Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem

We present a remarkable finding that a recently discovered [G. S. Uhrig, Phys. Rev. Lett. 98, 100504 (2007)10.1103/PhysRevLett.98.100504] series of pulse sequences, designed to optimally restore coherence to a qubit in the spin-boson model of decoherence, is in fact completely model independent and generically valid for arbitrary dephasing Hamiltonians given sufficiently short delay times between pulses. The series maximizes qubit fidelity versus number of applied pulses for sufficiently short delay times because the series, with each additional pulse, cancels successive orders of a time expansion for the fidelity decay. The "magical" universality of this property, which was not appreciated earlier, requires that a linearly growing set of "unknowns" (the delay times) must simultaneously satisfy an exponentially growing set of nonlinear equations that involve arbitrary dephasing Hamiltonian operators.     

Electron spin decoherence in isotope-enriched silicon

Silicon is promising for spin-based quantum computation because nuclear spins, a source of magnetic noise, may be eliminated through isotopic enrichment. Long spin decoherence times T2 have been measured in isotope-enriched silicon but come far short of the T2=2T1 limit. The effect of nuclear spins on T2 is well established. However, the effect of background electron spins from ever present residual phosphorus impurities in silicon can also produce significant decoherence. We study spin decoherence decay as a function of donor concentration, 29Si concentration, and temperature using cluster expansion techniques specifically adapted to the problem of a sparse dipolarly coupled electron spin bath. Our results agree with the existing experimental spin echo data in Si:P and establish the importance of background dopants as the ultimate decoherence mechanism in isotope-enriched silicon.     

Quenching spin decoherence in diamond through spin bath polarization

We experimentally demonstrate that the decoherence of a spin by a spin bath can be completely eliminated by fully polarizing the spin bath. We use electron paramagnetic resonance at 240 GHz and 8 T to study the electron-spin coherence time T2 of nitrogen-vacancy centers and nitrogen impurities in diamond from room temperature down to 1.3 K. A sharp increase of T2 is observed below the Zeeman energy (11.5 K). The data are well described by a suppression of the flip-flop induced spin bath fluctuations due to thermal electron-spin polarization. T2 saturates at approximately 250 micros below 2 K, where the polarization of the electron-spin bath exceeds 99%.     

Hybridization and spin decoherence in heavy-hole quantum dots

We theoretically investigate the spin dynamics of a heavy hole confined to an unstrained III-V semiconductor quantum dot and interacting with a narrowed nuclear-spin bath. We show that band hybridization leads to an exponential decay of hole-spin superpositions due to hyperfine-mediated nuclear pair flips, and that the accordant single-hole-spin decoherence time T2 can be tuned over many orders of magnitude by changing external parameters. In particular, we show that, under experimentally accessible conditions, it is possible to suppress hyperfine-mediated nuclear-pair-flip processes so strongly that hole-spin quantum dots may be operated beyond the "ultimate limitation" set by the hyperfine interaction which is present in other spin-qubit candidate systems.     

Microcanonical relation between continuous and discrete spin models

A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of an Ising model defined on the same lattice suggests an approximate expression for the microcanonical density of states. Based on this approximation we conjecture that if a O(n) model with ferromagnetic interactions on a lattice has a phase transition, its critical energy density is equal to that of the n=1 case, i.e., an Ising system with the same interactions. The conjecture holds true in the case of long-range interactions. For nearest-neighbor interactions, numerical results are consistent with the conjecture for n=2 and n=3 in three dimensions. For n=2 in two dimensions (XY model) the conjecture yields a prediction for the critical energy of the Bere?inskij-Kosterlitz-Thouless transition, which would be equal to that of the two-dimensional Ising model. We discuss available numerical data in this respect.     

Pairwise decoherence in coupled spin qubit networks

Experiments involving phase coherent dynamics of networks of spins, such as echo experiments, will only work if decoherence can be suppressed. We show here, by analyzing the particular example of a crystalline network of Fe8 molecules, that most decoherence typically comes from pairwise interactions (particularly dipolar interactions) between the spins, which cause "correlated errors." However, at very low T these are strongly suppressed. These results have important implications for the design of quantum information processing systems using electronic spins.     

