Generation of Multi-ion Graph States with Trapped Ions in Thermal Motion

We propose a scheme for generating multi-ion graph states using many trapped ions in thermal motion. Our generation scheme is insensitive to external state since the interaction between ions and laser fields does not involve the external degree of freedom. The scheme can be well realized within the current experimental technique.     

Generation of Arbitrary Pure States for Three-Dimensional Motion of a Trapped Ion

In this paper, we propose a scheme for generating an arbitrary three-dimensional pure state of vibrational motion of a trapped ion. Our scheme is based on a sequence of laser pulses, which are tuned to the appropriate vibrational sidebands with respect to the appropriate electronic transition.     

Robust Entanglement for Multiple Trapped Ions in Thermal Motion

A robust scheme is proposed for producing maximally entangled states for many trapped ions in thermal motion. In the scheme the ions are simultaneously illuminated by two standing-wave laser fields. During the operation the phases of the lasers are inverted, which not only cancels the vibration-dependent parts in the evolution operator, but also suppresses direct off-resonant coupling of the internal states. Thus, our scheme allows the production of entanglement for hot trapped ions with laser fields of high intensity, which makes the entanglement speed extremely high.     

Storage of Entangled States with Multiple Trapped Ions in Thermal Motion

This paper presents an alternative scheme to realize the storage of entangled states for multiple trapped ions including W state, Bell states, and GHZ states even with ions which exchange vibrational energy with a heating surrounding. Our scheme requires that the ions be simultaneously excited by two laser beams with different frequencies.In this scheme the vibrational degrees of freedom are only regarded as intermediate states and the ions exchange energy via the mediation of the vibration of the vibrational mode in coupling processes. The scheme is insensitive to both the initial vibrational state and heating if the system remains in the Lamb-Dicke regime. Since the effective Rabi frequency has a small dependence on the vibrational quantum number the heating will have no direct effect on the internal state evolution.     

Preparation of Cluster States with Trapped Ions in Thermal Motion

A potential scheme is proposed for generating cluster states of many trapped ions in thermal motion, in which the effective Hamiltonian does not involve the external degree of freedom and thus the scheme is insensitive to the external state, allowing it to be thermal state. The required experimental techniques of the schemes are within the scope that can be obtained in the ion-trap setup.     

一个囚禁离子运动压缩数态的制备

本文提出一个方案以制备一个被囚禁在谐势阱中的离子质心运动的压缩数态。在本方案中，这个离子受到两个分别调到第一高、低振动边带的激光场和一个与离子共振的激光场的轮流激发。系统最后被制备到运动压缩数态与电子基态的直积。     

Generation of SU(1,1) Intelligent States for the Motion of Two Trapped Ions

We propose a method for generating SU (1, 1) intelligent states for the center of mass and relative motionalmodes for two trapped ions. In our scheme, only three laser beams are employed, and their directions are all the sameas the direction of the two trapped ions‘ alignment. Under certain conditions, our desired states are obtained as thesteady-state solution of the master equation of the system.     

Generation of SU（1,1） Intelligent States for the Motion of Two Trapped Ions

We propose a method for generating SU(1, 1) intelligent states for the center of mass and relative motional modes for two trapped ions. In our scheme, only three laser beams are employed, and their directions are all the same as the direction of the two trapped ions‘ alignment. Under certain conditions, our desired states are obtained as the steady-state solution of the master equation of the system.     

Cluster States from Quantum Logic Gates with Trapped Ions in Thermal Motion

Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86 （2001） 910], a procedure is proposed for one-step realizing quantum control phase gates with two trapped ions in thermal motion. It is shown that the scheme can also be used to create a new special type of entangled states, i.e., cluster states of many trapped ions. In the scheme the two-trapped ions are simultaneously excited by a single laser beam and the frequency of the laser beam is slightly off resonance with the first lower vibration sideband of the trapped ions. The distinct advantage of the scheme is that it does not use the vibrational mode as the data bus. Furthermore, our scheme is insensitive to both the initial motional state and heating （or decay） as long as the system remains in the Lamb-Dicke regime.     

