Abstract

A simple scheme is proposed to generate a N-qubit W state of spatially separated single molecule magnets (SMM) in a cavity-fiber-cavity system. In the present scheme, the framework consisting of entangled qubits can be expediently designed according to our needs. By quantitatively discussing the case of N=4, we show that the effects of SMM’s spontaneous decay and photon leakage out of fiber can be suppressed in our scheme due to the presence of virtual excited processes in SMM and fiber modes. Moreover, we also show that the present scheme is robust with respect to some deviations of experimental parameters, and as a result, the present investigation provides a research clue for realizing multi-partite entanglement between distant SMMs solid-state nanostructures, which may result in a substantial impact on the progress of multi-node quantum information network.

© 2009 Optical Society of America

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2007

M. Hossein-Zadeh, and K. Vahala, "Free ultra-high-Q microtoroid: a tool for designing photonic devices," Optics Express 15166-175 (2007).
[CrossRef] [PubMed]

2006

Hiroki Takesue, "Long-distance distribution of time-bin entanglement generated in a cooled fiber," Optics Express,  14, 3453-3460 (2006).
[CrossRef] [PubMed]

Y.-F. Xiao, Z.-F. Han, J. Gao and G.-C. Guo, "Generation of multi-atom Dicke states through the detection of cavity decay," J. Phys. B: At. Mol. Opt. Phys. 39, 485-491 (2006).
[CrossRef]

2004

C. F. Roos, M. Riebe, H. Haffner, W. Hansel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, "Control and Measurement of Three-Qubit Entangled States," Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

B. Yu, Z.-W. Zhou and G.-C. Guo, "The generation of multi-atom entanglement via the detection of cavity decay," J. Opt. B: Quantum Semiclass. Opt. 6, 86-90 (2004).
[CrossRef]

Y. Wu and L. Deng, "Achieving multifrequency mode entanglement with ultraslow multiwave mixing," Optics Letters 29, 1144-1146 (2004).
[CrossRef] [PubMed]

2003

K. J. Vahala,"Optical microcavities," Nature,  424839-846 (2003).
[CrossRef] [PubMed]

2001

J. M. Raimond, M. Brune, and S. Haroche,"Manipulating quantum entanglement with atoms and photons in a cavity," Rev. Mod. Phys.,  73565-582 (2001).
[CrossRef]

M. N. Leuenberger and D. Loss, "Quantum computing in molecular magnets," Nature (London) 410789-793 (2001).
[CrossRef] [PubMed]

H. J. Briegel and R. Raussendorf, "Persistent Entanglement in Arrays of Interacting Particles," Phys. Rev. Lett. 86, 910-913 (2001).
[CrossRef] [PubMed]

2000

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, "Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement," Nature (London) 403, 515-519 (2000);D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, "Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement," Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef] [PubMed]

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, "Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement," Nature (London) 403, 515-519 (2000);D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, "Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement," Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef] [PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, and C. M. D. J. Wineland, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef] [PubMed]

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, "Step-by-step engineered multiparticle entanglement," Science 288, 2024-2028 (2000).
[CrossRef] [PubMed]

C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature (London) 404, 247-255 (2000).
[CrossRef]

1999

M. Hillery, V. Buˇzek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829-1834 (1999).
[CrossRef]

W. Wernsdorfer and R. Sessoli, "Quantum Phase Interference and Parity Effects in Magnetic Molecular Clusters," Science 284133-135 (1999).
[CrossRef] [PubMed]

Y. Wu and P. T. Leung, "Lasing threshold for whispering-gallery-mode microsphere lasers," Phys. Rev. A 60, 630-633 (1999).
[CrossRef]

1998

A. Karlsson and M. Bourennane, "Quantum teleportation using three-particle entanglement," Phys. Rev. A 58, 4394-4400 (1998).
[CrossRef]

1997

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

N. Gisin and S. Massar, "Optimal Quantum Cloning Machines," Phys. Rev. Lett. 79, 2153-2156 (1997).
[CrossRef]

T. Pellizzari, "Quantum Networking with Optical Fibres," Phys. Rev. Lett. 79, 5242-5245 (1997).
[CrossRef]

D. W. Vernooy and H. J. Kimble, "Quantum structure and dynamics for atom galleries," Phys. Rev. A 551239 (1997).
[CrossRef]

Y.-F. Xiao, Z.-F. Han, and G.-C. Guo, "Quantum computation without strict strong coupling on a silicon chip," Phys. Rev. A 551239 (1997).

