Abstract

We present the transfer function of an all-optical atomic spin gyroscope through a series of differential equations and validate the transfer function by experimental test. A transfer function is the basis for further control system design. We build the differential equations based on a complete set of Bloch equations describing the all-optical atomic spin gyroscope, and obtain the transfer function through application of the Laplace transformation to these differential equations. Moreover, we experimentally validate the transfer function in an all-optical CsXe129 atomic spin gyroscope through a series of step responses. This transfer function is convenient for analysis of the form of control system required. Furthermore, it is available for the design of the control system specifically to improve the performance of all-optical atomic spin gyroscopes.

© 2013 Optical Society of America

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  1. N. Barbour, “Inertial sensor technology trends,” IEEE Sens. J. 1, 332–339 (2001).
    [CrossRef]
  2. T. W. Kornack, R. K. Ghosh, and M. V. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
    [CrossRef]
  3. M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett. 107, 171604 (2011).
    [CrossRef]
  4. J. C. Fang and J. Qin, “Advances in atomic gyroscope: a view from application for inertial navigation,” Sensors 12, 6331–6346 (2012).
    [CrossRef]
  5. J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull. 58, 1512–1515 (2013).
  6. T. W. Kornack, “A test of CPT and Lorentz symmetry using a K-3He comagnetometer,” Ph.D. dissertation (Princeton University, 2005).
  7. S. J. Seltzer, “Developments in alkali-metal atomic magnetometry,” Ph.D. dissertation (Princeton University, 2008).
  8. R. Stoner and R. Walsworth, “Collisions give sense of direction,” Nat. Phys. 2, 17–18 (2006).
    [CrossRef]
  9. J. M. Brown, “A new limit on Lorentz- and CPT-violating neutron spin interactions using a K-3He comagnetometer,” Ph.D. dissertation (Princeton University, 2011).
  10. B. Yu, Navigation Technology (Aeronautic Industry, 1987).
  11. V. Apostolyuk and F. E. H. Tay, “Dynamics of micromechanical coriolis vibratory gyroscopes,” Sensor Lett. 2, 252–259 (2005).
    [CrossRef]
  12. J. C. Fang, S. A. Wan, Y. Chen, and R. J. Li, “Light-shift measurement and suppression in atomic spin gyroscope,” Appl. Opt. 51, 7714–7717 (2012).
    [CrossRef]

2013

J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull. 58, 1512–1515 (2013).

2012

J. C. Fang, S. A. Wan, Y. Chen, and R. J. Li, “Light-shift measurement and suppression in atomic spin gyroscope,” Appl. Opt. 51, 7714–7717 (2012).
[CrossRef]

J. C. Fang and J. Qin, “Advances in atomic gyroscope: a view from application for inertial navigation,” Sensors 12, 6331–6346 (2012).
[CrossRef]

2011

M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett. 107, 171604 (2011).
[CrossRef]

2006

R. Stoner and R. Walsworth, “Collisions give sense of direction,” Nat. Phys. 2, 17–18 (2006).
[CrossRef]

2005

V. Apostolyuk and F. E. H. Tay, “Dynamics of micromechanical coriolis vibratory gyroscopes,” Sensor Lett. 2, 252–259 (2005).
[CrossRef]

T. W. Kornack, R. K. Ghosh, and M. V. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[CrossRef]

2001

N. Barbour, “Inertial sensor technology trends,” IEEE Sens. J. 1, 332–339 (2001).
[CrossRef]

Apostolyuk, V.

V. Apostolyuk and F. E. H. Tay, “Dynamics of micromechanical coriolis vibratory gyroscopes,” Sensor Lett. 2, 252–259 (2005).
[CrossRef]

Barbour, N.

N. Barbour, “Inertial sensor technology trends,” IEEE Sens. J. 1, 332–339 (2001).
[CrossRef]

Brown, J. M.

M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett. 107, 171604 (2011).
[CrossRef]

J. M. Brown, “A new limit on Lorentz- and CPT-violating neutron spin interactions using a K-3He comagnetometer,” Ph.D. dissertation (Princeton University, 2011).

Chen, Y.

