• Laser & Optoelectronics Progress
  • Vol. 59, Issue 3, 0327001 (2022)
Fu Yu1, Tian Xiao2, Gaoqian He1, and Qinghong Liao1、*
Author Affiliations
  • 1Department of Electronic Information Engineering, Information Engineering School, Nanchang University, Nanchang , Jiangxi 330031, China
  • 2School of Future Technology, Nanchang University, Nanchang , Jiangxi 330031, China
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    DOI: 10.3788/LOP202259.0327001 Cite this Article Set citation alerts
    Fu Yu, Tian Xiao, Gaoqian He, Qinghong Liao. Probe Absorption Properties of a Superconducting Qubit Coupled to Microwave Cavity and Mechanical Resonator[J]. Laser & Optoelectronics Progress, 2022, 59(3): 0327001 Copy Citation Text show less

    Abstract

    A scheme based on the interaction of photon-superconducting qubit-phonon three-body hybrid quantum system is proposed, which is specifically composed of a microwave cavity and a micromechanical resonator coupled with a superconducting charge qubit. The probe absorption properties of the superconducting qubit coupled microwave cavity and mechanical resonator system are analyzed in detail through the first-order linear susceptibility which is solved by the quantum Langevin equation. The results show that the dual-field detecting method can accurately measure the coupling strength between the qubit and the microwave cavity according to the width between the double peaks in the absorption spectrum of the signal field. At the same time, according to the positions of the absorption peak and gain peak, accurate measurement of the vibration frequency is achieved. The new measurement scheme proposed in this paper is of great significance to the fields of precision measurement, quantum computing and quantum information processing.
    Hq-c=-μEpσ+exp-iωpt+σ-expiωpt-μEsσ+exp-iωst+σ-expiωst,
    H=ΔpσZ+Δaa+a+gσ+a+σ-a++ωbb+b+gmσ+b+σ-b+-Ωpσ++σ--μEsσ+exp-iδt+σ-expiδt,
    dσzdt=-Γ1σz+1-igσ+a-σ-a+-igmσ+b-σ-b++iΩpσ+-σ-+iμEsσ+exp-iδt-σ-expiδt,
    dσ-dt=-iΔp+Γ2σ-+2igσza+2igmσzb-2iΩpσz-2iμEsσzexp-iδt+τint,
    dadt=-iΔa+κa/2a-igσ-+aint,
    dbdt=-iωb+κb/2b-igmσ-+bint,
    σZt=σ0Z+σ+Zexp-iδt+σ-Zexpiδt,
    σ-t=σ0+σ+exp-iδt+σ-expiδt,
    at=a0+a+exp-iδt+a-expiδt,
    bt=b0+b+exp-iδt+b-expiδt,
    0=-Γ1σ0Z+1-igσ0*a0-σ0a0*-igmσ0*b0-σ0b0*+iΩpσ0*-σ0,
    -iδσ+Z=-Γ1σ+Z-igσ0*a++σ-*a0-σ0a-*+σ+a0*-igmσ0*b++σ-*b0-σ0b-*+σ+b0*+iΩpσ-*-σ++iμEsσ0*,
    iδσ-Z=-Γ1σ-Z-igσ0*a-+σ+*a0-σ0a+*+σ-a0*-igmσ0*b-+σ+*b0-σ0b+*+σ-b0*+iΩpσ+*-σ--iμEsσ0,
    0=-iΔp+Γ2σ0+2igσ0Za0+2igmσ0Zb0-2iΩpσ0Z,
    -iδσ+=-iΔp+Γ2σ++2igσ0Za++σ+Za0+2igmσ0Zb++σ+Zb0-2iΩpσ+Z-2iμEsσ0Z,
    iδσ-=-iΔp+Γ2σ-+2igσ0Za-+σ-Za0+2igmσ0Zb-+σ-Zb0-2iΩpσ-Z,
    0=-iΔa+ka/2a0-igσ0,
    -iδa+=-iΔa+ka/2a+-igσ+,
    iδa-=-iΔa+ka/2a--igσ-,
    0=-iΔb+kb/2b0-igmσ0,
    -iδb+=-iΔb+kb/2b+-igmσ+,
    iδb-=-iΔb+kb/2b--igmσ-
    Γ1σ0Z+12σ0Zg2Γ2κa-2ΔaΔpωb2+κb2/4+gm2Γ2κb-2ωbΔpΔa2+κa2/4+4σ0Z2g4ωb2+κb2/4+gm4Δa2+κa2/4+g2gm22Δaωb+κ2κb/2+Δp2+Γ22Δa2+κa2/4ωb2+κb2/4-4Ωp2σ0ZΓ2Δa2+κa2/4ωb2+κb2/4=0
    χ1ωseff=μσ+/Es=μ2/Γ2χ1ωs
    χ1ωs=Γ2-Π1*Π1γ6γ10*+Λ3*Π1γ7-2iΛ3*σ0ZΛ1Λ3*-Π1*Π1γ6γ9*
    Fu Yu, Tian Xiao, Gaoqian He, Qinghong Liao. Probe Absorption Properties of a Superconducting Qubit Coupled to Microwave Cavity and Mechanical Resonator[J]. Laser & Optoelectronics Progress, 2022, 59(3): 0327001
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