1996

Y. Wu, "Effective Raman theory for a three-level atom in the configuration," Phys. Rev. A 54, 1586-1592 (1996).
[CrossRef] [PubMed]

L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, B. Barbara, "Macroscopic quantum tunnelling of magnetization in a single crystal of nanomagnets," Nature (London) 383145-147 (1996).
[CrossRef]

1995

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, "Conditional Quantum Dynamics and Logic Gates," Phys. Rev. Lett. 74, 4083-4086 (1995).
[CrossRef] [PubMed]

I. L. Chuang and Y. Yamamoto, "Simple quantum computer," Phys. Rev. A 52, 3489-3496 (1995).
[CrossRef] [PubMed]

D.P. DiVincenzo, "Quantum Computation," Science 270, 255-261 (1995).
[CrossRef]

1993

R. Sessoli, D. Gatteschi, A. Caneschi, M. A. Novak, "Magnetic bistability in a metal-ion cluster," Nature (London) 365141-143 (1993).
[CrossRef]

1991

A. K. Ekert, "Quantum cryptography based on Bells theorem," Phys. Rev. Lett. 67, 661-663 (1991).
[CrossRef] [PubMed]

1990

D. M. Greenberger, M. A. Horne, A. Shimony, A. Zeilinger, "Bell’s theorem without inequalities," Am. J. Phys. 58, 1131-1143 (1990).
[CrossRef]

Bahr, S.

K. Petukhov, S. Bahr, W. Wernsdorfer, A.-L. Barra, and V. Mosser, "Magnetization dynamics in the singlemolecule magnet Fe8 under pulsed microwave irradiation," Phys. Rev. B 75 064408(1-12) (2007).
[CrossRef]

Bai, Y.-K.

Y.-K. Bai and Z. D. Wang, "Multipartite entanglement in four-qubit cluster-class states," Phys. Rev. A 77, 032313(1-6) (2008).
[CrossRef]

Ballou, R.

L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, B. Barbara, "Macroscopic quantum tunnelling of magnetization in a single crystal of nanomagnets," Nature (London) 383145-147 (1996).
[CrossRef]

Barbara, B.

L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, B. Barbara, "Macroscopic quantum tunnelling of magnetization in a single crystal of nanomagnets," Nature (London) 383145-147 (1996).
[CrossRef]

Barclay, P. E.

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, "Integration of fiber-coupled high-Q SiNx microdisks with atom chips," Appl. Phys. Lett. 89, 131108(1-3) (2006).
[CrossRef]

Barenco, A.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, "Conditional Quantum Dynamics and Logic Gates," Phys. Rev. Lett. 74, 4083-4086 (1995).
[CrossRef] [PubMed]

Barna, J.

M. Misiorny and J. Barna, "Magnetic switching of a single molecular magnet due to spin-polarized current," Phys. Rev. B, 75 134425(1-5) (2007).
[CrossRef]

Barra, A.-L.

K. Petukhov, S. Bahr, W. Wernsdorfer, A.-L. Barra, and V. Mosser, "Magnetization dynamics in the singlemolecule magnet Fe8 under pulsed microwave irradiation," Phys. Rev. B 75 064408(1-12) (2007).
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Figures (7)

Fig. 1.
Fig. 1.

(Color online) (a) The basal configuration for cavity-fiber-cavity system. An assistant SMM is trapped in a central cavity (cavity M) and N entangled SMMs are individually trapped in N cavities (cavity n), which connect with the central cavity together via N fibers. (b) The level configuration of each SMM.