J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull. 58, 1512–1515 (2013).

J. C. Fang, S. A. Wan, Y. Chen, and R. J. Li, “Light-shift measurement and suppression in atomic spin gyroscope,” Appl. Opt. 51, 7714–7717 (2012).
[CrossRef]

Cheuk, L. W.

M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett. 107, 171604 (2011).
[CrossRef]

Fang, J. C.

J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull. 58, 1512–1515 (2013).

J. C. Fang and J. Qin, “Advances in atomic gyroscope: a view from application for inertial navigation,” Sensors 12, 6331–6346 (2012).
[CrossRef]

J. C. Fang, S. A. Wan, Y. Chen, and R. J. Li, “Light-shift measurement and suppression in atomic spin gyroscope,” Appl. Opt. 51, 7714–7717 (2012).
[CrossRef]

Ghosh, R. K.

T. W. Kornack, R. K. Ghosh, and M. V. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[CrossRef]

Kornack, T. W.

T. W. Kornack, R. K. Ghosh, and M. V. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[CrossRef]

T. W. Kornack, “A test of CPT and Lorentz symmetry using a K-3He comagnetometer,” Ph.D. dissertation (Princeton University, 2005).

Li, R. J.

J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull. 58, 1512–1515 (2013).

J. C. Fang, S. A. Wan, Y. Chen, and R. J. Li, “Light-shift measurement and suppression in atomic spin gyroscope,” Appl. Opt. 51, 7714–7717 (2012).
[CrossRef]

Qin, J.

J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull. 58, 1512–1515 (2013).

J. C. Fang and J. Qin, “Advances in atomic gyroscope: a view from application for inertial navigation,” Sensors 12, 6331–6346 (2012).
[CrossRef]

Romalis, M. V.

M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett. 107, 171604 (2011).
[CrossRef]

T. W. Kornack, R. K. Ghosh, and M. V. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[CrossRef]

Seltzer, S. J.

S. J. Seltzer, “Developments in alkali-metal atomic magnetometry,” Ph.D. dissertation (Princeton University, 2008).

Smiciklas, M.

M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett. 107, 171604 (2011).
[CrossRef]

Smullin, S. J.

M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett. 107, 171604 (2011).
[CrossRef]

Stoner, R.

R. Stoner and R. Walsworth, “Collisions give sense of direction,” Nat. Phys. 2, 17–18 (2006).
[CrossRef]

Tay, F. E. H.

V. Apostolyuk and F. E. H. Tay, “Dynamics of micromechanical coriolis vibratory gyroscopes,” Sensor Lett. 2, 252–259 (2005).
[CrossRef]

Walsworth, R.

R. Stoner and R. Walsworth, “Collisions give sense of direction,” Nat. Phys. 2, 17–18 (2006).
[CrossRef]

Wan, S. A.

J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull. 58, 1512–1515 (2013).

J. C. Fang, S. A. Wan, Y. Chen, and R. J. Li, “Light-shift measurement and suppression in atomic spin gyroscope,” Appl. Opt. 51, 7714–7717 (2012).
[CrossRef]

Yu, B.

B. Yu, Navigation Technology (Aeronautic Industry, 1987).

Appl. Opt.

Chin. Sci. Bull.

J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull. 58, 1512–1515 (2013).

IEEE Sens. J.

N. Barbour, “Inertial sensor technology trends,” IEEE Sens. J. 1, 332–339 (2001).
[CrossRef]

Nat. Phys.

R. Stoner and R. Walsworth, “Collisions give sense of direction,” Nat. Phys. 2, 17–18 (2006).
[CrossRef]

Phys. Rev. Lett.

T. W. Kornack, R. K. Ghosh, and M. V. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[CrossRef]

M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett. 107, 171604 (2011).
[CrossRef]

Sensor Lett.

V. Apostolyuk and F. E. H. Tay, “Dynamics of micromechanical coriolis vibratory gyroscopes,” Sensor Lett. 2, 252–259 (2005).
[CrossRef]

Sensors

J. C. Fang and J. Qin, “Advances in atomic gyroscope: a view from application for inertial navigation,” Sensors 12, 6331–6346 (2012).
[CrossRef]

Other

J. M. Brown, “A new limit on Lorentz- and CPT-violating neutron spin interactions using a K-3He comagnetometer,” Ph.D. dissertation (Princeton University, 2011).

