Trapped-ion quantum simulation of tunable-range Heisenberg chains
Tóm tắt
Quantum-optical techniques allow for generating controllable spin-spin interactions between ions, making trapped ions an ideal quantum simulator of Heisenberg chains. A single parameter, the detuning of the Raman coupling, allows to switch between ferromagnetic and antiferromagnetic chains, and to modify the range of the interactions. On the antiferromagnetic side, the system can be tuned from an extreme long-range limit, in which any pair of ions interacts with almost equal strength, to interactions with a
decay. By exact diagonalization, we study how a system of up to 20 ions behaves upon tuning the interactions. We find that it undergoes a transition from a dimerized state with extremely short-ranged correlations towards a state with quasi long-range order, that is, algebraically decaying correlations. The dynamical evolution of the system after a local quench is shown to strongly vary in the two regimes: While in the dimerized limit, the excitation remains localized for long times, propagating spinons characterize the dynamics of the quasi-long-range ordered system. Taking a look onto the ferromagnetic side of the system, we demonstrate the feasibility of witnessing non-locality of quantum correlations by measuring two-particle correlators.
Tài liệu tham khảo
Auerbach A: Interacting Electrons and Quantum Magnetism. Springer, Berlin; 1994.
Lewenstein M, Sanpera A, Ahufinger V: Ultracold Atoms in Optical Lattices - Simulating Quantum Many-Body Systems. Oxford University Press, Oxford; 2012.
Romero-Isart O, Eckert K, Rodó C, Sanpera A: Transport and entanglement generation in the Bose-Hubbard model. J Phys A, Math Theor 2007., 40(28): Article ID 8019 Article ID 8019
Hauke P, Tagliacozzo L: Spread of correlations in long-range interacting quantum systems. Phys Rev Lett 2013., 111: Article ID 207202 Article ID 207202
Schachenmayer J, Lanyon BP, Roos CF, Daley AJ: Entanglement growth in quench dynamics with variable range interactions. Phys Rev X 2013., 3: Article ID 031015 Article ID 031015
Lamata L, León J, Schätz T, Solano E: Dirac equation and quantum relativistic effects in a single trapped ion. Phys Rev Lett 2007., 98: Article ID 253005 Article ID 253005
Gerritsma R, Kirchmair G, Zähringer F, Solano E: Quantum simulation of the Dirac equation. Nature 2010., 463: Article ID 68 Article ID 68
Schmied R, Wesenberg JH, Leibfried D: New J Phys. 2011., 13: Article ID 115011 Article ID 115011
Casanova J, Mezzacapo A, Lamata L, Solano E: Quantum simulation of interacting fermion lattice models in trapped ions. Phys Rev Lett 2012., 108: Article ID 190502 Article ID 190502
Pons M, Ahufinger V, Wunderlich C, Sanpera A, Braungardt S, Sen(De) A, Sen U, Lewenstein M: Trapped ion chain as a neural network: error resistant quantum computation. Phys Rev Lett 2007., 98: Article ID 023003 Article ID 023003
Mintert F, Wunderlich C: Ion-trap quantum logic using long-wavelength radiation. Phys Rev Lett 2001., 87: Article ID 257904 Article ID 257904
Porras D, Cirac JI: Effective quantum spin systems with trapped ions. Phys Rev Lett 2004., 92: Article ID 207901 Article ID 207901
Friedenauer A, Schmitz H, Glueckert JT, Porras D, Schaetz T: Simulating a quantum magnet with trapped ions. Nat Phys 2008, 4(10):757–761. 10.1038/nphys1032
Kim K, Chang M-S, Islam R, Korenblit S, Duan L-M, Monroe C: Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes. Phys Rev Lett 2009., 103: Article ID 120502 Article ID 120502
Kim K, Chang MS, Korenblit S, Islam R, Edwards EE, Freericks JK, Lin GD, Duan LM, Monroe C: Quantum simulation of frustrated Ising spins with trapped ions. Nature 2010, 465: 590–593. 10.1038/nature09071
Britton JW, Sawyer BC, Keith AC, Wang C-CJ, Freericks JK, Uys H, Biercuk MJ, Bollinger JJ: Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 2012, 484(7395):489–492. 10.1038/nature10981
Richerme P, Gong Z-X, Lee A, Senko C, Smith J, Foss-Feig M, Michalakis S, Gorshkov AV, Monroe C: arXiv:1401.5088; 2014.
Jurcevic P, Lanyon BP, Hauke P, Hempel C, Zoller P, Blatt R, Roos CF: arXiv:1401.5387; 2014.
