Abstract

We will discuss a model with ultracold atoms confined in optical superlattices. In particular, we will study the ground-state properties of two spin-1 bosons trapped in a double-well potential. Depending on the external magnetic field and biquadratic interactions, different phases of magnetic order are realized. Applying von Neumann entropy and the number of relevant orbitals, we will quantify the bipartite entanglement between particles. Changing the values of the parameters determining the superlattices, we can switch the system between differently entangled states.

© 2014 Optical Society of America

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2013 (7)

S. K. Goyal and T. Konrad, “Teleporting photonic qudits using multimode quantum scissors,” Sci. Rep. 3, 3548 (2013).
[Crossref]

K. Bartkiewicz, K. Lemr, A. Cernoch, J. Soubusta, and A. Miranowicz, “Experimental eavesdropping based on optimal quantum cloning,” Phys. Rev. Lett. 110, 173601 (2013).
[Crossref]

J. Pietraszewicz, T. Sowiński, M. Brewczyk, M. Lewenstein, and M. Gajda, “Spin dynamics of two bosons in an optical lattice site: a role of anharmonicity and anisotropy of the trapping potential,” Phys. Rev. A 88, 013608 (2013).
[Crossref]

T. Sowiński, M. Łącki, O. Dutta, J. Pietraszewicz, P. Sierant, M. Gajda, J. Zakrzewski, and M. Lewenstein, “Tunneling-induced restoration of the degeneracy and the time-reversal symmetry breaking in optical lattices,” Phys. Rev. Lett. 111, 215302 (2013).
[Crossref]

H. Katsura and H. Tasaki, “Ground states of the spin-1 Bose–Hubbard model,” Phys. Rev. Lett. 110, 130405 (2013).

A. Miranowicz, M. Paprzycka, Y. X. Liu, J. Bajer, and F. Nori, “Two-photon and three-photon blockades in driven nonlinear systems,” Phys. Rev. A 87, 023809 (2013).
[Crossref]

T. V. Gevorgyan, A. R. Shahinyan, L. Y. Chew, and G. Y. Kryuchkyan, “Bistability and chaos at low levels of quanta,” Phys. Rev. E 88, 022910 (2013).
[Crossref]

2012 (7)

T. V. Gevorgyan, A. R. Shahinyan, and G. Y. Kryuchkyan, “Generation of Fock states and qubits in periodically pulsed nonlinear oscillators,” Phys. Rev. A 85, 053802 (2012).
[Crossref]

P. Chen, Z.-L. Xue, I. P. McCulloch, M.-C. Chung, and S.-K. Yip, “Dimerized and trimerized phases for spin-2 bosons in a one-dimensional optical lattice,” Phys. Rev. A 85, 011601(R) (2012).
[Crossref]

F. Pinheiro, J.-P. Martikainen, and J. Larson, “Confined p-band Bose–Einstein condensates,” Phys. Rev. A 85, 033638 (2012).
[Crossref]

T. Sowiński, “Creation on demand of higher orbital states in a vibrating optical lattice,” Phys. Rev. Lett. 108, 165301 (2012).
[Crossref]

P. Hauke, F. M. Cucchietti, L. Tagliacozzo, I. Deutsch, and M. Lewenstein, “Can one trust quantum simulators?” Rep. Prog. Phys. 75, 082401 (2012).
[Crossref]

R. Blatt and C. F. Roos, “Quantum simulations with trapped ions,” Nat. Phys. 8, 277–284 (2012).
[Crossref]

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[Crossref]

2011 (8)

C. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
[Crossref]

C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
[Crossref]

M. Bartkowiak, A. Miranowicz, X. Wang, Y. X. Liu, W. Leoński, and F. Nori, “Sudden vanishing and reappearance of nonclassical effects: general occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses,” Phys. Rev. A 83, 053814 (2011).
[Crossref]

J. Simon, W. S. Bakr, R. Ma, M. E. Tai, P. M. Preiss, and M. Greiner, “Quantum simulation of antiferromagnetic spin chains in an optical lattice,” Nature 472, 307–312 (2011).
[Crossref]

K. Rodriguez, A. Argüelles, A. K. Kolezhuk, L. Santos, and T. Vekua, “Field-induced phase transitions of repulsive spin-1 bosons in optical lattices,” Phys. Rev. Lett. 106, 105302 (2011).
[Crossref]

G. De Chiara, M. Lewenstein, and A. Sanpera, “Bilinear–biquadratic spin-1 chain undergoing quadratic Zeeman effect,” Phys. Rev. B 84, 054451 (2011).
[Crossref]

A. Wagner, C. Bruder, and E. Demler, “Spin-1 atoms in optical superlattices: single-atom tunneling and entanglement,” Phys. Rev. A 84, 063636 (2011).
[Crossref]

W. Leoński and A. Kowalewska-Kudłaszyk, “Quantum scissors finite-dimensional states engineering,” Prog. Opt. 56, 131–185 (2011).
[Crossref]

2010 (7)

A. Kowalewska-Kudłaszyk and W. Leoński, “Squeezed vacuum reservoir effect for entanglement decay in the nonlinear quantum scissor system,” J. Phys. B 43, 205503 (2010).
[Crossref]

D. J. Papoular, G. V. Shlyapnikov, and J. Dalibard, “Microwave-induced Fano–Feshbach resonances,” Phys. Rev. A 81, 041603(R) (2010).
[Crossref]

Y. X. Liu, A. Miranowicz, Y. B. Gao, J. J. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

V. V. Semenaka, O. V. Nesterova, V. N. Kokozay, V. V. Dyakonenko, R. I. Zubatyuk, O. Shishkin, R. Boča, J. Jezierska, and A. Ozarowski, “CrIII-CrIII interactions in two alkoxo-bridged heterometallic Zn2Cr2 complexes self-assembled from zinc oxide, Reinecke’s salt, and diethanolamine,” Inorg. Chem. 49, 5460–5471 (2010).
[Crossref]

X. Peng, J. Zhang, J. Du, and D. Suter, “Ground-state entanglement in a system with many-body interactions,” Phys. Rev. A 81, 042327 (2010).
[Crossref]

J. L. Guo and H. S. Song, “Entanglement and teleportation through a two-qubit Heisenberg xxz model with the Dzyaloshinskii–Moriya interaction,” Eur. Phys. J. D 56, 265–269 (2010).
[Crossref]

T. Sowiński, M. Brewczyk, M. Gajda, and K. Rzążewski, “Dynamics and decoherence of two cold bosons in a one-dimensional harmonic trap,” Phys. Rev. A 82, 053631 (2010).
[Crossref]

2009 (4)

D. Sych and G. Leuchs, “A complete basis of generalized Bell states,” New J. Phys. 11, 013006 (2009).
[Crossref]

A. Kowalewska-Kudłaszyk, J. K. Kalaga, and W. Leoński, “Long-time fidelity and chaos for a kicked nonlinear oscillator system,” Phys. Lett. A 373, 1334–1340 (2009).
[Crossref]

M. Hermele, V. Gurarie, and A. M. Rey, “Mott insulators of ultracold fermionic alkaline earth atoms: underconstrained magnetism and chiral spin liquid,” Phys. Rev. Lett. 103, 135301 (2009).
[Crossref]

L.-A. Wu, A. Miranowicz, X. B. Wang, Y. X. Liu, and F. Nori, “Perfect function transfer and interference effects in interacting boson lattices,” Phys. Rev. A 80, 012332 (2009).
[Crossref]

2008 (4)

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964 (2008).
[Crossref]

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
[Crossref]

J. Zhang, X. Peng, N. Rajendran, and D. Suter, “Detection of quantum critical points by a probe qubit,” Phys. Rev. Lett. 100, 100501 (2008).
[Crossref]

A. Bencini and F. Totti, “On the importance of the biquadratic terms in exchange coupled systems: a post-HF investigation,” Inorg. Chim. Acta 361, 4153–4156 (2008).

