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The nitrogen-vacancy center structure of diamond has attracted widespread attention due to its high sensitivity in quantum precision measurement. In this paper, a coupled phonon field is used to resonantly regulate the atomic spins of the nitrogen-vacancy center for improving the spin transition efficiency. Firstly, the interaction between phonons and lattice energy is analyzed based on the relationship between the wave function and the lattice displacement vector. The spin transition mechanism is investigated based on phonon resonance regulation, and the strain-induced energy transferable phonon-spin interaction coupling excitation model is established. Secondly, the coefficient matrix satisfying Bloch’s theorem is adopted to develop the phonon spectrum model of the first Brillouin zone characteristic region for different axial nitrogen-vacancy centers. Considering the thermal expansion, the thermal balance properties of phonon resonance system are analyzed and its specific heat model is studied based on the Debye model. Finally, the structure optimization model of different axial nitrogen-vacancy centers under the phonon model is built up based on the molecular dynamics simulation software CASTEP and density functional theory for first-principles research. The structural characteristics, phonon characteristics, and thermodynamic properties of nitrogen-vacancy centers are analyzed. The research results show that the evolution of phonon mode depends on the occupation of the nitrogen-vacancy center. A decrease in thermodynamic entropy accompanies the strengthening of the phonon mode. The covalent bond of diamond with nitrogen-vacancy center is weaker than that of a defect-free diamond. The thermodynamic properties of a defect-free diamond are more unstable. The primary phonon resonance frequency of diamond with nitrogen-vacancy centers are on the order of THz, and the secondary phonon resonance frequency is about in a range of 800 and 1200 MHz. A surface acoustic wave resonance mechanism with an interdigital width of 1.5 μm is designed according to the secondary resonance frequency, and its center frequency is about 930 MHz. The phonon resonance control method can effectively increase the spin transition probability of nitrogen-vacancy center under suitable phonon resonance control parameters, and thus realizing the increase of atomic spin manipulation efficiency.
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NV色心轴向 晶格动力学矩阵元不对称关系 NV色心轴向 晶格动力学矩阵元不对称关系 无NV色心 $\left\{ \begin{aligned}&{ {D_{xy} }\left( {{q} } \right) = {D_{yx} }\left( {{q} } \right)}\\&{ {D_{yz} }\left( {{q} } \right) = {D_{zy} }\left( {{q} } \right)}\\&{ {D_{xz} }\left( {{q} } \right) = {D_{zx} }\left( {{q} } \right)}\end{aligned} \right.