B. Yu, Navigation Technology (Aeronautic Industry, 1987).

T. W. Kornack, “A test of CPT and Lorentz symmetry using a K-3He comagnetometer,” Ph.D. dissertation (Princeton University, 2005).

S. J. Seltzer, “Developments in alkali-metal atomic magnetometry,” Ph.D. dissertation (Princeton University, 2008).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the all-optical atomic spin gyroscope. (a) Alkali atoms and noble-gas atoms are polarized along the bias field Bc. (b) SB is able to automatically track and compensate for changes in the external magnetic field, thus isolating the external magnetic field sensed by SA. (c) Simple block diagram of an atomic spin gyroscope in a control system.

Fig. 2.
Fig. 2.

Experimental apparatus of the all-optical atomic spin gyroscope. The pump laser transmits in the z direction with frequency detuned to the D1 line of Cs. The probe laser propagates in the x direction from the D2 line of Cs, and the Faraday modulation method is used for probing the direction of atomic spin to measure the output signal of the all-optical atomic spin gyroscope.

Fig. 3.
Fig. 3.

Test apparatus for the transfer function of the all-optical atomic spin gyroscope.

Fig. 4.
Fig. 4.

Step responses of the all-optical atomic spin gyroscope. (a) The eight total step responses according to alternate step input. (b) The elaborate first step response of the eight total step responses shown in (a).

Tables (1)

Tables Icon

Table 1. Values of Relevant Parameters of the Eight Total Step Responses Shown in Fig. 4a

Equations (36)

