Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session X33: Focus Session: Quantum Information at the AMO/Condensed-Matter Interface |
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Sponsoring Units: GQI DAMOP Chair: Barry Sanders, University of Calgary Room: Colorado Convention Center 403 |
Friday, March 9, 2007 8:00AM - 8:36AM |
X33.00001: Quantum simulation of magnetism using optical lattices Invited Speaker: Physical simulation as a means for resolving outstanding quantum many-body problems was first proposed by Feynmann in 1981. Since then, physicists have dreamed of using physical quantum simulation as a quantitative tool. Ultra-cold atoms trapped in an optical lattice are now emerging as an ideal tool for quantum simulation of a wide range of many-body quantum models, including the Hubbard model and quantum magnetism. I will review the developing field of quantum simulation using ultra-cold atoms and highlight our progress on simulating quantum magnetism. [Preview Abstract] |
Friday, March 9, 2007 8:36AM - 8:48AM |
X33.00002: Quantum phase transitions of light Charles Tahan, Andrew Greentree, Jared Cole, Lloyd Hollenberg Recently, condensed matter and atomic experiments have reached a length-scale and temperature regime where new quantum collective phenomena emerge. Finding such physics in systems of photons, however, is problematic, as photons typically do not interact with each other and can be created or destroyed at will. Here, we introduce a physical system of photons that exhibits strongly correlated dynamics on a meso-scale. By adding photons to a two-dimensional array of coupled optical cavities each containing a single two-level atom in the photon-blockade regime, we form dressed states, or polaritons, that are both long-lived and strongly interacting. Our zero temperature results predict that this photonic system will undergo a characteristic Mott insulator (excitations localised on each site) to superfluid (excitations delocalised across the lattice) quantum phase transition. Each cavity's impressive photon out-coupling potential may lead to actual devices based on these quantum many-body effects, as well as observable, tunable quantum simulators. We explicitly show that such phenomena may be observable in micro-machined diamond containing nitrogen-vacancy colour centres and superconducting microwave strip-line resonators. (Nature Physics, December 2006) [Preview Abstract] |
Friday, March 9, 2007 8:48AM - 9:00AM |
X33.00003: Universal and measurable entanglement in the spin-boson model Angela Kopp, Karyn Le Hur We study the entanglement between a qubit and its environment by calculating the von Neumann entropy of the spin in the delocalized phase of the spin-boson model. Using a well-known mapping between the spin-boson model with Ohmic dissipation and the anisotropic Kondo model, we obtain exact results for the entanglement entropy $E$ at arbitrary dissipation strength $\alpha$ and level asymmetry $h$. We show that the Kondo energy scale $T_K$ controls the entanglement between the qubit and the bosonic environment. For $h \ll T_K$, we find that $E=E(h=0)-\frac{2e^{b/(2-2\alpha)} \Gamma[1+1/(2-2\alpha)]}{\pi \ln 2 \Gamma[1+\alpha/(2-2\alpha)]} (\frac{h}{T_K})^2$, where $b=\alpha \ln \alpha + (1-\alpha) \ln (1-\alpha)$. The universal $(h/T_K)^2$ scaling reflects the Fermi liquid nature of the Kondo ground state. In the limit $h \gg T_K$, E vanishes as $(T_K/h)^{2-2\alpha}$, up to a logarithmic correction. We thoroughly explore the phase space $(\alpha, h)$; for a given $h$, the maximal entanglement occurs in the crossover regime $h \sim T_K$. We also emphasize the possibility of measuring this entanglement using charge qubits subject to electromagnetic noise. [Preview Abstract] |
Friday, March 9, 2007 9:00AM - 9:12AM |
X33.00004: Quantum Information Transport in Nuclear Spin Chains. Paola Cappellaro, David Cory In many solid-state proposals for quantum computers, the transport of information over relatively short distances inside the quantum processor itself is an essential task, and one for which relying on photons, and therefore on a frequent exchanging of information between solid-state and light qubits, could be too costly. Quantum wires based on spins could be a viable alternative leading to much theoretical work on quantum information transfer in linear spin chains. Experimental studies on nuclear spin systems in solid-state by NMR (the most natural implementation of such models) has been up to now prevented by the unavailability of the desired (Heisenberg) Hamiltonian, since the naturally occurring interaction assumes the dipolar form. We present here a similarity transformation between the Heisenberg Hamiltonian and an interaction which is achievable with the collective control provided by rf pulses in NMR. Not only this second Hamiltonian allows us to simulate the information transport in a spin chain, but it also provides a means to observe its signature experimentally. With this scheme it will be possible to study experimentally, in solid-state NMR systems, the transport of polarization beyond exactly solvable models. [Preview Abstract] |