State transfer in intrinsic decoherence spin channels

By analytically solving the master equation, we investigate quantum state transfer, creation and distribution of entanglement in the model of Milburn’s intrinsic decoherence. Our results reveal that the ideal spin channels will be destroyed by the intrinsic decoherence environment, and the detrimental effects become severe as the decoherence rate γ and the spin chain length N increase. For infinite evolution time, both the state transfer fidelity and the concurrence of the created and distributed entanglement approach steady state values, which are independent of the decoherence rate γ and decrease as the spin chain length N increases. Finally, we present two modified spin chains which may serve as near perfect spin channels for long distance state transfer even in the presence of intrinsic decoherence environments.     

Electron spin decoherence in quantum dots due to interaction with nuclei

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei. The decay is caused by the spatial variation of the electron wave function within the dot, leading to a nonuniform hyperfine coupling A. We evaluate the spin correlation function and find that the decay is not exponential but rather power (inverse logarithm) lawlike. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by (planck)N/A, where N is the number of nuclei inside the dot, and the amplitude of precession decays to a finite value. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.     

On the environmental decoherence and spin interference in mesoscopic loop structures

Mechanisms of ‘environmental decoherence’ such as surface scattering, Elliot–Yafet process and precession mechanisms, as well as their influence on the spin phase relaxation are considered and compared. It is shown that the ‘spin ballistic’ regime is possible, when the phase relaxation length for the spin part of the wave function (L^(s)) is much greater than the phase relaxation length for the ‘orbital part’ (L^(e)). In the presence of an additional magnetic field, the spin part of the electron's wave function (WF) acquires a phase shift due to additional spin precession about that field. If the structure length L is chosen to be L^(s)>L>L^(e), it is possible to ‘wash out’ the quantum interference related to the phase coherence of the ‘orbital part’ of the WF, retaining at the same time that related to the phase coherence of the spin part and, hence, to reveal corresponding conductance oscillations.     

Superstrings in AdS superbackgrounds and their integrability

This contribution is mainly based on results of [1, 2]. We review the structure of Green-Schwarz superstrings on AdS backgrounds with the emphasis on peculiarities of those cases which are not maximally supersymmetric. In particular, we discuss complications which one encounters with the proof of classical integrability of non-maximally supersymmetric string sigma-models and describe a method of the construction of a Lax representation of the equations of motion which is capable to provide evidence for the integrability of sigma-models whose target space is not a semi-symmetric super-coset manifold.     

Relaxation and decoherence of orbital and spin degrees of freedom in quantum dots

The phonon induced mechanisms of relaxation/decoherence in quantum dots are analysed. A non-perturbative technique - a modification of the Davydov transformation appropriate to the localised particles is applied for solving the electron-phonon eigenvalue problem in a quantum dot at magnetic field presence. The decay rates for polaron relaxation via the anharmonicity induced channel are analysed in details. In particular, it is indicated that previous, of perturbative type, estimations of the anharminicity induced relaxation rates were too severe and after including the coherence effects they are of, at least, one order longer. The process of exciton dressing with phonons is also analysed as the unavoidable source of picosecond scale decoherence in optically driven nanostructures. A break-down of an instant Pauli spin blocking mechanism and a large enhancement of the Fröhlich constant for confined electrons are also addressed.     

On the origin of integrability in matrix models

The matrix integrals involved in 2d lattice gravity are studied at finiteN. The integrable systems that arise in the continuum theory are shown to result directly from the formulation of the matrix integrals in terms of orthogonal polynomials. The partition function proves to be a tau function of the Toda lattice hierarchy. The associated linear problem is equivalent to finding the polynomial basis which diagonalizes the partition function. The cases of one Hermitian matrix, one unitary matrix, and Hermitian matrix chains all fall within the Toda framework.Research supported in part by DOE contract DE-FG02-90ER-40560, an NSF Presidential Young Investigator Award, and the Alfred P. Sloan Foundation     

Yangian symmetries and integrability of the Dirac equation with spin symmetry

We show that a Yangian symmetry, namely, Y(su(2))$Y\left(su\left(2\right)\right)$, exists in the Dirac equation with spin symmetry when the potential term takes a Coulomb form. We construct the generators of Y(su(2))$Y\left(su\left(2\right)\right)$ explicitly and get the energy spectrum of this model from the representation theory for Y(su(2))$Y\left(su\left(2\right)\right)$. We also show that this model is integrable, from RTT relations.     

