Quantum simulation of the Klein paradox with trapped ions

We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.     

Entangling quantum gate in trapped ions via Rydberg blockade

We present a theoretical analysis of the implementation of an entangling quantum gate between two trapped Ca⁺ ions which is based on the dipolar interaction among ionic Rydberg states. In trapped ions, the Rydberg excitation dynamics is usually strongly affected by mechanical forces due to the strong couplings between electronic and vibrational degrees of freedom in inhomogeneous electric fields. We demonstrate that this harmful effect can be overcome using dressed states that emerge from the microwave coupling of nearby Rydberg states. At the same time. these dressed states exhibit long-range dipolar interactions which we use to implement a controlled adiabatic phase gate. Our study highlights a route toward a trapped ion quantum processor in which quantum gates are realized independently of the vibrational modes.     

Geometric Phases for Mixed States in Trapped Ions

The generalization of geometric phase from the pure states to the mixed states may have potential applications in constructing geometric quantum gates. We here investigate the mixed state geometric phases and visibilities of the trapped ion system in both non-degenerate and degenerate cases. In the proposed quantum system, the geometric phases are determined by the evolution time, the initial states of trapped ions, and the initial states of photons. Moreover, special periods are gained under which the geometric phases do not change with the initial states changing of photon parts in both non-degenerate and degenerate cases. The high detection efficiency in the ion trap system implies that the mixed state geometric phases proposed here can be easily tested.     

Geometric Phases for Mixed States in Trapped Ions

The generalization of geometric phase from the pure states to the mixed states may have potential applications in constructing geometric quantum gates. We here investigate the mixed state geometric phases and visibilities of the trapped ion system in both non-degenerate and degenerate cases. In the proposed quantum system, the geometric phases are determined by the evolution time, the initial states of trapped ions, and the initial states of photons. Moreover,special periods are gained under which the geometric phases do not change with the initial states changing of photon parts in both non-degenerate and degenerate cases. The high detection efficiency in the ion trap system implies that the mixed state geometric phases proposed here can be easily tested.     

Fast scheme for generating quantum-interference states and GHZ state of N trapped ions

We propose a fast scheme to generate the quantum-interference states of N trapped ions. In the scheme the ions are driven by a standing-wave laser beam whose carrier frequency is tuned such that the ion transition can take place. We also propose a simple and fast scheme to produce the GHZ state of N hot trapped ions and this scheme is insensitive to the heating of vibrational motion, which is important from the viewpoint of decoherence.     

Motional Quantum-State Engineering and Implementation of a Quantum Phase-Gate for Multiple Trapped Ions

We propose a scheme to generate a superposition of motional coherent states with arbitrary coefficients on a line in phase space and implement a quantum controlled phase-gate for multiple trapped ions with a single standing-wave laser pulse whose carrier frequency is tuned to the ions transition. In the scheme each ion does not need to be exactly positioned at the node of the standing wave, which is very important from viewpoint of experiment. Furthermore, our scheme may allow the generation of a superposition of coherent states with large mean phonon number for a large number of trapped ions in a fast way by choosing suitable laser intensity. We show that it can also be used to generate maximally entangled states of multiple trapped ions.     

Motional Quantum-State Engineering and Implementation of a Quantum Phase-Gate for Multiple Trapped Ions

We propose a scheme to generate a superposition of motional coherent states with arbitrary coefficients on a line in phase space and implement a quantum controlled phase-gate for multiple trapped ions with a single standing-wave laser pulse whose carrier frequency is tuned to the ions transition. In the scheme each ion does not need to be exactly positioned at the node of the standing wave, which is very important from viewpoint of experiment, Furthermore, our scheme may allow the generation of a superposition of coherent states with large mean phonon number for a large number of trapped ions in a fast way by choosing suitable laser intensity. We show that it can also be used to generate maximally entangled states of multiple trapped ions.     

Optimum electrode configurations for fast ion separation in microfabricated surface ion traps

For many quantum information implementations with trapped ions, effective shuttling operations are important. Here, we discuss the efficient separation and recombination of ions in surface ion trap geometries. The maximum speed of separation and recombination of trapped ions for adiabatic shuttling operations depends on the secular frequencies the trapped ion experiences in the process. Higher secular frequencies during the transportation processes can be achieved by optimising trap geometries. We show how two different arrangements of segmented static potential electrodes in surface ion traps can be optimised for fast ion separation or recombination processes. We also solve the equations of motion for the ion dynamics during the separation process and illustrate important considerations that need to be taken into account to make the process adiabatic.     

Efficient Scheme for Greenberger-Horne-Zeilinger State and Cluster State with Trapped Ions

We propose a scheme to generate the Greenberger-Horne-Zeilinger （GHZ） states and the cluster states of many trapped ions. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. The scheme only requires resonant interactions. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed, which is important in view of decoherence.     

