Generation of unconventional geometric phase gates in ion trap-optical cavity system by squeezed operators

Based on squeezed operators this paper has implemented an ideal unconventional geometric quantum gate (GQG) in ion trap-optical cavity system by radiating the trapped ions with the cavity field of frequency w_c and an external laser field of frequency w_L. It can ensure that the gate time is shorter than the coherence time for qubits and the decay time of the optical cavity by appropriately tuning the ionic transition frequency w₀, the frequencies of the cavity mode w_c and the vibrational mode ν. It has also realized the unconventional GQG under the influence of the cavity decay based on the squeezed-like operators and found that the present scheme works well for the smaller cavity decay by investigating the corresponding fidelity and success probability.     

Coupling a single atomic quantum bit to a high finesse optical cavity

The quadrupole S(1/2)-D(5/2) optical transition of a single trapped Ca+ ion, well suited for encoding a quantum bit of information, is coherently coupled to the standing wave field of a high finesse cavity. The coupling is verified by observing the ion's response to both spatial and temporal variations of the intracavity field. We also achieve deterministic coupling of the cavity mode to the ion's vibrational state by selectively exciting vibrational state-changing transitions and by controlling the position of the ion in the standing wave field with nanometer precision.     

Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave

We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.     

囚禁离子非线性J-C模型量子态保真度

用全量子理论研究驻波激光场与囚禁离子相互作用系统中量子态保真度,详细讨论离子质心在驻波激光场中位置及离子初始状态对保真度的影响.结果表明:随着囚禁离子从远离驻波激光场波节处向波节处移动,量子态保真度振荡频率越来越高,振荡幅度几乎不变,且保真度到达第一个极小值所用时间越来越短,但不会出现信息完全失真;随着囚禁离子处于基态概率增加,量子态保真度振荡频率几乎不变,振荡幅度越来越小,也不会出现信息完全失真;在信息储存或传递过程中,囚禁离子量子态失真比系统和驻波场量子态失真小.     

Influence of second sideband excitation on the dynamics of trapped ions in a cavity

We study the dynamics of a trapped ion placed at an antinode of the standing wave inside a high finesse cavitywith consideration of the second sideband excitation between the ionic internal levels and the light field. We investigatethe entanglement of the three subsystems embodying the ionic internal levels, the vibrational mode of the ion and thecavity field.     

Coherent coupling of a single <Superscript>40</Superscript>Ca<Superscript>+</Superscript> ion to a high-finesse optical cavity

We demonstrate coherent coupling of the quadrupole S_1/2D_5/2 optical transition of a single trapped ⁴⁰Ca⁺ ion to the standing wave field of a high-finesse cavity. The dependence of the coupling on temporal dynamics and spatial variations of the intracavity field is investigated in detail. By precisely controlling the position of the ion in the cavity standing wave field and by selectively exciting vibrational state-changing transitions the ion’s quantized vibration in the trap is deterministically coupled to the cavity mode. We confirm coherent interaction of ion and cavity field by exciting Rabi oscillations with short resonant laser pulses injected into the cavity, which is frequency-stabilized to the atomic transition. Received: 23 August 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. E-mail: christoph.becher@uibk.ac.at RID="**" ID="**"Present address: Time and Frequency Division, National Institute of Standards and Technology, Boulder, CO 80305, USA     

驻波激光场中囚禁离子的线性熵和量子态转移研究

运用量子纠缠和线性熵理论,研究了驻波激光场中囚禁离子的线性熵和量子态转移.讨论了相干角、离子的相对位相、离子与驻波激光场之间的耦合强度以及失谐量、Lamb-Dicke参数对离子线性熵的影响.结果表明,在一定的条件下可以实现囚禁离子的内态到振动态的相干转移,线性熵随时间的演化呈现非周期性的振荡行为.离子线性熵的最大值随着相干角、离子与激光场之间的耦合强度以及失谐量的增大而减小,随着Lamb-Dicke参数的增大而增大.并且可以通过调节驻波激光场来调节离子与驻波激光场之间的耦合强度和失谐量,从而达到对离子线性熵的控制与操纵,理论上提供了一种调控纠缠的方式.     

驻波激光场中囚禁离子的线性熵和量子态转移研究

运用量子纠缠和线性熵理论,研究了驻波激光场中囚禁离子的线性熵和量子态转移。讨论了相干角、离子的相对位相、离子与驻波激光场之间的耦合强度以及失谐量、Lamb-Dicke参数对离子线性熵的影响。结果表明,在一定的条件下可以实现囚禁离子的内态到振动态的相干转移,线性熵随时间的演化呈现非周期性的振荡行为。离子线性熵的最大值随着相干角、离子与激光场之间的耦合强度以及失谐量的增大而减小,随着Lamb-Dicke参数的增大而增大。并且可以通过调节驻波激光场来调节离子与驻波激光场之间的耦合强度和失谐量,从而达到对离子线性熵的控制与操纵,理论上提供了一种调控纠缠的方式。     

Laser cooling with electromagnetically induced transparency: application to trapped samples of ions or neutral atoms

A novel method of ground-state laser cooling of trapped atoms utilizes the absorption profile of a three- (or multi-) level system that is tailored by a quantum interference. With cooling rates comparable to conventional sideband cooling, lower final temperatures may be achieved. The method was experimentally implemented to cool a single Ca⁺ ion to its vibrational ground state. Since a broad band of vibrational frequencies can be cooled simultaneously, the technique will be particularly useful for the cooling of larger ion strings, thereby being of great practical importance for initializing a quantum register based on trapped ions. We also discuss its application to different level schemes and for ground-state cooling of neutral atoms trapped by a far-detuned standing wave laser field. Received: 10 July 2001 / Published online: 23 November 2001     

Squeezing transfer from vibrations to a cavity field in an ion-trap laser

We present a novel way to produce squeezed light in an optical cavity. The main idea is to transfer vibrational squeezing from the motion of a trapped ion to the photons in a cavity. We use the dipolar coupling of the motion of a three-level ion with one cavity mode and two different kind of pumps. The first pump is an oscillating electric field that drives the ion into a vibrational squeezed state. The second pump consists of two lasers resonant with the ionic levels that makes the transfer possible.     

