum computing and un-

dertake quantum communication using light, we would

need optical-to-microwave quantum transduction capa-

bility [5,6]. Such transduction usually involves the faith-

ful transfer of quantum information encoded in a set of

bosonic operators ({ˆa†

j}) to another set of bosonic opera-

tors ({ˆ

b†

j}). This could be possible with distinct bosons,

such as photons and phonons, or the same kind of boson

but with dissimilarity in the values within atleast one

degree-of-freedom, such as electromagnetic ﬁeld modes

at non-identical frequencies [7–9].

When it comes to optical-to-microwave transduction,

the primary problem is the large diﬀerence between

the mode-frequencies that lead to oﬀ-resonant interac-

tions [1,10]. Intermediate systems, such as atomic en-

sembles [11–16] and magnons [17,18] that couple to both

modes - optical and microwave signals, can facilitate the

bridging of the energy-gap [19]. Optoelectromechanical

approaches can provide an eﬃcient interface for under-

taking quantum transduction, with optomechanics using

elements such as photoelasticity [20–23] and electrome-

chanics using an interfacing capacitive element [24–28].

∗Electronic address: mguhamajumdar@fas.harvard.edu

†Electronic address: chandracm@iisc.ac.in

Double-cavity optomechanical systems are the centre-

point of a standard method for realisation of optical-to-

microwave transduction. Such a system couples a mi-

crowave resonator mode C1with resonance frequency

ωC,1to the vibrational mode of a mechanical resonator

with frequency ωm, that is, simultaneously coupled to an

optical cavity mode C2with resonance frequency ωC,2.

The mediating phononic mode in the optoelectrome-

chanical realisation of quantum transduction is usually

generated in a Silicon nitride (SiN) nanomembrane. It

has been experimentally demonstrated by Andrews et

al. [29] wherein SiN nanomembrane is used as one of

the mirrors in a Fabry-Perot cavity while constituting

the capacitive coupling to a superconductor microwave

resonator. In the experiment, bidirectional transduction

was performed with 10% net eﬃciency, albeit with about

1700 noise quanta generated at cryogenic temperatures.

The eﬃciency of conversion was limited by microwave

resonator losses and imperfect mode-matching, although

the two main sources of noise were the thermal vibra-

tional noise and spurious mechanical modes in the mem-

brane. In another experiment, mechanically mediated

electro-optic conversion in an alternative feed- forward

framework was used to demonstrate microwave to opti-

cal conversion with 47% conversion eﬃciency [30].

For eﬃcient transduction, we must remove these spu-

rious mechanical modes, have low-loss optical transmis-

sion platform as well as large opto- and electromechani-

cal coupling rates. The use of photonic ﬁbers optimises

transmission of optical quantum signals, and thereby the

use of the same in any transduction framework can help

achieve high eﬃciency in the process. In this paper, we

propose the use of traveling-wave optomechanical inter-

actions known as Brillouin interactions using rare-earth

aluminosilicate glass microwires. A pressure or force den-

sity on the material results from electrostriction or radi-

ation pressure when optical modes of a waveguide inter-

arXiv:2210.01581v2 [quant-ph] 7 Jan 2023

fere with one another. In the event that there is conser-

vation of momentum and energy during the interaction,

this pressure then stimulates an acoustic wave. As a re-

sult of the acoustic ﬁeld’s stresses altering the medium’s

dielectric characteristics and perturbing its boundaries,

light is essentially scattered across distinct optical modes.

The new proposed scheme using rare-earth aluminosil-

icate glass microwires also oﬀers a conversion rate of

≈45%, far higher than any other scheme using silicon

based membrane as transduction medium.

II. PHYSICAL INTERACTIONS AT COUPLING

INTERFACES

Our scheme for undertaking optical-to-microwave

transduction involves two distinct physical interactions

at the coupling interfaces: opto-acoustic interactions us-

ing Brillouin scattering and dielectric-modulated mag-

netic response at the acousto-electric interface [31–33].

A. Opto-acoustic Interaction with Brillouin

Scattering

Certain underlying processes in optically isotropic

material substrates result in opto-acoustic interactions

[33]. The electromagnetic ﬁeld can produce mechanical

strains in the waveguide through electrostriction [34].

