Degrees of controllability for quantum systems and applications to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio

First Order Static Excitation Potential: Scheme for Excitation Energies and Transition Moments

We present an approximation scheme for the calculation of the principal excitation energies and transition moments of finite many-body systems. The scheme is derived from a first order approximation to the self energy of a recently proposed extended particle-hole Green's function. A hermitian eigenvalue problem is encountered of the same size as the well-known Random Phase Approximation (RPA). We find that it yields a size consistent description of the excitation properties and removes an inconsistent treatment of the ground state correlation by the RPA. By presenting a hermitian eigenvalue problem the new scheme avoids the instabilities of the RPA and should be well suited for large scale numerical calculations. These and additional properties of the new approximation scheme are illuminated by a very simple exactly solvable model.Comment: 15 pages revtex, 1 eps figure included, corrections in Eq. (A1) and Sec. II

Constructive control of quantum systems using factorization of unitary operators

We demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise and decay times or Gaussian wavepackets. To illustrate the technique it is applied to find control schemes to achieve population transfers for pure-state systems, complete inversions of the ensemble populations for mixed-state systems, create arbitrary superposition states and optimize the ensemble average of dynamic observables.Comment: 28 pages, IoP LaTeX, principal author has moved to Cambridge University ([email protected]

Review of biorthogonal coupled cluster representations for electronic excitation

Single reference coupled-cluster (CC) methods for electronic excitation are based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in terms of excited CC states, also referred to as correlated excited (CE) states, and an associated set of states biorthogonal to the CE states, the latter being essentially configuration interaction (CI) configurations. The bCC representation generates a non-hermitian secular matrix, the eigenvalues representing excitation energies, while the corresponding spectral intensities are to be derived from both the left and right eigenvectors. Using the perspective of the bCC representation, a systematic and comprehensive analysis of the excited-state CC methods is given, extending and generalizing previous such studies. Here, the essential topics are the truncation error characteristics and the separability properties, the latter being crucial for designing size-consistent approximation schemes. Based on the general order relations for the bCC secular matrix and the (left and right) eigenvector matrices, formulas for the perturbation-theoretical (PT) order of the truncation errors (TEO) are derived for energies, transition moments, and property matrix elements of arbitrary excitation classes and truncation levels. In the analysis of the separability properties of the transition moments, the decisive role of the so-called dual ground state is revealed. Due to the use of CE states the bCC approach can be compared to so-called intermediate state representation (ISR) methods based exclusively on suitably orthonormalized CE states. As the present analysis shows, the bCC approach has decisive advantages over the conventional CI treatment, but also distinctly weaker TEO and separability properties in comparison with a full (and hermitian) ISR method

Monte Carlo simulations of spin transport in a strained nanoscale InGaAs field effect transistor

Spin-based logic devices could operate at very high speed with very low energy consumption and hold significant promise for quantum information processing and metrology. Here, an in-house developed, experimentally verified, ensemble self-consistent Monte Carlo device simulator with a Bloch equation model using a spin-orbit interaction Hamiltonian accounting for Dresselhaus and Rashba couplings is developed and applied to a spin field effect transistor (spinFET) operating under externally applied voltages on a gate and a drain. In particular, we simulate electron spin transport in a \SI{25}{nm} gate length \chem{In_{0.7}Ga_{0.3}As} metal-oxide-semiconductor field-effect transistor (MOSFET) with a CMOS compatible architecture. We observe non-uniform decay of the net magnetization between the source and gate and a magnetization recovery effect due to spin refocusing induced by a high electric field between the gate and drain. We demonstrate coherent control of the polarization vector of the drain current via the source-drain and gate voltages, and show that the magnetization of the drain current is strain-sensitive and can be increased twofold by strain induced into the channel

General methods to control right-invariant systems on compact Lie groups and multilevel quantum systems

For a right-invariant system on a compact Lie group G, I present two methods to design a control to drive the state from the identity to any element of the group. The first method, under appropriate assumptions, achieves exact control to the target but requires estimation of the `size' of a neighborhood of the identity in G. The second method, does not involve any mathematical difficulty, and obtains control to a desired target with arbitrary accuracy. A third method is then given combining the main ideas of the previous methods. This is also very simple in its formulation and turns out to be generically more efficient as illustrated by one of the examples we consider. The methods described in the paper provide arbitrary constructive control for any right-invariant system on a compact Lie group. I give examples including closed multilevel quantum systems and lossless electrical networks. In particular, the results can be applied to the coherent control of general multilevel quantum systems

From bi-layer to tri-layer Fe nanoislands on Cu3Au(001)

Self assembly on suitably chosen substrates is a well exploited root to control the structure and morphology, hence magnetization, of metal films. In particular, the Cu3Au(001) surface has been recently singled out as a good template to grow high spin Fe phases, due to the close matching between the Cu3Au lattice constant (3.75 Angstrom) and the equilibrium lattice constant for fcc ferromagnetic Fe (3.65 Angstrom). Growth proceeds almost layer by layer at room temperature, with a small amount of Au segregation in the early stage of deposition. Islands of 1-2 nm lateral size and double layer height are formed when 1 monolayer of Fe is deposited on Cu3Au(001) at low temperature. We used the PhotoElectron Diffraction technique to investigate the atomic structure and chemical composition of these nanoislands just after the deposition at 140 K and after annealing at 400 K. We show that only bi-layer islands are formed at low temperature, without any surface segregation. After annealing, the Fe atoms are re-aggregated to form mainly tri-layer islands. Surface segregation is shown to be inhibited also after the annealing process. The implications for the film magnetic properties and the growth model are discussed.Comment: Revtex, 5 pages with 4 eps figure