Superfluid properties of a Bose-Einstein condensate in an optical lattice confined in a cavity

We study the effect of a one dimensional optical lattice in a cavity field with quantum properties on the superfluid dynamics of a Bose-Einstein condensate (BEC). In the cavity the influence of atomic backaction and the external driving pump become important and modify the optical potential. Due to the coupling between the condensate wavefunction and the cavity modes, the cavity light field develops a band structure. This study reveals that the pump and the cavity emerges as a new handle to control the superfluid properties of the BEC.     

非线性激光场中量子噪声之间的耦合效应

用二维气体激光模型对量子噪声的实部和虚部存在耦合的激光场进行了理论分析，通过福克－普朗克方程导出了定态激光光场强度和位相的分布函数，算出了定态激光强度和位相的平均值，方差和偏斜度，与量子噪声的两个分量为独立随机变量的激光场相比，噪声间的耦合极大地改变了激光场强度和位相的涨落，并引起了激光场强度与位相之间的耦合。     

On quantum gauge theories in two dimensions

Two dimensional quantum Yang-Mills theory is studied from three points of view: (i) by standard physical methods; (ii) by relating it to the largek limit of three dimensional Chern-Simons theory and two dimensional conformal field theory; (iii) by relating its weak coupling limit to the theory of Reidemeister-Ray-Singer torsion. The results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces.Research supported in part by NSF Grant PHY86-20266     

Renormalizable 4D Quantum Gravity as a Perturbed Theory from CFT

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.     

Magnetization plateaus induced by a coupling to the lattice

We present a novel mechanism for the appearance of magnetization plateaus in quasi-one-dimensional quantum spin systems, which is induced by the coupling to the underlying lattice. We investigate in detail a simple model of a frustrated spin-1/2 Heisenberg chain coupled to adiabatic phonons under an external magnetic field, but the present mechanism is expected to be more general. Using field theoretic methods complemented by extensive density matrix renormalization group techniques, we show that magnetization plateaus at nontrivial rational values of the magnetization can be stabilized by the lattice coupling. We suggest that such a scenario could be relevant for some low dimensional frustrated spin-Peierls compounds.     

基态精细结构能级之间的量子相干引起的非线性效应

讨论了级联四能级系统中基态精细结构能级之间的量子相干引起的非线性效应。耦合场同时激励激发态的下精细结构能级和基态的两个精细结构能级之间的光学跃迁使系统中出现新吸收峰。研究结果表明,基态精细结构能级之间的粒子弛豫速率越小,量子相干效应越显著,但是增大耦合场的Rabi频率会削弱这种量子相干效应。     

基态精细结构能级之间的量子相干引起的非线性效应

讨论了级联四能级系统中基态精细结构能级之间的量子相干引起的非线性效应。耦合场同时激励激发态的下精细结构能级和基态的两个精细结构能级之间的光学跃迁使系统中出现新吸收峰。研究结果表明,基态精细结构能级之间的粒子弛豫速率越小,量子相干效应越显著,但是增大耦合场的Rabi频率会削弱这种量子相干效应。     

Octonion massive electrodynamics

In this paper, we have made an attempt to reformulate the generalized field equation and various quantum equations of massive dyons in terms of octonion eight dimensional space as the combination of two (external and internal) four dimensional spaces. The octonion forms of generalized potential and current equations of massive dyons are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion massive electrodynamics in manifestly covariant and consistent manner.     

The ground- and first-excited states of magnetopolarons in two-dimensional quantum dots for all coupling strengths

The ground- and first-excited state energies of a magnetopolaron in a two dimensional parabolic quantum dot are studied within a variational calculation for all coupling strength. The Lee-Low-Pines-Huybrecht variational technique that is developed previously for all coupling strength has been extented for polarons in a magnetic field. The dependence of the polaronic correction on the magnetic field and the confinement length is investigated. The polarization potential and the renormalized cyclotron masses as a function of electron-phonon coupling strength and the strength of both confinement potential and magnetic field are also studied within the same approach. Received 16 December 2002 / Received in final form 14 April 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: kandemir@science.ankara.edu.tr     

磁场对非对称量子点中极化子性质的影响

采用线性组合算符和幺正变换方法研究磁场对非对称量子点中弱耦合磁极化子性质的影响.导出了非对称量子点中弱耦合磁极化子的振动频率、基态能量和基态结合能随量子点的横向和纵向有效受限长度、磁场和电子-声子耦合强度的变化关系.数值计算结果表明:非对称量子点中弱耦合磁极化子的基态能量和基态结合能随量子点的横向和纵向有效受限长度的增加而迅速增大.随回旋频率的增加而增大,随电子-声子耦合强度的增加而减小.     

Thermalization of Fermionic Quantum Walkers

We consider the discrete time dynamics of an ensemble of fermionic quantum walkers moving on a finite discrete sample, interacting with a reservoir of infinitely many quantum particles on the one dimensional lattice. The reservoir is given by a fermionic quasifree state, with free discrete dynamics given by the shift, whereas the free dynamics of the non-interacting quantum walkers in the sample is defined by means of a unitary matrix. The reservoir and the sample exchange particles at specific sites by a unitary coupling and we study the discrete dynamics of the coupled system defined by the iteration of the free discrete dynamics acting on the unitary coupling, in a variety of situations. In particular, in absence of correlation within the particles of the reservoir and under natural assumptions on the sample’s dynamics, we prove that the one- and two-body reduced density matrices of the sample admit large times limits characterized by the state of the reservoir which are independent of the free dynamics of the quantum walkers and of the coupling strength. Moreover, the corresponding asymptotic density profile in the sample is flat and the correlations of number operators have no structure, a manifestation of thermalization.     

