We propose a new entanglement switch of qubits consisting of electric
dipoles, oriented along or against an external electric field and coupled by
the electric dipole-dipole interaction. The pairwise entanglement can be tuned
and controlled by the ratio of the Rabi frequency and the dipole-dipole
coupling strength. Tuning the entanglement can be achieved for one, two and
three-dimensional arrangements of the qubits. The feasibility of building such
an entanglement switch is also discussed.Comment: 6 pages and 4 figures. To be published on Journal of Chemical Physic

Ficek Z.

Krems R.

Nielsen M. A.

Qi Wei

Sabre Kais

Yong P. Chen

English

arXiv

We propose a new entanglement switch of qubits consisting of electric dipoles oriented along or against an external electric field and coupled by the electric dipole-dipole interaction. The pairwise entanglement can be tuned and controlled by the ratio of the Rabi frequency and the dipole-dipole coupling strength. Tuning the entanglement can be achieved for one, two, and three-dimensional arrangements of the qubits. The feasibility of building such an entanglement switch is also discussed

Wei, Qi

Kais, Sabre

Chen, Yong P

Purdue E-Pubs

Purdue UniversityPurdue e-PubsBirck and NCN Publications Birck Nanotechnology Center3-2010Communications: Entanglement switch for dipolearraysQi WeiPurdue University - Main CampusSabre KaisBirck Nanotechnology Center and Department of Chemistry, Purdue University, kais@purdue.eduYong P. ChenPurdue University - Main Campus, yongchen@purdue.eduFollow this and additional works at: http://docs.lib.purdue.edu/nanopubPart of the Nanoscience and Nanotechnology CommonsThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Wei, Qi; Kais, Sabre; and Chen, Yong P., "Communications: Entanglement switch for dipole arrays" (2010). Birck and NCNPublications. Paper 655.http://dx.doi.org/10.1063/1.3366522Communications: Entanglement switch for dipole arraysQi Wei,1 Sabre Kais,1,a and Yong P. Chen21Department of Chemistry and Birck Nanotechnology Center, Purdue University, West Lafayette,Indiana 47907, USA2Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette,Indiana 47907, USAReceived 25 January 2010; accepted 25 February 2010; published online 29 March 2010We propose a new entanglement switch of qubits consisting of electric dipoles oriented along oragainst an external electric field and coupled by the electric dipole-dipole interaction. The pairwiseentanglement can be tuned and controlled by the ratio of the Rabi frequency and the dipole-dipolecoupling strength. Tuning the entanglement can be achieved for one, two, and three-dimensionalarrangements of the qubits. The feasibility of building such an entanglement switch is alsodiscussed. © 2010 American Institute of Physics. doi:10.1063/1.3366522Entanglement is a quantum mechanical property that de-scribes a correlation between quantum mechanical systems.It has no classical analog and has been lying in the heart ofthe foundation of quantum mechanics. The desire to under-stand, tune, and manipulate quantum entanglement is of fun-damental importance in the field of quantum information andcomputation.1–4 Recently, we studied a set of localized spinscoupled through exchange interaction and subject to an ex-ternal magnetic field.5–8 We demonstrated for such a class ofone-dimensional magnetic systems, that entanglement can becontrolled and tuned by varying the anisotropy parameter inthe Hamiltonian and by introducing impurities into thesystems.4 In this letter, we propose a new entanglementswitch of qubits consisting of the electric dipole moment ofdiatomic polar molecules, oriented along or against an exter-nal electric field and coupled