2007 (4)

R. Bastardis, N. Guihèry, and C. de Graaf, “Microscopic origin of isotropic non-Heisenberg behavior in s = 1 magnetic systems,” Phys. Rev. B 76, 132412 (2007).
[Crossref]

K. Eckert, L. Zawitkowski, M. J. Leskinen, A. Sanpera, and M. Lewenstein, “Ultracold atomic Bose and Fermi spinor gases in optical lattices,” New J. Phys. 9, 133 (2007).
[Crossref]

T. Hirano and Y. Hatsugai, “Entanglement entropy of one-dimensional gapped spin chains,” J. Phys. Soc. Jpn. 76, 074603 (2007).
[Crossref]

S. K. Ozdemir, K. Bartkiewicz, Y. X. Liu, and A. Miranowicz, “Teleportation of qubit states through dissipative channels: conditions for surpassing the no-cloning limit,” Phys. Rev. A 76, 042325 (2007).
[Crossref]

2006 (2)

A. Kitaev and J. Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96, 110404 (2006).
[Crossref]

C. Wu, “Hidden symmetry and quantum phases in spin-3/2 cold atomic systems,” Mod. Phys. Lett. B 20, 1707–1738 (2006).
[Crossref]

2005 (4)

X. Peng, J. Du, and D. Suter, “Quantum phase transition of ground-state entanglement in a Heisenberg spin chain simulated in an NMR quantum computer,” Phys. Rev. A 71, 012307 (2005).
[Crossref]

A. Miranowicz, “Optical-state truncation and teleportation of qudits by conditional eight-port interferometry,” J. Opt. B 7, 142–150 (2005).
[Crossref]

O. E. Alon, A. I. Streltsov, and L. S. Cederbaum, “Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 95, 030405 (2005).
[Crossref]

V. W. Scarola and S. Das Sarma, “Quantum phases of the extended Bose–Hubbard Hamiltonian: possibility of a supersolid state of cold atoms in optical lattices,” Phys. Rev. Lett. 95, 033003 (2005).
[Crossref]

2004 (5)

G. M. Nikolopoulos, D. Petrosyan, and P. Lambropoulos, “Coherent electron wavepacket propagation and entanglement in array of coupled quantum dots,” Europhys. Lett. 65, 297–303 (2004).
[Crossref]

M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, “Perfect state transfer in quantum spin networks,” Phys. Rev. Lett. 92, 187902 (2004).
[Crossref]

G. C. Levine, “Entanglement entropy in a boundary impurity model,” Phys. Rev. Lett. 93, 266402 (2004).
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J. J. Garcia-Ripoll, M. A. Martin-Delgado, and J. I. Cirac, “Implementation of spin Hamiltonians in optical lattices,” Phys. Rev. Lett. 93, 250405 (2004).
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A. Miranowicz and W. Leoński, “Dissipation in systems of linear and nonlinear quantum scissors,” J. Opt. B 6, S43–S46 (2004).
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2003 (4)

A. Imambekov, M. Lukin, and E. Demler, “Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic, and dimerized phases,” Phys. Rev. A 68, 063602 (2003).
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S.-K. Yip, “Dimer state of spin-1 bosons in an optical lattice,” Phys. Rev. Lett. 90, 250402 (2003).
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L. Zhou, H. S. Song, Y. Q. Guo, and C. Li, “Enhanced thermal entanglement in an anisotropic Heisenberg xyz chain,” Phys. Rev. A 68, 024301 (2003).
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S. Ghosh, T. F. Rosenbaum, G. Aeppli, and S. N. Coppersmith, “Entangled quantum state of magnetic dipoles,” Nature 425, 48–51 (2003).
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2002 (4)

A. Osterloh, L. Amico, G. Falci, and R. Fazio, “Scaling of entanglement close to a quantum phase transition,” Nature 416, 608–610 (2002).
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T. J. Osborne and M. A. Nielsen, “Entanglement in a simple quantum phase transition,” Phys. Rev. A 66, 032110 (2002).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).
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2000 (2)