可扩展的用于量子信息处理的刻槽平面离子芯片设计

研究设计了一个有效的可扩展的二维刻槽离子芯片。为了减少激光在离子芯片表面的散射,使被囚禁离子更加稳定,并使激光容易控制和探测成行的被囚禁离子,在每两个平行的射频电极中间刻槽使冷却光和探测光路径可穿过芯片。把控制离子运动的直流电极跟射频电极分开,减轻了不同电压对被囚禁离子的干扰,改进了对离子的控制。用有限元分析的方法对芯片表面上方的电势分布做了计算模拟。模拟结果表明,在这种新型的刻槽可扩展芯片上可以生成一个可扩展的离子阱阵列。这种结构提供了一个新颖的刻槽二维平面离子芯片,被囚禁其上的线形离子阵列可用来进行大型的量子信息处理。     

A New Approach to Measurement of Heating Rate of Trapped Ions

We propose a new scheme to estimate the heating rate of trapped ions inthermal states. By applying a controlled-U gate between the internal and themotional states of one of the trapped ions, we could obtain the mean phononnumber from the population of the internal state of the ion. The imperfection due to fluctuations of the relevant parameters in real experiments is considered and we analyze the experimental feasibility of our scheme with sophisticated ion trap techniques.     

Observation of laser-cooled Be+ -ion clouds in a Penning trap

Be⁺ ions trapped in a Penning trap are laser-cooled to about 10 mK. The excitation spectra of ion clouds containing about 500 ions are obtained by scanning the frequency of the cooling laser and discontinuities in these spectra are observed because of phase transitions. When the cooled ions are heated electrically by applying an rf voltage, no phase transition occurs and the spectra become continuous. Two-dimensional measurement of the ion clouds is carried out and the abrupt change in the shape of the ion cloud due to the phase transition is observed. When many ions are trapped and cooled, the phase transition occurs partially and a transient state where two states are mixed can be observed. The static properties of the ions are also measured by using an additional probe laser and the results of experimental measurements are compared with theoretical predictions.     

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.     

Trapped-ion state detection through coherent motion

We demonstrate a general method for state detection of trapped ions that can be applied to a large class of atomic and molecular species. We couple a spectroscopy ion (27Al+) to a control ion (25Mg+) in the same trap and perform state detection through off-resonant laser excitation of the spectroscopy ion that induces coherent motion. The motional amplitude, dependent on the spectroscopy ion state, is measured either by time-resolved photon counting or by resolved sideband excitations on the control ion. The first method provides a simplified way to distinguish clock states in 27Al+, which avoids ground-state cooling and sideband transitions. The second method reduces spontaneous emission and optical pumping on the spectroscopy ion, which we demonstrate by nondestructively distinguishing Zeeman sublevels in the (1)S0 ground state of 27Al+.     

Preparation of Motional Mesoscopic Superpositions of Squeezed Coherent States of N Trapped Ions

A scheme is proposed to generate arbitrary, discrete superpostions of squeezed coherent states of the squeezed center of mass of $N$ trapped ions along a straight line in phase space. The scheme is based on a resonant bichromatic excitation of each trapped ion that generates displacement and squeezing in the vibrational motion conditioned to each internal state. In this paper, we also show that such a method can be used for the engineering of motional quantum states.     

Measurement of the Wigner Characteristic Function for the Center-of-Mass Motion of Two Trapped Ions

We proposed a scheme for the reconstruction of the quantum states for the center-of-mass vibrationalmode of two trapped ions. In the scheme the ions are multichromatically excited by three lasers. Then measurementof the difference between probabilities of the ions being both in electronic ground and excited states directly yields theWigner characteristic function for the center-of-mass vibrational state. The scheme can also be used to prepare entangledcoherent states for the center-of-mass and relative vibrational modes.     

Effective quantum spin systems with trapped ions

We show that the physical system consisting of trapped ions interacting with lasers may undergo a rich variety of quantum phase transitions. By changing the laser intensities and polarizations the dynamics of the internal states of the ions can be controlled, in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analogue quantum simulator of spin systems with trapped ions, and observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins.     

Measurement of the Wigner Characteristic Function for the Center－of－Mass Motion of Two Trapped Ions

We proposed a scheme for the reconstruction of the quantum states for the center-of-mass vibrational mode of two trapped ions. In the scheme the ions are multichromatically excited by three lasers. Then measurement of the difference between probabilities of the ions being both in electronic ground and excited states directly yields the Wigner characteristic function for the center-of-mass vibrational state. The scheme can also be used to prepare entangled coherent states for the center-of-mass and relative vibrational modes.