Uncertainty principle limit to the energy sensitivity of SQUID's and other linear amplifiers

SQUID's (Superconducting quantum interference devices) and other amplifiers are modeled by ideal noiseless linear amplifiers with current in and voltage en noise sources in their input circuits. For independent sources at frequency v the uncertainty principle requires that (e 2ni2n)1/2 ≳2hv, where h is Planck's constant. This limits the intrinsic energy sensitivity ε=Φ2n/2L of a SQUID of inductance L and effective flux noise power Φ2n to ε≳ε min=(e2ni2n) 1/2 /2πν=h/π. Correlation of the noise sources or mismatch of the SQUID inductance is shown to degrade εmin.