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Noise Types in a Dilution Fridge.md

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Critical Equations & Formulas for Noise Types in a Dilution Refrigerator

Noise Type Equation Description
Thermal Noise (P_{\text{thermal}} = k_B T) Thermal energy per mode due to temperature.
(k_B T \ll \hbar \omega) Mitigation condition: Thermal noise is negligible below the energy splitting.
Phonon Noise (n_{\text{phonon}} = \frac{1}{e^{\hbar \omega / k_B T} - 1}) Average number of thermal phonons.
(n_{\text{phonon}} \to 0) at low (T) Mitigation condition: Phonon noise is suppressed as temperature decreases.
Resistive Noise (S_V = 4 k_B T R) Voltage noise power spectral density due to resistance.
(R = 0) (superconductors) (\Rightarrow S_V = 0) Mitigation condition: Resistive noise is eliminated in superconducting states.
Blackbody Radiation (I(\nu, T) = \frac{2 h \nu^3}{c^2} \frac{1}{e^{h \nu / k_B T} - 1}) Spectral radiance of blackbody radiation.
(I(\nu, T) \to 0) at low (T) Mitigation condition: Blackbody radiation intensity is suppressed at low (T).
Magnetic Noise (M_T \propto \sqrt{k_B T}) Thermal magnetization fluctuation.
(M_T \to 0) at low (T) Mitigation condition: Magnetic noise is minimized by reducing temperature.
Quasiparticle Noise (n_{\text{qp}} \propto e^{-\Delta / k_B T}) Quasiparticle density decreases exponentially with lower temperature.
(n_{\text{qp}} \to 0) at low (T) Mitigation condition: Quasiparticles are suppressed at ultra-low temperatures.
Vibration-Induced Noise (F = m a) Force due to mechanical vibrations.
Vibration isolation minimizes (a) Mitigation strategy: Reduces mechanical noise effects.
Residual Gas Noise (\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}) Mean free path of gas molecules.
(P \to 0) at low (T) Mitigation condition: Residual gas noise is eliminated as pressure drops.