$ [–1, 1, –1]轴向 $\left\{ {\begin{aligned}&{{D_{xy}}\left( {{q}} \right) = - {k_{[ - 1, 1, - 1]}}{D_{yx}}\left( {{q}} \right)}\\&{{D_{yz}}\left( {{q}} \right) = - {k_{[ - 1, 1, - 1]}}{D_{zy}}\left( {{q}} \right)}\\&{{D_{xz}}\left( {{q}} \right) = {k_{[ - 1, 1, - 1]}}{D_{zx}}\left( {{q}} \right)}\end{aligned}} \right.$ [1, 1, 1]轴向 $\left\{ {\begin{aligned}&{{D_{xy}}\left( {{q}} \right) = {k_{[1, 1, 1]}}{D_{yx}}\left( {{q}} \right)}\\&{{D_{yz}}\left( {{q}} \right) = {k_{[1, 1, 1]}}{D_{zy}}\left( {{q}} \right)}\\&{{D_{xz}}\left( {{q}} \right) = {k_{[1, 1, 1]}}{D_{zx}}\left( {{q}} \right)}\end{aligned}} \right.$ [–1, –1, 1]轴向 $\left\{ {\begin{aligned}&{{D_{xy}}\left( {{q}} \right) = {k_{[ - 1, - 1, 1]}}{D_{yx}}\left( {{q}} \right)}\\&{{D_{yz}}\left( {{q}} \right) = - {k_{[ - 1, - 1, 1]}}{D_{zy}}\left( {{q}} \right)}\\&{{D_{xz}}\left( {{q}} \right) = - {k_{[ - 1, - 1, 1]}}{D_{zx}}\left( {{q}} \right)}\end{aligned}} \right.$ [1, –1, –1]轴向 $\left\{ {\begin{aligned}&{{D_{xy}}\left( {{q}} \right) = - {k_{[1, - 1, - 1]}}{D_{yx}}\left( {{q}} \right)}\\&{{D_{yz}}\left( {{q}} \right) = {k_{[1, - 1, - 1]}}{D_{zy}}\left( {{q}} \right)}\\&{{D_{xz}}\left( {{q}} \right) = - {k_{[1, - 1, - 1]}}{D_{zx}}\left( {{q}} \right)}\end{aligned}} \right.$ 
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特征线 声子谱波矢条件 声子谱函数 极化向量 Λ线 $ {{q}}_{{x}}={{q}}_{y}={{q}}_{{z}}={q} $ $\left\{\begin{aligned}&{\omega }_{1}=\sqrt {{ {A} }_ {[1, 1, 1]} ^ {\varLambda } + {2}{B} _ {[1, 1, 1]} ^ {\varLambda }} \\ &{\omega }_{2}=\sqrt {{ {A} }_ {[1, 1, 1]} ^ {\varLambda } {-}{ {B} }_ {[1, 1, 1]} ^ {\varLambda } } \\ &{\omega }_{3}=\sqrt{ { {A} }_ {[1, 1, 1]} ^ {\varLambda } {-}{ {B} }_ {[1, 1, 1]} ^ {\varLambda } }\end{aligned}\right.$ $ \left\{\begin{aligned}&{{e}}_{{q}{1}}=\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)\\ &{{e}}_{{q}{2}}=\left({-}\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}{, 0}\right)\\ &{{e}}_{{q}{3}}=\left({-}\frac{1}{\sqrt{{6}}}{, -}\frac{1}{\sqrt{{6}}}, \frac{\sqrt{{6}}}{3}\right)\end{aligned}\right. $ $ \varDelta $线
(ΓF线)
(ZQ线)$ {{q}}_{{x}}={{q}}_{{z}}{=0} $ $\left\{\begin{aligned}&{\omega }_{1}=\sqrt{ { {A} }_{[1, 1, 1]}^{\varDelta }+{ {B} }_{[1, 1, 1]}^{\varDelta} }\\ &{\omega }_{2}=\sqrt{ { {B} }_{[1, 1, 1]}^{\varDelta } }\\ &{\omega }_{3}=\sqrt{ { {B} }_{[1, 1, 1]}^{\varDelta} }\end{aligned}\right.$ $ \left\{\begin{aligned}&{{e}}_{{q}{1}}=\left({0, 1, 0}\right)\\ &{{e}}_{{q}{2}}=\left({1, 0, 0}\right)\\ &{{e}}_{{q}{3}}=\left({0, 0, 1}\right)\end{aligned}\right. $ Σ线 ${ {q} }_{ {x} }={ {q} }_{y}={q},$
$ {{q}}_{{z}}= 0 $$\left\{\begin{aligned}&{\omega }_{1}=\sqrt{ { {A} }_{ [1, 1, 1] }^{\varSigma }+{ {B} }_ {[1, 1, 1]} ^ {\varSigma } }\\ &{\omega }_{2}=\sqrt{ { {A} }_{[1, 1, 1]} ^ {\varSigma } {-}{ {B} }_{[1, 1, 1]} ^ {\varSigma } } \\ &{\omega }_{3}=\sqrt{ { {C} }_ {[1, 1, 1]} ^{\varSigma } } \end{aligned}\right.$ $ \left\{\begin{aligned}&{{e}}_{{q}{1}}=\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}{, 0}\right)\\ &{{e}}_{{q}{2}}=\left({-}\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}{, 0}\right)\\ &{{e}}_{{q}{3}}=\left({0, 0, 1}\right)\end{aligned}\right. $ M线
