Exponential decay in a spin bath

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.Comment: 4+ pages, 3 figures; v2: 9 pages, 3 figures (added four appendices with extensive technical details, version to appear in Phys. Rev. B

Singlet-triplet decoherence due to nuclear spins in a double quantum dot

We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 1/2, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law ($\sim 1/t^{3/2}$) when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\pi/4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence, and find that there is an optimal operating point where orbital dephasing becomes negligible.Comment: 12 pages, 4 figure

Free-induction decay and envelope modulations in a narrowed nuclear spin bath

We evaluate free-induction decay for the transverse components of a localized electron spin coupled to a bath of nuclear spins via the Fermi contact hyperfine interaction. Our perturbative treatment is valid for special (narrowed) bath initial conditions and when the Zeeman energy of the electron $b$ exceeds the total hyperfine coupling constant $A$: $b>A$. Using one unified and systematic method, we recover previous results reported at short and long times using different techniques. We find a new and unexpected modulation of the free-induction-decay envelope, which is present even for a purely isotropic hyperfine interaction without spin echoes and for a single nuclear species. We give sub-leading corrections to the decoherence rate, and show that, in general, the decoherence rate has a non-monotonic dependence on electron Zeeman splitting, leading to a pronounced maximum. These results illustrate the limitations of methods that make use of leading-order effective Hamiltonians and re-exponentiation of short-time expansions for a strongly-interacting system with non-Markovian (history-dependent) dynamics.Comment: 13 pages, 9 figure

Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics

We have performed a systematic calculation for the non-Markovian dynamics of a localized electron spin interacting with an environment of nuclear spins via the Fermi contact hyperfine interaction. This work applies to an electron in the s -type orbital ground state of a quantum dot or bound to a donor impurity, and is valid for arbitrary polarization p of the nuclear spin system, and arbitrary nuclear spin I in high magnetic fields. In the limit of p=1 and I=1/2, the Born approximation of our perturbative theory recovers the exact electron spin dynamics. We have found the form of the generalized master equation (GME) for the longitudinal and transverse components of the electron spin to all orders in the electron spin--nuclear spin flip-flop terms. Our perturbative expansion is regular, unlike standard time-dependent perturbation theory, and can be carried-out to higher orders. We show this explicitly with a fourth-order calculation of the longitudinal spin dynamics. In zero magnetic field, the fraction of the electron spin that decays is bounded by the smallness parameter \delta=1/p^{2}N, where N is the number of nuclear spins within the extent of the electron wave function. However, the form of the decay can only be determined in a high magnetic field, much larger than the maximum Overhauser field. In general the electron spin shows rich dynamics, described by a sum of contributions with non-exponential decay, exponential decay, and undamped oscillations. There is an abrupt crossover in the electron spin asymptotics at a critical dimensionality and shape of the electron envelope wave function. We propose a scheme that could be used to measure the non-Markovian dynamics using a standard spin-echo technique, even when the fraction that undergoes non-Markovian dynamics is small.Comment: 22 pages, 8 figure

Hall effect in quasi one-dimensional organic conductors

We study the Hall effect in a system of weakly coupled Luttinger Liquid chains, using a Memory function approach to compute the Hall constant in the presence of umklapp scattering along the chains. In this approximation, the Hall constant decomposes into two terms: a high-frequency term and a Memory function term. For the case of zero umklapp scattering, where the Memory function vanishes, the Hall constant is simply the band value, in agreement with former results in a similar model with no dissipation along the chains. With umklapp scattering along the chains, we find a power-law temperature dependance of the Hall constant. We discuss the applications to quasi 1D organic conductors at high temperatures.Comment: Proceedings of the ISCOM conference "Sixth International Symposium on Crystalline Organic Metals, Superconductors, and Ferromagnets", Key West, Florida, USA (Sept. 2005), to be plublished in the Journal of Low Temperature Physic

Rigorous Born Approximation and beyond for the Spin-Boson Model

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by $\sqrt{\alpha}$, where $\alpha$ is the coupling strength to the environment. We also explore the calculation of the next order Born approximation: we show that, at the expense of very large computational complexity, interesting physical quantities can be rigorously computed at fourth order using computer algebra, presented completely in an accompanying Mathematica file. We compute the $O(\alpha)$ corrections to the long time behavior of the system density matrix; the result is identical to the reduced density matrix of the equilibrium state to the same order in $\alpha$. All these calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.Comment: Greatly extended version of short paper cond-mat/0304118. Accompanying Mathematica notebook fop5.nb, available in Source, is an essential part of this work; it gives full details of the fourth-order Born calculation summarized in the text. fop5.nb is prepared in arXiv style (available from Wolfram Research

Microscopic Theory for the Markovian Decay of Magnetization Fluctuations in Nanomagnets

We present a microscopic theory for the phonon-driven decay of the magnetization fluctuations in a wide class of nanomagnets where the dominant energy is set by isotropic exchange and/or uniaxial anisotropy. Based on the Zwanzig-Mori projection formalism, the theory reveals that the magnetization fluctuations are governed by a single decay rate $\omega_c$, which we further identify with the zero-frequency portion of the associated self-energy. This dynamical decoupling from the remaining slow degrees of freedom is attributed to a conservation law and the discreteness of the energy spectrum, and explains the omnipresent mono-exponential decay of the magnetization over several decades in time, as observed experimentally. A physically transparent analytical expression for $\omega_c$ is derived which highlights the three specific mechanisms of the slowing down effect which are known so far in nanomagnets.Comment: 7 page

Relating chaos to deterministic diffusion of a molecule adsorbed on a surface

Chaotic internal degrees of freedom of a molecule can act as noise and affect the diffusion of the molecule on a substrate. A separation of time scales between the fast internal dynamics and the slow motion of the centre of mass on the substrate makes it possible to directly link chaos to diffusion. We discuss the conditions under which this is possible, and show that in simple atomistic models with pair-wise harmonic potentials, strong chaos can arise through the geometry. Using molecular-dynamics simulations, we demonstrate that a realistic model of benzene is indeed chaotic, and that the internal chaos affects the diffusion on a graphite substrate

Magnetization reversal driven by spin-injection : a mesoscopic spin-transfer effect

A mesoscopic description of spin-transfer effect is proposed, based on the spin-injection mechanism occurring at the junction with a ferromagnet. The effect of spin-injection is to modify locally, in the ferromagnetic configuration space, the density of magnetic moments. The corresponding gradient leads to a current-dependent diffusion process of the magnetization. In order to describe this effect, the dynamics of the magnetization of a ferromagnetic single domain is reconsidered in the framework of the thermokinetic theory of mesoscopic systems. Assuming an Onsager cross-coefficient that couples the currents, it is shown that spin-dependent electric transport leads to a correction of the Landau-Lifshitz-Gilbert equation of the ferromagnetic order parameter with supplementary diffusion terms. The consequence of spin-injection in terms of activation process of the ferromagnet is deduced, and the expressions of the effective energy barrier and of the critical current are derived. Magnetic fluctuations are calculated: the correction to the fluctuations is similar to that predicted for the activation. These predictions are consistent with the measurements of spin-transfer obtained in the activation regime and for ferromagnetic resonance under spin-injection.Comment: 20 pages, 2 figure

Path Integral for Quantum Operations

In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe