Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session W33: Quantum Entanglement 
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Sponsoring Units: GQI Chair: Ivette FuentesSchuller, University of Nottingham, UK Room: E143 
Thursday, March 18, 2010 11:15AM  11:27AM 
W33.00001: Entanglement of Dirac fields in an expanding spacetime Ivette FuentesSchuller, Robert B. Mann, Shahpoor Moradi We study the entanglement generated between Dirac field modes in a ddimensional RobertsonWalker expanding universe. In the twodimensional case, we compare the bosonic and fermionic entanglement generated by the expansion of the Universe. We find qualitative differences, in particular, we show that the entanglement generated between fermionic field modes is considerably lower than the bosonic case. This result, together with previous investigations on entanglement in noninertial frames, suggest that entanglement between fermionic modes is less affected by the underlying spacetime. [Preview Abstract] 
Thursday, March 18, 2010 11:27AM  11:39AM 
W33.00002: Entanglement Entropy in Critical Harmonic Chains with Even Dynamical Exponents Layla Hormozi, Nick Bonesteel, Kun Yang We study the behavior of the entanglement entropy in a chain of coupled harmonic oscillators at the critical regime and in the absence of conformal symmetry. We consider a specific class of the socalled ``squared'' interactions [1], namely interactions leading to the dispersion $\omega_k = (2 Sin (k/2))^z$ with even dynamical exponent, $z$, in which up to the $z^{th}$ nearest neighbors are coupled. Similar to the conformally symmetric case, we find a logarithmic scaling for the entanglement entropy, with a coefficient that can be calculated analytically and depends only on $z$. \\[4pt] [1] M. B. Plenio, J. Eisert, J. Drei{\ss}ig, and M. Cramer, Phys. Rev. Lett. {\bf94}, 060503 (2005) [Preview Abstract] 
Thursday, March 18, 2010 11:39AM  11:51AM 
W33.00003: Quench dynamics of entanglement entropy in the toric code Armin Rahmani, Claudio Chamon We calculate analytically the timedependent entanglement entropy of a spin system described by the toric code Hamiltonian when quenched from a fully magnetized initial state. We argue that, in the presence of disorder, the entanglement entropy saturates to values which, due to integrability, scale as the area of the subsystem as opposed to its volume. This sudden quantum quench from the magnetic phase into the topological phase does not create any topological order. Finally we study the effects of integrabilitybreaking perturbations on the quench dynamics. [Preview Abstract] 
Thursday, March 18, 2010 11:51AM  12:03PM 
W33.00004: Holographic Entanglement Spectrum Noah BrayAli We evaluate the entanglement spectrum (singular value decomposition of the wavefunction) of paired states of fermions in two dimensions that break parity and timereversal symmetries. The spectrum takes a quasiparticle form within the BCS approximation and contains a onedimensional Majorana fermion excitation in the weakpairing (BCS) phase. Experimentally relevant systems include condensates of pwave Feshbach resonant atoms in a pancake trap and quantum Hall liquids in a halffilled Landau level. [Preview Abstract] 
Thursday, March 18, 2010 12:03PM  12:15PM 
W33.00005: Entanglement Entropy in Heisenberg Ladders with Valence Bond QMC Ann Kallin, Iv\'{a}n Gonz\'{a}lez, Matthew Hastings, Roger Melko Entanglement has arisen as a new paradigm for the study of correlations in condensed matter systems. Traditionally entanglement is measured through the von Neumann entanglement entropy (vNEE). Unfortunately, calculating vNEE requires access to the wavefunction of the system, which is not available in quantum Monte Carlo (QMC). Recently a new quantity has been proposed, the valence bond entanglement entropy (VBEE), which is easily calculated using QMC in the valence bond basis and seems to share many characteristics with the vNEE [1,2]. \\ I will discuss our recent paper in which we directly compare the VBEE and the vNEE on Heisenberg ladders using QMC to calculate VBEE and density matrix renormalization group (DMRG) simulations to calculate vNEE. We find in some cases, the VBEE is greater than the vNEE, while in other cases VB EE is less than the vNEE. Hence the VBEE cannot provide a bound for the vNEE. We confirm the previous result [1,2] that the VB EE gives a logarithmic correction to the area law in the 2D limit of the N\'{e}el ground state, however results from DMRG show the vNEE in this system obeys the area law without correction. We relate the VBEE to the bondlength distribution in the QMC. \\ {[}1] F. Alet, et. al., Phys. Rev. Lett. 99, 117204 (2007). \\ {[}2] R. W. Chhajlany, et. al., Phys. Rev. Lett. 99, 167204 (2007). [Preview Abstract] 
