广义非简谐振子的多尺度微扰理论

应用多尺度微扰理论到广义非简谐振子, 得到了一阶经典和量子微扰解. 特别是 我们的量子解在极限条件下能方便地转变为经典解, 并且坐标和动量算符的对易 关系的简化十分自然. 与Taylor级数解相比较, 无论是在经典还是在量子解 中频率移动都出现在各阶振动表达式中, 所以多尺度微扰解是弱耦合非简谐振动的较好解法.     

具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模(英文)

基于Hartree-Fock方法和多标度方法,我们考察了具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模,量子磁振子的波函数由量子包络孤子来描述.在布里渊区边界,量子包络孤子变成了量子内禀局域模,它的量子本征频率在简谐波带的顶部上方,量子磁振子主要集中在中心位置j=j0的附近.     

Quantum Solitary Wave Solutions in a Ferromagnetic Chain with Nearest- and Next-Nearest-Neighbor Interaction

The quantum solitary wave solutions in a one-dimensional ferromagnetic chain is investigated by using the Hartree-Fock approach and the multiple-scale method. It is shown that quantum solitary wave solutions can exist in a ferromagnetic system with nearest- and next-nearest-neighbor exchange interaction, and at the certain value of the first Brillouin zone, the solitary wave solution of the Hartree wave function becomes the intrinsic localized mode.     

加强的量子汉明限

通过研究具有相同重量的算子集合的性质,找到了任意维数纯量子稳定子码参数的新的解析上限.与目前所知最优的解析上限——著名的量子汉明限相比,本文提出的码限强于量子汉明限. 关键词： 量子汉明限 量子稳定子码 量子纠错码 量子信息     

Quantum Solitary Wave Solutions in a Ferromagnetic Chain with Nearest- and Next-Nearest-Neighbor Interaction

The quantum solitary wave solutions in a one-dimensional ferromagnetic chain is investigated by using the Hartree-Fock approach and the multiple-scale method. It is shown that quantum solitary wave solutions can exist in a ferromagnetic system with nearest- and next-nearest-neighbor exchange interaction, and at the certain value of the first Brillouin zone, the solitary wave solution of the Hartree wave function becomes the intrinsic localized mode.     

Quantum Discord in Two-Qubit System Constructed from the Yang–Baxter Equation

Quantum correlations among parts of a composite quantum system are a fundamental resource for several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way, we investigate the quantum discord of the two-qubit system constructed from the Yang-Baxter Equation. The density matrix of this system is generated through the unitary Yang-Baxter matrix R. The analytical expression and numerical result of quantum discord and geometric measure of quantum discord are obtained for the Yang-Baxter system. These results show that quantum discord and geometric measure of quantum discord are only connect with the parameter θ, which is the important spectral parameter in Yang Baxter equation.     

Quantum Solitons and Breathers in an Anisotropic Ferromagnet with Octupole-Dipole Interaction

By using a full quantum approach based on the time-dependent Hartree approximation and the semidiscrete multiple-scale method, we study quantum nonlinear excitations in a one-dimensional ferromagnetic chain with octupole-dipole interaction and on-site uniaxial anisotropy. We find that quantum solitons and breathers can exist in the ferromagnetic chain, and analyze existence conditions of these excitations. Since the system states corresponding to quantum breathers are stationary states, we can get the energy level formula of such quantum breathers.     

Measured Composite Collision Models: Quantum Trajectory Purities and Channel Divisibility

We investigate a composite quantum collision model with measurements on the memory part, which effectively probe the system. The framework allows us to adjust the measurement strength, thereby tuning the dynamical map of the system. For a two-qubit setup with a symmetric and informationally complete measurement on the memory, we study the divisibility of the resulting dynamics in dependence of the measurement strength. The measurements give rise to quantum trajectories of the system and we show that the average asymptotic purity depends on the specific form of the measurement. With the help of numerical simulations, we demonstrate that the different performance of the measurements is generic and holds for almost all interaction gates between the system and the memory in the composite collision model. The discrete model is then extended to a time-continuous limit.     

Quantum cloning machines and their implementation in physical systems

We review the basic theory of approximate quantum cloning for discrete variables and some schemes for implementing quantum cloning machines. Several types of approximate quantum clones and their expansive quantum clones are intro- duced. As for the implementation of quantum cloning machines, we review some design methods and recent experimental results.     

Leptogenesis from first principles in the resonant regime

The lepton asymmetry generated by the out-of-equilibrium decays of heavy Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly enhanced. In this work, we study this scenario within a first-principle approach. The quantum field theoretical treatment is applicable for mass splittings of the order of the width of the Majorana neutrinos, for which the enhancement is maximally large. The non-equilibrium evolution of the mixing Majorana neutrino fields is described by a formal analytical solution of the Kadanoff–Baym equations, that is obtained by neglecting the back-reaction. Based on this solution, we derive approximate analytical expressions for the generated asymmetry and compare them to the Boltzmann result. We find that the resonant enhancement obtained from the Kadanoff–Baym approach is smaller compared to the Boltzmann approach, due to additional contributions that describe coherent transitions between the Majorana neutrino species. We also discuss corrections to the masses and widths of the degenerate pair of Majorana neutrinos that are relevant for very small mass splitting, and compare the approximate analytical result for the lepton asymmetry with numerical results.     

Approximate Good Quantum Numbers in Cs Stark States

Using Cs atom zero-field wavefunctions from a kind of atomic potential model, and the mean value of z-component of spin angular momentum (S_z) in each Stark state, we numerically investigate the approximate good quantum numbers in Cs Stark states. Our results quantitatively confirm the concept that m_t and m_s, can be taken as the approximate good quantum numbers in two cases, except for some Stark states in a few special field points or ranges; however we also find that m_t and m_s, cannot be treated as the approximate good quantum numbers for these special Stark states.     

