Nonidentical Coupling－based N－atom W Entanglement

ZHANG Ying－qiao

（Department of Physics，College of Science，Yanbian University，Yanji 133002，China）

Nonidentical Coupling－based N－atom W Entanglement

ZHANG Ying－qiao

（Department of Physics，College of Science，Yanbian University，Yanji 133002，China）

Based on the nonidentical coupling of N atoms with a single－mode cavity，a scheme for generation of an N－atom W state is proposed in cavity QED.Under the condition of the large－detuned interactionΔ≫gj，the influence of cavity decay is negligible.Such multiple－qubit entanglement will have wide applications to largescale quantum communication and quantum computation.

N－atom W state；three－level atom；cavity QED

1 Introduction

Quantum entanglement is an important physical resource in quantum communication［1－3］and quantum computation.So far，a lot of schemes［4－11］have been proposed to generate entanglements based on various of physical systems both in theory and experiment.Most of these schemes are focused on generation of two－qubit or three－qubit entanglements.For example，Turchette et al［6］have produced the deterministic entangled states of two trapped ions.In this scheme，the two qubits are constituted by the internal states of two trapped ions in both the Bell－like singlet and triplet states.Reina et al［7］have prepared the maximally entangled Bell and Greenberger－Horne－Zeilinger states by optically driven the coupled quantum dots.An alternative scheme［8］to generate three－qubit W state via nonlinear optical state truncation using quantum scissors is proposed.Using atom interferometric techniques，the generation of Bell，NOON and W states of an electromagnetic field in high－Q cavities are also proposed［9］.

However，multiple－qubit entanglements are often required to a large－scale quantum information processing.Therefore，the generation of multiple－qubit enanglements have attracted increasingly attentions.For example，an experimental demonstration of five－photon entanglement［10］was provided by generating a four－photon entangled state with two entangled photon pairs and then combining itwith a single－photon state.Based on rf SQUID，a simple scheme was presented to generate the N－qubit W states by adiabatic passage［11］.

Based on the nonidentical coupling of the three three－level atoms with a resonant single－mode vacuum cavity field［12］and the large－detuning interaction of two identical two－level atoms with a singlemode cavity field［13］in cavity QED，as well as the combination of the coherent dynamics of the above two schemes［14］，we propose a scheme for generation of an N－atom W state.Though it is a generalization of the previous three－atom W state scheme［15］，it is universal to multiple－qubit case.

This paper is organized as follows：In Sec.Ⅱ we describe the coupling dynamics of N atoms interaction with a single－mode cavity.In Sec.Ⅲ we describe the generation of an N－atom W state.Conclusion is given in Sec.Ⅳ.

2 Coupling Dynamics of N Atoms Interaction with a Single－mode Cavity

We consider that N three－level atoms simultaneously interact with a single－mode cavity field.Each atom has one excited state｜e〉and two ground states｜g〉and｜r〉.In our scheme，the state｜r〉is not involved in the interaction with the cavity mode.In the rotating－wave approximation，the interaction Hamiltonian in the interaction picture can be written as（assumingħ＝1）

where S＋j＝｜e〉j〈g｜，S－j＝｜g〉j〈e｜（j＝1，2，…，N）.a†and a are the creation and annihilation operators of the single－mode cavity，respectively.gjis the coupling constant of the j th atom to the cavity mode.Δ＝ω0－ωwithω0andωbeing the atomic transition frequency and cavity frequency，respectively.In the case ofΔ≫gj，there is no energy exchange between the atomic system and the cavity，the effective Hamiltonian is

whereλj＝g2j／Δandλjk＝gjgk／Δ.The first two terms denote the photon－number dependent Stark shifts，and the third term denotes the cavity mode－induced dipole coupling among the N atoms.Assuming that the coupling constant for the first atom with the cavity is g1and the coupling constants for the other atoms with the cavity are g ＝gj（j＝2，3，…，N）.If the cavity field is in the vacuum state initially，the effective Hamiltonian becomes

whereλ1＝g21／Δand g2／Δ.

3 Generation of an N－atom W State

We assume that the N atoms are in the state〉，initially.The state evolution is

where

If the interaction time satisfy t＝ （2k＋1）π／［（N－1）l＋1］λ1（k is an integer）and the parameters that related to nonidentical atom－cavity coupling satisfywe obtain

Therefore we have generated an N－atom W state

4 Conclusion

In conclusion，we have proposed an universal scheme for generation of an N－atom W state based on the nonidentical coupling of N atoms with a single－mode cavity.Under the large－detuned interaction of the N atoms with the single－mode cavity（Δ≫gj），the influence of cavity decay is negligible.Such multiple－qubit entanglements are often required to a large－scale quantum communication and quantum computation.

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1004－4353（2011）03－0242－03

基于非全同耦合的N－ 原子W纠缠态

张英俏
（延边大学理学院 物理系，吉林 延吉133002）

在腔QED中利用N个原子与一个单模腔的非全同耦合提出一个制备N原子W纠缠 态的方案.在大失谐相互作用Δ≫gj的条件下，腔衰减的影响可以忽略.此类多比特纠缠态可广泛应用于级联量子通讯和量子计算中.

N原子W态；三能级原子；腔QED

2011 -05 -14

张英俏（1978—），女，理学博士，讲师，研究方向为量子信息学.

0365；4250

A