Generation of Vibrational Entangled Coherent States of Two Trapped Ions

We propose a scheme for the generation of entangled coherent states for the center-of-mass and relative vibrational modes of two trapped ions. In the scheme the ions are simultaneously illuminated by a single standing-wave laser tuned to the carrier. The scheme allows the production of an entangled coherent states with a considerably high speed as long as a laser field of sufficiently high intensity is available.     

Generation of Vibrational Entangled Coherent States of Two Trapped Ions

We propose a scheme for the generation of entangled coherent states for the center-of-mass and relative vibrational modes of two trapped ions. In the scheme the ions are simultaneously illuminated by a single standing-wave laser tuned to the carrier. The scheme allows the production of an entangled coherent states with a considerably high speed as long as a laser field of sufficiently high intensity is available.     

Realization of Nonclassical States and Two-Mode Coupling in the Motion of Two Trapped Ions

We propose a scheme to generate various nonclassical vibrational states in the collective motion of twotrapped ions, such as squeezed states, Schrodinger cat states, and SU(2) states. It is based on Raman-type excitations.Two-mode coupling between the center-of-mass and relative vibrational modes can also be realized.     

Generation of Three-Qutrit Singlet States with Two-Level Trapped Ions

We propose an adiabatic-passage scheme for the generation of three-qutrit singlet states with two-level trapped ions. Distinctly different from previous proposals, we encode qutrits in Dicke states with two-level ions and use the adiabatic-evolution techniques in order not to exactly control the laser pulses, making the realization of the scheme much easier. Furthermore, the phonon is only virtually excited in the procedure, so the effect of the phonon losses can be reduced.     

Generation of Three-Qutrit Singlet States with Two-Level Trapped Ions

We propose an adiabatic-passage scheme for the generation of three-qutrit singlet states with two-level trapped ions. Distinctly different from previous proposals, we encode qutrits in Dicke states with two-level ions and use the adiabatic-evolution techniques in order not to exactly control the laser pulses, making the realization of the scheme much easier. Furthermore, the phonon is only virtually excited in the procedure, so the effect of the phonon losses can be reduced.     

Realization of Nonclassical States and Two-Mode Coupling in the Motion of Two Trapped Ions

We propose a scheme to generate various nonclassical vibrational states in the collective motion of two trapped ions, such as squeezed states, Schrödinger cat states, and SU(2) states. It is based on Raman-type excitations. Two-mode coupling between the center-of-mass and relative vibrational modes can also be realized.     

Generation of Superpositions of Two-Mode Coherent States for the Motion of Two Trapped Ions

We propose a method for the generation of superpositions of two-mode coherent states for the center-of-mass and relative vibrational modes of two trapped ions. In the scheme the ions are driven by a single travelling-wave laser field tuned to the carrier. Then a measurement of the internal states collapses the vibrational modes to the entangled coherent state.     

Generation of Superpositions of Two-Mode Coherent States for the Motion of Two Trapped Ions

We propose a method for the generation of superpositions of two-mode coherent states for the center-of-mass and relative vibrational modes of two trapped ions. In the scheme the ions are driven by a single travelling-wave laser field tuned to the carrier. Then a measurement of the internal states collapses the vibrational modes to the entangled coherent state.     

Two Schemes for Generation of Entanglement for Vibronic Collective States of Multiple Trapped Ions

We propose two schemes to prepare entanglement for the vibronic collective states of multiple trapped ions. The first scheme aims to generating multipartite entanglement for vibrational modes of trapped ions, which only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the mediated excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Beyond their fundamental importance, these states may be of interest for experimental studies on decoherence since the present scheme operates in a fast way. The second scheme aims to preparing the continuous variable multimode maximal1y Greenberger-Horne-Zeilinger state. The distinct advantage is that the operation time is only limited by the available laser intensity, not by the inherent mechanisms such as off-resonant excitations. This makes it promising to obtain entanglernent of multiple coherent and squeezing states with desired amplitudes in a reasonable time.     

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.