Mesoscopic LC Circuit Research Articles

OPERATOR JOSEPHSON EQUATION FOR A JOSEPHSON JUNCTION CONNECTED INTO A MESOSCOPIC LC CIRCUIT

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.

Modified Josephson equations for the mesoscopic LC circuit including two coupled Josephson junctions**Work supported by the National Natural Science Foundation of China under Grant 10574060 and the Natural Science Foundation of Liaocheng University under Grant X071049.

Based on the entangled state representation and Feynman's idea that ‘electron pairs are bosons, …, a bound pair acts as a Bose particle’, we present a cooper-pair number-phase quantization scheme for the mesoscopic LC circuit including two coupled Josephson junctions (JJs). Then we use the Heisenberg equation of motion to obtain the modified current equation and voltage equation across each JJ, as well as the equation for realizing quantum control. Besides, we investigate how the phases in two JJs are affected mutually through the capacitor coupling and the coupled JJs.

The energy and thermal effects of mesoscopic capacitance coupling LC circuit at finite temperature

For the mesoscopic capacitance coupling LC circuit, the Hamiltonian is given by the canonical quantization. The Hamiltonian operator is diagonalized by a unitary transformation. The ensemble average energy and its fluctuations are derived by ensemble theory. In virtue of the generalized Hellmann-Feynman theorem, the quantum fluctuations of charge and self-conductance magnetic flux for the system at finite temperature are investigated. It is found that, the quantum fluctuations of charge and self-conductance magnetic flux depend on the temperature as well as the parameters of the circuit components.

The complete solution of zero-state response in mesoscopic LC circuit

The exact solution of time evolution operator was obtained by applying the gauge transform of algebra dynamic. Such an operator describes the quantum state of time dependence of mesoscopic LC circuit containing voltage source. The zero-state response in mesoscopic LC circuit was researched, and the charge and current zero-state response of the import signal were also acquired. The result showed that the system of mesoscopic LC circuit has linear time invariant feature, and the response in mesoscopic LC circuit is the same as in the macroscopic LC circuit.

GEOMETRIC PHASE IN A MESOSCOPIC LC CIRCUIT WITH ALTERNATING SOURCE

In this paper, we examine a mesoscopic LC circuit with alternating source and solve its time-dependent Schrödinger equation by selecting a proper Hermitian invariant operator. We study LR geometric phase in mesoscopic circuit system. Our results indicate that LR geometric phase is present at all times. In the evolution of the circuit system, it is a geometric phase factor accumulated by the wavefunction of external source's interaction with circuit system after nonadiabatic and noncyclic evolution. Its property lies in that it depends on the evolution path of the system wavefunction in the parameter space.

The time evolution of charge and current in mesoscopic LC circuit with charge discreteness

This Letter mainly investigates dynamic behavior of charge and current in a mesoscopic LC circuit with charge discreteness by considering coupling energy of the mesoscopic capacitor. The results indicate that the time evolution function of charge or current is the Jacobi elliptic function instead of a sine one, and the squeezing effect appears periodically in the circuit.

Thermodynamics of squeezed states in mesoscopic circuits

Based on the information theory, we present a density matrix to discuss coherent and squeezed states in a mesoscopic LC circuit with time-dependent frequency. With the relevant operators included in the density matrix, a connection between the appearance of coherent and squeezed states is established, i.e., the quantum state evolution of the system is closely related to the initial state. Generally speaking, due to the effect of environment temperature, the mesoscopic LC circuit will evolve to a squeezed state when it initially lies in an excited state. In particular, at a low temperature, step changes of circuit parameters will result in a squeezed minimum uncertainty state if the resonance frequency remains the same after the change.

Quantum effects of the mesoscopic LC electric circuit in thermal Kerr state

Based on the fact that a mesoscopic capacitor can be regarded as a mesoscopic tunnel junction, we quantized the mesoscopic LC circuit by using the rotating -wave approximation.The study shows: Considering the coupled energy of the meso scopic capacitor, the system of the mesoscopic LC circuit will be equivalent to a Kerr system. We also used the thermal field dynamic theory to investigate the thermal Kerr state at a definite temperature and calculated the quantum fluc tuation of both charge and magnetic flux, and discussed the results.

COLLAPSE AND REVIVAL EFFECT IN A MESOSCOPIC LC CIRCUIT

This paper studied the time evolution of quantum state in a mesoscopic LC circuit with the coupling energy caused by mesoscopic capacitor acting as a tunnel junction. It indicates that the state of the junction evolves into the quantum superposition of two coherent states and, in the state, nonclassical squeezing properties of the circuit appear. It also indicates that the dynamic behavior of the current shows collapse and revival phenomenon. The research in the paper will be helpful to miniaturize integrate circuits and electric components. It will be also important for the utilization of mesoscopic circuits to evolve the quantum states, which work as information carriers.

Preparation of Schr?dinger cat state via a mesoscopic LC circuit

A scheme is presented for preparing the superposition of coherent states,i.e.,Schr?dinger cat states. These states can be generated by the action of an external impulse functional signal on initial vaccum state of a mesoscopic LC circuit. The nonclassical squeezing properties appear in the circuit under the Schr?dinger cat states.

Behaviors of mesoscopic LC circuit in the external magnetic field

The phenomenon of Coulomb gap can be caused by Coulomb force in a mesoscopic circuit. We have investigated the tunnelling process in this circuit. The results indicate that, by varying the external direct voltage, the steps on the current–voltage characteristic curve can be observed. But when this circuit is placed in an external magnetic field varying with sine, not only the relation of current–voltage of the circuit is nonlines but also the phenomenon of step disappears.

Preparation of squeezed even coherence state and its nonclassical properties

By keeping the frequency of non-dissipative mesoscopic LC circuit a constant and its parameter varying with the step function, the quantum state of the circuit evolves to a squeezed even coherent state from the initial even coherent state. The nonclassical properties, not only squeezing but also antibunching effects, appear in the circuit by adjusting its inductor parameter under the squeezed even coherent state.

Shapiro effect in mesoscopic LC circuit

In this paper we consider the movement of an electron in the single electron tunnel process through a mesoscopic capacitor. The results show that, due to the Coulomb force, there is a threshold voltage Vt in the mesoscopic LC circuit. When the external voltage is lower than the threshold voltage, the tunnel current value is zero and the Coulomb blockade phenomenon arises. Furthermore, considering that the mesoscopic dimension is comparable to the coherence length in which charge carriers retain the phase remembrance, a weak coupling can be produced through the proximity effect of the normal metal electrons of both electrodes of a mesoscopic capacitor. By varying the external voltage, we can observe the Shapiro current step on the current-voltage characteristic curve of a mesoscopic LC circuit.