Thursday, March 18, 2010 12:15PM  12:27PM 
W33.00006: Entanglement Entropy of Random Fractional Quantum Hall Systems Barry Friedman, Darwin Luna The entanglement entropy of fractional quantum Hall systems is studied numerically in the presence of a short range random potential. The numerical method used is direct diagonalization and two questions will be considered. Firstly, can the topological entanglement entropy be reliably computed for accessible system sizes? Secondly, can the entanglement entropy be practically used to detect phase transitions as a function of the disorder strength? [Preview Abstract] 
Thursday, March 18, 2010 12:27PM  12:39PM 
W33.00007: Entanglement Entropy and Mutual Information in BoseEinstein Condensates Kun Yang, Wenxin Ding We study the entanglement properties of free nonrelativistic Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system, and find that it diverges logarithmically ($\frac{1}{2} \ln N$) with the particle number in the subsystem. For finite temperatures, we study the mutual information between the two blocks. We first analytically study an infiniterange hopping model, then numerically study a set of longrange hopping models in onedimension that exhibit BoseEinstein condensation. In both cases we find that a BoseEinstein condensate, if present, makes a divergent contribution to the mutual information which is proportional to the logarithm of the number of particles in the condensate in the subsystem. Below $T_C$ the prefactor of the logarithmic divergent term is 1/2 for the infiniterange hopping model, and model dependent ($<$1/2) for the longrange hopping models. [Preview Abstract] 
Thursday, March 18, 2010 12:39PM  12:51PM 
W33.00008: Fluctuation Length Scales in Random Singlet Phases Huan Tran, Nick Bonesteel For any disorder strength, the ground state of the randombond spin1/2 AFM Heisenberg chain flows to an infiniterandomness fixed point and a random singlet (RS) state forms on long length scales.\footnote{D. S. Fisher, PRB \textbf{50}, 3799 (1994).} This state can be characterized by its valencebond entanglement entropy,\footnote{F. Alet, \emph{et al.}, PRL \textbf{99}, 117204 (2007).} defined to be $\overline{\langle n_L\rangle}$, the average number of valence bonds leaving a block of $L$ spins, as well the fluctuations of this number, $\sigma_{L}^2 = \overline{\langle n_L^2\rangle  \langle n_L\rangle^2}$, (angle brackets denote amplitude weighted averages over valencebond states in the ground state, and overbar denotes disorder average). For large $L$, $\overline{\langle n_L \rangle}$ scales logarithmically, indicating a powerlaw distribution of valencebond lengths, while $\sigma^2_L$ {\it saturates} at a crossover length scale $\xi$, beyond which the valence bonds ``lock" into a particular RS configuration.\footnote{H. Tran and N. E. Bonesteel, arXiv:0909.0038.} Using valencebond Monte Carlo, we have studied the dependence of $\xi$ on disorder strength in the limit of weak disorder for both the Heisenberg chain and the critical random transversefield Ising model. We compare our results with previous calculations of related crossover length scales in these models.\footnote{N. Laflorencie \emph{et al.}, PRB \textbf{70}, 054430 (2004).} [Preview Abstract] 
Thursday, March 18, 2010 12:51PM  1:03PM 
W33.00009: Von Neumann and Renyi Entanglement Entropies in Spin Ladders Ivan Gonzalez, Ann B. Kallin, Matthew B. Hastings, Roger G. Melko Density matrix renormalization group (DMRG) algorithm has proven a useful tool to calculate entanglement properties of one and quasionedimensional condensed matter systems, due to the fact that the reduced density matrix eigenvalue spectrum for some bipartitions of the system is avaliable as a byproduct of the algorithm. In this talk, I will present calculations of the von Neumann and Renyi entanglement entropies (EE) on Heisenberg ladders up to seven legs using DMRG. For a bipartition into subregions A and B, the EE for evenleg ladders is constant for subregion sizes larger than the correlation length, while for oddleg ladders has a logarithmic dependence on the subregion size. Our results indicate that in the limit of a large number of legs the von Neumann EE obeys an area law. [Preview Abstract] 
Thursday, March 18, 2010 1:03PM  1:15PM 