by the electric dipole-dipoleinteraction.Recent progress in methods for producing, trapping, andcontrolling cold polar molecules make them an excellentcandidate for quantum computation.9–12 Trapped polar mol-ecules was proposed as a novel physical realization of aquantum computer by a number of authors.12–20 In this pro-posal, the qubits are the molecular electric dipole momentswhich can only orient along 0 or against 1 the externalelectric fields. Each qubit is one polar molecule with equalspacing along the axis. For such a system, tuning and con-trolling the entanglement between the dipoles is of great im-portance.The Hamiltonian of N-trapped dipoles in an externalelectric field reads21H = i=1NiŜiz + ijNijŜi+Ŝj−, 1where Ŝ’s are the dipole operators and related to Pauli ma-trices, Ŝi+ and Ŝj− represent dipole excitation and de-excitation, respectively. i is the transition frequency of thedipole on site i, which is a function of dipole moment andexternal electric fields at site i.i = d · E  , 2where d is the electric dipole moment which we assume thesame for each site. ij is the dipole-dipole coupling constantbetween sites i and j, which is determined by the strength ofdipole moment, the direction of the external electric field andthe lattice constant of the dipole array.ij =d 21 – 3 cos2 rij3, 3where  is the angle between rij and external electric field.We will expand the Hamiltonian in pure standard basis,00 , 01 , 10 , 11	, and all the eigenstates will beobtained by diagonalizing the Hamiltonian matrix. For ex-ample, for N=2, we obtained the following four eigenvec-tors: 1= 00 , 2= 1 /201− 10 , 3= 1 /201+ 10 , 4= 11 with corresponding eigenvalues:E1=0 , E2=− , E3=+ , E4=2. For the ratio  /1, 2 is fully entangled ground state. However, for /1 the nonentangled state 1 is the ground state. Thus,we have a curve crossing at  /=1.The concept of entanglement of formation is related tothe amount of entanglement needed to prepare the state 	,where 	 is the density matrix. It was shown by Wootters22that concurrence is a good measure of entanglement.23 Theconcurrence C is given by22C	 = max0,1 − 2 − 3 − 4	 . 4For a general state of two qubits, i’s are the eigenvalues, indecreasing order, of the Hermitian matrix R		̃	 where	 is the density matrix and 	̃ is the spin-flipped state definedas	̃ = y  y	y  y , 5where the 	 is the complex conjugate of 	 and is taken inthe standard basis, which for a pair of two level particles is00 , 01 , 10 , 11	.aAuthor to whom correspondence should be addressed. Electronic mail:kais@purdue.edu.THE JOURNAL OF CHEMICAL PHYSICS 132, 121104 20100021-9606/2010/13212/121104/4/$30.00 © 2010 American Institute of Physics132, 121104-1Downloaded 28 Oct 2010 to 128.210.126.199. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissionsIn order to calculate thermal entanglement, we need thetemperature dependent density matrix and the density matrixfor a system in equilibrium at a temperature T reads:	=e−Ĥ/Z with =1 /kT and Z is the partition function,Z=Tre−Ĥ. In this case, the partition function isZT = igie−i, 6where i is the ith eigenvalue and gi is the degeneracy. Andthe corresponding density matrix can be written	T =1ZiNe−iii , 7where i is the ith eigenfunction. For pairwise thermal en-tanglement, we can get reduced density matrix as a functionof temperature in the same way, which leads to temperaturedependent entanglement.In Fig. 1 we show the tuning of the pairwise entangle-ment, measured by concurrence, of one-dimensional arrange-ments of the dipoles as one varies the ratio  / at differenttemperatures for N=9 dipoles. Here we took all transitionfrequencies to be the same, i=, and the nearest neighbordipole-dipole interaction to be the same, i,i+1=i,i−1=.All other dipole-dipole coupling constants i,ji1 can beexpressed in terms of . Thus, we have two parameters tovary, the ratio  / and temperature kT. At kT0 one has aconstant entanglement over a long ratio  / and sharp tran-sitions or jumps to lower values at other values of  /. It isworth mentioning that for  /0.634, entanglement isonly between dipoles 1 and 2. For 0.634 /1.14 di-pole one becomes entangled also with dipole 3 and withother dipoles until we reach  /1.74, above this value theconcurrence is zero between all sites. As one increases thetemperature, the curve becomes smoother as mixing occurwith higher states. Calculations for N=3,4 , . . .8 gave similarbehavior of tuning and controlling entanglement as for thecase N=9. To show how the populations changes at the tran-sition point, we present in Fig. 2 the coefficients ofthe wave function for N=4 before and after the transitionpoint  /=0.64. When  /0.64, the ground state waveFIG. 1. Pairwise concurrence Eq. 4 of one-dimensional arrangements ofthe dipoles as one varies the ratio  / at kT=10−4, 10−2, and 10−1 ,respectively, for N=9 dipoles.FIG. 2. Pairwise concurrence Eq. 4 and coefficients of the wave functionof one-dimensional arrangements of the dipoles as one varies the ratio  /at kT=10−4  for N=4 dipoles.121104-2 Wei, Kais, and Chen J. Chem. Phys. 132, 121104 2010Downloaded 28 Oct 2010 to 128.210.126.199. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissionsfunction is  =0.19↓↓ ↑↑−0.51↓↑ ↓↑+0.45↓↑ ↑↓+0.45↑↓ ↓↑−0.51↑↓ ↑↓+0.19↑↑ ↓↓, however, when /0.64, the ground state wave function becomes  =0.36↓↓ ↓↑−0.61↓↓ ↑↓+0.61↓↑ ↓↓−0.36↑↓ ↓↓. Fig-ures 3 and 4 show a similar phenomena for two and three-dimensional arrangements of the dipoles. The pairwise en-tanglement decreases as one increases the dimensionality ofthe system and the temperature.There have been rapid advances made recently in cool-ing, trapping and manipulating atomic Rydberg24–26 andmolecular dipoles.10,11,27–29 For example, a wide variety ofground state polar molecules with large electric dipole mo-ments several debyes, where 1 D 3.310−30 C m havebeen cooled to ultracold mK or below regime, some evennear quantum degeneracy.29 These developments provide ex-citing opportunities to experimentally realize the entangle-ment switch described above, which requires tuning  /around 1, and cooling the dipoles to temperatures T corre-sponding to a fraction of the dipole-dipole interaction energy.30 For a dipole moment p of few debyes, and a typicalexperimental electric field 105 V /m, required for the di-pole moment to actually manifest itself12,31, dipole-dipole separation d on the order of 10 nm is required for /1. Such d is much shorter than what can be achievedin typical optical lattices as envisaged in Ref. 12 whichcorresponds to the regime of  /1, but can be realizedwith arrays of nanoscale plasmon-enhanced electric/electro-optical traps recently proposed32,33 where extremely tight,few-nanometer confinement, and trap frequencies exceeding100 MHz are shown to be possible. At such short d, thedipole-dipole interaction = p2 /40d3 is on the order of0.1 K. Cooling to a small fraction of such a temperature scaleis easily within the current experimental technology. Further-more,  / can be tuned experimentally by the electricalfield, and/or by d e.g., by varying the microtrap configura-tion.In summary, we presented a new way to construct anentanglement switch in an optical lattice and discussed theexperimental feasibility of building such switch. The realiza-tion of such a scheme will have a profound impact on theimplementation of quantum gates in quantum computingwith trapped polar molecules. The similar idea could