Spinon excitations in the XX chain: spectra, transition rates, observability

The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1=2 XX model on a lattice with an even or odd number N of lattice sites and periodic boundary conditions. Exact product formulas for the transition rates derived via Bethe ansatz are used to calculate asymptotic expressions of the 2-spinon and 4-spinon parts (for large even N) as well as of the 1-spinon and 3-spinon parts (for large odd N) of the dynamic spin structure factors. The observability of these spectral contributions is assessed for finite and infinite N.Comment: 19 pages, 10 figure

Optimization of Short Coherent Control Pulses

The coherent control of small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the non-commutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for $\pi$ and $\frac{\pi}{2}$ pulses.Comment: 9 pages, 6 figures; published versio

Generalization of short coherent control pulses: extension to arbitrary rotations

We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.Comment: 6 pages, no figures; published versio

High Order Coherent Control Sequences of Finite-Width Pulses

The performance of sequences of designed pulses of finite length $\tau$ is analyzed for a bath of spins and it is compared with that of sequences of ideal, instantaneous pulses. The degree of the design of the pulse strongly affects the performance of the sequences. Non-equidistant, adapted sequences of pulses, which equal instantaneous ones up to $\mathcal{O}(\tau^3)$, outperform equidistant or concatenated sequences. Moreover, they do so at low energy cost which grows only logarithmically with the number of pulses, in contrast to standard pulses with linear growth.Comment: 6 pages, 5 figures, new figures, published versio

Optimized pulses for the perturbative decoupling of spin and decoherence bath

In the framework of nuclear magnetic resonance, we consider the general problem of the coherent control of a spin coupled to a bath by means of composite or continuous pulses of duration $\tau_\mathrm{p}$. We show explicity that it is possible to design the pulse in order to achieve a decoupling of the spin from the bath up to the third order in $\tau_\mathrm{p}$. The evolution of the system is separated in the evolution of the spin under the action of the pulse and of the bath times correction terms. We derive the correction terms for a general time dependent axis of rotation and for a general coupling between the spin and the environment. The resulting corrections can be made vanish by an appropriate design of the pulse. For $\pi$ and $\pi/2$ pulses, we demonstrate explicitly that pulses exist which annihilate the first and the second order corrections even if the bath is fully quantum mechanical, i.e., it displays internal dynamics. Such pulses will also be useful for quantum information processing.Comment: 9 pages, 7 figures. Published versio

Transport Control in Low-Dimensional Spin-1/2 Heisenberg Systems

We analyze transport of local magnetization and develop schemes to control transport behavior in finite spin-1/2 Heisenberg chains and spin-1/2 Heisenberg two-leg ladders at zero temperature. By adjusting parameters in the Hamiltonians, these quantum systems may show both integrable and chaotic limits. We provide examples of chaotic systems leading to diffusive and to ballistic transport. In addition, methods of coherent quantum control to induce a transition from diffusive to ballistic transport are proposed.Comment: 8 pages, 5 figure

Manipulation of the dynamics of many-body systems via quantum control methods

We investigate how dynamical decoupling methods may be used to manipulate the time evolution of quantum many-body systems. These methods consist of sequences of external control operations designed to induce a desired dynamics. The systems considered for the analysis are one-dimensional spin-1/2 models, which, according to the parameters of the Hamiltonian, may be in the integrable or non-integrable limits, and in the gapped or gapless phases. We show that an appropriate control sequence may lead a chaotic chain to evolve as an integrable chain and a system in the gapless phase to behave as a system in the gapped phase. A key ingredient for the control schemes developed here is the possibility to use, in the same sequence, different time intervals between control operations.Comment: 10 pages, 3 figure

Direct Observation of Field-Induced Incommensurate Fluctuations in a One-Dimensional S=1/2 Antiferromagnet

Neutron scattering from copper benzoate, Cu(C6D5COO)2 3D2O, provides the first direct experimental evidence for field-dependent incommensurate low energy modes in a one-dimensional spin S = 1/2 antiferromagnet. Soft modes occur for wavevectors q=\pi +- dq(H) where dq(H) ~ 2 \pi M(H)/g\mu_B as predicted by Bethe ansatz and spinon descriptions of the S = 1/2 chain. Unexpected was a field-induced energy gap $\Delta(H) \propto H^\alpha$, where $\alpha = 0.65(3)$ as determined from specific heat measurements. At H = 7 T (g\mu_B H/J = 0.52), the magnitude of the gap varies from 0.06 - 0.3 J depending on the orientation of the applied field.Comment: 11 pages, 5 postscript figures, LaTeX, Submitted to PRL 3/31/97, e-mail comments to [email protected]

Search for CP violation in D+→ϕπ+ and D+s→K0Sπ+ decays

A search for CP violation in D + → ϕπ + decays is performed using data collected in 2011 by the LHCb experiment corresponding to an integrated luminosity of 1.0 fb−1 at a centre of mass energy of 7 TeV. The CP -violating asymmetry is measured to be (−0.04 ± 0.14 ± 0.14)% for candidates with K − K + mass within 20 MeV/c 2 of the ϕ meson mass. A search for a CP -violating asymmetry that varies across the ϕ mass region of the D + → K − K + π + Dalitz plot is also performed, and no evidence for CP violation is found. In addition, the CP asymmetry in the D+s→K0Sπ+ decay is measured to be (0.61 ± 0.83 ± 0.14)%