Deng X-L, Porras D, Cirac JI: Effective spin quantum phases in systems of trapped ions. Phys Rev A 2005., 72: Article ID 063407 Article ID 063407
Graß T, Juliá-Díaz B, Kuś M, Lewenstein M: Quantum chaos in su(3) models with trapped ions. Phys Rev Lett 2013., 111: Article ID 090404 Article ID 090404
Koffel T, Lewenstein M, Tagliacozzo L: Entanglement entropy for the long-range Ising chain in a transverse field. Phys Rev Lett 2012., 109: Article ID 267203 Article ID 267203
Haldane FDM:Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-(1/2 antiferromagnetic Heisenberg chain with 1/ r 2 exchange. Phys Rev Lett 1988, 60: 635–638. 10.1103/PhysRevLett.60.635
Shastry BS:Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions. Phys Rev Lett 1988, 60: 639–642. 10.1103/PhysRevLett.60.639
Greiter M: Mapping of Parent Hamiltonians: from Abelian and Non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains. Springer, Berlin; 2011.
Majumdar CK, Ghosh DK: J Math Phys. 1969., 10: Article ID 1388 Article ID 1388
Lipkin H, Meshkov N, Glick AJ: Nucl Phys. 1965., 62: Article ID 188 Article ID 188
Tura J, Augusiak R, Sainz AB, Vértesi T, Lewenstein M, Acín A: arXiv:1306.6860; 2013.
Laughlin RB: Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys Rev Lett 1983., 50: Article ID 1395 Article ID 1395
Gebhard F, Vollhardt D: Correlation functions for Hubbard-type models: the exact results for the Gutzwiller wave function in one dimension. Phys Rev Lett 1987, 59: 1472–1475. 10.1103/PhysRevLett.59.1472
Affleck I: Critical behavior of two-dimensional systems with continuous symmetries. Phys Rev Lett 1985, 55: 1355–1358. 10.1103/PhysRevLett.55.1355
Okamoto K, Nomura K:Fluid-dimer critical point in s=12 antiferromagnetic Heisenberg chain with next nearest neighbor interactions. Phys Lett A 1992, 169(6):433–437. 10.1016/0375-9601(92)90823-5
Eggert S: Numerical evidence for multiplicative logarithmic corrections from marginal operators. Phys Rev B 1996, 54: 9612–9615. 10.1103/PhysRevB.54.R9612
Schneider C, Porras D, Schaetz T: Experimental quantum simulations of many-body physics with trapped ions. Rep Prog Phys 2012., 75(2): Article ID 024401 Article ID 024401
Korenblit S, Kafri D, Campbell WC, Islam R, Edwards EE, Gong Z-X, Lin G-D, Duan L-M, Kim J, Kim K, Monroe C: Quantum simulation of spin models on an arbitrary lattice with trapped ions. New J Phys 2012., 14(9): Article ID 095024 Article ID 095024
Kim K, Korenblit S, Islam R, Edwards EE, Chang M-S, Noh C, Carmichael H, Lin G-D, Duan L-M, Wang CCJ, Freericks JK, Monroe C: Quantum simulation of the transverse Ising model with trapped ions. New J Phys 2011., 13(10): Article ID 105003 Article ID 105003
Sandvik AW: Ground states of a frustrated quantum spin chain with long-range interactions. Phys Rev Lett 2010., 104: Article ID 137204 Article ID 137204
Chhajlany RW, Tomczak P, Wójcik A, Richter J: Entanglement in the Majumdar-Ghosh model. Phys Rev A 2007., 75: Article ID 032340 Article ID 032340
Laflorencie N, Sørensen ES, Chang M-S, Affleck I: Boundary effects in the critical scaling of entanglement entropy in 1d systems. Phys Rev Lett 2006., 96: Article ID 100603 Article ID 100603
Them K: arXiv:1308.2882; 2013.
Brunner N, Cavalcanti D, Pironio S, Scarani V, Wehner S: Bell nonlocality. Rev. Mod. Phys. 2014, 86: 419. 10.1103/RevModPhys.86.419
Bell JS: Physics. 1964., 1: Article ID 195 Article ID 195
Douglas JS, Habibian H, Gorshkov AV, Kimble HJ, Chang DE: arXiv:1312.2435; 2013.
Noguchi A, Toyoda K, Urabe S: Generation of Dicke states with phonon-mediated multilevel stimulated Raman adiabatic passage. Phys Rev Lett 2012., 109: Article ID 260502 Article ID 260502
Blanes S, Casas F, Oteo JA, Ros J: The magnus expansion and some of its applications. Phys Rep 2009, 470(5–6):151–238. 10.1016/j.physrep.2008.11.001