Quantum tomography of current and voltage states in nanoelectric circuits

Nanoelectric circuit with small variable capacitance C(t) and inductance L(t) considered as quantum parametric oscillator with varying frequency is studied. Current and voltage in quantum circuits play the role of conjugate “position” and “momentum” of the parametric oscillator with the wave function (density matrix) depending on current (voltage). The physical realization of electric circuits with varying capacitance and inductance by Josephson junctions used in superconducting devices is discussed in the context of possibilities to use an analog of nonstationary Casimir effect to create current (voltage) in the circuits by varying the Josephson junction parameters. The idea to observe the analog of nonstationary Casimir effect proposed in [1]-[5] is accompanied by the possibility to introduce the tomographic probability description of the current and voltage state. The equation for optical and symplectic quantum tomograms of evolving current (voltage) states in nanoelectric circuits is obtained in expli...