Squeezed -Light -Enhanced Dispersive Gyroscope based Optical Microcavities XIAOYANG CHANG 1 WENXIU LI1 HAO ZHANG2 YANG ZHOU2 ANPING

2025-05-03 0 0 751.73KB 13 页 10玖币

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Squeezed-Light-Enhanced Dispersive

Gyroscope based Optical Microcavities

XIAOYANG CHANG,1 WENXIU LI1 , HAO ZHANG2*, YANG ZHOU2, ANPING

HUANG1,AND ZHISONG XIAO1,2,3

1 School of Physics, Beihang University, Beijing 100191, China

2 Research Institute of Frontier Science, Beihang University, Beijing 100191, China

3 Beijing Academy of Quantum Information Sciences, Beijing 100193, China

*Corresponding author: haozhang@buaa.edu.cn

Abstract: Optical gyroscope based on the Sagnac effect have excellent potential in the

application of high-sensitivity inertial rotation sensors. In this paper, we demonstrate that for

an optical resonance gyroscope with normal dispersion, the measurement sensitivity can be

increased by two orders of magnitude through coupling into a squeezed vacuum light, which

is different from that in the classical situation. When the system is operated under critical

anomalous dispersion condition, injecting a squeezed vacuum light allows the measurement

sensitivity beyond the corresponding standard quantum limit by five orders of magnitude,

with a minimum value of 3.8×10-5 Hz. This work offers a promising possibility for

developing optical gyroscopes that combine high sensitivity with tiny size.

Agreement

1. Introduction

Optical gyroscopes based on microcavity have remarkable advantages in weight, size, cost,

and power consumption and have become one of the focuses of inertial rotation sensors[1].

Physically, the optical gyroscope is based on the Sagnac effect[2]. That is to say, if two

beams are counter-propagating in an optical loop, a phase or frequency shift between the

clockwise (CW) and counterclockwise (CCW) beams is generated when the loop is rotating

around the axis, which is proportional to the angular rotation rate of the loop. The

accumulated phase or frequency shift in the loop, which comes from the Sagnac effect, is

proportional to the effective area of the optical cavity. Therefore, the Sagnac phase shift

accumulated in an optical microcavity gyro is seriously bounded, limiting its measurement

sensitivity due to the tiny effective area. In many applications such as vehicles, spacecraft,

and satellites, the size and weight of the gyro are strictly limited, but high sensitivity is

required simultaneously.

In order to make a microcavity optical gyro have high measurement sensitivity, various

coupled resonator optical waveguides (CROWs) were proposed, and the normal dispersion

effect in these structures is also discussed[3–8]. Subsequent studies have shown that even

with optimized parameters, the sensitivity of the CROW gyro is equal to that of a Ring laser

gyro under equal loop loss conditions. Physically, normal dispersion is a resultant feature of

the CROW structure and is not directly correlated with sensitivity enhancement. In addition,

the sensitivity of a resonator-based optical gyroscope can be enhanced by introducing

anomalous dispersion effect[9]. Typically, there are two experimental regimes for achieving

anomalous dispersion, utilizing the alkali metal vapors and optical coupled resonators[9–24].

However, the alkali metal vapors approach is unsuitable for reducing the weight and size of a

gyro because the experimental system is rather complex. Optical coupled microresonators can

achieve anomalous dispersion only by using passive elements, thus avoiding the complexities

of modulating the dispersion in alkali metal vapors.

Nevertheless, most of the previous research on dispersion enhancing the sensitivity of an

optical gyroscope is based on classical light. As a result, these devices are forcing an

inevitable quantum-mechanical limit on the sensitivity in detecting angular rotation rate[25].

David D. Smith et al. have shown that a cavity containing rubidium atomic gas dispersion

medium, the sensitivity to resonant frequency shift can be increased by two orders of

magnitude at critical anomalous dispersion point under ideal conditions (classical sources in

the cavity can be neglected, e.g., temperature and mechanical fluctuations) [26]. This increase

above corresponds to the standard quantum limit (SQL) dispersion enhancement of the

system due to the bound of the quantum-mechanical photon shot noise. Fortunately, the SQL

is a limit that can be reached when the measurement device uses classical light, but it is not

the limit that theoretical is allowed. Besides, the SQL can be exceeded by using non-classical

light[27], such as the Fock states[28], the NOON states[29], and the squeezed states of light.

In particular, squeezed vacuum light has a particular advantage in exceeding the SQL due to

its intrinsic nature of the noise distribution on the two quadrature components[30–32].

In this paper, we present a scheme that a squeezed vacuum light coupling into a three-

dimensional vertically coupled resonator system (3D-VCRS) with dispersion to improve the

measurement sensitivity on angular rotation rate. The rest of this article is organized as

follows. In Section 2, we calculated the dispersion condition and derived the expression of

scale factor enhancement and the uncertainty of frequency measurement of the system. In

Section 3, we discussed the sensitivity enhancement factor and the measurement sensitivity of

the system operating under different situations. In Section 4, we conclude with a summary.

