Generating Entanglement and Squeezed States of Nuclear Spins in Quantum Dots

Entanglement generation and detection are two of the most sought-after goals in the field of quantum control. Besides offering a means to probe some of the most peculiar and fundamental aspects of quantum mechanics, entanglement in many-body systems can be used as a tool to reduce fluctuations below the standard quantum limit. For spins, or spin-like systems, such a reduction of fluctuations can be realized with so-called squeezed states. Here we present a scheme for achieving coherent spin squeezing of nuclear spin states in few-electron quantum dots. This work represents a major shift from earlier studies in quantum dots, which have explored classical "narrowing" of the nuclear polarization distribution through feedback involving stochastic spin flips. In contrast, we use the nuclear-polarization-dependence of the electron spin resonance (ESR) to provide a non-linearity which generates a non-trivial, area-preserving, "twisting" dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips.Comment: 8 pgs, 3 fgs. References added, text update

Spin Decoherence from Hamiltonian dynamics in Quantum Dots

The dynamics of a spin-1/2 particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied, as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a gaussian decay, and at later times it revives displaying nonmonotonic time dependence. The decoherence time scale dep ends on moments of the bath-spin distribuition, and also on the polarization strengths in various bath-spin channels. The bath polarizations have a tendency to increase the decoherence time scale. The effective dynamics of the central spin polarization is shown to be describ ed by a master equation with non-markovian features.Comment: 11 pages, 6 figures Accepted for publication in Phys.Rev

Visualisation of an entangled channel spin-1 system

Co-variance matrix formalism gives powerful entanglement criteria for continuous as well as finite dimensional systems. We use this formalism to study a mixed channel spin-1 system which is well known in nuclear reactions. A spin-j state can be visualized as being made up of 2j spinors which are represented by a constellation of 2j points on a Bloch sphere using Majorana construction. We extend this formalism to visualize an entangled mixed spin-1 system.Comment: 4 pages,4 figure

Spin decay and quantum parallelism

We study the time evolution of a single spin coupled inhomogeneously to a spin environment. Such a system is realized by a single electron spin bound in a semiconductor nanostructure and interacting with surrounding nuclear spins. We find striking dependencies on the type of the initial state of the nuclear spin system. Simple product states show a profoundly different behavior than randomly correlated states whose time evolution provides an illustrative example of quantum parallelism and entanglement in a decoherence phenomenon.Comment: 6 pages, 4 figures included, version to appear in Phys. Rev.