Optimal control theory for unitary transformations

The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory (OCT) is used to solve the inversion problem irrespective of the initial input state. A unified formalism, based on the Krotov method is developed leading to a new scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X^1\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\Sigma^+_u$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Out of the schemes studied the square modulus scheme converges fastest. A study of the implementation of the $Q$ qubit Fourier transform in the Na$_2$ molecule was carried out for up to 5 qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.Comment: 32 pages, 6 figure

The manipulation of massive ro-vibronic superpositions using time-frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing

Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in Time-Frequency-Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 1000 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated frequency-resolved CARS, while the third-order coherence is captured using time-gated frequency-resolved CARS. The Fourier filtering provided by time integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing - all single qubit operations and the two-qubit controlled-NOT (CNOT) gate - are available in time resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally "wired" for carrying out all single qubit operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-qubit CNOT gate, wherein the vibrational qubit controls the switching of the targeted electronic qubit.Comment: PDF format. 59 pages, including 22 figures. To appear in Chemical Physic

Theory of Quantum Optical Control of Single Spin in a Quantum Dot

We present a theory of quantum optical control of an electron spin in a single semiconductor quantum dot via spin-flip Raman transitions. We show how an arbitrary spin rotation may be achieved by virtual excitation of discrete or continuum trion states. The basic physics issues of the appropriate adiabatic optical pulses in a static magnetic field to perform the single qubit operation are addressed

Rhinomanometric reference intervals for normal total nasal airflow resistance

Background: Reference intervals (Rls) or mean values for normal total nasal airflow resistance are essential for the diagnosis of nasal obstruction. Data relating to nasal airflow are not standardised, and valid and reliable Rls do not exist for the time being. This meta-analysis aimed to determine such standard95%-Rls. Methodology: Research of related literature listed in Medline, Embase, Cochrane, and Web of Science databases. Results: Airflow resistance data were gathered from 38 studies using active anterior rhinomanometry at a differential pressure of 150Pa to examine patients under congested and decongested mucosal conditions. In the meta-analysis overall values and Rls for normal total nasal airflow resistance under congested nasal mucosal conditions were calculated for all subjects at 0.25Pa/ cm(3)/s (95%-RI 0.10-0.40Pa/cm(3)/s), adults regardless of gender at 0.25Pa/cm(3)/s (95%-RI 0.12-0.38Pa/cm(3)/s), men at 0.24Pa/cm(3)/s (95%-RI 0.09-0.39Pa/cm(3)/s), and women at 0.26Pa/cm(3)/s (95%-RI 0.08-0.44Pa/cm(3)/s). Asian, African and Caucasian ethnic groups exhibited rising airflow resistance mean values: 0.23Pa/cm(3)/s (95%-RI 0.08-0.39Pa/cm(3)/s), 0.25Pa/cm(3)/s (95%-RI 0.11-0.38Pa/cm(3)/s) and 0.26Pa/cm(3)/s (95%-RI 0.13-0.38Pa/cm(3)/s), respectively. Lower overall mean values resulted under decongested nasal mucosal conditions. Conclusion:The reference intervals and mean values ascertained in this meta-analysis improve the diagnosis of nasal obstruction and may represent a useful supplement in existing guidelines for the standardisation of rhinomanometric measurements

Diagnostics of spectrally resolved transient absorption : surface plasmon resonance of metal nanoparticles

Time and frequency resolved transient absorption measurements yield two-dimensional images that map the dynamical correlation between the center and width of the scattering function. Global analysis of such data allows unique diagnostics of the mechanics underlying the time evolution. We specialize in the case of surface plasmon resonances of optically driven nanoparticles. We present a catalog of 2D maps that can be used to fingerprint physically meaningful cases, and we provide two experimental examples to illustrate the diagnostic value of the maps and their utility in extracting the various time constants at play. In silver nanorods, the experiment shows a π/2 phase shift between the oscillations of the center and the width of the plasmon resonance. Inspection of the maps allows the assignment that the center of the plasmon resonance tracks the strain in shape-oscillations, while the width tracks the strain rate. This finding is the basis of the novel mechanism of plasmon damping due to electron scattering from the electrophoretic potential generated by the motion of the interfacial double layer in colloidal nanoparticles. Measurements in gold nanoparticles show over-damped oscillations, which obscure the phase correlation between the center and width of the plasmon. The damping is dominated by inhomogeneous dephasing, and the time dependence of the width, which follows the temperature of the nanoparticles, and is diagnostic of the interband transition contribution to the plasmon resonance

Broadband similariton : applications to ultrafast optics and photonics

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