• Photonics Research
  • Vol. 11, Issue 2, 150 (2023)
Lin Jiao and Jun-Hong An*
Author Affiliations
  • Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
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    DOI: 10.1364/PRJ.469779 Cite this Article Set citation alerts
    Lin Jiao, Jun-Hong An. Noisy quantum gyroscope[J]. Photonics Research, 2023, 11(2): 150 Copy Citation Text show less

    Abstract

    Gyroscope for rotation sensing plays a key role in inertial navigation systems. Developing more precise gyroscopes than the conventional ones bounded by the classical shot-noise limit by using quantum resources has attracted much attention. However, existing quantum gyroscope schemes suffer severe deterioration under the influence of decoherence, which is called the no-go theorem of noisy metrology. Here, by using two quantized optical fields as the quantum probe, we propose a quantum gyroscope scheme breaking through the constraint of the no-go theorem. Our exact analysis of the non-Markovian noise reveals that both the evolution time as a resource in enhancing the sensitivity and the achieved super-Heisenberg limit in the noiseless case are asymptotically recoverable when each optical field forms a bound state with its environment. The result provides a guideline for realizing high-precision rotation sensing in realistic noisy environments.
    H^S=ω0l=1,2a^la^l+Ω(a^1a^1a^2a^2),

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    minδΩ=[2tN(2+N)]1,

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    H^=H^S+l=1,2k[ωk,lb^k,lb^k,l+gk,l(a^lb^k,l+H.c.)],

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    ρ˙(t)=l=1,2{iϖl(t)[a^la^l,ρ(t)]+γl(t)D^lρ(t)},

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    u˙l(t)+iωlul(t)+0tf(tτ)ul(τ)dτ=0,

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    Π¯(t)=x[4m1(m2*m1*p22)+4m2(m1*m2*p12)+(1p1p2)2+16|m1m2|2]1/2,

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    δΩBA(t)=(2e2tκ+NCe2tκ)C8N(N+2)t|sin(4Ωt)|,

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    Yl(El)ωl0J(ω)ωEldω=El,El=izl.

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    limtδΩ(t)=F2F42N(2+N)Z12Z22t(Z1+Z2)|sin(2Gt)|,

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    ρ(α¯f,αf;t)=dμ(αi)dμ(αi)J(α¯f,αf;t|α¯i,αi;0)×ρ(α¯i,αi;0),(A1)

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    J(α¯f,αf;t|α¯i,αi;0)=exp{l=12{ul(t)α¯lfαli+u¯l(t)α¯liαlf+[1|ul(t)|2]α¯liαli}},(A2)

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    u˙l(t)+iωlul(t)+0tf(tτ)ul(τ)=0,(A3)

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    ρ(α¯i,αi;0)=1cosh2rexp[itanhr2l(α¯li2αli2)].(A4)

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    ρ(α¯f,αf;t)=xexp[l(mlα¯lf2+m¯lαlf2+plα¯lfαlf)],(A5)

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    ρout=dμ(αf)dμ(αf)ρ(α¯f,αf;t)×|α1f+iα2f2,α2f+iα1f2α¯1fiα¯2f2,α¯2fiα¯2f2|.(A6)

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    Π¯=x[4m1(m2*m1*p22)+4m2(m1*m2*p12)+(1p1p2)2+16|m1m2|2]1/2,(A7)

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    u˙l(t)+0tdτ0dωJ(ω)ei(ωωl)(tτ)ul(τ)=0.(B1)

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    δΩBA(t)=(2e2tκ+NCe2tκ)C8N(N+2)t|sin(4Ωt)|,(B2)

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    ul(t)=12πiiσ+iσeiEltElωl+0J(ω)ωEldωdE,(C1)

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    Yl(El)ωl0J(ω)ωEldω=El.(C2)

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    ul(t)=ZleiEb,lt+0Θ(E)eiEtdE,(C3)

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    Zl=[1+0J(ω)(Eb,lω)2dω]1(C4)

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    limtul(t)={0,Yl(0)0ZleiEb,ltYl(0)<0.(C5)

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    limtδΩ(t)=F2F42N(2+N)|Ω(Z12+Z221)24+2N+Z12Z22[t(Z1+Z2)sin(2Gt)2Ωln(Z1Z2)cos2(Gt)]|1,(C6)

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    limtδΩ(t)F2F42N(2+N)Z12Z22t(Z1+Z2)|sin(2Gt)|.(C7)

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    limNlimtδΩ(t)N.(C8)

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    limZ1,Z21limtδΩ(t)=[2tN(2+N)]1,(C9)

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