Spin projection chromatography

We formulate the many-body spin dynamics at high temperature within the non-equilibrium Keldysh formalism. For the simplest XY interaction, analytical expressions in terms of the one particle solutions are obtained for linear and ring configurations. For small rings of even spin number, the group velocities of excitations depend on the parity of the total spin projection. This should enable a dynamical filtering of spin projections with a given parity i.e. a Spin projection chromatography.Comment: 13 pages, 3 figure

A Quantum Many-Body Instability in the Thermodynamic Limit

Intrinsic decoherence in the thermodynamic limit is shown for a large class of many-body quantum systems in the unitary evolution in NMR and cavity QED. The effect largely depends on the inability of the system to recover the phases. Gaussian decaying in time of the fidelity is proved for spin systems and radiation-matter interaction.Comment: 11 pages, 1 figure. Final version accepted for publication in Modern Physics Letters

Decoherence as attenuation of mesoscopic echoes in a spin-chain channel

An initial local excitation in a confined quantum system evolves exploring the whole system, returning to the initial position as a mesoscopic echo at the Heisenberg time. We consider a two weakly coupled spin chains, a spin ladder, where one is a quantum channel while the other represents an environment. We quantify decoherence in the quantum channel through the attenuation of the mesoscopic echoes. We evaluate decoherence rates for different ratios between sources of amplitude fluctuation and dephasing in the inter-chain interaction Hamiltonian. The many-body dynamics is seen as a one-body evolution with a decoherence rate given by the Fermi golden rule.Comment: 12 pages, 7 figure

Quantum parallelism as a tool for ensemble spin dynamics calculations

Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local". It resorts a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.Comment: 5 pages, 3 figures, improved version of the manuscrip

Thermodynamic Limit and Decoherence: Rigorous Results

Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. In a many-body system has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence more and more small as the number of particles increases. This effect has been observed experimentally. More generally, a theorem about coherence of bulk matter can be proved. All this takes us to the conclusion that a well definite boundary for the quantum to classical world does exist and that can be drawn by the thermodynamic limit, extending in this way the deep link between statistical mechanics and quantum evolution to a high degree.Comment: 5 pages, no figures. Contribution to proceedings of DICE 2006 (Piombino, Italy, September 11-15, 2006

Effective one-body dynamics in multiple-quantum NMR experiments

A suitable NMR experiment in a one-dimensional dipolar coupled spin system allows one to reduce the natural many-body dynamics into effective one-body dynamics. We verify this in a polycrystalline sample of hydroxyapatite (HAp) by monitoring the excitation of NMR many-body superposition states: the multiple-quantum coherences. The observed effective one-dimensionality of HAp relies on the quasi 1d structure of the dipolar coupled network that, as we show here, is dynamically enhanced by the quantum Zeno effect. Decoherence is also probed through a Loschmidt echo experiment, where the time reversal is implemented on the double-quantum Hamiltonian, I_{i,+}I_{j,+} + I_{i,-}I_{j,-}. We contrast the decoherence of adamantane, a standard 3d system, with that of HAp. While the first shows an abrupt Fermi-type decay, HAp presents a smooth exponential law.Comment: 8 pages, 6 figure

Quantum Dynamical Echoes in the Spin 'Diffusion' in Mesoscopic Systems

The evolution of local spin polarization in finite systems involves interference phenomena that give rise to {\bf quantum dynamical echoes }and non-ergodic behavior. We predict the conditions to observe these echoes by exploiting the NMR sequences devised by Zhang et al. [Phys. Rev. Lett. {\bf % 69}, 2149 (1992)], which uses a rare $^{13}$C as {\bf local probe }for a dipolar coupled $^1$H spin system. The non-ideality of this probe when testing mesoscopic systems is carefully analyzed revealing the origin of various striking experimental features.Comment: 4 pages, Revtex, 3 Figures available upon reques

Perfect state transfers by selective quantum interferences within complex spin networks

We present a method that implement directional, perfect state transfers within a branched spin network by exploiting quantum interferences in the time-domain. That provides a tool to isolate subsystems from a large and complex one. Directionality is achieved by interrupting the spin-spin coupled evolution with periods of free Zeeman evolutions, whose timing is tuned to be commensurate with the relative phases accrued by specific spin pairs. This leads to a resonant transfer between the chosen qubits, and to a detuning of all remaining pathways in the network, using only global manipulations. As the transfer is perfect when the selected pathway is mediated by 2 or 3 spins, distant state transfers over complex networks can be achieved by successive recouplings among specific pairs/triads of spins. These effects are illustrated with a quantum simulator involving 13C NMR on Leucine's backbone; a six-spin network.Comment: 5 pages, 3 figure

Decoherence under many-body system-environment interactions: a stroboscopic representation based on a fictitiously homogenized interaction rate

An environment interacting with portions of a system leads to multiexponential interaction rates. Within the Keldysh formalism, we fictitiously homogenize the system-environment interaction yielding a uniform decay rate facilitating the evaluation of the propagators. Through an injection procedure we neutralize the fictitious interactions. This technique justifies a stroboscopic representation of the system-environment interaction which is useful for numerical implementation and converges to the natural continuous process. We apply this procedure to a fermionic two-level system and use the Jordan-Wigner transformation to solve a two-spin swapping gate in the presence of a spin environment.Comment: 11 pages, 3 figures, title changed, some typos change

Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation

Quantum Information Processing relies on coherent quantum dynamics for a precise control of its basic operations. A swapping gate in a two-spin system exchanges the degenerate states |+,-> and |-,+>. In NMR, this is achieved turning on and off the spin-spin interaction b=\Delta E that splits the energy levels and induces an oscillation with a natural frequency \Delta E/\hbar. Interaction of strength \hbar/\tau_{SE}, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale \tau_{\phi}. While the experimental frequency \omega and decoherence time \tau_{\phi} were expected to be roughly proportional to b/\hbar and \tau_{SE} respectively, we present here experiments that show drastic deviations in both \omega and \tau_{\phi}. By solving the many spin dynamics, we prove that the swapping regime is restricted to \Delta E \tau_{SE} > \hbar. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/\tau_{\phi} \propto (b/\hbar)^2 \tau_{SE}. The transition between quantum dynamical phases occurs when \omega \propto \sqrt{(b/\hbar)^{2}-(k/\tau_{SE})^2} becomes imaginary, resembling an overdamped classical oscillator. Here, 0<k^2<1 depends only on the anisotropy of the system-environment interaction, being 0 for isotropic and 1 for XY interactions. This critical onset of a phase dominated by the Quantum Zeno effect opens up new opportunities for controlling quantum dynamics.Comment: Final version. One figure and some equations corrected, 10 pages, 4 figure