Optimal Control of One-Qubit Gates

We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy spent in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions.Comment: 5 page

Complete controllability of quantum systems

Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised 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

Influence of chromophores on quarternary structure of phycobiliproteins from the cyanobacterium, Mastigocladus laminosus

Chromophores of C-phycocyanin and phycoerythrο-cyanin have been chemically modified by reduction to rubins , bleaching , photoisomerization , or perturbation with bulky substituents. Pigments containing modified chromophores, or hybrids containing modified and unmodified chromophores in individual protomers have been prepared. All modifications inhibit the association of the (aß)-protomers of these pigments to higher aggregates. The results demonstrate a pronounced effect of the state of the chromophores on biliprotein quaternary structure. It may be important in phycobi1isome assembly , and also in the dual function of biliproteins as (i) antenna pigments for photosynthesis and (ii) reaction centers for photomor-phogenesis

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

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]

Self-consistent Green's function approaches

We present the fundamental techniques and working equations of many-body Green's function theory for calculating ground state properties and the spectral strength. Green's function methods closely relate to other polynomial scaling approaches discussed in chapters 8 and 10. However, here we aim directly at a global view of the many-fermion structure. We derive the working equations for calculating many-body propagators, using both the Algebraic Diagrammatic Construction technique and the self-consistent formalism at finite temperature. Their implementation is discussed, as well as the inclusion of three-nucleon interactions. The self-consistency feature is essential to guarantee thermodynamic consistency. The pairing and neutron matter models introduced in previous chapters are solved and compared with the other methods in this book.Comment: 58 pages, 14 figures, Submitted to Lect. Notes Phys., "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor

Photophysics of phycoerythrocyanins from the cyanobacterium Westiellopsis prolifica studied by time-resolved fluorescence and coherent anti-Stokes Raman scattering spectroscopy

Three building blocks of the antenna complexes of the cyanobacterium Westiellopsis prolifica were studied: PEC(X), which is similar to the α-subunit of phycoerythrocyanin (PEC), trimers of PEC and monomers derived from these by deaggregation with KSCN. The fit of the fluorescence decay curve of PEC(X) requires at least four exponentials, although it supposedly contains only one chromophore. The coherent anti-Stokes Raman scattering (CARS) spectra indicate that the heterogeneity observed is due to geometrical isomers, which are in part generated by photoinduced processes. A similar heterogeneity in chromophore structure and properties is also found in the monomers, where four exponentials are needed to fit the fluorescence decay curve. As in trimers, there is a long-lived, low-amplitude component, which can be assigned to impurities and/or oxidation products. The energy transfer time between the two phyocyanobilin chromophores in the β-subunit is about 500 ps; the lifetime of the fluorescing β-chromophore is 1.5 ns. The phycoviolobilin chromophore in the α-subunit adopts different geometries characterized by fluorescence lifetimes of about 240 and 800 ps. No evidence was found for energy transfer between the α-chromophore and the β-chromophores. This energy transfer occurs in trimers on a time scale of less than 20 ps; the energy transfer time between the two different types of β-chromophore is about 250 ps and the lifetime of the terminal emitter is about 1.5 ns. The excited state kinetics are therefore similar to those of PEC trimers from Mastigocladus laminosus, as are the CARS spectra, indicating a similar chromophore—protein arrangement. In comparison with phycocyanin, the ordering of the excited states of chromophores β84 and β155 may be changed. Although PEC trimers of Westiellopsis prolifica show almost as good a photostability as trimers of Mastigocladus laminosus, monomers are so photolabile that no CARS spectra could be recorded

Symmetric Informationally Complete Measurements of Arbitrary Rank

There has been much interest in so-called SIC-POVMs: rank 1 symmetric informationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs which are symmetric and informationally complete but not necessarily rank 1. This class of POVMs is of some independent interest. In particular it includes a POVM which is closely related to the discrete Wigner function. However, it is interesting mainly because of the light it casts on the problem of constructing rank 1 symmetric informationally complete POVMs. In this connection we derive an extremal condition alternative to the one derived by Renes et al.Comment: Contribution to proceedings of International Conference on Quantum Optics, Minsk, 200