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
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J. Lou, T. Xiang, and Z. Su, “Thermodynamics of the bilinear–biquadratic spin-one Heisenberg chain,” Phys. Rev. Lett. 85, 2380–2383 (2000).
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1999 (1)

P. Millet, F. Mila, F. C. Zhang, M. Mambrini, A. B. Van Oosten, V. A. Pashchenko, A. Sulpice, and A. Stepanov, “Biquadratic interactions and spin-Peierls transition in the spin-1 chain LiVGe2O6,” Phys. Rev. Lett. 83, 4176–4179 (1999).
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1998 (3)

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
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D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A 57, 120–126 (1998).
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D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
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1997 (1)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eible, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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1996 (1)

W. Leoński, “Quantum and classical dynamics for a pulsed nonlinear oscillator,” Physica A 233, 365–378 (1996).
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1995 (1)

A. Drzewiński and R. Dekeyser, “Renormalization of the anisotropic linear xy model,” Phys. Rev. B 51, 15218–15228 (1995).
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1994 (3)

A. Drzewiński and J. M. J. van Leeuwen, “Renormalization of the Ising model in a transverse field,” Phys. Rev. B 49, 403–408 (1994).
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1991 (1)

G. J. Milburn and C. A. Holmes, “Quantum coherence and classical chaos in a pulsed parametric oscillator with a Kerr nonlinearity,” Phys. Rev. A 44, 4704–4711 (1991).
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1990 (1)

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1982 (1)

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1959 (1)

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L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
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Bajer, J. J.

Y. X. Liu, A. Miranowicz, Y. B. Gao, J. J. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
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Bakr, W. S.

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C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
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I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
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C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
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I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964 (2008).
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).
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V. V. Semenaka, O. V. Nesterova, V. N. Kokozay, V. V. Dyakonenko, R. I. Zubatyuk, O. Shishkin, R. Boča, J. Jezierska, and A. Ozarowski, “CrIII-CrIII interactions in two alkoxo-bridged heterometallic Zn2Cr2 complexes self-assembled from zinc oxide, Reinecke’s salt, and diethanolamine,” Inorg. Chem. 49, 5460–5471 (2010).
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Boschi, D.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
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D. Bouwmeester, J. W. Pan, K. Mattle, M. Eible, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
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J. Pietraszewicz, T. Sowiński, M. Brewczyk, M. Lewenstein, and M. Gajda, “Spin dynamics of two bosons in an optical lattice site: a role of anharmonicity and anisotropy of the trapping potential,” Phys. Rev. A 88, 013608 (2013).
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T. Sowiński, M. Brewczyk, M. Gajda, and K. Rzążewski, “Dynamics and decoherence of two cold bosons in a one-dimensional harmonic trap,” Phys. Rev. A 82, 053631 (2010).
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A. Wagner, C. Bruder, and E. Demler, “Spin-1 atoms in optical superlattices: single-atom tunneling and entanglement,” Phys. Rev. A 84, 063636 (2011).
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D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
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P. Rungta, W. J. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, “Qudit entanglement,” in Directions in Quantum Optics, H. J. Carmichael, R. J. Glauber, and M. O. Scully, eds., Vol. 561 of Lecture Notes in Physics (Springer-Verlag, 2001), pp. 149–164.

Cederbaum, L. S.

O. E. Alon, A. I. Streltsov, and L. S. Cederbaum, “Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 95, 030405 (2005).
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K. Bartkiewicz, K. Lemr, A. Cernoch, J. Soubusta, and A. Miranowicz, “Experimental eavesdropping based on optimal quantum cloning,” Phys. Rev. Lett. 110, 173601 (2013).
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P. Chen, Z.-L. Xue, I. P. McCulloch, M.-C. Chung, and S.-K. Yip, “Dimerized and trimerized phases for spin-2 bosons in a one-dimensional optical lattice,” Phys. Rev. A 85, 011601(R) (2012).
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C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
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T. V. Gevorgyan, A. R. Shahinyan, L. Y. Chew, and G. Y. Kryuchkyan, “Bistability and chaos at low levels of quanta,” Phys. Rev. E 88, 022910 (2013).
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Chin, C.

C. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
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Christandl, M.

M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, “Perfect state transfer in quantum spin networks,” Phys. Rev. Lett. 92, 187902 (2004).
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Chung, M.-C.

P. Chen, Z.-L. Xue, I. P. McCulloch, M.-C. Chung, and S.-K. Yip, “Dimerized and trimerized phases for spin-2 bosons in a one-dimensional optical lattice,” Phys. Rev. A 85, 011601(R) (2012).
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Cirac, J. I.

J. J. Garcia-Ripoll, M. A. Martin-Delgado, and J. I. Cirac, “Implementation of spin Hamiltonians in optical lattices,” Phys. Rev. Lett. 93, 250405 (2004).
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D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
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Coppersmith, S. N.

S. Ghosh, T. F. Rosenbaum, G. Aeppli, and S. N. Coppersmith, “Entangled quantum state of magnetic dipoles,” Nature 425, 48–51 (2003).
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Cucchietti, F. M.

P. Hauke, F. M. Cucchietti, L. Tagliacozzo, I. Deutsch, and M. Lewenstein, “Can one trust quantum simulators?” Rep. Prog. Phys. 75, 082401 (2012).
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Dalibard, J.

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
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D. J. Papoular, G. V. Shlyapnikov, and J. Dalibard, “Microwave-induced Fano–Feshbach resonances,” Phys. Rev. A 81, 041603(R) (2010).
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I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964 (2008).
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V. W. Scarola and S. Das Sarma, “Quantum phases of the extended Bose–Hubbard Hamiltonian: possibility of a supersolid state of cold atoms in optical lattices,” Phys. Rev. Lett. 95, 033003 (2005).
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M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, “Perfect state transfer in quantum spin networks,” Phys. Rev. Lett. 92, 187902 (2004).
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G. De Chiara, M. Lewenstein, and A. Sanpera, “Bilinear–biquadratic spin-1 chain undergoing quadratic Zeeman effect,” Phys. Rev. B 84, 054451 (2011).
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R. Bastardis, N. Guihèry, and C. de Graaf, “Microscopic origin of isotropic non-Heisenberg behavior in s = 1 magnetic systems,” Phys. Rev. B 76, 132412 (2007).
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De Martini, F.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
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A. Drzewiński and R. Dekeyser, “Renormalization of the anisotropic linear xy model,” Phys. Rev. B 51, 15218–15228 (1995).
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Demler, E.

A. Wagner, C. Bruder, and E. Demler, “Spin-1 atoms in optical superlattices: single-atom tunneling and entanglement,” Phys. Rev. A 84, 063636 (2011).
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A. Imambekov, M. Lukin, and E. Demler, “Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic, and dimerized phases,” Phys. Rev. A 68, 063602 (2003).
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Deuar, P.

P. Rungta, W. J. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, “Qudit entanglement,” in Directions in Quantum Optics, H. J. Carmichael, R. J. Glauber, and M. O. Scully, eds., Vol. 561 of Lecture Notes in Physics (Springer-Verlag, 2001), pp. 149–164.

Deutsch, I.

