Analytical solution of the time evolution of an entangled electron spin pair in a double quantum dot nanostructure

Using master equations we present an analytical solution of the time evolution of an entangled electron spin pair which can occupy 36 different quantum states in a double quantum dot nanostructure. This solution is exact given a few realistic assumptions and takes into account relaxation and decoherence rates of the electron spins as phenomenological parameters. Our systematic method of solving a large set of coupled differential equations is straightforward and can be used to obtain analytical predictions of the quantum evolution of a large class of complex quantum systems, for which until now commonly numerical solutions have been sought.Comment: 23 pages, 3 figure

Giant phase-conjugate reflection with a normal mirror in front of an optical phase-conjugator

We theoretically study reflection of light by a phase-conjugating mirror preceded by a partially reflecting normal mirror. The presence of a suitably chosen normal mirror in front of the phase conjugator is found to greatly enhance the total phase-conjugate reflected power, even up to an order of magnitude. Required conditions are that the phase-conjugating mirror itself amplifies upon reflection and that constructive interference of light in the region between the mirrors takes place. We show that the phase-conjugate reflected power then exhibits a maximum as a function of the transmittance of the normal mirror.Comment: 8 pages, 3 figures, RevTe

An analytical decomposition protocol for optimal implementation of two-qubit entangling gates

This paper addresses the question how to implement a desired two-qubit gate U using a given tunable two-qubit entangling interaction H_int. We present a general method which is based on the K_1 A K_2 decomposition of unitary matrices in SU(4) to calculate analytically the smallest number of two-qubit gates U_int [based on H_int] and single-qubit rotations, and the explicit sequence of these operations that are required to implement U. We illustrate our protocol by calculating the implementation of (1) the transformation from standard basis to Bell basis, (2) the CNOT gate, and (3) the quantum Fourier transform for two kinds of interaction - Heisenberg exchange interaction and quantum inductive coupling - and discuss the relevance of our results for solid-state qubits.Comment: 16 pages, published versio

Suppression of Conductance in a Topological Insulator Nanostep Junction

We investigate quantum transport via surface states in a nanostep junction on the surface of a 3D topological insulator that involves two different side surfaces. We calculate the conductance across the junction within the scattering matrix formalism and find that as the bias voltage is increased, the conductance of the nanostep junction is suppressed by a universal factor of 1/3 compared to the conductance of a similar planar junction based on a single surface of a topological insulator. We also calculate and analyze the Fano factor of the nanostep junction and predict that the Fano factor saturates at 1/5, five times smaller than for a Poisson process

Detecting entanglement of two electron spin qubits with witness operators

We propose a scheme for detecting entanglement between two electron spin qubits in a double quantum dot using an entanglement witness operator. We first calculate the optimal configuration of the two electron spins, defined as the position in the energy level spectrum where, averaged over the nuclear spin distribution, 1) the probability to have two separated electrons, and 2) the degree of entanglement of the quantum state quantified by the concurrence are both large. Using a density matrix approach, we then calculate the evolution of the expectation value of the witness operator for the two-spin singlet state, taking into account the effect of decoherence due to quantum charge fluctuations modeled as a boson bath. We find that, for large interdot coupling, it is possible to obtain a highly entangled and robust ground state.Comment: 4 pages, 3 figure

A spin pump turnstile: parametric pumping of a spin-polarized current through a nearly-closed quantum dot

We investigate parametric pumping of a spin-polarized current through a nearly-closed quantum dot in a perpendicular magnetic field. Pumping is achieved by tuning the tunnel couplings to the left and right lead - thereby operating the quantum dot as a turnstile - and changing either the magnetic field or a gate-voltage. We analyze the quantum dynamics of a pumping cycle and the limiting time scales for operating the quantum dot turnstile as a pure spin pump. The proposed device can be used as a fully controllable double-sided and bipolar spin filter and to inject spins "on demand".Comment: 5 pages, 2 figures, one reference correcte

Energy Spectrum and Exact Cover in an Extended Quantum Ising Model

We investigate an extended version of the quantum Ising model which includes beyond-nearest neighbour interactions and an additional site-dependent longitudinal magnetic field. Treating the interaction exactly and using perturbation theory in the longitudinal field, we calculate the energy spectrum and find that the presence of beyond-nearest-neighbour interactions enhances the minimal gap between the ground state and the first excited state, irrespective of the nature of decay of these interactions along the chain. The longitudinal field adds a correction to this gap that is independent of the number of qubits. We discuss the application of our model to implementing specific instances of 3-satisfiability problems (Exact Cover) and make a connection to a chain of flux qubits.Comment: 9 pages, 3 figures, published versio