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The quantization scheme between double enhanced charge phase-slip (ECPS) qubits is given. In this system, there exist quantum entanglement phenomenona. The entanglement characteristic is discussed by employing the concurrence. An interesting conclusion is obtained, i.e., if one desire to change the entanglement between two ECPS qubits, the mutual inductance should be considered first, but it is also a good choice to tune symmetric and asymmetric combination of two gate voltages.

Starting from the classical equation of the motion of a domain wall in the ferromagnetic systems, the quantum energy levels of the wall and the corresponding eigenfunctions in the case of considering damping term are given by using the canonical quantization method and unitary transformation. The quantum fluctuations of displacement and momentum of the moving wall has also been given as well as the uncertain relation.

In the newly constructed entangled state representation embodying quantum entanglement of Einstein, Podolsky and Rosen, the usual wave function of atomic coherent state ∣τ〉 = exp (μJ+-μ*J-)∣j, -j〉 turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j, where j is the spin value. We then prove that a two-dimensional time-independent anisotropic harmonic oscillator in a uniform magnetic field possesses energy eigenstates which can be classified as the states ∣τ〉 in terms of the spin values j.

The properties of the even and odd negative binomial states are investigated. Mainly we concentrate on the statistical properties for such states and we consider the squeezing phenomenon by examining the variation in the quadrature variances. Using the Pegg–Barnett formalism of phase operator, the phase probability distributions of the states are discussed, and also the phase and number squeezing with different parameters are studied. The numerical computation results show that the phase probability distributions for the even and odd NBSs can clearly exhibit the different features of quantum effects.

By introducing the entangled state representation and following Feynman's assumption that "electron pairs are bosons … A bound pair acts as a Bose particle", we construct a Hamiltonian operator for the Josephson transmission line (JTL) detector, then we use the Heisenberg equation of motion to derive the modified Josephson equation. Based on the modified Josephson equation, the measurement dynamics of JTL detector is investigated, which will be helpful for us to analyze the quantum measurement of JTL detector.

We find that when a single Josephson junction is inserted into a mesoscopic LC circuit, the operator Josephson equation is modified accompanying with the modification of Farady equation describing the inductance. By virtue of the entangled state representation and using the appropriate phase operator in bosonic form we derive the modified equations.

Based on Feynman's explanation about Cooper pair that "a bound pair acts as a Bose particle" and the bosonic operator Hamiltonian of the Josephson junction, we realize that the quantum state of the Josephson junction is a Cooper pair number-phase entangled state constructed by the phase operator across the junction. Its Schmidt decomposition is derived. The Cooper pair number-phase squeezed state's projection onto this entangled state leads to a geometric distribution.

Based on Feynman's explanation about the Cooper pair that "a bound pairs act as a Bose particle" and the bosonic operator Hamiltonian of Josephson junction (H.-Y. Fan, Int. J. Mod. Phys. B17 (2003) 2599) as well as the entangled state representation, we establish a possible number–phase squeezing mechanism for the Cooper-pair and the phase difference between the two sides of the junction. We find that when an extra energy (e.g. microwave radiation) is provided to the junction, then this squeezing mechanism can happen.

We reveal that Weyl ordering of operators is invariant under general n-mode similar transformations. The technique of integration within a Weyl ordered product of operators is employed to prove our statement. Application of this property in obtaining generalized squeezed state via similar transformation is discussed.

In this paper, we investigate the dynamical evolution and the decoherence of a single flux qubit due to its coupling with the external environment bath. We consider two typical baths: boson bath and spin bath. It is shown that, at low but finite temperature, if the two typical baths have smooth and continuous spectrum, the dynamics of the system is in general non-Markovian though of finite memory time. Most important of all, affected by the external environment bath, the flux qubit exhibits resonance of the coherence of the qubit. Comparing with the spin bath, the boson bath's destruction of the coherence is more serious.