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P⃗et=γeQ(B⃗+λMnP⃗n+L⃗)×P⃗eΩ⃗×P⃗e+(Rps⃗p+RseenP⃗nRtotP⃗e)/Q,P⃗nt=γn(B⃗+λMeP⃗e)×P⃗nΩ⃗×P⃗n+RseneP⃗eRtotnP⃗n,
[PxetPyetPxntPynt]=[RtotQγe(Bz+λMnPzn+Lz)QRseenQγeQλMnPzeγe(Bz+λMnPzn+Lz)QRtotQγeλMnPzeQRseenQRseneγnλMePznRtotnγn(Bz+λMePzze)γnλMePznRseneγn(Bz+λMePze)Rtotn]×[PxePyePxnPyn]+[γeQPze(By+Ly)PzeΩγeQPze(Bx+Lx)γnPznByPznΩγnPznBx].
[P˜etP˜nt]=[ABCD][P˜eP˜n]+[γeQPze(By+Ly)PzeΩ+1Q(Rp+Rmsm)+i[γeQPze(Bx+Lx)1Q(Rp+Rmsm)]γnPznByPznΩiγnPznBx],
A=RtotQ+iγeQ(Bz+λMnPzn+Lz),B=RseenQiγeQλMnPzeC=RseneiγnλMePzn,D=Rtotn+iγn(Bz+λMePze).
P˜e¨(A+D)P˜e˙(BCAD)P˜e=W,W=D{γeQPze(By+Ly)PzeΩ+i[γeQPze(Bx+Lx)]}(γnPznByPznΩiγnPznBx).
U¨+2ζω0U˙+ω02U=ω02kHSω,
r2(A+D)r(BCAD)=0.
r1,2=(A+D)±(A+D)2+4(BCAD)2.
(A+D)2+4(BCAD)={(1QRtot2γeγnλMnPznλMePzeRtot)i[γeQ(Bz+λMnPzn+Lz)γn(Bz+λMePze)]}2.
r1=12RtotnγeγnλMnPznλMePzeRtot+iγn(Bz+λMePze),r2=RtotQ+γeγnλMnPznλMePzeRtot+iγeQ(Bz+λMnPzn+Lz).
P˜e(t)=c1er1t+c2er2t+P˜e*,
P˜e*=W(ADBC).
Pxe(t)=Re[P˜e(t)]=c1eΓ1tcos(ω1t)+c2eΓ2tcos(ω2t)+Re[P˜e*],
Γ1=12RtotnγeγnλMnPznλMePzeRtot,ω1=γn(Bz+λMePze),Γ2=RtotQ+γeγnλMnPznλMePzeRtot,ω2=γeQ(Bz+λMnPzn+Lz),
Re[P˜e*]=PzeγeRtot[Rtot2+γe2(Bz+λMnPzn+Lz)2]×{(Bz+λMnPzn+Lz)(Bz+λMePze)By+Ly+γeRtot(Bz+λMnPzn+Lz)Lx+γeRtot(Bz+λMnPzn+Lz)2(Bz+λMePze)Bx+(1γn1γeQ)Ω},
Bz=λMePzeλMnPzn.
γnλMnPznγeQλMePze.
ω1=ω2=γnλMnPzn.
[s2(A+D)s(BCAD)]P˜e(s)=(DPze+Pzn)Ω(s).
G(s)=Pxe(s)Ω(s)=Re[G˜(s)],
G˜(s)=P˜e(s)Ω(s)=(DPze+Pzn)s2(A+D)s(BCAD)=(DPze+Pzn)(sr1)(sr2).
G(s)=Pxe(s)Ω(s)=Re[G˜(s)]=N[(sΓ1)2+ω12][(sΓ2)2+ω22]=(RtotnPze+Pzn)(sz1)(sz2)[(sΓ1)2+ω12][(sΓ2)2+ω22],
N=(RtotnPze+Pzn)s2+[γn(Bz+λMePze)(ω1+ω2)(Γ1+Γ2)RtotnPze]s+(Γ1Γ2ω1ω2)(RtotnPze+Pzn)γn(Bz+λMePze)(ω1Γ2+ω2Γ1),Γ1=12RtotnγeγnλMnPznλMePzeRtot,ω1=γn(Bz+λMePze),Γ2=RtotQ+γeγnλMnPznλMePzeRtot,ω2=γeQ(Bz+λMnPzn+Lz),
s1,2=Γ1±jω1,s3,4=Γ2±jω2,Γ1=12RtotnγeγnλMnPznλMePzeRtot,ω1=γn(Bz+λMePze),Γ2=RtotQ+γeγnλMnPznλMePzeRtot,ω2=γeQ(Bz+λMnPzn+Lz).
Γ2Γ1=RtotQ+γeγnλMnPznλMePzeRtot+12RtotnRtotQ(1QγnλMnPznRtot·γeλMePzeRtot)0,
RtotRtotn105,RtotγeλMePze10102,RtotγnλMnPzn10102.
z1,2=[γn(Bz+λMePze)(ω1+ω2)(Γ1+Γ2)RtotnPze]±Δ2(RtotnPze+Pzn),
Δ=[γn(Bz+λMePze)(ω1+ω2)(Γ1+Γ2)RtotnPze]24(RtotnPze+Pzn)[(Γ1Γ2ω1ω2)(RtotnPze+Pzn)γn(Bz+λMePze)(ω1Γ2+ω2Γ1)]=[γn(Bz+λMePze)(ω1+ω2)]2+[(Γ1Γ2)RtotnPze]2+4(RtotnPze)2ω1ω2+2γnRtotnPze(Bz+λMePze)(ω2ω1)(Γ1Γ2)0.
[γn(Bz+λMePze)(ω1+ω2)(Γ1Γ2)RtotnPze]2Δ[γn(Bz+λMePze)(ω1+ω2)+(Γ1Γ2)RtotnPze]2,
|γn(Bz+λMePze)(ω1+ω2)(Γ1Γ2)RtotnPze|Δ[γn(Bz+λMePze)(ω1+ω2)+(Γ1Γ2)RtotnPze],
z1Γ1,z2Γ2.
G(s)=(RtotnPze+Pzn)(sΓ1)2+ω12=RtotnPze+Pzns22Γ1s+Γ12+ω12.
G(s)=kωn2s2+2ζωns+ωn2.
d=A1A2,
D=lnd=2πζ1ζ2,
ωd=ωn1ζ2,

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