Figure 3 Probability density (B). The probability density with squeezing parameters r 1 = r 2 = 0.7 and ϕ 1 = ϕ 2 = 1.5 is shown here as a function of q 1 and t. Various values we have taken are q 2 = 0, n 1 = n 2 = 2, , R 0 = R 1 = R 2 = 0.1, L 0 = L 1 = L 2 = 1, C 1 = 1, C 2 = 1.2, p 1c (0) = p 2c (0) = 0, and δ = 0. The values of are (0,0,0,0) (a), (0.5,0.5,10,4) (b), and (0.5,0.5,0.5,0.53)(c). You can see the check details effects of squeezing from Figure 3. The probability densities in the DSN are more significantly distorted than
those of the DN. We can see from Figure 3b,c that the time behavior of probability densities is highly affected by external power source. If there is no power source in the circuit, the displacement of charge, specified with an initial condition, may gradually disappear according to its dissipation induced by resistances in the circuit. This is the same as that interpreted from the DN and exactly coincides with
classical analysis of the system. While various means and technologies to generate squeezed and/or displaced light are developed in the context of quantum optics after the seminal work of Slusher et selleckchem al.  for observing squeezed light in the mid 1980s, (displaced) squeezed number state with sufficient degree of squeezing for charges and Blasticidin S mw currents in a circuit quantum electrodynamics is first realized not long ago by Marthaler et al.  as far as Glutamate dehydrogenase we know. The circuit they designed not only undergoes sufficiently low dissipation but its potential energy also contains a positive quartic term that leads to achieving strong squeezing. Another method to squeeze quantum states of mechanical oscillation of charge carriers in a circuit is to use the technique of back-action evasion [33, 34] that is originally devised in order to measure one of two arbitrary conjugate quadratures with high precision beyond
the standard quantum limit. Though it is out of the scope of this work, the superpositions of any two DSNs may also be interesting topics to study, thanks to their nonclassical features that have no classical analogues. The quantum properties such as quadrature squeezing, quantum number distribution, purity, and the Mandel Q parameter for the superposition of two DSNs out of phase with respect to each other are studied in the literatures (see, for example, ). Quantum fluctuations Now let us see the quantum fluctuations and uncertainty relations for charges and currents in the DSN for the original system. It is well known that quantum energy and any physical observables are temporarily changed due to their quantum fluctuations. The theoretical study for the origin and background physics of quantum fluctuations have been performed in  by introducing stochastic and microcanonical quantizations.