Closed-loop dual-atom-interferometer inertial sensor with continuous cold atomic beams Zhi-Xin Meng 孟至欣124 Pei-Qiang Yan 颜培强12 Sheng-Zhe Wang 王圣

2025-04-29 1 0 3.15MB 8 页 10玖币

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Closed-loop dual-atom-interferometer inertial sensor

with continuous cold atomic beams

Zhi-Xin Meng(孟至欣)1,2,4, Pei-Qiang Yan(颜培强)1,2, Sheng-Zhe Wang(王圣

哲)1,2, Xiao-Jie Li(李晓杰)1,2, Hong-Bo Xue(薛洪波)3, Yan-Ying Feng(冯焱颖)1,2∗

1State Key Laboratory of Precision Measurement Technology and Instruments, Tsinghua University, Beijing 100084, China

2Department of Precision Instrument, Tsinghua University, Beijing, 100084, China

3State Key Laboratory of Space Weather, National Space Science Center,

Chinese Academy of Sciences, Beijing 100190, China and

4Beijing Institute of Aerospace Control Devices, Beijing 100039, China

(Dated: April 16, 2024)

We demonstrate a closed-loop light-pulse atom interferometer inertial sensor that can realize

continuous decoupled measurements of acceleration and rotation rate. The sensor operates with

double-loop atom interferometers, which share the same Raman light pulses in a spatially separated

Mach-Zehnder conﬁguration and use continuous cold atomic beams propagating in opposite direc-

tions from two 2D+magneto-optical trappings. Acceleration and the rotation rate are decoupled

and simultaneously measured by the sum and diﬀerence of dual atom-interferometer signals, respec-

tively. The sensitivities of inertial measurements are also increased to be approximately 1.86 times

higher than that of a single atom interferometer. The acceleration phase shift is compensated in

real time by phase-locking these interferometers via the Raman laser phases from the sum interfer-

ometer signal, and the gyroscope perfomance is improved. We achieve long-term stabilities of 6.1µg

and 840 nrad/s for the acceleration and the rotation rate, respectively, using a short interrogation

time of 0.87ms (interference area A= 0.097 mm2). This work provides a building block for an

atomic interferometer based inertial measurement unit for use in ﬁeld applications that require a

high data-rate and high stability.

I. INTRODUCTION

Over more than 30 years of development [1–4],

light-pulse atom interferometers (LPAIs) have demon-

strated their potential for use as high-sensitivity quan-

tum sensors for measuring inertial quantities, including

acceleration[5, 6], rotation rate [4, 7], gravity, and grav-

ity gradient [3, 8, 9]. Various applications are available

for LPAI-based inertial sensors, such as high-precision

inertial navigation [10–12], fundamental physics [13–17],

geophysics [18, 19], and quantum metrology [20]. In re-

cent years, attempts have been made to move LPAI-based

inertial sensors from laboratory environments to ﬁeld ap-

plications [21–24], but several bottleneck challenges have

yet to be overcome, e.g., problems with low data rates

and low dynamic ranges [6, 25–28].

After the early stage of development, in which thermal

atomic beams were used as matter-wave sources [1, 4],

most research into atom interferometry focused on using

of a pulsed cold atom source [29]. For inertial sensing,

these cold LPAIs oﬀer advantages in terms of interroga-

tion time and system volume over LPAIs with thermal-

atom beam sources because they have slower longitudinal

mean velocities and narrower longitudinal velocity distri-

butions [30, 31]. Furthermore, the narrower horizontal

velocity distribution of a cold atomic cloud usually pro-

duces a higher static fringe contrast because more atoms

are involved in the Doppler-sensitive Raman transition

and thus contribute to the interferometer signal [32, 33].

∗yyfeng@tsinghua.edu.cn

A cold LPAI gyroscope has been demonstrated with sen-

sitivity and stability that can compete with those of the

best strategic-grade ﬁber-optic gyroscopes [7]. However,

it is a major challenge for LPAIs with pulsed cold atomic

sources to measure time-varying signals because of their

low data rates (∼a few Hz) [7, 33, 34], which suﬀer from

their time sequential operating mode and the loading

times required for the magneto-optical traps (MOTs).