2. Theoretical mode and analysis

A schematic view of squeezed vacuum light coupling with the 3D-VCRS is shown in Fig. 1.

The system consists of two ring resonators, Ring 1 and 2, and an input waveguide. A coherent

light

ˆc

passes through a 50/50 beam splitter (BS) and launches into the input waveguide at

the bottom of the system, then couples to the stacked vertically coupled ring resonators. A

squeezed vacuum light (quadrature phase squeezed light)

ˆin

is reflected by the BS and

coupled into the 3D-VCRS together with the coherent light

ˆc

as input light

ˆin

. A blocker is

placed between the squeezed light source and the BS, and the blocker is opened or closed,

corresponding to

ˆin

is squeezed vacuum light or vacuum field. The output light

ˆout

detected by a photodetector (PD). The advantage of 3D-VCRS is that the input light

ˆin

transmitted in the same direction in both Ring 1 and 2, which allows the Sagnac phase shift to

accumulate. Thus avoid the cancellation of the Sagnac phase shift in the unfolded LC coupled

ring resonators structure[33]. We assume that the BS and the input waveguide are lossless and

that the loss coefficients of Ring 1 and 2 are a1 and a2, respectively. r1, r2, and t1, t2 are the

amplitude reflection and transmission coefficients in the two coupling regions, i.e., the

coupling region between Ring 1 and 2, and the region between Ring 2 and the input

waveguide, respectively. Here, we neglect the loss in the coupling region, and it can be shown

that rj2 + tj2 =1 (i=1, 2).

The complex transmission coefficient in the coupling region between Ring 2 and 1 can be

written as[34]

( ) ( )

2 1 1 1 11

0 1 1 1

exp( ) ,

1 exp( )

E r a i t t e

E a r i







−

= = =

−

(1)

Fig. 1. Schematic of squeezed light coupling with the 3D-VCRS structure

here

1 , 1

2R eff R







is the one round trip phase shift in Ring 1, where rR1, neff,R1,



, and

c are the radius, the effective index of Ring 1, angular frequency of the cavity mode, and the

speed of light in vacuum, respectively. The complex transmission coefficient of the 3D-

VCRS is

( )

( ) ( ) ( )

2 2 1 2

4 2 2 1 2

exp( ) ,

1 exp( )

r a t i

E a r t i



   





−

= = =

−

(2)

here

( )

c q q

   

=−

is the one round trip phase shift in Ring 2, where



and

()e



are the

qth cavity mode frequency of Ring 2 with and without dispersion, respectively[35].



is the

round trip time of light in Ring 2. When Ring 1 is removed (empty cavity without dispersion),

the transmission coefficient in the coupling region between Ring 2 and the input waveguide

can be written as

( ) ( )

2 2 2

exp( ) .

1 exp( )

r a i

t t e

a r i









−

(3)

The effective group index ng of the 3D-VCRS can be given as

g eff R

nn L







(4)

here the effective length LR2 is



(rR2 is the radius of Ring 2), and the effective index of

Ring 2 is neff,R2,



is the argument of

( )



For a passive coupled resonator, it exhibits normal dispersion (1<ng) when it is over-

coupled and anomalous dispersion (0<ng<1) when it is under-coupled, which can be achieved

by tuning the coupled coefficient between Ring 1 and 2, i.e., by tailoring the value of r1. In

order to determine the detailed parameters with which the system operates under normal or

anomalous dispersion conditions, ng calculated from Eq. (4) versus





with different

values of r1 is plotted in Fig. 2.





is the detuning between the angular frequency of input

light and the resonance frequency of the 3D-VCRS. The fixed values are

1 2 0 ,

50 /

R R eff R

L L n



01064nm



, neff,R1=neff,R2,=2,

10.94a=

2 2 2

exp( 2 )



=−

where

23/dB cm



is the propagation loss in Ring 2.

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Squeezed-Light-EnhancedDispersiveGyroscopebasedOpticalMicrocavitiesXIAOYANGCHANG,1WENXIULI1,HAOZHANG2*,YANGZHOU2,ANPINGHUANG1,ANDZHISONGXIAO1,2,31SchoolofPhysics,BeihangUniversity,Beijing100191,China2ResearchInstituteofFrontierScience,BeihangUniversity,Beijing100191,China3BeijingAcademyofQuantumInfo...

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Squeezed -Light -Enhanced Dispersive Gyroscope based Optical Microcavities XIAOYANG CHANG 1 WENXIU LI1 HAO ZHANG2 YANG ZHOU2 ANPING

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