in prin-ciple also be applied to other systems with electric dipoles,such as quantum dots and excitons in nanostructures.We would like to thank the ARO for financial support.Y.P.C. acknowledges partial support from National ScienceFoundation Grant CCF No. 0829918.1 M. A. Nielsen and I. L. Chuang, Quantum Computation and QuantumInformation University Press, Cambridge, 2000.2 L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 5172008.3 V. Vedral, Nature London 453, 1004 2008.4 S. Kais, Adv. Chem. Phys. 134, 493 2007.5 O. Osenda, Z. Huang, and S. Kais, Phys. Rev. A 67, 062321 2003.6 Z. Huang, O. Osenda, and S. Kais, Phys. Lett. A 322, 137 2004.7 Z. Huang and S. Kais, Int. J. Quantum Inf. 3, 483 2005.8 Z. Huang and S. Kais, Phys. Rev. A 73, 022339 2006.9 R. Krems, W. C. Stwalley, and B. Friedrich, Cold Molecules: Theory,Experiment, Applications Taylor Francis, London, 2009.10 D. Herschbach, Faraday Discuss. 142, 9 2009.11 B. Friedrich and J. M. Doyle, ChemPhysChem 10, 604 2009.12 D. DeMille, Phys. Rev. Lett. 88, 067901 2002.13 G. K. Brennen, I. H. Deutsch, and P. S. Jessen, Phys. Rev. A 61, 0623092000.14 G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, Phys. Rev.Lett. 82, 1060 1999.15 A. Micheli, G. K. Brennen, and P. Zoller, Nat. Phys. 2, 341 2006.16 M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I.Cirac, and P. Zoller, Phys. Rev. Lett. 87, 037901 2001.17 D. Jaksch, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 85, 2208 2000.18 S. F. Yelin, K. Kirby, and R. Cote, Phys. Rev. A 74, 050301R 2006.19 E. Charron, P. Milman, A. Keller, and O. Atabek, Phys. Rev. A 75,033414 2007.20 E. Kuznetsova, R. Cote, K. Kirby, and S. F. Yelin, Phys. Rev. A 78,012313 2008.21 Z. Ficek and S. Swain, Quantum Interference and Coherence Theory andExperiment Springer, New York, 2004.22 W. K. Wootters, Phys. Rev. Lett. 80, 2245 1998.FIG. 3. Pairwise concurrence Eq. 4 for different two-dimensional ar-rangements of the dipoles as one varies the ratio  / at kT=10−4 . Theexternal electric field is perpendicular to the 2-d plane.FIG. 4. Pairwise concurrence Eq. 4 of three-dimensional simple cubicarrangements of the dipoles as one varies the ratio  / at kT=10−4 .Here  is the dipole-dipole coupling constant between dipole 1 and dipole2, =12. The external electric field is along dipoles 1 to 5.121104-3 Entanglement switch for dipole arrays J. Chem. Phys. 132, 121104 2010Downloaded 28 Oct 2010 to 128.210.126.199. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions23 S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 1997.24 E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G.Walker, and M. Saffman, Nat. Phys. 5, 110 2009.25 T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemuller, Phys. Rev.Lett. 104, 013001 2010.26 R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Low, and T.Pfau, Phys. Rev. Lett. 100, 033601 2008.27 K. K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Pe’er, B. Neyenhuis, J.J. Zirbel, S. Kotochigova, P. S. Julienne, D. S. Jin, and J. Ye, Science322, 231 2008.28 J. Deiglmayr, A. Grochola, M. Repp, K. Mörtlbauer, C. Glück, J. Lange,O. Dulieu, R. Wester, and M. Weidermüller, Phys. Rev. Lett. 101,133004 2008.29 L. D. Carr, D. DeMille, R. V. Krems and J. Ye, New J. Phys. 11, 0550492009.30 M. Aymar and O. Dulieua, J. Chem. Phys. 122, 204302 2005.31 J. L. Bohn, e-print arXiv:0901.0276.32 D. E. Chang, J. D. Thompson, H. Park, V. Vuletić, A. S. Zibrov, P. Zoller,and M. D. Lukin, Phys. Rev. Lett. 103, 123004 2009.33 B. Murphy and L. V. Hau, Phys. Rev. Lett. 102, 033003 2009.121104-4 Wei, Kais, and Chen J. Chem. Phys. 132, 121104 2010Downloaded 28 Oct 2010 to 128.210.126.199. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