Low data rates and low bandwidths are bottleneck prob-

lems that limit the application of LPAI-based inertial

sensors in dynamic environments, especially application

to high-precision inertial navigation.

Among the various trials of high-date-rate LPAIs

[6, 25], LPAIs based on continuous atomic beams have

shown the potential to achieve higher data rates (∼100

Hz) without loss of sensitivity [4]. A high data rate makes

it easier for an LPAI inertial sensor to tune the interfer-

ometer’s phase using Raman frequencies or phases. A

continuous operating mode is also helpful for performing

real-time compensation of the rotation rate and acceler-

ation and realizing a closed-loop system, which generally

demonstrates a broader dynamic range, better robust-

ness, and improved long-term stability when compared

with open-loop systems. In addition, LPAIs with contin-

uous atomic beams inherently work in a zero-dead-time

operating mode that cancels the aliasing noises caused by

the Dick eﬀect [35]. The ﬁrst continuous cold LPAI was

demonstrated by our group using a low-velocity intense

source (LVIS) of cold atoms [36]. An LPAI with a contin-

uous three-dimensional (3D) cold atomic beam operating

at sub-Doppler temperatures (15 µK) was demonstrated

recently with an inferred short-term phase measurement

arXiv:2210.15346v3 [physics.atom-ph] 15 Apr 2024

noise of 530(20) µrad/√Hz [37, 38].

Among the diﬀerent measurement protocols, the fringe

ﬁtting technique leads to great long-term stability for an

atom-interferometer gyroscope [4, 39, 40]. When com-

pared with fringe ﬁtting technique, the closed-loop ap-

proach oﬀers better time resolution to achieve a shorter

time constant for the lock loop [39]. A closed-loop system

locked into mid-fringe operation has been realized on an

atom-interferometer gyroscope with two atomic clouds

[40]. By feeding the error signal back to the common

piezo stepper motor mounted on the Raman mirrors, the

acceleration phase of the second interferometer can be

corrected for slow drift. Another closed-loop technique

uses the mid-fringe locking to cause LPAIs to work within

a linear regime with maximal sensitivity [7, 41, 42]. This

approach was realized by modulating the interferometer

phase by ±π/2 and feeding the error signal back onto

the Raman relative phase, which is computed from two

successive alternate measurements taken on both sides

of a fringe. These locking schemes demonstrate advan-

tages that include shorter time constants, higher sensitiv-

ity, improved robustness, and long-term stability [39, 41].

Closed-loop locking technology is easier to implement in

LPAIs with continuous atomic beams because of the suc-

cessive output signals.

In this work, we report the experimental realization

of an LPAI inertial sensor with dual closed-loop phase-

locked interferometers. Simultaneous, decoupled, and

continuous measurements of the accelerations and ro-

tation rates are realized by the sensor using continuous

cold atomic beams of 87Rb generated from 2D+MOTs

and Raman laser beams with Mach-Zehnder-type geome-

try. The diﬀerential dual-atom-interferometer operating

mode eﬀectively suppresses the common-mode noise of

the gyroscope, and improves the measurement sensitiv-

ity. The vibration noise of the gyroscope is suppressed

by feeding the sum signal back in a closed-loop mode.

We measure the acceleration and rotation rate, and eval-

uate the sensor’s long-term stabilities in terms of Allan

deviations. Long-term stabilities of 6.1µg for the accel-

eration and 840 nrad/s for the rotation rate are demon-

strated with a spatially separated interference length of

only L= 9.5 mm and a corresponding interrogation time

of T= 0.87 ms. Furthermore, the LPAI inertial sensor

can track a continuously changing rotation rate well by

applying an external force on the platform, thus enabling

real-world sensor applications.

II. EXPERIMENTAL SETUP

The conﬁguration of the proposed closed-loop dual-

atom-interferometer inertial sensor is shown in Fig. 1.

