Neutral skyrmion configurations in the low-energy effective theory of spinor condensate ferromagnets

We study the low-energy effective theory of spinor condensate ferromagnets for the superfluid velocity and magnetization degrees of freedom. This effective theory describes the competition between spin stiffness and a long-ranged interaction between skyrmions, topological objects familiar from the theory of ordinary ferromagnets. We find exact solutions to the non-linear equations of motion describing neutral configurations of skyrmions and anti-skyrmions. These analytical solutions provide a simple physical picture for the origin of crystalline magnetic order in spinor condensate ferromagnets with dipolar interactions. We also point out the connections to effective theories for quantum Hall ferromagnets.Comment: 13 pages, 7 figure

Entropy and Correlation Functions of a Driven Quantum Spin Chain

We present an exact solution for a quantum spin chain driven through its critical points. Our approach is based on a many-body generalization of the Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The resulting nonequilibrium state of the system, while being a pure quantum state, has local properties of a mixed state characterized by finite entropy density associated with Kibble-Zurek defects. The entropy, as well as the finite spin correlation length, are functions of the rate of sweep through the critical point. We analyze the anisotropic XY spin 1/2 model evolved with a full many-body evolution operator. With the help of Toeplitz determinants calculus, we obtain an exact form of correlation functions. The properties of the evolved system undergo an abrupt change at a certain critical sweep rate, signaling formation of ordered domains. We link this phenomenon to the behavior of complex singularities of the Toeplitz generating function.Comment: 16 pgs, 7 fg

Bell inequalities for three systems and arbitrarily many measurement outcomes

We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define facets of the polytope of local correlations. We investigate the quantum violations of these inequalities, in particular with respect to the Hilbert space dimension. We provide strong evidence that the maximal quantum violation can only be reached using systems with local Hilbert space dimension exceeding the number of measurement outcomes. This suggests that our inequalities can be used as multipartite dimension witnesses.Comment: v1 6 pages, 4 tables; v2 Published version with minor typos correcte

A phenomenological model of the superconducting state of the Bechgaard salts

We present a group theoretical analysis of the superconducting state of the Bechgaard salts, e.g., (TMTSF)_2PF_6 or (TMTSF)_2ClO_6. We show that there are eight symmetry distinct superconducting states. Of these only the (fully gapped, even frequency, p-wave, triplet) 'polar state' is consistent with the full range of the experiments on the Bechgaard salts. The gap of the polar state is d(k) (psi_uk,0,0), where psi_uk may be any odd parity function that is translationally invariant.Comment: 4 pages, no figure

The physics of dipolar bosonic quantum gases

This article reviews the recent theoretical and experimental advances in the study of ultracold gases made of bosonic particles interacting via the long-range, anisotropic dipole-dipole interaction, in addition to the short-range and isotropic contact interaction usually at work in ultracold gases. The specific properties emerging from the dipolar interaction are emphasized, from the mean-field regime valid for dilute Bose-Einstein condensates, to the strongly correlated regimes reached for dipolar bosons in optical lattices.Comment: Review article, 71 pages, 35 figures, 350 references. Submitted to Reports on Progress in Physic

Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point

We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of the asymptotics of the transition probability when the tuning parameter slowly changes in the finite range. Then we apply this perturbation theory to many-particle systems with low energy spectrum characterized by quasiparticle excitations. Within this approach we derive the scaling of various quantities such as the density of generated defects, entropy and energy. We discuss the applications of this approach to a specific situation where the system crosses a quantum critical point. We also show the connection between adiabatic and sudden quenches near a quantum phase transitions and discuss the effects of quasiparticle statistics on slow and sudden quenches at finite temperatures.Comment: 20 pages, 3 figures, contribution to "Quantum Quenching, Annealing and Computation", Eds. A. Das, A. Chandra and B. K. Chakrabarti, Lect. Notes in Phys., Springer, Heidelberg (2009, to be published), reference correcte

An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling

The Hubbard model, containing only the minimum ingredients of nearest neighbor hopping and on-site interaction for correlated electrons, has succeeded in accounting for diverse phenomena observed in solid-state materials. One of the interesting extensions is to enlarge its spin symmetry to SU(N>2), which is closely related to systems with orbital degeneracy. Here we report a successful formation of the SU(6) symmetric Mott insulator state with an atomic Fermi gas of ytterbium (173Yb) in a three-dimensional optical lattice. Besides the suppression of compressibility and the existence of charge excitation gap which characterize a Mott insulating phase, we reveal an important difference between the cases of SU(6) and SU(2) in the achievable temperature as the consequence of different entropy carried by an isolated spin. This is analogous to Pomeranchuk cooling in solid 3He and will be helpful for investigating exotic quantum phases of SU(N) Hubbard system at extremely low temperatures.Comment: 20 pages, 6 figures, to appear in Nature Physic

Quantum Computing and Quantum Simulation with Group-II Atoms

Recent experimental progress in controlling neutral group-II atoms for optical clocks, and in the production of degenerate gases with group-II atoms has given rise to novel opportunities to address challenges in quantum computing and quantum simulation. In these systems, it is possible to encode qubits in nuclear spin states, which are decoupled from the electronic state in the $^1$S$_0$ ground state and the long-lived $^3$P$_0$ metastable state on the clock transition. This leads to quantum computing scenarios where qubits are stored in long lived nuclear spin states, while electronic states can be accessed independently, for cooling of the atoms, as well as manipulation and readout of the qubits. The high nuclear spin in some fermionic isotopes also offers opportunities for the encoding of multiple qubits on a single atom, as well as providing an opportunity for studying many-body physics in systems with a high spin symmetry. Here we review recent experimental and theoretical progress in these areas, and summarise the advantages and challenges for quantum computing and quantum simulation with group-II atoms.Comment: 11 pages, 7 figures, review for special issue of "Quantum Information Processing" on "Quantum Information with Neutral Particles

Dynamics of a Quantum Phase Transition and Relaxation to a Steady State

We review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase, and apparent relaxation of an excited system after a sudden quench of a parameter in its Hamiltonian. Accordingly the review is divided into two parts. The first part revolves around a quantum version of the Kibble-Zurek mechanism including also phenomena that go beyond this simple paradigm. What they have in common is that excitation of a gapless many-body system scales with a power of the driving rate. The second part attempts a systematic presentation of recent results and conjectures on apparent relaxation of a pure state of an isolated quantum many-body system after its excitation by a sudden quench. This research is motivated in part by recent experimental developments in the physics of ultracold atoms with potential applications in the adiabatic quantum state preparation and quantum computation.Comment: 117 pages; review accepted in Advances in Physic