From Random Telegraph to Gaussian Stochastic Noises: Decoherence and Spectral Diffusion in a Semiconductor Quantum Dot

<table>Standard deviation <svg height="10.475" id="M95" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 9.875 10.475" width="9.875" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">Σ</tspan>
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</svg> of the frequency versus ratio of the jump processes characteristic times <svg height="16.299999" id="M96" style="vertical-align:-4.5044pt" version="1.1" viewbox="0 0 32.900002 16.299999" width="32.900002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.3)">
<g transform="translate(72,-58.96)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜏</tspan>
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<text transform="matrix(1,0,0,-1,-65.55,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">↓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.58,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">𝜏</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0">↑</tspan>
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</svg>. The dotted line indicates the maximum value of the standard deviation <svg height="21.075001" id="M97" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 63.912498 21.075001" width="63.912498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.075)">
<g transform="translate(72,-55.14)">
<text transform="matrix(1,0,0,-1,-71.95,58.42)">
<tspan style="font-size: 12.50px; " x="0" y="0">Σ</tspan>
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<text transform="matrix(1,0,0,-1,-64.15,55.29)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan>
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<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
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<text transform="matrix(1,0,0,-1,-32.69,58.42)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
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</svg> <svg height="10.6875" id="M98" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">Ω</tspan>
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</svg>/2 that is reached for symmetric jump processes <svg height="12.425" id="M99" style="vertical-align:-4.5044pt" version="1.1" viewbox="0 0 47.9375 12.425" width="47.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.425)">
<g transform="translate(72,-62.06)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜏</tspan>
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<text transform="matrix(1,0,0,-1,-65.55,63.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">↓</tspan>
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<text transform="matrix(1,0,0,-1,-57.11,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">𝜏</tspan>
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<text transform="matrix(1,0,0,-1,-38.67,63.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">↑</tspan>
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</svg>.</table>

Advances in Mathematical Physics

fig3

Figure 3

Figure 3: From Random Telegraph to Gaussian Stochastic Noises: Decoherence and Spectral Diffusion in a Semiconductor Quantum Dot 