Fig. 2.
Fig. 2.

(Color online) The four-qubitWstate in the configurations of square [panel (a)] and regular tetrahedron [panel (b)].

Fig. 3.
Fig. 3.

(Color online) The fidelity FW of realizing four-qubit W state ∣Ψ W 〉 versus time Ω M t. The parameters are chosen as Ω en =0.5Ω eM , ηn = 25ΩeM (n=1,2,3,4).

Fig. 4.
Fig. 4.

(Color online) The fidelity FW of realizing four-qubit W state ∣Ψ W 〉 versus time ΩeMt and proportional coefficient s [panel (a)] and versus s when t= 4.95ΩeM [panel (b)].

Fig. 5.
Fig. 5.

(Color online) The fidelity FW of realizing four-qubit W state ∣Ψ W 〉versus time Ω eMt and coupling constant η [panel (a)] and versus η when t= [panel (b)].

Fig. 6.
Fig. 6.

(Color online) The fidelity FW of realizing the four-qubit W state ∣Ψ W 〉 versus time γt for different decay rates κ (γa = γf = κ). The corresponding system parameters are chosen as: γn = 8γ (n=1-4), gM = 16γ, Ω n = 10γ, Ω M = 10γ, η = 25γ, and Δ M = Δ n = 100γ.

Fig. 7.
Fig. 7.

(Color online) Fidelity of realizing the W state ∣Ψ W 〉versus κ and γa [panel (a)]; versus κ and γf [panel (b)]; when γt =3.16. The other system parameters are the same as in Fig. 6

Equations (32)

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̂=̂0S+0F+̂,
̂0S=DŜMz2+̂trgμBŜMxH0 +n=1N(DŜnz2+̂trgμBŜnxH0),
̂0F=ħ vM âM âM +n=1Nħvnânân,
̂=[gμB2(ŜM·HMeiωMt+ŜM·MâM)
gμB2 n=1N(Ŝn·Hneiωnt+Ŝn·nân)+H.c. ] ,
HIsc=ΔM 2M2|+(ΩM2M1+GMaM0M2+H.c.)
+n=1N[Δn2n2+(Gnan2n0Ωn1n2+H.c.)],
ΩM(t)=gμBHM(t)2ħ2ŜMy1,GM=gμBM(t)ħ2ŜMx0,
Ωn(t)=gμBHn(t)2ħ2Ŝny1,Gn=gμBn(t)ħ2Ŝnx0,
Heffsc=[ΩeMaM1M1+n=1NΩenan1n0+H.c.] ,
HIcf=n=1N[ηnaMbn+ηnbnan+H.c.] ,
HI=Heffsc+HIcf
=[ΩeMaM0M1+n=1N(ηnaMbn+ηnbnan+Ωenan1n0)+H.c.].
itψ(t)=HIψ(t),
ϕ1=1M0102030400000c0000f,
ϕ2=0M0102030410000c0000f,
ϕ3=0M0102030400000c1000f,
ϕ4=0M0102030401000c0000f,
ϕ5=0M1102030400000c0000f,
ϕ6=0M0102030400000c0100f,
ϕ7=0M0102030400100c0000f,
ϕ8=0M0102030400000c0000f,
ϕ9=0M0102030400000c0010f,
ϕ10=0M0102030400010c0000f,
ϕ11=0M0102130400000c0000f,
ϕ12=0M0102030400000c0001f,
ϕ13=0M0102030400001c0000f,
ϕ14=0M0102031400000c0000f,
ρ˙w=i[HIsc+HIcf,ρ]κM2(aMaMρ2aMρaM+ρaMaM)
i=0,1γaMei2(σeeMρ2σieMρσeiM+ρσeeM)
n=14[γfn2(bnbnρ2bnρbn+ρbnbn)+κn2(ananρ2anρan+ρanan)]
n=14i=0,1γanei2(σeenρ2σienρσein+ρσeen),

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