Squeezing effect induced by the Joule heat of resistance in mesoscopic steady-state circuit

Building on Louisell’s proposal for a quantization scheme of a mesoscopic LC electric circuit treated as a harmonic oscillator, we establish that when a LC circuit includes a resistance R, its ground state is a squeezed vacuum state of the enforced oscillator. We then investigate how it dissipates in an amplitude damping channel with the damping coefficient k by deriving its final density operator. In addition, we calculate the oscillator’s de-excitation number, which evolves according to a damping factor e−2kt, clearly illustrating the reduction in the oscillator’s excitation number. This indicates that a larger damping coefficient of the channel leads to faster dissipation of squeezing.