Entanglement of a three-level trapped atom in the presence of another three-level trapped atom

A new version of two multi-level trapped atoms interacting with laser fields is under consideration. This system is based on a three-level trapped atom interacting with laser fields in the presence of another three-level trapped atom taking into account the time-dependent atom-field couplings and phase shift. The entanglement due to the concurrence is calculated and its time evolution phenomena is demonstrated within the framework of the presented theory. Our results establish an explicit relationship between the concurrence and the entanglement through the two three-level atoms and the fields interaction. We show that different nonclassical effects arise in the dynamics of the atomic population inversion, due to the initial states of the system as well as the values of the Lamb-Dicke parameter.     

Manipulating mixed state entanglement between a time-dependent field and a three-level trapped ion

In this paper, we extend earlier investigations (Q.C. Zhou, S.N. Zhu, Opt. Commun. 248 (2005) 437) on the pure state entanglement to the mixed state entanglement. In particular, analysis of the pattern of entanglement arising in the interaction between a three-level trapped ion with a time-dependent frequency interacting with a laser field is presented. By working out an exact analytic solution, we conclusively calculate the mixed state entanglement formula. Numerical calculations under current experimental conditions are carried out. Depending on the initial state of the system and in the presence of a time-dependent interaction, long surviving entanglement between the trapped ion and field can be obtained.     

Entanglement concentration for non-maximally entangled states of qudits

Entanglement concentration for higher dimensional quantum systems, qudits, is studied. In particular, we study a concentration protocol based on entanglement swapping of non-maximally entangled qudits via quantum state discrimination. We compare this protocol to a concentration scheme based on copies of the state to be concentrated, local transformations and two-way communications. We show that the success probability of the first scheme is equal to or larger than the success probability of the latter.     

Generation of entangled states of qudits using twin photons

We report an experiment to generate entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D slits in the arms of the twin photons define the qudit space. By manipulating the pump beam correctly, the twin photons will pass only by symmetrically opposite slits, generating entangled states between these different paths. Experimental results for qudits with D = 4 and 8 are shown. We demonstrate that the generated states are entangled states.     

利用弱交叉科尔效应实现多光子任意高维空间纠缠态的确定性制备

提出两种实现多光子高维空间纠缠态的制备方案.首先给出一种基于后验选择技术的实现方案,此方案以一定的概率实现.然后以基于弱交叉科尔效应的控制路径(C-path)门为基础,给出任意双光子任意维度的空间纠缠态的制备方案,并将此方案推广到任意多光子任意维度的空间纠缠态的制备.这一制备方案的最大优点在于可以确定性的得到纠缠态,并且不需要复杂的后验选择技术,可以很方便的应用于量子信息过程,同时该方案在目前的实验条件下是可行的.     

Non Abelian structures and the geometric phase of entangled qudits

In this work, we address some important topological and algebraic aspects of two-qudit states evolving under local unitary operations. The projective invariant subspaces and evolutions are connected with the common elements characterizing the su(d)$\mathfrak{s}\mathfrak{u}\left(d\right)$ Lie algebra and their representations. In particular, the roots and weights turn out to be natural quantities to parametrize cyclic evolutions and fractional phases. This framework is then used to recast the coset contribution to the geometric phase in a form that generalizes the usual monopole-like formula for a single qubit.     

The entropy of entangled three-level atoms interacting with entangled cavity fields: Entanglement swapping

The dynamics of an entangled atomic system, partially interacting with entangled cavity fields and characterizing an entanglement swapping, has been studied through their von Neumann entropies. The aforementioned interaction is implemented via a two-photon process, given by either the full microscopical Hamiltonian approach or the two-photon Jaynes-Cummings model. Numerical simulations furnish the explicit expressions for each sub-system entropy, which allow us to estimate the multiperiodicity in the evolution of the entangled atom-field system. The effects of the detuning parameter upon the period and the amplitude of the entropies are also discussed as well as the power spectrum of the entropy.     

Dynamics of a two-level trapped ion in a cavity

In the present paper we consider the case of a two-level ion in a cavity in the presence of a single mode field linearly polarized. We suppose that the ion is free to move along the polarization direction and trapped by a harmonic potential along the other two directions. By multiple path integration we derive the density matrix of the system and we study its dynamics. We assume an initial electromagnetic vacuum. This initial condition for the present system, compared with any other initial photonic state, gives new and higher order leading terms with respect to an expansion in powers of the inverse of the volume. Further after such an expansion there appears a first order term that originates from the combined interaction of the two-level system (qubit) with the quantum motion of the ion and the electromagnetic field in the cavity. We notice that the dynamics of the present system is very rich and can be studied exhaustively in the present framework.     

Quantum chaos of an ion trapped in a linear ion trap

We describe the transition to quantum chaos of an ion trapped in a linear ion trap and interacting with two laser fields. Under the conditions of adiabatic illumination of the upper level of the ion, and when the frequencies of the two laser beams are slightly different, the system is reduced to a quantum linear oscillator interacting with a monochromatic wave. The property of localization over the quantum resonance cells is proposed to exploit in order to facilitate the process of measurement of the probability distribution of an ion on the vibrational levels. In the regime of strong chaos the time-averaged values of the energy and dispersion of energy are computed and compared with the corresponding classical quantities for different values of the perturbation amplitude. In the exact resonance case, the classical analog of the system possesses an infinite inhomogeneous stochastic web. We analyze the quantum dynamics inside the inhomogeneous web. It is shown that the quantum system mimics on average the dynamics of the corresponding classical system. Formation of the quantum resonance cells is illustrated in the case of a finite detuning from the exact resonance, and under increasing of the wave amplitude. The parameters of the model and the initial conditions are close to the real physical situation which can be realized in the system of cold trapped ion perturbed by two lasers fields with close frequencies. (c) 2000 American Institute of Physics.     