P. Hauke, F. M. Cucchietti, L. Tagliacozzo, I. Deutsch, and M. Lewenstein, “Can one trust quantum simulators?” Rep. Prog. Phys. 75, 082401 (2012).
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DiVincenzo, D. P.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
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D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A 57, 120–126 (1998).
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A. Drzewiński and R. Dekeyser, “Renormalization of the anisotropic linear xy model,” Phys. Rev. B 51, 15218–15228 (1995).
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A. Drzewiński and J. M. J. van Leeuwen, “Renormalization of the Ising model in a transverse field,” Phys. Rev. B 49, 403–408 (1994).
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T. Sowiński, M. Łącki, O. Dutta, J. Pietraszewicz, P. Sierant, M. Gajda, J. Zakrzewski, and M. Lewenstein, “Tunneling-induced restoration of the degeneracy and the time-reversal symmetry breaking in optical lattices,” Phys. Rev. Lett. 111, 215302 (2013).
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V. V. Semenaka, O. V. Nesterova, V. N. Kokozay, V. V. Dyakonenko, R. I. Zubatyuk, O. Shishkin, R. Boča, J. Jezierska, and A. Ozarowski, “CrIII-CrIII interactions in two alkoxo-bridged heterometallic Zn2Cr2 complexes self-assembled from zinc oxide, Reinecke’s salt, and diethanolamine,” Inorg. Chem. 49, 5460–5471 (2010).
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R. Grobe, K. Rzążewski, and J. H. Eberly, “Measure of electron–electron correlations in atomic physics,” J. Phys. B 27, L503–L508 (1994).
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K. Eckert, L. Zawitkowski, M. J. Leskinen, A. Sanpera, and M. Lewenstein, “Ultracold atomic Bose and Fermi spinor gases in optical lattices,” New J. Phys. 9, 133 (2007).
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D. Bouwmeester, J. W. Pan, K. Mattle, M. Eible, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, “Perfect state transfer in quantum spin networks,” Phys. Rev. Lett. 92, 187902 (2004).
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C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
[Crossref]

Esslinger, T.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).
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Falci, G.

A. Osterloh, L. Amico, G. Falci, and R. Fazio, “Scaling of entanglement close to a quantum phase transition,” Nature 416, 608–610 (2002).
[Crossref]

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L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
[Crossref]

A. Osterloh, L. Amico, G. Falci, and R. Fazio, “Scaling of entanglement close to a quantum phase transition,” Nature 416, 608–610 (2002).
[Crossref]

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R. P. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21, 467–488 (1982).
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C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
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J. Pietraszewicz, T. Sowiński, M. Brewczyk, M. Lewenstein, and M. Gajda, “Spin dynamics of two bosons in an optical lattice site: a role of anharmonicity and anisotropy of the trapping potential,” Phys. Rev. A 88, 013608 (2013).
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T. Sowiński, M. Łącki, O. Dutta, J. Pietraszewicz, P. Sierant, M. Gajda, J. Zakrzewski, and M. Lewenstein, “Tunneling-induced restoration of the degeneracy and the time-reversal symmetry breaking in optical lattices,” Phys. Rev. Lett. 111, 215302 (2013).
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T. Sowiński, M. Brewczyk, M. Gajda, and K. Rzążewski, “Dynamics and decoherence of two cold bosons in a one-dimensional harmonic trap,” Phys. Rev. A 82, 053631 (2010).
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Gao, Y. B.

Y. X. Liu, A. Miranowicz, Y. B. Gao, J. J. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
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Garcia-Ripoll, J. J.

J. J. Garcia-Ripoll, M. A. Martin-Delgado, and J. I. Cirac, “Implementation of spin Hamiltonians in optical lattices,” Phys. Rev. Lett. 93, 250405 (2004).
[Crossref]

Gardiner, C. W.

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
[Crossref]

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C. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
[Crossref]

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T. V. Gevorgyan, A. R. Shahinyan, L. Y. Chew, and G. Y. Kryuchkyan, “Bistability and chaos at low levels of quanta,” Phys. Rev. E 88, 022910 (2013).
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T. V. Gevorgyan, A. R. Shahinyan, and G. Y. Kryuchkyan, “Generation of Fock states and qubits in periodically pulsed nonlinear oscillators,” Phys. Rev. A 85, 053802 (2012).
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Ghosh, S.

S. Ghosh, T. F. Rosenbaum, G. Aeppli, and S. N. Coppersmith, “Entangled quantum state of magnetic dipoles,” Nature 425, 48–51 (2003).
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Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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S. K. Goyal and T. Konrad, “Teleporting photonic qudits using multimode quantum scissors,” Sci. Rep. 3, 3548 (2013).
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J. Simon, W. S. Bakr, R. Ma, M. E. Tai, P. M. Preiss, and M. Greiner, “Quantum simulation of antiferromagnetic spin chains in an optical lattice,” Nature 472, 307–312 (2011).
[Crossref]

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).
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Grobe, R.