Dimensional crossover of a Rabi-coupled two-component Bose–Einstein condensate in an optical lattice

Dimensionality is a central concept in developing the theory of low-dimensional physics.However,previous research on dimensional crossover in the context of a Bose-Einstein condensate(BEC) has focused on the single-component BEC.To our best knowledge,further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking.In this work,we are motivated to investigate the dimensional crossover in a three-dimensional(3D) Rabi-coupled two-compon...     

Local Tomography and the Jordan Structure of Quantum Theory

Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i) individual systems are Jordan algebras (equivalently, their cones of unnormalized states are homogeneous and self-dual), (ii) composites are locally tomographic (meaning that states are determined by the joint probabilities they assign to measurement outcomes on the component systems) and (iii) at least one system has the structure of a qubit. Using this result, we also characterize finite dimensional quantum theory among probabilistic theories having the structure of a dagger-monoidal category.     

Spin-orbit coupling and anisotropy of spin splitting in quantum dots

In lateral quantum dots, the combined effect of both Dresselhaus and Bychkov-Rashba spin-orbit coupling is equivalent to an effective magnetic field +/- B(SO) which has the opposite sign for s(z)= +/- 1/2 spin electrons. When the external magnetic field is perpendicular to the planar structure, the field B(SO) generates an additional splitting for electron states as compared to the spin splitting in the in-plane field orientation. The anisotropy of spin splitting has been measured and then analyzed in terms of spin-orbit coupling in several AlGaAs/GaAs quantum dots by means of resonant tunneling spectroscopy. From the measured values and sign of the anisotropy we are able to determine the dominating spin-orbit coupling mechanism.     

A complete action for the spinning string

We present an action for the Neveu-Schwarz-Ramond model from which follow both the field equations and the gauge and supergauge constraints. This is done by coupling the free-field action to two-dimensional supergravity in a geometrically clear way. The constraints arise as the supergravity field equations, the supergravity fields playing the role of Lagrange multipliers. The action is invariant under local supersymmetry transformations and, as a consequence, the field equations and the constraints are consistent. The commutator structure of the local supersymmetry algebra is exhibited. It is also shown that there exists a special gauge in which the action, the field equations and the constraints take the free-field from of the usual formulation of the Neveu-Schwarz-Ramond model.     

Quantum Torus Symmetry of the KP,KdV and BKP Hierarchies

In this paper, we construct the quantum torus symmetry of the KP hierarchy and further derive the quantum torus constraint on the tau function of the KP hierarchy. That means we give a nice representation of the quantum torus Lie algebra in the KP system by acting on its tau function. Comparing to the W _∞ symmetry, this quantum torus symmetry has a nice algebraic structure with double indices. Further by reduction, we also construct the quantum torus symmetries of the KdV and BKP hierarchies and further derive the quantum torus constraints on their tau functions. These quantum torus constraints might have applications in the quantum field theory, supersymmetric gauge theory and so on.     

Some topological states in one-dimensional cold atomic systems

Ultracold atoms trapped in optical lattices nowadays have been widely used to mimic various models from condensed-matter physics. Recently, many great experimental progresses have been achieved for producing artificial magnetic field and spin–orbit coupling in cold atomic systems, which turn these systems into a new platform for simulating topological states. In this paper, we give a review focusing on quantum simulation of topologically protected soliton modes and topological insulators in one-dimensional cold atomic system. Firstly, the recent achievements towards quantum simulation of one-dimensional models with topological non-trivial states are reviewed, including the celebrated Jackiw–Rebbi model and Su–Schrieffer–Heeger model. Then, we will introduce a dimensional reduction method for systematically constructing high dimensional topological states in lower dimensional models and review its applications on simulating two-dimensional topological insulators in one-dimensional optical superlattices.     

Novel structure of single-electron two-channel multiplexer/demultiplexer

We propose a novel structure of single-electron two-channel multiplexer and demultiplexer based on three coupled single-dopant quantum dots defined by enhancement gates on AlGaAs/GaAs heterostructure. Two side-gates next to the dots are designed for applying a lateral switching field to the structure. A simple model of spherical parabolic quantum dot within effective-mass approximation demonstrates that the coupling strengths of the dots are adjustable by applying a lateral field. This gives the promise on achieving the functions of multiplexing and demultiplexing through the proposed structure.     

Quantum well excitons in an electric field: two versus three dimensional behavior

Previous calculations have shown a transition between two dimensional and three dimensional behavior of excitons confined in a semiconducting quantum well structure as a function of electric field. We here present calculations of the exciton binding energy as a function of electric field using a two parameter variational wave function of the form used in the absence of the electric field by Matsuura and Shinozuka. Our calculations were performed using a finite potential barrier model for the confinement of the exciton in the quantum well. The results of our calculations confirm the validity of the conclusion that the variational exciton wave function goes from being of a purely 2D hydrogenic type at small well widths and/or low electric fields to a 3D hydrogenic type in wide wells and/or high electric fields.