Witnessing quantum phase transition in a non-Hermitian trapped ion system via quantum Fisher information

Quantum Fisher information is used to witness the quantum phase transition in a non-Hermitian trapped ion system with balanced gain and loss,from the viewpoint of quantum parameter estimation.We formulate a general non-unitary dynamic of any two-level non-Hermitian system in the form of state vector.The sudden change in the dynamics of quantum Fisher information occurs at an exceptional point characterizing quantum criticality.The dynamical behaviors of quantum Fisher information are classified into two different ways which depends on whether the system is located in symmetry unbroken or broken phase regimes.In the phase regime where parity and time reversal symmetry are unbroken,the oscillatory evolution of quantum Fisher information is presented,achieving better quantum measurement precision.In the broken phase regime,quantum Fisher information undergoes the monotonically decreasing behavior.The maximum value of quantum estimation precision is obtained at the exceptional point.It is found that the two distinct kinds of behaviors can be verified by quantum entropy and coherence.Utilizing quantum Fisher information to witness phase transition in the non-Hermitian system is emphasized.The results may have potential applications to non-Hermitian quantum information technology.

Quantum teleportation by entanglement swapping with trapped ions

An effective teleportation scheme for an unknown ionic internal state via trapped ions is proposed without joint Bell-state measurement （BSM）. In the constructed quantum channel process, we make use of entanglement swapping to avoid decrease in entanglement during the distributing of particles. Thus our scheme provides new prospects for quantum teleportatlon in a longer distance. The distinct advant.age of our scheme is insensitive to the heating of vibrational mode. Furthermore, our scheme has no any individual optical access, and the successful probability also can reach 1.

Generation of Multi-mode Entangled Coherent States for N Trapped Ions in Strong-Excitation Regime

We propose a scheme to generate entangled coherent states for the vibrational modes of N trapped ions.In the scheme the first ion is sequentially excited by two travelling wave laser fields tuned to the ion transition. The scheme works in the strong-excitation regime, which is of experimental importance in view of decoherence.

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%.

Squeezing properties of a trapped ion in the running-wave laser beyond the Lamb-Dicke limit

Beyond the Lamb-Dicke limit, this paper investigates the squeezing properties of the trapped ion in the travelling- wave laser. It shows that the squeezing properties of the trapped ion in the travelling-wave laser are strongly affected by the sideband number k, the Lamb-Dicke parameter η and the initial average phonon number.

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.

Preparation of Squeezed State and Entanglement State Between Vibrational Motion of Trapped Ion and Light

Several schemes have been proposed to prepare two-mode squeezed state and entanglement state betweenmotional states of a single trapped ion and light.Preparation of two-mode squeezed state is based on interaction ofa trapped ion located in light cavity with cavity field.Preparation of entanglement state is based on interaction of atrapped ion located in light cavity with cavity field and a traveling wave light field.

A scheme for the implementation of unconventional geometric phase gates with trapped ions

We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identical two-level ions, In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser pulse with its pulse frequency being tuned to the ionic transition. The gate operation time can be much shorter, making the system robust against decoherence. In addition, we choose the appropriate experimental parameters to construct the geometric phase gate in one step, and thus avoid implementing the pure geometric single qubit operation.

An Analytical Solution to the Model for Single Three-Level Trapped Ion Driven by External Fields

The interaction of a single three-level trapped ion with two laser beams has been studied theoretically. With application of two successive unitary transformations, an analytical solution to this quantum system has been obtained.

Superdense Coding via Hot Trapped Ions

Superdense coding plays an important role in quantum information and can be performed with trapped ions. By confining the ions in a linear trap or a trap-cavity setup, we propose schemes to implement a reliable superdense coding by means of bichromatic radiation method. Experimental feasibility and reliability for achieving our schemes is discussed in detail.

Quantum computation and simulation with vibrational modes of trapped ions

Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource,beyond the role as a mediator for entangling quantum operations on internal degrees of freedom,because of the large available Hilbert space.The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions.Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes,including bosonic encoding schemes in quantum information,reliable and efficient measurement techniques,and quantum operations that allow various quantum simulations and quantum computation algorithms.We describe experiments using the vibrational modes,including the preparation of non-classical states,molecular vibronic sampling,and applications in quantum thermodynamics.We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.

Telecloning Quantum States with Trapped Ions

We propose a scheme for telecloning quantum states with trapped ions. The scheme is based on a single ion interacting with a single laser pulse. In the protocol, an ion is firstly measured to determine whether the telecloning succeeds or not, and then another ion is detected to complete the whole procedure. The required experimental techniques are within the scope of what can be obtained in the ion-trap setup.

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 cavlty, in which the trap works beyond the Lamb--Dicke limit. When the light field is resonant with the atomic transition ｜g） →← ｜e） 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.

Probe of topological invariants using quantum walks of a trapped ion in coherent state space

We present a protocol to realize topological discrete-time quantum walks,which comprise a sequence of spindependent flipping displacement operations and quantum coin tossing operations,with a single trapped ion.It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space.Interestingly,the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process.Furthermore,we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence.Our work provides a simple method to measure bulk topological features in discrete-time quantum walks,which can be experimentally realized in the system of single trapped 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.

Quantum Decoherence of a Single Trapped Ion due to Engineered Reservoir

Known as an engineered reservoir due to fluctuations in trap parameter,a classical source of quantum decoherence is considered for a single trapped ion theoretically.For simplicity it is assumed that the fluctuations involved are white noise processes,which enables us to give a simple master equation description of this source of decoherence.Our results show that the decoherence rate depends on the vibrational quantum number in different ways corresponding to the vibrational excitation sideband used there.Besides,this source of decoherence also leads to occurrence of dissipation in the ion system.

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.

Quantum feedback cooling of two trapped ions

We present a sub-Doppler cooling scheme of a two-trapped-ion crystal by quantum feedback control method. In the scheme, we obtain the motional information by continuously measuring the spontaneous emission photons from one single ion of the crystal, and then apply a feedback force to cool the whole chain down.We derive the cooling dynamics of the cooling scheme using quantum feedback theory and quantum regression theorem. The result shows that with experimentally achievable parameters, our scheme can achieve lower temperature and faster cooling rate than Doppler cooling.

Generation of Entangled Displacement Fock State of Trapped Ion Manipulated by a Laser Beam

The interaction of a single two-level two-mode trapped ion with a laser beam has been studied theoretically. With application of a unitary transformation, an analytical solution to this quantum system has been obtained without performing the Lamb-Dicke approximation. In this system the entangled displacement Fock state is produced.

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.