Two continuous cold 87Rb atomic beams, designated 1

and 2, are generated from 2D+MOTs located at both

ends of the sensor. These beams propagate along the

same path but in opposite directions, as demonstrated

in our previous work [43–45]. The vacuum apparatus

volume is approximately 1.5 m×0.3 m×0.3 m, and two

ion pumps are used to evacuate the detection and inter-

ferometry zone. In the 2D+MOT zone, a set of four

rectangular coils generates a quadrupole ﬁeld with a line

of zero magnetic ﬁeld along the symmetry axis. Two

pairs of counterpropagating cooling laser beams are per-

pendicular to each other with a power of 200 mW and

size of 100 mm×25 mm. A continuous cold atomic beam

is generated through an optical pressure imbalance, that

is induced by a 30-mW pushing laser beam (ϕ25 mm)

and a retro-refecting mirror with a 1-mm hole drilled at

its center.

The ﬂuxes of these cold atomic beams are measured

to be up to 2 ×109atoms/s with a mean longitudinal

velocity of 10.9(1) m/s and a longitudinal velocity dis-

tribution of 3.0(1) m/s using the time-of-ﬂight (TOF)

method. We measured Doppler-sensitive Raman transi-

tion spectra of cold atomic beams using a counterpropa-

gating Raman beam with a 1mm width and a detection

light situated approximately 600mm from the exit of the

2D+MOT. The linewidth (full width at half maximum,

FWHM) was calculated to be 2π·(224 ±4) kHz, corre-

sponding to an eﬀective atomic transverse temperature of

14.1(5) µK. The linearly polarized state preparation laser

beams prepare approximately 85% of the atoms into the

|F= 1, mF= 0⟩ground state with wavevectors oriented

parallel to the direction of the Raman bias magnetic ﬁeld,

tuned to the |F= 2⟩→|F′= 1⟩and |F= 1⟩→|F′= 0⟩

D2transition line.

Three spatially separated Raman light pulses with a

2−π−π

2sequence coherently split, reﬂect, and recom-

bine the atomic wave-packets for two atomic beams by

stimulated Raman transitions, and form two spatial do-

main atom interferometers (AIs) of the Mach-Zehnder

type. The interference phase shifts are measured via

the atomic numbers populated in the 

52S1/2, F = 2

state by collecting light-induced ﬂuorescence signals us-

ing PMTs (H7422-50, Hamamatsu, Japan) with a detec-

tion laser beam that has a power of 250µW and size of

20 mm×4 mm. Each of the two AIs operates as an in-

ertial sensor that is sensitive to the acceleration aalong

the direction of the Raman eﬀective wavevector keﬀ and

the rotation Ωalong the normal direction of the interfer-

ence area. The AI phase shifts are modulated at a fre-

quency of 81 Hz using a piezoelectric transducer (PZT;

PAL 20 VS12, NanoMotions, China), mounted behind

one of the planar mirrors for the π/2 Raman pulse. The

other two Raman laser beams are reﬂected by a rect-

angular mirror mounted on a home-made mount. The

demodulated signals acquired via two lock-in ampliﬁers

(LIAs) from the two AIs are added and then fed to a

proportional-integral-derivative (PID) controller. Then

the signal from the PID controller is fed back to the PZT

driver for real-time phase-shift compensation. The max-

imum measurement sensitivity is realized by locking the

zero crossing of the interference signals[42, 46, 47].

The Raman beam is detuned by −1.23 GHz from

the master laser frequency using a double-pass acousto-

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Closed-loopdual-atom-interferometerinertialsensorwithcontinuouscoldatomicbeamsZhi-XinMeng(孟至欣)1,2,4,Pei-QiangYan(颜培强)1,2,Sheng-ZheWang(王圣哲)1,2,Xiao-JieLi(李晓杰)1,2,Hong-BoXue(薛洪波)3,Yan-YingFeng(冯焱颖)1,2∗1StateKeyLaboratoryofPrecisionMeasurementTechnologyandInstruments,TsinghuaUniversity,Beijing100084,C...

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Closed-loop dual-atom-interferometer inertial sensor with continuous cold atomic beams Zhi-Xin Meng 孟至欣124 Pei-Qiang Yan 颜培强12 Sheng-Zhe Wang 王圣

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