Intrapulse depolarization in optical fibers: a classical analog of spin decoherence

We show that the combination of cross-phase modulation and polarization-mode dispersion inside optical fibers leads to a novel phenomenon of intrapulse depolarization manifested as different random states of polarization across the pulse profile. Such polarization evolution of optical pulses is directly analogous to the phenomenon of spin decoherence in semiconductors or pseudospin relaxation in atoms.     

Detection of single spin decoherence in a quantum dot via charge currents

We consider a quantum dot attached to leads in the Coulomb blockade regime that has a spin 1 / 2 ground state. We show that, by applying an ESR field to the dot spin, the stationary current in the sequential tunneling regime exhibits a new resonance peak whose linewidth is determined by the single spin decoherence time T2. The Rabi oscillations of the dot spin are shown to induce coherent current oscillations from which T2 can be deduced in the time domain. We describe a spin inverter which can be used to pump current through a double dot via spin flips generated by ESR.     

Statistical-acoustics models of energy decay in systems of coupled rooms and their relation to geometrical acoustics

An improved statistical-acoustics model of high-frequency sound fields in coupled rooms is developed by incorporating into prior models geometrical-acoustics corrections for both energy decay within subrooms and energy transfer between subrooms. The conditions under which statistical-acoustics models of coupled rooms are valid approximations to geometrical acoustics are examined by comparison of computational geometrical-acoustics predictions of decay curves in two- and three-room systems with those of both improved and prior statistical-acoustics models. The accuracy of the decay model used within subrooms is found to have a primary influence on the accuracy of predictions in coupled systems. Likewise, nondiffuse transfer of energy is shown to significantly affect decay of energy in systems of coupled rooms. The decrease in energy density of the reverberant field with distance from the source, which is predicted by geometrical acoustics, is found to result in spatial dependence of decay-curve shape for certain coupling geometries. Geometrical effects are shown to contribute to the failure of statistical-acoustics models in the case of strong coupling between subrooms; thus, previously proposed statistical-acoustics criteria cannot predict the point at which the models break down with consistent accuracy.     

Coupled chaotic oscillators and their relation to a central pattern generator for artificial quadrupeds

Animal locomotion employs different periodic patterns known as animal gaits. In 1993, Collins and Stewart recognized that gaits possessed certain symmetries and characterized the gaits of quadrupeds and bipeds using permutation symmetry groups, which impose constraints on the locomotion center called the central pattern generator (CPG) in the animal brain. They modeled the CPG by coupling four nonlinear oscillators and found that it was possible to reproduce all symmetries of the gaits by changing the coupling strength. Here we propose to extend this idea using coupled chaotic oscillators synchronized using the Pyragas method in order to characterize the CPG symmetries. We also evaluate the time series behavior when the foot is in contact with the ground: this has potential robotic applications.     

Thermal and phase decoherence effects on entanglement dynamics of the quantum spin systems

Entanglement dynamics of the N-qubit XY model in thermal and dephasing environments are investigated by solving the Lindblad form of the master equation. Analytical solutions for the two-qubit case and numerical solutions for the multi-qubit case are obtained. For the two-qubit case, our results revealed two main features for entanglement evolution from different initial states. First, the thermal reservoir always induces degradation of the entanglement, and the entanglement may undergo sudden death during certain intervals of the evolution time. Second, the dephasing environment induces damped oscillation of the entanglement for initially separable states and mixed states with relative large values of Δ or J; however, it always induces exponentially decay of the entanglement for the initial Bell states. For the multi-qubit case, our results show that the entanglement decreases monotonically as the time evolves for the initial W state, and behaves as damped oscillation for the initial “one-particle” state. Particularly, for system with large number of qubits, the curves of the concurrence C₁₂ with different N are almost overlapped in dephasing environment.