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.     

Quantum state swap for two trapped Rydberg atoms

The quantum swap gate is one of the most useful gates for quantum computation. Two-qubit entanglement and a controlled-NOT quantum gate in a neutral Rydberg atom system have been achieved in recent experiments. It is therefore very interesting to propose a scheme here for swapping a quantum state between two trapped neutral atoms via the Rydberg blockade mechanism. The atoms interact with a sequence of laser pulses without individual addressing. The errors of the swap gate due to imprecision of pulse length, finite Rydberg interaction, and atomic spontaneous emission are discussed.     

A scheme of quantum phase gate for trapped ion

We propose a scheme to implement two-qubit controlled quantum phase gate(CQPG) via a single trapped two-level ion located in the standing wave field of a quantum cavity, in which the trap works beyond the Lamb--Dicke limit. When the light field is resonant with the atomic transition $|g\rangle\leftrightarrow|e\rangle$ of the ion located at the antinode of the standing wave, we can perform CQPG between the internal and external states of the trapped ion; while the frequency of the light field is chosen to be resonant with the first red sideband of the collective vibrational mode of the ion located at the node of the standing wave, we can perform CQPG between the cavity mode and the collective vibrational mode of the trapped ion. Neither the Lamb--Dicke approximation nor the assistant classical laser is needed. Also we can generate a GHZ state if assisted with a classical laser.     

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.     

Long-range quantum gates using dipolar crystals

We propose the use of dipolar spin chains to enable long-range quantum logic between distant qubits. In our approach, an effective interaction between remote qubits is achieved by adiabatically following the ground state of the dipolar chain across the paramagnet to crystal phase transition. We demonstrate that the proposed quantum gate is particularly robust against disorder and derive scaling relations, showing that high-fidelity qubit coupling is possible in the presence of realistic imperfections. Possible experimental implementations in systems ranging from ultracold Rydberg atoms to arrays of nitrogen vacancy defect centers in diamond are discussed.     

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.     

Collisional and radiative processes with participation of highly excited states of atoms and molecules

A number of processes in which highly excited states of atoms and molecules participate are investigated. These processes are of interest for the kinetics of a low-temperature plasma, for atomic and molecular spectroscopy, and for astrophysics. A quasiclassical theory is developed for transitions between Rydberg states with change of the principal quantum number, and also for the processes of direct and associative ionization of highly excited atoms, which result from collisions between a neutral particle and its atomic core. The state of the inner electrons of a quasimolecular (molecular) ion is not altered by transitions of the outer electrons. Specific calculations are carried out for the case of the collision of hydrogen H(n) with helium He (1s²) atoms. It is shown that the cross sections and the rate constants of these processes are determined in this case by the mechanism investigated in the paper, and not by scattering of the Rydberg electron by the neutral particle. The cross sections for dipole excitation and dissociation of molecular ions from high vibrational energy levels by electron impact is calculated in the Born-Coulomb approximation. The cross sections and the rates of dissociative and three-particle attachment of electrons to ions are determined. The processes of autoionization and autodissociation decay of Rydberg states of vibrationally excited molecules are determined. Also investigated are radiative transitions near the dissociation limit of diatomic molecular ions and neutral molecules, viz., photodissociation and radiative decay of high vibrational levels, and photodissociation and translational (inverse-bremsstrahlung) absorption in collision of atomic particles.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. Lebedeva AN SSSR, Vol. 145, pp. 80–130, 1984.     

Geometric phase gate with trapped ions in thermal motion by adiabatic passage

We propose a scheme for implementing two-qubit geometric phase gate via the adiabatic evolution for trapped ions in thermal motion, leveraging on the stimulated Raman adiabatic passage with the geometric phase mechanism. Evolution along a dark state makes our scheme not only immune from decoherence due to spontaneous emission from excited states, but also rid off the dynamical phase. Furthermore, due to the opposite detuning of the driving lasers, the vibrational states of the trapped ions are only virtually excited during the operations, so our scheme is also insensitive to the occupation number of the vibrational mode.     

ns6s里德堡分子的势能曲线

里德堡电子与基态原子的低能电子散射形成长程里德堡分子,这种分子具有大的轨道半径,丰富的振动能级和永久电偶极矩等特点。本文考虑铯里德堡ns态与(n-4)l(n为主量子数,l为角量子数且l2)近简并态的非绝热耦合与p-波共振现象,数值计算了长程铯里德堡分子的势能曲线。分析ns6s(n=32-36)态分子最外层势阱,研究了长程里德堡分子的势阱深度、平衡距离与主量子数n的关系,为实验研究长程里德堡分子提供理论依据。     

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.     

Cold atoms and molecules in self-assembled dipolar lattices

We study the realization of lattice models, where cold atoms and molecules move as extra particles in a dipolar crystal of trapped polar molecules. The crystal is a self-assembled floating mesoscopic lattice structure with quantum dynamics given by phonons. We show that within an experimentally accessible parameter regime extended Hubbard models with tunable long-range phonon-mediated interactions describe the effective dynamics of dressed particles.     

Rydberg states in the condensed phase studied by fluorescence depletion spectroscopy

Higher Rydberg states of NO trapped in rare gas matrices have been studied by inducing Rydberg-Rydberg transitions from the lowest Rydberg state and detecting its fluorescence depletion. This technique unravels Rydberg states, which cannot be accessed by ground state absorption. However, no clear cut Rydberg series show up. The data show a compression of the n-(n + 1) splittings between Rydberg states, as well as of the splittings. The results are rationalised in terms of the quantum defect model and the lack of extended Rydberg series is due to the compression of high-n Rydberg states in a tiny energy region below the ionisation potential. Finally, fluorescence depletion data of NO trapped in amorphous sites (the so-called red sites) of solid Ar can be interpreted in terms of the gas phase NO-Ar van der Waals data. A general discussion on the fate of Rydberg states in van der Waals complexes, in liquids, and in solids is presented in an attempt to relate the data in these different media. Received 28 July 1999 and Received in final form 8 November 1999     

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.     

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.     

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.     

Quantum Nondemolition Measurement of the Collective Motional Energy of Two Trapped Ions

We propose a quantum nondemolition measurement of the collective motional energy of two trapped ions for the first time.It is based on the excitation of the two ions by two lasers with appropriate frequencies and amplitudes.The scheme also provides a new possibility of preparing vibrational Fock states and laser cooling.     

Mode shaping in mixed ion crystals of 40Ca2+ and 40Ca+

We present studies of mixed Coulomb crystals of ⁴⁰Ca⁺ and ⁴⁰Ca²⁺ ions in a linear Paul trap. Doubly charged ions are produced by photoionization of trapped ⁴⁰Ca⁺ with a vacuum ultraviolet laser source and sympathetically cooled via Doppler cooled ⁴⁰Ca⁺ ions. We investigate experimentally and theoretically the structural configurations and the vibrational modes of these mixed crystals. Our results with ⁴⁰Ca²⁺ are an important step towards experimental realization of the proposals for mode shaping in a linear crystal and spin-dependent configuration changes from zigzag to linear as proposed by Li et al. (Phys Rev A 87:052304, 2013) and Li and Lesanovsky (Phys Rev Lett 108:023003, 2012) using ions excited to Rydberg states.     

Robust entanglement

It is common belief among physicists that entangled states of quantum systems lose their coherence rather quickly. The reason is that any interaction with the environment which distinguishes between the entangled sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca⁺ ions and observe robust entanglement lasting for more than 20 s.     

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