Communications: Entanglement switch for dipole arrays

We propose a new entanglement switch of qubits consisting of electric dipoles                 oriented along or against an external electric field and coupled by the electric                 dipole-dipole interaction. The pairwise entanglement can be tuned and controlled by                 the ratio of the Rabi frequency and the dipole-dipole coupling strength. Tuning the                 entanglement can be achieved for one, two, and three-dimensional arrangements of the                 qubits. The feasibility of building such an entanglement switch is also             discussed

Wei, Q.

Kais, S.

Chen, Y. P.

PhysicsPhysics Research PublicationsPurdue University Year Communications: Entanglement switchfor dipole arraysQ. Wei S. KaisY. P. ChenThis paper is posted at Purdue e-Pubs.http://docs.lib.purdue.edu/physics articles/1341Communications: Entanglement switch for dipole arraysQi Wei,1 Sabre Kais,1,a and Yong P. Chen21Department of Chemistry and Birck Nanotechnology Center, Purdue University, West Lafayette,Indiana 47907, USA2Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette,Indiana 47907, USAReceived 25 January 2010; accepted 25 February 2010; published online 29 March 2010We propose a new entanglement switch of qubits consisting of electric dipoles oriented along oragainst an external electric field and coupled by the electric dipole-dipole interaction. The pairwiseentanglement can be tuned and controlled by the ratio of the Rabi frequency and the dipole-dipolecoupling strength. Tuning the entanglement can be achieved for one, two, and three-dimensionalarrangements of the qubits. The feasibility of building such an entanglement switch is alsodiscussed. © 2010 American Institute of Physics. doi:10.1063/1.3366522Entanglement is a quantum mechanical property that de-scribes a correlation between quantum mechanical systems.It has no classical analog and has been lying in the heart ofthe foundation of quantum mechanics. The desire to under-stand, tune, and manipulate quantum entanglement is of fun-damental importance in the field of quantum information andcomputation.1–4 Recently, we studied a set of localized spinscoupled through exchange interaction and subject to an ex-ternal magnetic field.5–8 We demonstrated for such a class ofone-dimensional magnetic systems, that entanglement can becontrolled and tuned by varying the anisotropy parameter inthe Hamiltonian and by introducing impurities into thesystems.4 In this letter, we propose a new entanglementswitch of qubits consisting of the electric dipole moment ofdiatomic polar molecules, oriented along or against an exter-nal electric field and coupled by the electric dipole-dipoleinteraction.Recent progress in methods for producing, trapping, andcontrolling cold polar molecules make them an excellentcandidate for quantum computation.9–12 Trapped polar mol-ecules was proposed as a novel physical realization of aquantum computer by a number of authors.12–20 In this pro-posal, the qubits are the molecular electric dipole momentswhich can only orient along 0 or against 1 the externalelectric fields. Each qubit is one polar molecule with equalspacing along the axis. For such a system, tuning and con-trolling the entanglement between the dipoles is of great im-portance.The Hamiltonian of N-trapped dipoles in an externalelectric field reads21H = i=1NiSˆ iz + ijNijSˆ i+Sˆ j−, 1where Sˆ ’s are the dipole operators and related to Pauli ma-trices, Sˆ i+ and Sˆ j− represent dipole excitation and de-excitation, respectively. i is the transition frequency of thedipole on site i, which is a function of dipole moment andexternal electric fields at site i.i = d · E  , 2where d is the electric dipole moment which we assume thesame for each site. ij is the dipole-dipole coupling constantbetween sites i and j, which is determined by the strength ofdipole moment, the direction of the external electric field andthe lattice constant of the dipole array.ij =d 21 – 3 cos2 rij3, 3where  is the