Friday, March 9, 2007 9:12AM - 9:24AM |
X33.00005: Cavity QED in the mesoscopic regime Pascal Degiovanni, Valentin Bonzom, Hichem Bouzidi, Arnaud Le Diffon, Clement Ruef, Tristan Meunier, Jean-Michel Raimond We report on a recent study of the behavior of N atoms resonantly coupled to a single electromagnetic field mode sustained by a high-Q cavity, containing a mesoscopic coherent field. Using a simple effective Hamiltonian model, we show that the strong coupling between the cavity and N atoms/qubits produces an atom-field entangled state, involving N+1 nearly coherent components slowly rotating at different paces in the phase plane. The periodic overlap of these components results in a complex collapse and revival pattern for the Rabi oscillation. Decoherence induced by cavity relaxation, qubit relaxation and dephasing are taken into account. We propose a simple model based on the stochastic quantum trajectories approach. Its results are successfully compared to numerical simulations. Explicit predictions for Rydberg atoms and circuit QED experiments are obtained and suggest that these effects may be observable in the near future. [Preview Abstract] |
Friday, March 9, 2007 9:24AM - 9:36AM |
X33.00006: Diverging Length Scale, Scaling, and Universality of Entanglement Near a Quantum Phase Transition Han-Dong Chen In this work, we show that an important quantity to study about entanglement near a quantum phase transition is the two-body entanglement S(i,j), which measures the entanglement between two separated degrees of freedom (ij) and the rest of system. We establish its relation to correlation functions in the long range limit. Away from the critical point, S(n) saturates with a characteristic length scale $\xi_E$, as the distance n increases. The entanglement length $\xi_E$ diverges near the critical point with the same critical exponent as correlation length. At the critical point, S(n) follows a power law. The universality and finite size scaling of entanglement are demonstrated in a class of exactly solvable spin model. [Preview Abstract] |
Friday, March 9, 2007 9:36AM - 9:48AM |
X33.00007: Landau-Zener dynamics in qubits-oscillator settings Sigmund Kohler, Martijn Wubs, Peter H\"anggi, Keiji Saito, Yosuke Kayanuma In a Cooper-pair box realization of a qubit, the energy splitting of the logical states can be tuned upon variation of the penetrating magnetic flux. Then the coupling of the qubit to a circuit QED oscillator can induce Landau-Zener transitions between the qubit levels. By summing a perturbation series to all orders, we obtained an exact expression for the corresponding LZ transition probability. Moreover, we determined the parameters for which a non-adiabatic transition is accompannied by single-photon generation and showed that LZ transitions can create qubit-oscillator entanglement in a controlled manner [1]. Replacing the oscillator by a quantum heat bath, we encounter a nontrivial problem of dissipative quantum mechanics which can be solved in a similar way. As a main application, we discuss the determination of both the reorganization energy and the integrated spectral density of the bath [2]. Moreover, this provides a convenient test bench for numerical schemes for real- time dissipative quantum dynamics. \\{} [1] K. Saito \textit{et al.}, Europhys.\ Lett.\ \textbf{76}, 22 (2006). \\{} [2] M.\ Wubs \textit{et al.}, Phys.\ Rev.\ Lett.\ \textbf{97}, 200404 (2006). [Preview Abstract] |
Friday, March 9, 2007 9:48AM - 10:00AM |
X33.00008: Coherence control via dynamical decoupling of an electron spin in a quantum dot Wenxian Zhang, V.V. Dobrovitski, Nikolaos Konstantinidis, Lea F. Santos, Lorenza Viola, B.N. Harmon An electron spin in a quantum dot is a promising system for applications in coherent spintronics and quantum computation, but the interaction with the nuclear spins leads to fast decoherence. Subjecting the electron spin to a suitable pulsed control field decouples it from the nuclear spin bath and suppresses decoherence. We study numerically and analytically several most promising decoupling protocols, taking into account the intra-bath coupling, using fully quantum mechanical treatment of the system plus bath dynamics. We show that some high-level protocols extend the coherence time by 3 orders of magnitude for an arbitrary initial spin state. Moreover, we present the protocols which preserve a known initial state with near-to-optimal fidelity for arbitrarily long times. [Preview Abstract] |