(ΓZ线)
(FQ线)$ {{q}}_{{x}}={{q}}_{y}={0} $ $\left\{\begin{aligned}&{\omega }_{1}=\sqrt{ { {A} }_ {[1, 1, 1]} ^{ {M} }+{ {B} }_ {[1, 1, 1]} ^{ {M} } }\\ &{\omega }_{2}=\sqrt{ { {B} }_ {[1, 1, 1]} ^{ {M} } }\\ &{\omega }_{3}=\sqrt{ { {B} }_ {[1, 1, 1]} ^{ {M} } }\end{aligned}\right.$ $ \left\{\begin{aligned}&{{e}}_{{q}{1}}=\left({0, 0, 1}\right)\\ &{{e}}_{{q}{2}}=\left({1, 0, 0}\right)\\ &{{e}}_{{q}{3}}=\left({0, 1, 0}\right)\end{aligned}\right. $ 注: $A_{[1, 1, 1]}^\varDelta = \left( {2{f_1}/3{k_{[1, 1, 1]}}M_l^\alpha } \right)\left[ {2 - 2\cos \left( {{q_y}a/2} \right)} \right]$, $B_{[1, 1, 1]}^\varDelta = \left( {2{f_1}/3{k_{[1, 1, 1]} }M_l^\alpha } \right)\left[ {\eta - \eta \cos \left( { {q_y}a} \right)} \right]$,
$A_{[1, 1, 1]}^\varSigma = \left( { {f_1}/3{k_{[1, 1, 1]} }M_l^\alpha } \right)\{ 3 - 2\cos \left( {qa/2} \right) - \cos \left( {qa} \right) + \left[ {2\eta - 2\eta \cos \left( {qa} \right)} \right]\}$, $B_{[1, 1, 1]}^\varSigma = \left( { {f_1}/3{k_{[1, 1, 1]} }M_l^\alpha } \right)\left[ {1 - \cos \left( {qa} \right)} \right]$,
$C_{[1, 1, 1]}^\varSigma = \left( {2{f_1}/3{k_{[1, 1, 1]} }M_l^\alpha } \right)\left[ {2 - 2\cos \left( {qa/2} \right)} \right]$, $A_{[1, 1, 1]}^M = \left( {2{f_1}/3{k_{[1, 1, 1]}}M_l^\alpha } \right)\left[ {2 - 2\cos \left( {{q_z}a/2} \right)} \right]$,
$B_{[1, 1, 1]}^M = \left( {2{f_1}/3{k_{[1, 1, 1]}}M_l^\alpha } \right)\left[ {\eta - \eta \cos \left( {{q_z}a} \right)} \right]$.DownLoad:
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声子极化方向 声子热平衡温度 声子极化方向 声子热平衡温度 $ {\varLambda } $线方向 ${T}_{ {\varLambda } }=\dfrac{ {-}{\hbar }\sqrt{ { {A} }_{ {[1, 1, 1]} }^{ {\varLambda } }+{ {2}{B} }_{ {[1, 1, 1]} }^{ {\varLambda } } } }{ {k}_{\rm{B} }{\ln}\left(\frac{\left\langle { {n} } \right\rangle}{ {1+}\left\langle { {n} } \right\rangle}\right)}$ $ {\varSigma } $线方向 ${T}_{ {\varSigma } }=\dfrac{ {-}{\hbar }\sqrt{ { {A} }_{ {[1, 1, 1]} }^{ {\varSigma } }+{ {B} }_{ {[1, 1, 1]} }^{ {\varSigma } } } }{ {k}_{\rm{B} }{\ln}\left(\frac{\left\langle { {n} } \right\rangle}{ {1+}\left\langle { {n} } \right\rangle}\right)}$ $ \varDelta $线方向 ${T}_{\varDelta }=\dfrac{ {-}{\hbar }\sqrt{ { {A} }_{ {[1, 1, 1]} }^{\varDelta }+{ {B} }_{ {[1, 1, 1]} }^{\varDelta } } }{ {k}_{\rm{B} }{\ln}\left(\frac{\left\langle { {n} } \right\rangle}{ {1+}\left\langle { {n} } \right\rangle}\right)}$ M线方向 ${T}_{ {M} }=\dfrac{ {-}{\hbar }\sqrt{ { {A} }_{ {[1, 1, 1]} }^{ {M} }+{ {B} }_{ {[1, 1, 1]} }^{ {M} } } }{ {k}_{\rm{B} }{\ln}\left(\frac{\left\langle { {n} } \right\rangle}{ {1+}\left\langle { {n} } \right\rangle}\right)}$ 注: 参数$ {{A}}_{{[1, 1, 1]}}^{{\varLambda }}, {{B}}_{{[1, 1, 1]}}^{{\varLambda }}, {{A}}_{{[1, 1, 1]}}^{\varDelta }, {{B}}_{{[1, 1, 1]}}^{\varDelta } $, $ {{A}}_{{[1, 1, 1]}}^{{\varSigma }}, {{B}}_{{[1, 1, 1]}}^{{\varSigma }}, {{A}}_{{[1, 1, 1]}}^{{M}} $和$ {{B}}_{{[1, 1, 1]}}^{{M}} $同表2. DownLoad:
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