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.     

Preparation of Highly Squeezed States and Multi—component Entangled Coherent States via the Raman Interaction

A method is presented for generating highly squeezed states of a cavity field via the atom-cavity field interaction of the Raman type.In the scheme a sequence of three-level Λ-type atoms interacts with a cavity field,displaced by a classical source,in a Raman manner.Then the atomic states are measured.By this way the cavity field may collapse onto a superposition of several coherent states,which exhibits strong squeezing.The scheme can also be used to prepare superpositions of many two-mode coherent states for two cavity fields.The coherent states in each mode are on a straight line.This is the first way for preparing multi-component entangled coherent states of this type in cavity QED.     

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.     

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.     

Preparation of multicomponent motional coherent and squeezed coherent states of a trapped ion

In this paper, we present a scheme for preparation of multicomponent motional coherent and squeezed coherent states of the quantized centre of mass of an ion trapped in a one-dimensional harmonic potential and driven by two travelling-wave laser beams tuned to the nth red and blue vibrational sidebands, respectively. In addition, our scheme also provides experimental possibility for quantum state engineering.     

Generation and classification of robust remote symmetric Dicke states

In this paper, we present an approach to generating arbitrary symmetric Dicke states with distant trapped ions and linear optics. Distant trapped ions can be prepared in the symmetric Dicke states by using two photon-number-resolving detectors and a polarization beam splitter. The atomic symmetric Dicke states are robust against decoherence, for atoms are in a metastable level. We discuss the experimental feasibility of our scheme with current technology. Finally, we discuss the classification of arbitrary n-qubit symmetric Dicke states under statistical local operation and classical communication and prove the existence of [n/2] inequivalent classes of genuine entanglement of n-qubit symmetric Dicke states.     

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 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. In the scheme the ions are trapped in a linear potential and interact with laser beams. Our scheme does not put any requirement on the Lamb-Dicke parameters.     

Vibratile Coherence and Squeezing in Two Trapped Ions

It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode,in Lamb-Dicke regime and under rotating wave approximation,is described by a Jaynes-Cummings model.For the initial condition that the motional state of center-of-mass mode is in vacuum state and the internal state is prepared in a coherent superposition of states,coherence and squeezing for the vibratile motion of center-of-mass mode are discussed,particularly,a“weak” coherent state and a “weak” squeezed vacuum state are obtained.Collapse and revival are also observed in this type of initial condition.     

Entanglement and Phase-Covariant Cloning for Multiple Trapped Ions via Adiabatic Passage

We describe a scheme for the generation of W states and implementation of phase-covariant cloning for n trapped ions. The scheme does not use the vibational mode as the memory and works beyond the Lamb-Dicke regime. The procedure is robust against moderate fluctuations of experimental parameters by using adiabatic passage.     

Realization of superposition and entanglement of coherent and squeezed states in circuit quantum electrodynamics

We propose a new scheme for generating the superposition and entanglement of the coherent states and squeezed states by considering N superconducting charge qubits (or artificial two-level atoms) interacting with photons in a high finesse cavity on a chip, assisted by a strong driving field. By virtue of the parameters of this system, we can generate novel quantum states, for example, multiparty entangled states and Schro¨dinger cat states among the superconducting qubits, coherent states and squeezed state...     

Preparation of the W State of Atoms in a Single Cavity or N Distant Cavities by Photon Interference

We suggest two schemes to generate the W state of N A-type three-level atoms. In the schemes, identical N three-level atoms are trapped in a cavity or N distant cavities. The success or failure of the generation of the W state can be determined by detecting the polarization of photon leaking out of the cavity. The result demonstrates that the W state is free from both the cavity loss and the spontaneous emission due to the fact that the two ground states (left and right) of the three-level atoms are stable states (or metastable states).     

Coupling Between the Group—Related Coherent States

When two representations of the Lie algebra are coupled,the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states,These kernels have a connection with usual coupling coefficients.The explicit expressions of these kernels for SU(2),SO(4) and SUq(2) are given.When the direct product of three representations is formed in two ways,the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced,and the relations between these kernels and the general recoupling coefficients are obtained.The properties of these kerels are discussed.     

Algebraic and group treatments to nonlinear displaced number states and their nonclassicality features:A new approach

Recently,nonlinear displaced number states(NDNSs) have been manually introduced,in which the deformation function f(n) has been artificially added to the previously well-known displaced number states(DNSs).Indeed,just a simple comparison has been performed between the standard coherent state and nonlinear coherent state for the formation of NDNSs.In the present paper,after expressing enough physical motivation of our procedure,four distinct classes of NDNSs are presented by applying algebraic and group treatments.To achieve this purpose,by considering the DNSs and recalling the nonlinear coherent states formalism,the NDNSs are logically defined through an algebraic consideration.In addition,by using a particular class of Gilmore–Perelomov-type of SU(1,1) and a class of SU(2) coherent states,the NDNSs are introduced via group-theoretical approach.Then,in order to examine the nonclassical behavior of these states,sub-Poissonian statistics by evaluating Mandel parameter and Wigner quasi-probability distribution function associated with the obtained NDNSs are discussed,in detail.     

Quantum Fisher Information of Entangled Coherent States in a Lossy Mach–Zehnder Interferometer

We give an analytical result for the quantum Fisher information of entangled coherent states in a lossy Mach-Zehnder interferometer recently proposed by Joo et al., [Phys. Rev. Lett. 107 （2011） 083601]. For small loss of photons, we find that the entangled coherent state can surpass the Heisenberg limit. Phrthermore, the formalism developed here is applicable to the study of phase sensitivity of multipartite entangled coherent states.     

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 Mechanical Version of z-Transform Related to Eigenkets of Boson Creation Operator

Using the completeness relation composed of the coherent state and of the eigenket of bosonic creation operator, we establish a one-to-one correspondence between the z-transform and the quantum-mechanical transform from the representation by number states |n) to the representation by coherent states |(z)) (Bargmann representation).In this way, the quantum-mechanical version of the various properties of z-transform are obtained and the operators for embodying these properties in the Fock space are derived, which may find applications in quantum states engineering.     

On Husimi Distribution for Systems with Continuous Spectrum

We propose a procedure to generalize the Husimi distribution to systems with continuous spectrum. We start examining a pioneering work, by Gazeau and Klauder, where the concept of coherent states for systems with discrete spectrum was extended to systems with continuous one. In the present article, we see the Husimi distribution as a representation of the density operator in terms of a basis of coherent states. There are other ways to obtain it, but we do not consider here. We specially discuss the problem of the continuous harmonic oscillator.     

Generation of Entangled Coherent States in Raman-Coupled Bose-Einstein Condensates

A method for producing entangled coherent states (ECSs) for atomic Bose-Einstein condensates (BECs) ispresented. The proposed method involves a BEC with three internal states and two classical laser beams ina three-level Lambda configuration. We show how to generate multi-state ECSs through properly manipulatingstrengths of these interactions and laser detunings. A maximally entangled coherent state is obtained explicitly.