Quantum logic gates with two-level trapped ions beyond Lamb--Dicke limit

In the system with two two-level ions confined in a linear trap, this paper presents a simple scheme to realize the quantum phase gate (QPG) and the swap gate beyond the Lamb--Dicke (LD) limit. These two-qubit quantum logic gates only involve the internal states of two trapped ions. The scheme does not use the vibrational mode as the data bus and only requires a single resonant interaction of the ions with the lasers. Neither the LD approximation nor the auxiliary atomic level is needed in the proposed scheme. Thus the scheme is simple and the interaction time is very short, which is important in view of decoherence. The experimental feasibility for achieving this scheme is also discussed.     

Gravity-sensitive quantum dynamics in cold atoms

We subject a falling cloud of cold cesium atoms to periodic kicks from a sinusoidal potential created by a vertical standing wave of laser light. By controllably accelerating the potential, we show quantum accelerator mode dynamics to be highly sensitive to the effective gravitational acceleration when close to specific, resonant values. This quantum sensitivity to a control parameter is reminiscent of that associated with classical chaos and promises techniques for precision measurement.     

Conditional quantum phase gate between two 3-state atoms

We propose a scheme for conditional quantum logic between two 3-state atoms that share a quantum data bus such as a single mode optical field in cavity QED systems, or a collective vibrational state of trapped ions. Making use of quantum interference, our scheme achieves successful conditional phase evolution without any real transitions of atomic internal states or populating the quantum data bus. In addition, it requires only common addressing of the two atoms by external laser fields.     

Squeezing properties of a trapped ion in the running-wave laser beyond the Lamb--Dicke limit

Beyond the Lamb--Dicke limit, this paper investigates the squeezing properties of the trapped ion in the travelling-wave laser. It shows that the squeezing properties of the trapped ion in the travelling-wave laser are strongly affected by the sideband number $k$, the Lamb--Dicke parameter $\eta$ and the initial average phonon number.     

非线性增光子热态的非经典特性

本文从描述驻波激光场与囚禁离子相互作用的非线性Jaynes-Cummings模型出发,引入一种新的量子态,即非线性增光子热态.采用理论分析和数值计算相结合的方法,研究了Lamb-Dicke参数,温度和激光场的初相位等参数对这种量子态的非经典效应的影响.结果表明:非线性增光子热态的Mandel Q因子随温度的变化存在一个极小值.Lamb-Dicke参数越大,非线性增光子热态的非经典效应就越强.此外驻波场的初相位也对该态的非经典效应有明显的影响.     

应用相位调制驻波光场制备囚禁离子的暗压缩态

基于囚禁离子与驻波激光场相互作用,应用驻波光场的相位调制的方法,我们提出了一种制备离子振动压缩态的新方法.研究了压缩振幅与调制振幅的关系.我们发现:适当选择调制振幅,可把离子制备在最佳压缩振动态上,并且它们的产生伴随着自发辐射的相消.提出了一种实验构想,并进行了讨论.     

辐射场的起伏对囚禁离子的量子相干性的影响

研究了囚禁离子与一随机相位的驻波场相互作用时的量子动力学行为,讨论了辐射场的起伏对囚禁离子的量子崩塌-回复特性的影响.对于相位扩散模型获得了这个问题的解析解.     

Preparation of Squeezed State and Entanglement State Between VibrationalMotion of Trapped Ion and Light

Several schemes have been proposed to prepare two-mode squeezed state and entanglement state between motional states of a single trapped ion and light. Preparation of two-mode squeezed state is based on interaction of a trapped ion located in light cavity with cavity field. Preparation of entanglement state is based on interaction of a trapped ion located in light cavity with cavity field and a traveling wave light field.     

Generation of multi-atom W states via Raman transitionin an optical cavity

A simple scheme is proposed to generate the W state of N Λ-type neutral atoms trapped in an optical cavity via Raman transition. Conditional on no photon leakage from the cavity, the N-qubit W state can be prepared perfectly by turning on a classical coupling field for an appropriate time. Compared with the previous ones, our scheme requires neither individual laser addressing of the atoms, nor demand for controlling N atoms to go through an optical cavity simultaneously with a constant velocity. We investigate the influence of cavity decay using the quantum jump approach and show that the preparation time decreases and the success probability increases with atom number because of a collective enhancement of the coupling.     

基于频率调制激光驱动的囚禁离子几何相位逻辑门

为了避免激光相位的起伏对几何相位逻辑门保真度的影响, 提出一种基于囚禁离子的量子几何相位逻辑门的新方案。该机制是利用一束频率调制的行波激光场作用于两个囚禁离子上实现的。它的优点有：操作简单,仅需一步就能实现。不灵敏于激光场的相位也不需要对囚禁离子进行个别寻址。