14 research outputs found
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
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
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
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
Time Reversal Mirror and Perfect Inverse Filter in a Microscopic Model for Sound Propagation
Time reversal of quantum dynamics can be achieved by a global change of the
Hamiltonian sign (a hasty Loschmidt daemon), as in the Loschmidt Echo
experiments in NMR, or by a local but persistent procedure (a stubborn daemon)
as in the Time Reversal Mirror (TRM) used in ultrasound acoustics. While the
first is limited by chaos and disorder, the last procedure seems to benefit
from it. As a first step to quantify such stability we develop a procedure, the
Perfect Inverse Filter (PIF), that accounts for memory effects, and we apply it
to a system of coupled oscillators. In order to ensure a many-body dynamics
numerically intrinsically reversible, we develop an algorithm, the pair
partitioning, based on the Trotter strategy used for quantum dynamics. We
analyze situations where the PIF gives substantial improvements over the TRM.Comment: Submitted to Physica
Quantum dynamics under coherent and incoherent effects of a spin bath in the Keldysh formalism: application to a spin swapping operation
We develop the Keldysh formalism for the polarization dynamics of an open
spin system. We apply it to the swapping between two qubit states in a model
describing an NMR cross-polarization experiment. The environment is a set of
interacting spins. For fast fluctuations in the environment, the analytical
solution shows effects missed by the secular approximation of the Quantum
Master Equation for the density matrix: a frequency decrease depending on the
system-environment escape rate and the quantum quadratic short time behavior.
Considering full memory of the bath correlations yields a progressive change of
the swapping frequency.Comment: 16 pages, 3 figures, final for
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