angle between rij and external electric field.We will expand the Hamiltonian in pure standard basis,00 , 01 , 10 , 11	, and all the eigenstates will beobtained by diagonalizing the Hamiltonian matrix. For ex-ample, for N=2, we obtained the following four eigenvec-tors: 1= 00 , 2= 1 /201− 10 , 3= 1 /201+ 10 , 4= 11 with corresponding eigenvalues:E1=0 , E2=− , E3=+ , E4=2. For the ratio  /1, 2 is fully entangled ground state. However, for /1 the nonentangled state 1 is the ground state. Thus,we have a curve crossing at  /=1.The concept of entanglement of formation is related tothe amount of entanglement needed to prepare the state 	,where 	 is the density matrix. It was shown by Wootters22that concurrence is a good measure of entanglement.23 Theconcurrence C is given by22C	 = max0,1 − 2 − 3 − 4	 . 4For a general state of two qubits, i’s are the eigenvalues, indecreasing order, of the Hermitian matrix R		˜	 where	 is the density matrix and 	˜ is the spin-flipped state definedas	˜ = y  y	y  y , 5where the 	 is the complex conjugate of 	 and is taken inthe standard basis, which for a pair of two level particles is00 , 01 , 10 , 11	.aAuthor to whom correspondence should be addressed. Electronic mail:kais@purdue.edu.THE JOURNAL OF CHEMICAL PHYSICS 132, 121104 20100021-9606/2010/13212/121104/4/$30.00 © 2010 American Institute of Physics132, 121104-1Downloaded 22 Apr 2011 to 128.211.161.17. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissionsIn order to calculate thermal entanglement, we need thetemperature dependent density matrix and the density matrixfor a system in equilibrium at a temperature T reads:	=e−Hˆ /Z with =1 /kT and Z is the partition function,Z=Tre−Hˆ. In this case, the partition function isZT = igie−i, 6where i is the ith eigenvalue and gi is the degeneracy. Andthe corresponding density matrix can be written	T =1ZiNe−iii , 7where i is the ith eigenfunction. For pairwise thermal en-tanglement, we can get reduced density matrix as a functionof temperature in the same way, which leads to temperaturedependent entanglement.In Fig. 1 we show the tuning of the pairwise entangle-ment, measured by concurrence, of one-dimensional arrange-ments of the dipoles as one varies the ratio  / at differenttemperatures for N=9 dipoles. Here we took all transitionfrequencies to be the same, i=, and the nearest neighbordipole-dipole interaction to be the same, i,i+1=i,i−1=.All other dipole-dipole coupling constants i,ji1 can beexpressed in terms of . Thus, we have two parameters tovary, the ratio  / and temperature kT. At kT0 one has aconstant entanglement over a long ratio  / and sharp tran-sitions or jumps to lower values at other values of  /. It isworth mentioning that for  /0.634, entanglement isonly between dipoles 1 and 2. For 0.634 /1.14 di-pole one becomes entangled also with dipole 3 and withother dipoles until we reach  /1.74, above this value theconcurrence is zero between all sites. As one increases thetemperature, the curve becomes smoother as mixing occurwith higher states. Calculations for N=3,4 , . . .8 gave similarbehavior of tuning and controlling entanglement as for thecase N=9. To show how the populations changes at the tran-sition point, we present in Fig. 2 the coefficients ofthe wave function for N=4 before and after the transitionpoint  /=0.64. When  /0.64, the ground state waveFIG. 1. Pairwise concurrence Eq. 4 of one-dimensional arrangements ofthe dipoles as one varies the ratio  / at kT=10−4, 10−2, and 10−1 ,respectively, for N=9 dipoles.FIG. 2. Pairwise concurrence Eq. 4 and coefficients of the wave functionof one-dimensional arrangements of the dipoles as one varies the ratio  /at kT=10−4  for N=4 dipoles.121104-2 Wei, Kais, and Chen J. Chem. Phys. 132, 121104 2010Downloaded 22 Apr 2011 to 128.211.161.17. