Physical Realization of Quantum C-Not Gate

We investigate a Heisenberg spin cluster with two particles controlled by a time-dependent magnetic field. The system is controlled by tuning the amplitude, frequency, and interaction time of the three-step time-dependent magnetic field. Then we solve the time-dependent Schrodinger equation of the two-particle system, and obtain the time evolution operator. By the three-timestep interaction, the wavefunction evolves from the initial state to the final state, and the total evolution operator can be expressed as a product of the three evolution operators. By adjusting the physical parameters, the key two-qubit logic gate, the C-Not gate, can be realized physically.     

Coherent states of the inverted Caldirola-Kanai oscillator with time-dependent singularities

The coherent states for a system of time-dependent singular potentials coupled to inverted CK (Caldirola-Kanai) oscillator are investigated by employing invariant operator method and Lie algebraic approach. We considered Coulomb potential and inverse quadratic potential as singularities of the system. The spectrum of quantum states is discrete for λ < 0 while continuous for λ ? 0. The probability densities for both Fock state and coherent state are converged to the center as time goes by according to the dissipation of energy. We confirmed that the probability density in the coherent state oscillates back and forth like a classical wave packet.     

Direct Evaluation of Transition Amplitude Using Determinant of Wave Operator in One-Dimensional Potential Scattering System

A determinantal formula is developed for direct evaluation of transition amplitude without solving the wave equation in a one-dimensional potential scattering system. Our formulation is 5ased on the principle that a desired quantity can be extracted from the wave operator, which is the master operator maintaining all the information of the system. This principle is tested in a simplified system, i.e,, in a one-dimensional potential scattering system. We are now developing a formula for direct evaluation of near-field amplitude to design a system, in which local field enhancement is desired.     

Admissible states in quantum phase space

We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a formula for the momentum correlations of arbitrary order and derive explicit expressions for the wave functions in terms of time-dependent and independent Wigner functions. We show that the pure state quantum condition is preserved by the Moyal (but not by the classical Liouville) time evolution and is consistent with a generic stargenvalue equation. As a by-product Baker's converse construction is generalized both to an arbitrary stargenvalue equation, associated to a generic phase space symbol, as well as to the time-dependent case. These results are properly extended to the mixed state quantum condition, which is proved to imply the Heisenberg uncertainty relations. Globally, this formalism yields the complete characterization of the kinematical structure of Wigner quantum mechanics. The previous results are then succinctly generalized for various quasi-distributions. Finally, the formalism is illustrated through the simple examples of the harmonic oscillator and the free Gaussian wave packet. As a by-product, we obtain in the former example an integral representation of the Hermite polynomials.     

Quantum treatment of the time-dependent coupled oscillators under the action of a random force

In this communication we introduce the problem of time-dependent frequency converter under the action of external random force. We have assumed that the coupling parameter and the phase pump are explicitly time dependent. Using the equations of motion in the Heisenberg picture the dynamical operators are obtained, however, under a certain integrability condition. When the system is initially prepared in the even coherent states the squeezing phenomenon is discussed. The correlation function is also considered and it has been shown that the nonclassical properties are apparent and sensitive to any variation in the integrability parameter. Furthermore, the wave function in Schrödinger picture is calculated and used it to derive the wave function in the coherent states. The accurate definition of the creation and annihilation operators are also introduced and employed to diagonalize the Hamiltonian system.     

含时量子系统传播子的ABCD形式

将含时量子系统状态的演化看成物质波波束沿时间轴的传输,引入束宽、发散角、曲率半径、品质因子和束熵表征波束的传输.发现品质因子守恒的量子系统,其动量算子和位置算子呈线性演化,传播子可以表达成ABCD的形式,最小波包(品质因子为1)的形式不随时间改变.讨论了对常数势能系统和谐振子系统的应用 关键词： 物质波束 光束 谐振子     

两粒子自旋系统量子纠缠的时间演化

研究了两个具有海森伯耦合的自旋为1/2的粒子在随时间变化的磁场中的运动情况.系统的哈密顿量具有SU（2）代数结构,运用代数动力学方法对此系统进行求解,得到了时间演化算子的严格解.基于严格解,求得两粒子体系随时间变化的波函数,从而计算得到两粒子体系的纠缠.对不同初始波函数,研究了系统纠缠随时间的变化情况.讨论了外场影响纠缠的条件. 关键词： 二粒子系统纠缠 代数动力学解法     

Exact L series solution of the Dirac-Coulomb problem for all energies

We obtain exact solution of the Dirac equation with the Coulomb potential as an infinite series of square integrable functions. This solution is for all energies, the discrete as well as the continuous. The spinor basis elements are written in terms of the confluent hypergeometric functions and chosen such that the matrix representation of the Dirac-Coulomb operator is tridiagonal. The wave equation results in a three-term recursion relation for the expansion coefficients of the wavefunction which is solved in terms of the Meixner-Pollaczek polynomials.     

Quantum mechanics of a general driven time-dependent oscillator

Summary In this paper we investigate the time evolution of a general driven time-dependent oscillator using the evolution operator method developed by Chenget al. We obtain an exact form of the time evolution operator which, in turn, enables us to find the exact wave functions and coherent states at any timet. Our analyses indicate that the time-dependent coherent state is equivalent to the well-known squeezed state, while the time-dependent number state is equivalent to the displaced and squeezed number state. Besides, we also calculate the time-dependent transition probabilities among the coherent states and number states of a simple harmonic oscillator associated with the initial HamiltonianH(0).     

