Tang-Kun Liu

Coulomb blockade and quantum fluctuations of mesoscopic inductance coupling circuit

The quantum theory for a mesoscopic inductance coupling circuit in accord with the discreteness of electric charges is developed. The finite-difference Schrodinger equation of the coupling circuit has been obtained. The results show that the Coulomb blockade will appear in the circuit and there exist quantum fluctuations of currents in the ground state of the system, and the quantum fluctuations in each component circuit are correlated

Nonclassical properties of even and odd generalized coherent states for an isotonic oscillator

We used the numerical method to study nonclassical properties of the even and odd generalized coherent states and superposition states of generalized coherent states for an isotonic oscillator. The following was shown. (1) The quantum statistical properties of the even and odd generalized coherent states are very different from those of the usual even and odd coherent states, and the Nth-order (N = 2m + 1, m = 0, 1, 2,...) squeezing and sub-Poisson distribution appear alternately for both the even and odd generalized coherent states in some ranges of z = \beta\(2) The weaker the isotonic oscillator potential, the narrower the ranges. (2) The superposition states of generalized coherent states may exhibit the Nth-order squeezing effect too, and this kind of higher-order squeezing effect appears periodically.

Quantum Fluctuations in a Mesoscopic Inductance Coupling Circuit

Starting from the equation of motion of a mesoscopic inductance coupling circuit,the quantum fluctuations of charge and current in the circuit are investigated inboth the eigenstates of the system and the squeezed vacuum state. The resultsshow that there exist quantum fluctuations of the charge and current in bothcases, and the fluctuations in each component circuit are connected.

A Class of Even and Odd Nonlinear Coherent States and Their Properties

A class of even and odd nonlinear coherent states are introduced. The properties of some related states, including quadrature squeezing, antibunching effect, and phase probability distribution, are studied.

Phase Properties of New Even and Odd Nonlinear Coherent States

Using the Pegg–Barnett formalism of phase operator, we obtain phase probability distributions of new even and odd nonlinear coherent states. It is shown that the distributions for the states are rather different, and unlike the case of ordinary even and odd coherent states the Pegg–Barnett distribution clearly reflects the different character of quantum interference in the case of the new even and odd coherent states.

Quantum statistical properties of orthonormalized eigenstates of the operator (â f (n̂))k

The completeness of the k orthonormalized eigenstates of the operator (âf())k (k≥3) is investigated. We introduce a new kind of higher-order squeezing and an antibunching. The properties of the Mth-order squeezing and the antibunching effect of the k states are studied. The result shows that these states may form a complete Hilbert space, and the Mth-order (M = (n + 1/2)k; n = 0,1,...) squeezing effects exist in all of the k states when k is even. There is an antibunching effect in all of the states. An alternative method for constructing the k states is proposed, and the result shows that all of them can be generated by linear superposition of the time-dependent nonlinear coherent states at different instants.

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.

Higher Order Squeezed States of Anharmonic Oscillators

In this paper the N eigenstates of the Nth powers (N ≥ 3) of the annihilationoperator of an anharmonic oscillator are constructed and their completeness isinvestigated. We introduce a new kind of higher order squeezing, Mth-order SU(1,1) squeezing. The properties of Mth-order SU(1, 1) squeezing and anticorrelationof the N states are studied. The result show that these states may form a completeHilbert space; the Mth-order [M = (n + 1/2)N;n = 0,1, ...] SU(1, 1) squeezingeffects exist in all of the N states when N is even. There is anticorrelation in allof them.

A Class of k-Quantum Nonlinear Coherent States and Some of Their Properties

AbstractA class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers Bk (k ≥ 3) of the annihilation operator