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissionsfunction is  =0.19↓↓ ↑↑−0.51↓↑ ↓↑+0.45↓↑ ↑↓+0.45↑↓ ↓↑−0.51↑↓ ↑↓+0.19↑↑ ↓↓, however, when /0.64, the ground state wave function becomes  =0.36↓↓ ↓↑−0.61↓↓ ↑↓+0.61↓↑ ↓↓−0.36↑↓ ↓↓. Fig-ures 3 and 4 show a similar phenomena for two and three-dimensional arrangements of the dipoles. The pairwise en-tanglement decreases as one increases the dimensionality ofthe system and the temperature.There have been rapid advances made recently in cool-ing, trapping and manipulating atomic Rydberg24–26 andmolecular dipoles.10,11,27–29 For example, a wide variety ofground state polar molecules with large electric dipole mo-ments several debyes, where 1 D 3.310−30 C m havebeen cooled to ultracold mK or below regime, some evennear quantum degeneracy.29 These developments provide ex-citing opportunities to experimentally realize the entangle-ment switch described above, which requires tuning  /around 1, and cooling the dipoles to temperatures T corre-sponding to a fraction of the dipole-dipole interaction energy.30 For a dipole moment p of few debyes, and a typicalexperimental electric field 105 V /m, required for the di-pole moment to actually manifest itself12,31, dipole-dipole separation d on the order of 10 nm is required for /1. Such d is much shorter than what can be achievedin typical optical lattices as envisaged in Ref. 12 whichcorresponds to the regime of  /1, but can be realizedwith arrays of nanoscale plasmon-enhanced electric/electro-optical traps recently proposed32,33 where extremely tight,few-nanometer confinement, and trap frequencies exceeding100 MHz are shown to be possible. At such short d, thedipole-dipole interaction = p2 /40d3 is on the order of0.1 K. Cooling to a small fraction of such a temperature scaleis easily within the current experimental technology. Further-more,  / can be tuned experimentally by the electricalfield, and/or by d e.g., by varying the microtrap configura-tion.In summary, we presented a new way to construct anentanglement switch in an optical lattice and discussed theexperimental feasibility of building such switch. The realiza-tion of such a scheme will have a profound impact on theimplementation of quantum gates in quantum computingwith trapped polar molecules. The similar idea could in prin-ciple also be applied to other systems with electric dipoles,such as quantum dots and excitons in nanostructures.We would like to thank the ARO for financial support.Y.P.C. acknowledges partial support from National ScienceFoundation Grant CCF No. 0829918.1 M. A. Nielsen and I. L. Chuang, Quantum Computation and QuantumInformation University Press, Cambridge, 2000.2 L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 5172008.3 V. Vedral, Nature London 453, 1004 2008.4 S. Kais, Adv. Chem. Phys. 134, 493 2007.5 O. Osenda, Z. Huang, and S. Kais, Phys. Rev. A 67, 062321 2003.6 Z. Huang, O. Osenda, and S. Kais, Phys. Lett. A 322, 137 2004.7 Z. Huang and S. Kais, Int. J. Quantum Inf. 3, 483 2005.8 Z. Huang and S. Kais, Phys. Rev. A 73, 022339 2006.9 R. Krems, W. C. Stwalley, and B. Friedrich, Cold Molecules: Theory,Experiment, Applications Taylor Francis, London, 2009.10 D. Herschbach, Faraday Discuss. 142, 9 2009.11 B. Friedrich and J. M. Doyle, ChemPhysChem 10, 604 2009.12 D. DeMille, Phys. Rev. Lett. 88, 067901 2002.13 G. K. Brennen, I. H. Deutsch, and P. S. Jessen, Phys. Rev. A 61, 0623092000.14 G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, Phys. Rev.Lett. 82, 1060 1999.15 A. Micheli, G. K. Brennen, and P. Zoller, Nat. Phys. 2, 341 2006.16 M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I.Cirac, and P. Zoller, Phys. Rev. Lett. 87, 037901 2001.17 D. Jaksch, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 85, 2208 2000.18 S. F. Yelin, K. Kirby, and R. Cote, Phys. Rev. A 74, 050301R 2006.19 E. Charron, P. Milman, A. Keller, and O. Atabek, Phys. Rev. A 75,033414 2007.20 E. Kuznetsova, R. Cote, K. Kirby, and S. F. Yelin, Phys. Rev. A 78,012313 2008.21 Z. Ficek and S. Swain, Quantum Interference and Coherence Theory andExperiment Springer, New York, 2004.22 W. K. Wootters, Phys. Rev. Lett. 80, 2245 1998.FIG. 3. 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Entanglement Switch for Dipole Arrays

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