Excitation of hydrogen atom by positron using hylleraas time-dependent approach

The time-dependent treatment of positron-hydrogen scattering for a zero total angular momentum has been presented. The initial wavefunction of the positron-hydrogen scattering system has been expanded in terms of three dimensional dynamical wave functions to include all higher angular momenta by solving a set of three coupled differential equations. This wavefunction is then time evolved using Taylor series expansion of the evolution operator. The excitation probabilities are monitored as the wavefunction propagates until there is no more change in the probabilities. The positron impact excitation cross-sections extracted from the final wavefunction are compared with the available results of converged close coupling approach. Received 23 July 2001 and Received in final form 25 November 2001     

Variance squeezing and information entropy squeezing via Bloch coherent states in two-level nonlinear spin models

The nonclassical squeezing effect emerging from a nonlinear coupling model (generalized Jaynes–Cummings model) of a two-level atom interacting resonantly with a bimodal cavity field via two-photon transitions is investigated in the rotating wave approximation. Various Bloch coherent initial states (rotated states) for the atomic system are assumed, i.e., (i) ground state, (ii) excited state, and (iii) linear superposition of both states. Initially, the atomic system and the field are in a disentangled state, where the field modes are in Glauber coherent states via Poisson distribution. The model is numerically tested against simulations of time evolution of the based Heisenberg uncertainty relation variance and Shannon information entropy squeezing factors. The quantum state purity is computed for the three possible initial states and used as a criterion to get information about the entanglement of the components of the system. Analytical expression of the total density operator matrix elements at t > 0 shows, in fact, the present nonlinear model to be strongly entangled, where each of the definite initial Bloch coherent states is reduced to statistical mixtures. Thus, the present model does not preserve the modulus of the Bloch vector.     

How to introduce time operator

Time operator can be introduced by three different approaches: by pertaining it to dynamical variables; by quantizing the classical expression of time; and taken as the restriction of energy shift generator to the Hilbert space of a physical system.     

On the quantum motion of a generalized time-dependent forced harmonic oscillator

In this work, we use linear invariants and the dynamical invariant method to obtain exact solutions of the Schrödinger equation for the generalized time-dependent forced harmonic oscillator in terms of solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations between coordinate and momentum. It is shown that the width of the Gaussian packet, fluctuations and correlations do not depend on the external force. As a particular case, we consider the forced Caldirola-Kanai oscillator.     

An extended class of L-series solutions of the wave equation

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such includes the discrete (for bound states) as well as the continuous (for scattering states) spectrum of the Hamiltonian. The problem translates into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. These are written in terms of orthogonal polynomials, some of which are modified versions of known polynomials. The examples given, which are not exhaustive, include problems in one and three dimensions.     

Quantum effects of periodic orbits for the kicked top

We analyze traces of powers of the time evolution operator of a periodically kicked top. Semiclassically, such traces are related to periodic orbits of the classical map. We derive the semiclassical traces in a coherent state basis and show how the periodic orbits can be recovered via a Fourier transform. A breakdown of the stationary phase approximation is detected. The quasi energy spectrum remains elusive due to lack of knowledge of sufficiently many periodic orbits. Divergencies of periodic orbit formulas are avoided by appealing to the finiteness of the quantum mechanical Hilbert space. The traces also enter the coefficients of the characteristic polynominal of the Floquet operator. Statistical properties of these coefficients give rise to a new criterion for the distinction of chaos and regular motion.     

Loss of nonclassical properties of quantum states in linear phase-insensitive processes with arbitrary time-dependent parameters

Conditions of disappearance of different “nonclassical” properties (usual and high-order squeezing, sub-Poissonian statistics, negativity of s-parametrized quasidistributions) are derived for a quantum oscillator, whose evolution is governed by the standard master equation of quantum optics with arbitrary time-dependent coefficients.     

Time inversion in dynamical systems

We consider the case of a dynamical system when the time evolution is generated by a nonhermitian superoperator on the states of the system. Assuming the left and right eigenvectors of this to provide complete basis sets, we propose a generalized scalar product which can be used to construct a monotonically changing functional of the state, a generalized entropy. Combining the time-dependent state with its time-reversed counterpart we can define the operation of time inversion even in this case of irreversible evolution. We require that both the forward and reversed time evolution can be obtained from a generalized action principle, and this demand serves to define the form of the time-reversed state uniquely. The work thus generalizes the quantum treatment from the unitary case to the irreversible one. We present a discussion of the approach and derive some of the direct consequences of our results.     

Persistence of quantum information

We study the flip-processes in a two-level system, which is triggered by the coupling to a classical bath. When the bath is represented by a stochastic field, the time evolution of the density matrix leads to a stochastic equation with a multiplicative noise. Accordingly the Fokker–Planck-equation (FPE) depends on the matrix elements of the underlying density operator. The solution of the FPE can be parametrized in terms of an inherent conserved quantity α, which is interpreted as a measure for the persistence of quantum information. We show that the FPE exhibits a single unique steady state solution different from Boltzmann's law. The exactly computable discrete spectrum of the relaxation times is characterized by two quantum numbers and the ratio of Planck's constant and the coupling strength to the bath. The total entropy is analyzed as function of the quantum number α  . In case of α=1$\alpha =1$ the system is in a pure state whereas for α≠1$\alpha \ne 1$ a mixed state is realized. In case of two, two-level systems, immersed in the common bath, the two noninteracting two-level systems become mutually entangled. The annealed entropy is in that case non-extensive.