Quantum feedback control: how to use verification theorems and viscosity solutions to find optimal protocols

While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called ‘verification theorems’ and ‘viscosity solutions’ provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest.     

Adaptive field-of-view imaging for efficient receive beamforming in medical ultrasound imaging systems

Quadrature demodulation-based phase rotation beamforming (QD-PRBF) is commonly used to support dynamic receive focusing in medical ultrasound systems. However, it is computationally demanding since it requires two demodulation filters for each receive channel. To reduce the computational requirements of QD-PRBF, we have previously developed two-stage demodulation (TSD), which reduces the number of lowpass filters by performing demodulation filtering on summation signals. However, it suffers from image quality degradation due to aliasing at lower beamforming frequencies. To improve the performance of TSD-PRBF with reduced number of beamforming points, we propose a new adaptive field-of-view (AFOV) imaging method. In AFOV imaging, the beamforming frequency is adjusted depending on displayed FOV size and the center frequency of received signals. To study its impact on image quality, simulation was conducted using Field II, phantom data were acquired from a commercial ultrasound machine, and the image quality was quantified using spatial (i.e., axial and lateral) and contrast resolution. The developed beamformer (i.e., TSD-AFOV-PRBF) with 1024 beamforming points provided comparable image resolution to QD-PRBF for typical FOV sizes (e.g., 4.6% and 1.3% degradation in contrast resolution for 160 mm and 112 mm, respectively for a 3.5 MHz transducer). Furthermore, it reduced the number of operations by 86.8% compared to QD-PRBF. These results indicate that the developed TSD-AFOV-PRBF can lower the computational requirement for receive beamforming without significant image quality degradation.     

Elastic scattering from a sapphire microsphere placed on a silica optical fiber coupler: Possible applications to biosensing

Elastic light scattering is performed in the original band of optical fiber communication at 1300 nm for a 500 μm sapphire microsphere placed on a silica optical fiber half coupler. The morphology dependent resonances (MDRs) are observed in the transverse magnetically (TM) polarized and transverse electrically (TE) polarized 0^° transmission and 90^° elastic scattering obtained from the sapphire microsphere. The TE and TM MDRs can be detected selectively with the use of a Glan polarizer. The TE and TM polarization selectivity provides the ability to select relative MDR to BG levels. The TM polarization provides higher MDR signal to background ratio (SBR) and is suitable for optical monitoring, biological sensing or any other optoelectronic application that requires a high resolution optical filter. The polar angular mode spacing of 0.36 nm of the resonances correlates well with the optical size of the sapphire microsphere. The autocorrelation of the 90^° elastic scattering spectra also shows peaks at 0.36 nm. The spectral linewidths of the resonances are on the order of 0.1 nm, which corresponds to quality factors on the order of 10⁴. A sapphire sphere with a radius of 500 μm and relative refractive index of 1.31, resonances will red-shift by 1.01 nm (0.077%). This shift is on the order of 10 linewidths, making sapphire biophotonic sensors an interesting alternative to silica biophotonic sensors.     

Interfacial differences in enhanced schottky barrier height Au/n-GaAs diodes deposited at 77 K

The use of cryogenic temperatures (∼77 K) during Au Schottky contact deposition onto n-GaAs produces an increase in barrier height from 0.73 eV for room temperature diodes to 0.82 eV. Not all Schottky metals show this enhancement—for example Pt and Ti do not show any significant change in barrier height whereas Au, Pd and Ni show increases between 7 and 18%. We used X-ray reflectivity to show that the main difference between Au deposited at 77 K and room temperature is a decreased metal roughness while the interfacial roughness between the Au and GaAs is basically the same. As the diodes are annealed to 300 °C both the difference in barrier height and interfacial roughness is lost. This is a simple method with potential for improving the performance of GaAs metal-semiconductor-field-effect-transistors (MESFETs).     

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where “surface fields” may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.     

Rapid state reduction of quantum systems using feedback control

We consider using Hamiltonian feedback control to increase the speed at which a continuous measurement purifies (reduces) the state of a quantum system, and thus to increase the speed of the preparation of pure states. For a measurement of an observable with equispaced eigenvalues, we show that there exists a feedback algorithm which will speed up the rate of state reduction by at least a factor of 2(N + 1)/3.     

Quantum Emulation of Extreme Non‐Equilibrium Phenomena with Trapped Atoms

Ultracold atomic physics experiments offer a nearly ideal context for the investigation of quantum systems far from equilibrium. We describe three related emerging directions of research into extreme non‐equilibrium phenomena in atom traps: quantum emulation of ultrafast atom‐light interactions, coherent phasonic spectroscopy in tunable quasicrystals, and realization of Floquet matter in strongly‐driven lattice systems. We show that all three should enable quantum emulation in parameter regimes inaccessible in solid‐state experiments, facilitating a complementary approach to open problems in non‐equilibrium condensed matter.     

Experimental vibrational spectra (Raman,infrared) and DFT calculations on monomeric and dimeric structures of 2‐ and 6‐bromonicotinic acid

In this work, the Fourier transform infrared and Raman spectra of 2‐bromonicotinic acid and 6‐bromonicotinic acid (abbreviated as 2‐BrNA and 6‐BrNA, C₆H₄BrNO₂) have been recorded in the region 4000–400 and 3500–50 cm⁻¹. The optimum molecular geometry, normal mode wavenumbers, infrared intensities and Raman scattering activities, corresponding vibrational assignments and intermolecular hydrogen bonds were investigated with the help of B3LYP density functional theory (DFT) method using 6‐311++G(d,p) basis set. Reliable vibrational assignments were made on the basis of total energy distribution (TED) calculated with scaled quantum mechanical (SQM) method. From the calculations, the molecules are predicted to exist predominantly as the C1 conformer. Copyright © 2009 John Wiley & Sons, Ltd.     

Port-Hamiltonian representation for pdes with second-order derivatives in the energy density

In this contribution we consider a port-Hamiltonian setting for partial differential equations. A crucial property of this system class is the property to be able to link a power balance relation to the structure of the equations. However, one has to take into account also the effects of energy flows via the boundary. This is straightforward when the Hamiltonian depends on derivative variables of first order, e.g. by using integration by parts. If second-order derivatives appear then integration by parts cannot be used without due care, thus we suggest an approach by using the so-called Cartan-form. We visualize the derivation of a power balance relation by using the Kirchhoff plate as an example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)