Feedback cooling of a single trapped ion

Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electromechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical master equation.     

Entanglement of three-level trapped ions with phonon trap modes

The entanglement between a single electron in the electronic states of a trapped three-level ion and the ionic vibrational modes of the trap is studied for an initially unentangled state of an electron level and a coherent phonon state. The effects of time-independent and time-dependent couplings are discussed.     

Dynamics of a cold trapped ion in a Bose-Einstein condensate

We investigate the interaction of a laser-cooled trapped ion (Ba+ or Rb+) with an optically confined ??Rb Bose-Einstein condensate. The system features interesting dynamics of the ion and the atom cloud as determined by their collisions and their motion in their respective traps. Elastic as well as inelastic processes are observed and their respective cross sections are determined. We demonstrate that a single ion can be used to probe the density profile of an ultracold atom cloud.     

A single trapped ion in a finite range trap

This paper presents a method to describe dynamics of an ion confined in a realistic finite range trap. We model this realistic potential with a solvable one and we obtain dynamical variables (raising and lowering operators) of this potential. We consider coherent interaction of this confined ion in a finite range trap and we show that its center-of-mass motion steady state is a special kind of nonlinear coherent states. Physical properties of this state and their dependence on the finite range of potential are studied.     

Atomic parity violation in a single trapped radium ion

Atomic parity violation (APV) experiments are sensitive probes of the electroweak interaction at low energy. These experiments are competitive with and complementary to high-energy collider experiments. The APV signal is strongly enhanced in heavy atoms and it is measurable by exciting suppressed (M1, E2) transitions. The status of APV experiments and theory are reviewed as well as the prospects of an APV experiment using one single trapped Ra^?+? ion. The predicted enhancement factor of the APV effect in Ra^?+? is about 50 times larger than in Cs atoms. However, certain spectroscopic information on Ra^?+? needed to constrain the required atomic many-body theory, was lacking. Using the AGOR cyclotron and the TRI??P facility at KVI in Groningen, short-lived ^212???214Ra^?+? ions were produced and trapped. First ever excited-state laser spectroscopy was performed on the trapped ions. These measurements provide a benchmark for the atomic theory required to extract the electroweak mixing angle to sub-1% accuracy and are an important step towards an APV experiment in a single trapped Ra^?+? ion.     

三能级原子与耦合腔相互作用系统中的纠缠特性

采用Negativity熵来度量两个子系统间的纠缠,利用数值计算方法研究了简并Λ型三能级原子和简并V型三能级原子与耦合腔共振相互作用系统中原子之间、腔场之间和原子与腔场间的纠缠特性.给出了系统初始激发数为1时系统态矢的演化公式;讨论了腔场间的耦合系数变化对纠缠特性的影响.研究结果表明:随腔场间的耦合系数增大,原子间的纠缠增强,腔场间的纠缠减弱.     

Control of motional states of a trapped ion

We propose a scheme to drive the vibrational motion of a trapped ion to an arbitrary quantum state from the vacuum state. In the scheme the ion is excited by a sequence of laser pulses tuned to the respective lower vibrational sidebands. Finally, the system evolves into a pure state given by the product of the ground electronic state with the desired vibrational state.     

All-quantized Jaynes-Cummings interaction for a trapped ultracold ion

We propose an all-quantized Jaynes-Cummings (JC) interaction between a trapped ultracold ion with a quantized radiation field. The carrier excitation gives the usual JC model in cavity QED, but the red and blue excitations will result in three-body interactions analogous to a two-mode problem in quantum optics.     

囚禁单离子的量子阻尼运动

用包含偶极和四极虚势能项的非厄米哈密顿算符来描述Paul阱中囚禁阻尼单离子在静电场下的量子运动.通过导出和分析系统的精确解,得到在PT对称和不对称情形下的不同实能谱与稳定量子态,以及PT不对称情形的虚能谱和衰减量子态,同时给出相应于不同态的参数区域和存活概率.结果发现该非厄米系统外场参数能惟一确定量子稳定态并导致波函数形态变化,据此提出非相干操控相应量子跃迁的方法.让量子态衰减导致的离子位置期待值的衰减与经典阻尼谐振子的衰减一致,得到虚势能参数与经典阻尼参数的对应关系.所得结果将进一步丰富具有广泛应用背景的囚禁离子动力学.     

反馈方法在离子阱Doppler冷却中的应用研究

离子阱中离子的快速有效冷却在量子信息处理、光频标等领域都有重要的意义.基于Steixner 等提出的量子反馈模型,将反馈方法应用于离子的Doppler冷却.首先理论分析了该模型下离子运动信息的获取方式以及反馈对离子运动的影响,并推导出了存在反馈时离子运动所满足的方程,然后进行了仿真计算. 计算结果表明,利用量子反馈可以明显的提高离子冷却速率.还分析了反馈参数对离子冷却效率的影响. 关键词： 离子阱 Doppler冷却 量子反馈