Generation of Superpositions of Two Bloch States in an Ion Trap

We propose a scheme for the generation of superpositions of two Bloch states for a collection of ions. Inthe scheme the ions are trapped in a linear potential and interact with laser beams. Our scheme does not put anyrequirement on the Lamb-Dicke parameters.     

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.     

Preparation of nonclassical states and measurement of the Wigner function for the collective motion of N trapped ions

We propose a scheme for generating nonclassical states for the centre-of-mass vibrational mode of N trapped ions,including superpositions of several coherent states on a circle and Fock states. In the scheme N trapped ions are driven by a laser beam tuned to the carrier. The scheme also provides a new prospect for laser cooling. The scheme can be used to measure the Wigner function of the collective vibrational mode.     

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.     

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.     

制备囚禁离子的簇态

提出一个方案用于制备囚禁离子的簇态,制备过程中振动模仅仅是被虚激发。方案用双能级离子制备簇态,只要一束激光照射两个相互作用的离子。方案简单易行,成功几率可达到100.     

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.     

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.     

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 Macroscopic Quantum-Interference States for a Collection of Trapped Ions Via a Single Geometric Operation

We describe a scheme for the generation of macroscopic quantum-interference states for a collection of trapped ions by a single geometric phase operation. In the scheme the vibrational mode is displaced along a circle with the radius proportional to the number of ions in a certain ground electronic state. For a given interaction time, the vibrational mode returns to the original state, and the ionic system acquires a geometric phase proportional to the area of the circle, evolving from a coherent state to a superposition of two coherent states. The ions undergo no electronic transitions during the operation. Taking advantage of the inherent fault-tolerant feature of the geometric operation, our scheme is robust against decoherence.     

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.     

Quantum logic gates for hot ions without a speed limitation

We propose a scheme for realizing two-qubit quantum phase gates with trapped ions in thermal motion. In the scheme, the ions are simultaneously illuminated by a standing-wave laser tuned to the carrier, which virtually excites several vibrational modes. The scheme puts no limitations on the intensity of the laser field, allowing the production of a quantum logic gate for hot ions with an arbitrarily high speed as long as a laser field of sufficiently high intensity is available.     

Tunable Nongeometric Phase Gates for Two Hot Ions via Adiabatic Evolution of Dark States

We propose a scheme for implementing nongeometric phase gates fbr two trapped ions via adiabatic passage of dark states. During the operation, the vibrational mode is only virtually excited, thus the scheme is insensitive to heating. Furthermore, the spontaneous emission is suppressed since the ions are always in the electronic ground states. The scheme is robust against small fluctuations of parameters, and the conditional phase is tunable.     

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.     

One-Step Scheme for Realizing N-Qubit Quantum Phase Gates with Hot Trapped Ions

A scheme is presented for realizing an N-qubit quantum phase gate with trapped ions. Taking advantage of the virtual excitation of the vibrational mode, the qubit system undergoes a full-cycle of Rabi oscillation in the selective symmetric Dicke subspace. The scheme only involves a single step and the operation is insensitive to thermal motion. Moreover, the scheme does not require individual addressing of the ions.     

Quantum state engineering for multiple hot trapped ions in the symmetric Dicke subspace

We propose a scheme for the generation of an arbitrary quantum states for multiple trapped ions in the symmetric Dicke subspace. One can manipulate the collective ion transition in a selective symmetric Dicke subspace via the virtual excitation induced inequidistant energy levels. All the states undergo the same phonon-number-dependent Stark shift and thus the scheme is insensitive to the thermal motion. Furthermore, the scheme does not require individual addressing of the ions.     

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.     

Cluster states prepared by using hot trapped ions

We propose a scheme for the preparation of one-dimensional and two-dimensional cluster states by using hot trapped ions. The scheme is based on the interaction between two ions and bichromatic radiation. The vibrational mode in our protocol is only virtually excited so that the system is insensitive to the thermal field. In addition, we only use two levels of ions as qubits and the successful probability may achieve 100%.