W33.00010: Entanglement dynamics in twomode JCmodel Mikhail Erementchouk, Michael Leuenberger We consider the problem of entanglement of quantum fields for the example of two mode JaynesCummings model, that is the twolevel atom interacting with electromagnetic field. The atomic transitions are characterized by definite helicity, so that electron with spin down at the ground level is moved to the state with spin up at the excited level by absorbing the photon with ``+"polarization and so on. We study the time evolution of entanglement, defined as the von Neumann entropy of the photon single particle density matrix (SPDM), of initially disentangled photon state. Despite the absence of the direct interaction between the different polarizations (the Hamiltonian is completely separable) entanglement develops with time and demonstrates nontrivial oscillatory behavior. In the limit of small number of photons, $N$, the oscillations are the result of superposition of harmonics with incommensurate frequencies and, thus, are quasiperiodic. With increasing the number of photons the quasiperiodic oscillations transform toward a regular pattern. The coherence of SPDM drops and revives with the period $\propto \sqrt{N}/\omega_R$, where $\omega_R$ is the Rabi frequency. The initial drop of coherence, and its time dependence near the revival instants, follows the Gaussian law with the characteristic time $\propto 1/\sqrt{\omega_R}$ independent of $N$. [Preview Abstract] 
Thursday, March 18, 2010 1:15PM  1:27PM 
W33.00011: Stability of Flip and Exchange Symmetric Entangled State Classes Mehmet Zafer Gedik Flip and exchange symmetric (FES) manyqubit states, which can be obtained from a state with the same symmetries by means of invertible local operations (ILO), constitute a oneparameter family of curves in the Hilbert space. Eigenstates of FES ILOs correspond to vectors that cannot be transformed to other FES states. Therefore, equivalence classes of states under ILO can be determined in a systematic way for an arbitrary number of qubits. More important, for entangled states, at the boundaries of neighboring equivalence classes, one can show that when the fidelity between the final state after an ILO and a state of the neighboring class approaches unity, probability of success decreases to zero. In other words, the classes are stable under ILOs. [Preview Abstract] 
Thursday, March 18, 2010 1:27PM  1:39PM 
W33.00012: Singleexperimentdetectable nonclassical correlation witness Robabeh Rahimi, Akira SaiToh We introduce an operational method to detect nonclassical correlation of bipartite states for the paradigm related to the zeroway quantum deficit, which claims that a bipartite state described by a density matrix having no product eigenbasis possesses nonclassical correlation. This method is called nonclassical correlation witness since it uses particular maps which in construction are close to the wellestablished entanglement witnesses. It is also proved that the witness may be generally decomposed into nonlocal operations in addition to local ensemble measurements. Hence the detection in bulkensemble systems is performed in a single run experiment. For further details, see arXiv:0911.3460. [Preview Abstract] 
Thursday, March 18, 2010 1:39PM  1:51PM 
W33.00013: Entanglement Capacity of Nonlocal Hamiltonians: A Geometric Approach Pramod Joag, Behzad Lari, Ali Hassan We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for $N$qubit pure states (Phys. Rev. A \textbf{77}, 062334 (2008)). This geometric method has the distinct advantage that it gives the experimentally implementable criteria to ensure the optimal entanglement production rate without requiring a detailed knowledge of the state of the two qubit system. For the production of entanglement in practice, we need criteria for optimal entanglement production which can be checked {\it in situ} without any need to know the state, as experimentally finding out the state of a quantum system is generally a formidable task. Further, we use our method to quantify the entanglement capacity in higher level and multipartite systems. We quantify the entanglement capacity for two qutrits and find the maximal entanglement generation rate and the corresponding state for the general isotropic interaction between qutrits, using the entanglement measure of $N$qudit pure states proposed by us (Phys. Rev. A \textbf{80}, 042302 (2009)). Next we quantify the genuine three qubit entanglement capacity for a general interaction between qubits. We obtain the maximum entanglement generation rate and the corresponding three qubit state for a general isotropic interaction between qubits. [Preview Abstract] 

W33.00014: ABSTRACT WITHDRAWN 
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