Quantum Darwinism in a Composite System: Objectivity versus Classicality

We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems.     

Realization of Quantum Circuits in Fock Space

In this letter, by using the method we offered in our paper [L. Ma and Y.D. Zhang, Commun. Theor. Phys. (Beijing, China) 36 (2001) 119], some extended quantum logic gates, such as quantum counter, quantum adder, are studied and their expressions are given. It may be useful for us to study the more complicated quantum logic circuits deeply.     

A Fisher Information-Based Incompatibility Criterion for Quantum Channels

We introduce a new incompatibility criterion for quantum channels based on the notion of (quantum) Fisher information. Our construction is based on a similar criterion for quantum measurements put forward by H. Zhu. We then study the power of the incompatibility criterion in different scenarios. First, we prove the first analytical conditions for the incompatibility of two Schur channels. Then, we study the incompatibility structure of a tuple of depolarizing channels, comparing the newly introduced criterion with the known results from asymmetric quantum cloning.     

Intrinsic Localized Spin Wave Modes and Modulational Instability in a Two-Dimensional Heisenberg Ferromagnet

An analytical study on the properties of intrinsic localized modes and modulational instability in a quantum two-dimensional ferromagnet with single-ion uniaxial anisotropy is completed in the semiclassical limit. By making use of the semidiscrete multiple-scale method, we obtain a line localized solution and a radially symmetric localized solution, and analyze their existence conditions. Taking into account that the existence of bright localized solutions is closely linked to the modulational instability of plane waves, we analytically study the discrete modulational instability of plane spin waves. The result of the modulational instability analysis show that the uniaxial anisotropy plays a key role in the appearance of our intrinsic localized spin wave modes.     

Evaporative cooling of an atomic beam

We present a theoretical analysis of the evaporative cooling of an atomic beam propagating in a magnetic guide. Cooling is provided by transverse evaporation. The atomic dynamics inside the guide is analyzed by solving the Boltzmann equation with two different approaches: an approximate analytical ansatz and a Monte-Carlo simulation. Within their domain of validity, these two methods are found to be in very good agreement with each other. They allow us to determine how the phase-space density and the flux of the beam vary along its direction of propagation. We find a significant increase for the phase-space density along the guide for realistic experimental parameters. By extrapolation, we estimate the length of the beam needed to reach quantum degeneracy. Received 24 September 1999     

Quantum corrections to the entropy in a driven quantum Brownian motion model

The quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics.In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. We obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy in the weak coupling limit. Moreover, we find that for the thermodynamic equilibrium initial state, all terms odd in h are exactly zero. Our results bring important insights to the understanding of entropy in open quantum systems.     

广义量子干涉原理及对偶量子计算机

我们综述最近提出的广义量子干涉原理及其在量子计算中的应用。广义量子干涉原理是对狄拉克单光子干涉原理的具体化和多光子推广,不但对像原子这样的紧致的量子力学体系适用,而且适用于几个独立的光子这样的松散量子体系。利用广义量子干涉原理,许多引起争议的问题都可以得到合理的解释,例如两个以上的单光子的干涉等问题。从广义量子干涉原理来看双光子或者多光子的干涉就是双光子和双光子自身的干涉,多光子和多光子自身的干涉。广义量子干涉原理可以利用多组分量子力学体系的广义Feynman积分表示,可以定量地计算。基于这个原理我们提出了一种新的计算机,波粒二象计算机,又称为对偶计算机。在原理上对偶计算机超越了经典的计算机和现有的量子计算机。在对偶计算机中,计算机的波函数被分成若干个子波并使其通过不同的路径,在这些路径上进行不同的量子计算门操作,而后这些子波重新合并产生干涉从而给出计算结果。除了量子计算机具有的量子平行性外,对偶计算机还具有对偶平行性。形象地说,对偶计算机是一台通过多狭缝的运动着的量子计算机,在不同的狭缝进行不同的量子操作,实现对偶平行性。目前已经建立起严格的对偶量子计算机的数学理论,为今后的进一步发展打下了基础。本文着重从物理的角度去综述广义量子干涉原理和对偶计算机。现在的研究已经证明,一台d狭缝的n比特的对偶计算机等同与一个n比特+一个d比特(qudit)的普通量子计算机,证明了对偶计算机具有比量子计算机更强大的能力。这样,我们可以使用一台具有n+log2d个比特的普通量子计算机去模拟一个d狭缝的n比特对偶计算机,省去了研制运动量子计算机的巨大的技术上的障碍。我们把这种量子计算机的运行模式称为对偶计算模式,或简称为对偶模式。利用这一联系反过来可以帮助我们理解广义量子干涉原理,因为在量子计算机中一切计算都是普通的量子力学所允许的量子操作,因此广义量子干涉原理就是普通的量子力学体系所允许的原理,而这个原理只是是在多体量子力学体系中才会表现出来。对偶计算机是一种新式的计算机,里面有许多问题期待研究和发展,同时也充满了机会。在对偶计算机中,除了幺正操作外,还可以允许非幺正操作,几乎包括我们可以想到的任何操作,我们称之为对偶门操作或者广义量子门操作。目前这已经引起了数学家的注意,并给出了广义量子门操作的一些数学性质。此外,利用量子计算机和对偶计算机的联系,可以将许多经典计算机的算法移植到量子计算机中,经过改造成为量子算法。由于对偶计算机中的演化是非幺正的,对偶量子计算机将可能在开放量子力学的体系的研究中起到重要的作用。