Invariants and Quantum Fluctuations of a Mesoscopic RLC Circuit in a Squeezed State and Squeezed Number State

The invariants for a mesoscopic RLC circuit with a power source are studied and used to construct the squeezed states and squeezed number states for the system. The quantum fluctuations of the mesoscopic RLC circuit in the squeezed states and squeezed number states are also investigated.     

Quantum Fluctuation in Thermal Vacuum State for a Mesoscopic RLC Circuit

By means of the thermal field dynamics theory invented by Takahashi and Umezawa, we study the quantum effects of a nondissipative mesoscopic RLC circuit at a finite temperature.     

The Quantum Fluctuations of Mesoscopic Damped Mutual Capacitance Coupled Double Resonance RLC Circuit in Excitation State of the Squeezed Vacuum State

Mesoscopic damped double resonance mutual capacitance coupled RLC circuit is quantized by the method of damped harmonic oscillator quantization. The Hamiltonian is diagonalized by unitary transformation. The eigenenergy spectra of this circuit are given. The quantum fluctuations of the charges and current of each loop are researched in excitation state of the squeezed vacuum state, the squeezed vacuum state and in vacuum state. It is show that, the quantum fluctuations of the charges and current are related to not only circuit inherent parameter and coupled magnitude, but also quantum number of excitation, squeezed coefficients, squeezed angle and damped resistance. And, because of damped resistance, the quantum fluctuation decay along with time. PACS numbers: 03.65.-w,42.50.Lc.     

RLC介观电路中的量子涨落

从线性谐振子哈氏量出发,通过正则变换,得到了受迫阻尼谐振子哈氏量,还讨论了在压缩态下的电荷和电流的量子涨落。     

Thermodynamics of Squeezed State for Mesoscopic RLC Circuits

We present a density matrix of a mesoscopic RLC circuits to make it possible to analyze the connection between the initial condition and the certain temperature. Our results show that the quantum state evolution will be closely related to the initial condition; the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially. In addition, we also obtain squeezed minimum uncertainty state with satisfying certain condition in mesoscopic RLC circuit.     

Quantum Effects of a Nondissipative Mesoscopic Capacitance Coupling Circuit in a Displaced Squeezed Fock State

Starting from the classical equation of motion for a mesoscopic capacitancecoupling circuit, we study the quantum fluctuations of charge and current of themesoscopic capacitance coupling circuit in a displaced squeezed Fock state. Itis found that the quantum fluctuations of charge and current in each componentcircuit depend on the devices of two circuits and the squeezing parameters, whilethe fluctuations do not depend on displacement parameters.     

介观RLC电路的精确波函数和压缩态

利用一系列幺正变换求出了介观RLC电路的精确波函数和基本不变量,并发现此系统基本不变量的本征态是压缩态,它可用介观RLC电路的精确波函数来构造。     

有源RLC介观电路的量子涨落

使用正则交换和幺正变换的方法，研究了有源RLC介观电路的量子涨落。结果表明电源电动势ε(t)的有无对电荷和电流的量子涨落没有影响。     

Coulomb Blockade of a Mesoscopic RLC Circuit

The quantum theory of the mesoscopic RLC circuit and the condition for Coulomb blockade are given by using canonical quantization and a unitary transformation from the classical equation of motion. Our results show that there is a threshold voltage _T in the circuit. The threshold voltage is related not only to the junction capacitance and inductance, but also to the resistance of the circuit. Generally speaking, the larger the resistance, the larger the threshold voltage. This clarifies the phenomenon of the Coulomb blockade of the dissipative mesoscopic circuit.     

The Squeezing Effect in a Mesoscopic RLC Circuit

Using the path integral method we derive quantum wave function and quantum fluctuations of charge andcurrent in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely,the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit.If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also findthat uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.     

Fluctuation of Mesoscopic RLC Circuit at Finite Temperature

We consider the fluctuation of mesoscopic RLC circuit at finite temperature since a resistance always produces Joule heat when the circuit is working. By virtue of the thermo field dynamics and the coherent thermo state representation we show that the quantum mechanical zero-point fluctuations of both charge and current increase with the rising temperature and the resistance value.     

Entangling Mesoscopic Squeezed Vacuum States and Mesoscopic Coherent States in Dissipative Cavity QED System

A scheme has been proposed for generating the macroscopic entanglement between the mesoscopic squeezed vacuum states and mesoscopic coherent states by considering both the two-photon interaction and the single photon interaction of N two-level atoms in cavities with high quality factor assisted by a strong driving field. Moreover, we derive the dissipative interaction models for single photon interaction and two-photon interaction, respectively. The corresponding analytical expressions of the fidelities can be given. Our scheme can be realized in the current techniques on the cavity QED.     

压缩真空态与压缩单光子态的相干叠加态的非经典性质

通过对量子比特态进行压缩操作,获得压缩真空态与压缩单光子态按一定的权重比例叠加而成的相干叠加态,此相干叠加态与压缩参数和权重因子有关,研究其非经典性和非高斯性.研究结果表明,通过压缩使得量子比特态的光子数分布范围变宽了.特别是从亚泊松分布和Wigner函数负定性情况分析了该量子态的非经典属性,从Wigner函数的边缘分布角度观察了该量子态的非高斯性.发现调节权重因子和压缩参数可以改善该态的非经典性和非高斯性.     

Quantum Effect in the Mesoscopic RLC Circuits with a Source

The research work on the quantum effects in mesoscopic circuits has undergone a rapid development recently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electric charge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrodinger equation of the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of durrents and square of the current are calculated. The results show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the design of the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopic quantum states.     

Quantum Effect in the Mesoscopic RLC Circuits with a Source

The research work on the quantum effects in mesoscopic circuits has undergone a rapid development recently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electric charge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrodinger equation of.the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of currents and square of the current are calculated. The results show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the design of the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopic quantum states.     

Quantum Effects of a Mesoscopic Capacitance Coupling Circuit with Resistances

We study the quantization of a mesoscopic capacitance coupling circuit with resistances, derive the density matrix of the system, and study the influence of temperature on the fluctuation of the system.     

Quantum Effects of a Dissipative Mesoscopic Circuit with Mutual Inductance

We study the quantum fluctuations of the charge and current of two L-C dissipative mcsoscopic circuit withthe mutual inductance in the vacuum state. Our results show that the system state will evolve to a squerzcd coherentstate under the effect of external source. We find that the squeezing amplitude parameter is relative to the parametersof circuit and the mutual-inductance coefficient in the existence of dissipation. Whcn the circuit has no dissipation orthere is complete coupling between two meshes, the squeezing amplitude parameter only depends on the capacitance'sratio.     

Quantum Effects of a Dissipative Mesoscopic Circuit with Mutual Inductance

We study the quantum fluctuations of the charge and current of two L-C dissipative mesoscopic circuit with the mutual inductance in the vacuum state.Our results show that the system state will evolve to a squeezed coherent state under the effect of external source.We find that the squeezing amplitude parameter is relative to the parameters of circuit and the mutual-inductance coefficient in the existence of dissipation.When the circuit has no dissipation or there is complete coupling between two meshes,the squeezing amplitude parameter only depends on the capacitance‘s ratio.     

双模光场的介观电路模型及电路的量子效应

通过量子化电容耦合双ＬＣ电路,给出双模光场的介观电路模型,研究双ＬＣ电路在激发相干态下的量子效应。