Friday, March 9, 2007 10:00AM - 10:12AM |
X33.00009: Entanglement entropy of bilinear fermionic systems Letian Ding, Noah Bray-Ali, Stephan Haas We work out a bound of the block entropy $S_L$ for systems of spinless fermions with generic, bilinear interactions. Experimentally relevant examples include p-wave superconductors and cold atom gases near a Feshbach resonance. We find that the block entropy does {\it not} obey an area law $S_L \sim cL^{d-1}$ law whenever the system has a $d-1$ dimensional surface of gapless excitations. For other systems, such as a p-wave superconductor with Fermi points, the block entropy does obey the area law, but with a coefficient that diverges as the gap closes. [Preview Abstract] |
Friday, March 9, 2007 10:12AM - 10:24AM |
X33.00010: Adiabatic Preparation of Topological Order Alioscia Hamma, Daniel Lidar Topological order characterizes those phases of matter that defy the standard description in terms of symmetry breaking and local order parameters. Topological order is found in nature in the fractional quantum Hall effect. Topologically ordered systems have ground state degeneracy that is robust against perturbations, which has given the root to topological quantum information processing. We discusss the second order quantum phase transition between a spin-polarized phase and a topologically ordered string-net condensed phase. Next we show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by $O(\sqrt{n})$. This provides a physically plausible method for constructing a topological quantum memory. We discuss applications to topological and adiabatic quantum computing. [Preview Abstract] |
Friday, March 9, 2007 10:24AM - 10:36AM |
X33.00011: Quantum phase transition from magnetic to topological order Alioscia Hamma, Wen Zhang, Stephan Haas, Daniel Lidar We present a numerical study of the quantum phase transition from the magnetically ordered phase to the topologically ordered phase of a $n$-spins $1/2$ system. We show that the derivative of von Neumann entropy of a plaquette diverges at the critical point, signaling a second order quantum phase transition. Moreover, we compute the finite-size scaling of the Topological Entropy, showing how this quantity detects the passage to the topologically ordered phase. [Preview Abstract] |
Friday, March 9, 2007 10:36AM - 10:48AM |
X33.00012: Replacing energy by von Neumann entropy in quantum phase transitions Xun Jia, Angela Kopp, Sudip Chakravarty In the thermodynamic limit two distinct states of matter cannot be analytic continuations of each other. Classical phase transitions are characterized by non-analyticities of the free energy. For quantum phase transitions the ground state energy often assumes the role of the free energy. But in a number of important cases this criterion fails, such as the three- dimensional metal-insulator transition of non-interacting electrons in a random potential. It is therefore essential that we find alternative criteria that can track fundamental changes in the internal correlations of the ground state wavefunction. Here we propose that QPTs are generally accompanied by non- analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine integer quantum Hall effect from this perspective. [Preview Abstract] |
Friday, March 9, 2007 10:48AM - 11:00AM |
X33.00013: Statistical quantum mechanics and entanglement in anisotropic Heisenberg model. You-Ling Chiang, Armen Kocharian, Chee Yang The single site quantum and thermal entanglement, concurrences, quantum phase transitions and corresponding quantum critical points are studied in small spin $s={1\over 2}$ and $1$ in ferromagnetic and antiferromagnetic Heisenberg dimers. The grand canonical ensemble of Heisenberg clusters is also used for exact calculations of thermal properties, quantum and thermal entanglements of the various spin and fermionic lattice models in the presence of magnetic field. We study the magnetic phase transitions and crossovers driven by external field and temperature. The comparison with the exact solution for Heisenberg model in thermodynamic limit for the limiting cases is also provided. The small Ising, Heisenberg and Hubbard clusters are also used for comparison with the exact Bethe ansatz solutions and predictions of traditional mean field theory and developed perturbation theory about generalized self- consistent solution. [Preview Abstract] |
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