The converse, in the phenomenon of photoelasticity,

is observed when stresses cause localized variations in

the dielectric permittivity [21]. Waveguide boundaries

may physically shift as a result of radiation pressure

caused by the electromagnetic waves reﬂecting oﬀ of

the boundaries of the structure, which in turn drives

acoustic waves. A localised variation in the electro-

magnetic characteristics is caused by the mobility of

structural boundaries brought about by mechanical

vibrations. Stimulated Brillouin Scattering (SBS) is

the nonlinear phenomenon whereby an injected pump

wave is scattered by an acoustic vibration into the

Stoke and anti-Stoke wave components [31,35–37]. In

1972, Ippen et al. achieved low-threshold stimulated

Brillouin scattering with input powers as low as 1 W [38].

When we couple and guide a coherent laser beam

into an optical microwire, the light gives rise to as well

as experiences various kinds of elastic waves that have

similar frequencies. While light is sensitive only to

longitudinal and shear bulk acoustic waves in standard

optical ﬁbers, the light and the evanescent ﬁeld access

the outer-surface as well, in the case of a sub-wavelength

optical ﬁber, thereby causing the shaking of the wire

due to electrostriction which leads to surface acoustic

waves (SAWs) being generated. The eﬀective refractive

index along the microwire varies periodically due to

these ripples, leading to Bragg scattering of the light in

the backward direction as per phasematching condition.

The velocity of the bulk and surface acoustic waves

diﬀer signiﬁcantly, with the surface wave travelling at a

velocity of around 0.9 that of a shear wave and giving

rise to other optical sidebands. Beugnot et al. found

the surface acoustic wave mode to travel at a velocity

of 3400 m/s and a frequency of 6 GHz, having studied

the generation of SAWs in an 8 cm. long silica optical

microwire that was drawn from a single-mode ﬁber using

the heat-brush method [39].

Photon silica microwires, fabricated by tapering

optical ﬁbers, have been seen to support stimulated

Brillouin scattering [39]. It is found that rare-earth

materials like Lanthana and Ytterbia have a ﬁnite eﬀect

on the Brillouin characteristics of silica-based oxide glass

optical ﬁbers, with emergent attributes such as a wide

Brillouin spectral width, low acoustic velocity and a

negative photoelastic constant [40]. Brillouin processes

can alternatively be visualised as the formation and

destruction of quasi-particles, in this case photons and

phonons [41]. It is typically advantageous to diﬀerentiate

interactions based on whether there is an absorption

or emission of the phonon. A phonon is produced

when a high-frequency photon undergoes the Stokes

Brillouin transition and changes into a lower-frequency

Stokes photon [42,43]. This transition may happen

naturally or may be stimulated. Anti-Stokes transitions,

wherein a phonon is absorbed while a lower-frequency

photon is changed to a higher-frequency photon, are also

conceivable [44]. Brillouin processes can be triggered

by either an optical seed from an auxiliary optical ﬁeld

at the Stokes frequency or by thermal phonons in the

waveguide, which scatter the pump photons [45].

In almost every system of practical importance, it

is infeasible to compute Brillouin scattering from ﬁrst

principles, for example by considering Maxwell’s equa-

tions nonlinearly linked to the Christoﬀel equation. This

is caused by a division of scales. To start, the optical

and acoustic problems’ temporal scales often diﬀer by

ﬁve orders of magnitude. Second, interaction lengths

on the millimetre scale are necessary for integrated

waveguides that have nonpareil and superlative gain

coeﬃcients to give a noticeable overall response - the

system scale is four orders of magnitude larger than the

acoustic wave length. A coupled mode description is

especially appropriate to Brillouin problems due to this

scaling divergence [46]. We can express the acoustic and

optical ﬁelds as eigenmodes of the waveguide, which are

weighted by envelop functions - an(z, t) for each optical

mode and b(z, t) for the acoustic ﬁeld, thereby giving us

the states [47],

|ψ(x, y, z, t)i=X

an(z, t)|Ψn(x, y)ieiknz−iωnt+c.c,

|φ(x, y, z, t)i=b(z, t)|Φ(x, y)ieiqz−iΩnt+c.c, (1)

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HarnessingBrillouinInteractioninRare-earthAluminosilicateGlassMicrowiresforOptoelectromechanicQuantumTransductionMrittunjoyGuhaMajumdar1,andC.M.Chandrashekar1,2,3,y1QuantumOptics&QuantumInformation,DepartmentofInstrumentationandAppliedPhysics,IndianInstituteofScience,Bengaluru560012,India2TheInstit...

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Harnessing Brillouin Interaction in Rare-earth Aluminosilicate Glass Microwires for Optoelectromechanic Quantum Transduction Mrittunjoy Guha Majumdar1and C. M. Chandrashekar1 2 3y

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