R. Grobe, K. Rzążewski, and J. H. Eberly, “Measure of electron–electron correlations in atomic physics,” J. Phys. B 27, L503–L508 (1994).
[Crossref]

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R. Bastardis, N. Guihèry, and C. de Graaf, “Microscopic origin of isotropic non-Heisenberg behavior in s = 1 magnetic systems,” Phys. Rev. B 76, 132412 (2007).
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L. Zhou, H. S. Song, Y. Q. Guo, and C. Li, “Enhanced thermal entanglement in an anisotropic Heisenberg xyz chain,” Phys. Rev. A 68, 024301 (2003).
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Figures (4)

Fig. 1.
Fig. 1.

Spectrum of the Hamiltonian (3) for λ=1 in two limiting situations: (a) vanishing biquadratic interaction θ=0 and (b) vanishing external magnetic field h=0. In (a), different colors correspond to states with different total spin Sz (Sz=0, black line; Sz=±1, red line; Sz=±2, blue line). In (b), the circled numbers denote the degree of degeneracy of the states.

Fig. 2.
Fig. 2.

Ground-state phase diagram of the system. For a given angle θ and a magnetic field h, the ground state of the system belongs to the one of three subspaces characterized by total spin Sz. Note that the properties of the ground state depend highly on the sign of the linear coupling term λ. The phase diagram for negative magnetic field h has identical phases, but with opposite total spin.

Fig. 3.
Fig. 3.

Ground-state properties for positive linear coupling λ in the phase with total spin Sz=0 as a function of mixing angle θ. (a) Number of relevant orbitals K (blue dashed line) and von Neumann entropy S (red solid line); (b) probabilities p0 and p± of finding the ground state in appropriate two-site product states (as explained in the main text); and (c) fidelity FS (FT) between the ground state of the system and the singlet (triplet) qutrit–qutrit Bell state.

Fig. 4.
Fig. 4.

Ground-state properties for negative linear coupling λ in the phase with total spin Sz=0 as a function of mixing angle θ. (a) Number of relevant orbitals K (blue dashed line) and von Neumann entropy S (red solid line); (b) probabilities p0 and p± of finding the ground state in appropriate two-site product states (as explained in the main text); and (c) fidelities FS and FT between the ground state of the system and the singlet and triplet qutrit–qutrit Bell states, respectively. In contrast to the case λ=1, the ground state remains almost perfectly in the triplet qutrit–qutrit Bell state |3,BT in a whole phase.

Equations (18)

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H=t(a^Lσa^Rσ+a^Rσa^Lσ)+U02i=L,Rn^i(n^i1)+U22i=L,R(S^i22n^i)γB·(S^L+S^R),
H=J0+J1S^L·S^R+J2(S^L·S^R)2γBz(S^Lz+S^Rz),
H=λS^L·S^R+tanθ(S^L·S^R)2h(S^Lz+S^Rz),
||1;±=|0,1±|1,02
||1;±=|0,1±|1,02
||0;0=|1,1|1,12,
||0;±=cosα±|1,1+|1,12±sinα±|0,0,
E0;0=λ+tanθ,
E0;±=(λ+tanθ±δ)/2,
K(ρ^L)=(iηi2)1,
S(ρ^L)=Tr(ρ^Llog2ρ^L)=iηilog2ηi.
|3,BS=13(|1,1+|1,1|0,0),
|3,BT=13(|1,1+|1,1+|0,0),
S=E0;δlog2(|E0;|2δ)+2(λ+tanθ)2δE0;log2(2(λ+tanθ)2δ|E0;|),
K=2δ2E0;28(λ+tanθ)4+E0;4.
|Gθπ/2|3,BT.
|2,BT=12(|1,1+|1,1).
|G==θ=0|3,BS,

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