Measuring fluorescence to track a quantum emitter's state: a theory review

We review the continuous monitoring of a qubit through its spontaneous emission, at an introductory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubit's state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and heterodyne monitoring and illustrate its equivalence to the stochastic master equation formalism throughout. Special emphasis is given to homodyne (phase-sensitive) monitoring of fluorescence. The examples we develop are used to illustrate basic methods in quantum trajectories, but also to introduce some more advanced topics of contemporary interest, including the arrow of time in quantum measurement, and trajectories following optimal measurement records derived from a variational principle. The derivations we perform lead directly from the development of a simple model to an understanding of recent experimental results.     

Sensing and compensation of femtosecond waveform distortion induced by all-order polarization mode dispersion at selected polarization states

We demonstrate full characterization of femtosecond pulse distortion induced by all-order polarization mode dispersion (PMD) at selected polarization states via second-harmonic generation (SHG) frequency-resolved optical gating (FROG) measurements at an average power of under 28 nW. By applying the inverse of the measured spectral phase via a programmable pulse shaper, we compress the distorted pulses from more than 3 ps to nearly bandwidth-limited durations of less than 500 fs. Our results show that SHG FROG measurements performed by using fiber-pigtailed aperiodically poled lithium niobate waveguides can serve as a robust and sensitive tool for characterization of PMD-induced spectral phase.     

Controlled release of ketorolac through nanocomposite films of hydrogel and LDH nanoparticles

A novel nanocomposite film for sustained release of anionic ophthalmic drugs through a double-control process has been examined in this study. The film, made as a drug-loaded contact lens, consists principally of a polymer hydrogel of 2-hydroxyethyl methacrylate (HEMA), in whose matrix MgAl-layered double hydroxide (MgAl-LDH) nanoparticles intercalated with the anionic drug are well dispersed. Such nanocomposite films (hydrogel-LDH-drug) contained 0.6–0.8 mg of MgAl-LDH and 0.08–0.09 mg of the ophthalmic drug (ketorolac) in 1.0 g of hydrogel. MgAl-drug-LDH nanoparticles were prepared with the hydrodynamic particle size of 40–200 nm. TEM images show that these nanoparticles are evenly dispersed in the hydrogel matrix. In vitro release tests of hydrogel-LDH-drug in pH 7.4 PBS solution at 32 °C indicate a sustained release profile of the loaded drug for 1 week. The drug release undergoes a rapid initial burst and then a monotonically decreasing rate up to 168 h. The initial burst release is determined by the film thickness and the polymerization conditions, but the following release rate is very similar, with the effective diffusion coefficient being nearly constant (3.0 × 10⁻¹² m²/s). The drug release from the films is mechanistically attributed to anionic exchange and the subsequent diffusion in the hydrogel matrix.     

Two-dimensional Quantum Random Walk

We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting shape of the feasible region is, however, quite different. The limit region turns out to be an algebraic set, which we characterize as the rational image of a compact algebraic variety. We also compute the probability profile within the limit region, which is essentially a negative power of the Gaussian curvature of the same algebraic variety. Our methods are based on analysis of the space-time generating function, following the methods of Pemantle and Wilson (J. Comb. Theory, Ser. A 97(1):129–161, 2002).     

Exact crossover Green function in the two-channel and two-impurity Kondo models

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.     

Measurement of ultraweak transitions in the visible region of molecular oxygen

A highly sensitive cavity-enhanced frequency modulation spectroscopy technique has been used to measure ultraweak transitions in molecular oxygen that had not previously been characterized. The self-broadened half-width and line intensity of the measured transitions are reported. We include 12 high J transitions in the band of ¹⁶O₂ (the so-called A band), 59 transitions in the hot band of ¹⁶O₂, and 17 high J transitions in the band of ¹⁶O¹⁸O. Our measurements of line positions of the ¹⁶O¹⁸O transitions are used to determine improved molecular constants for the excited state of ¹⁶O¹⁸O.     

Vibrational spectra and crystal structure of the di‐amino acid peptide cyclo(L‐Met‐L‐Met): comparison of experimental data and DFT calculations

Experimental Raman and FT‐IR spectra of solid‐state non‐deuterated and N‐deuterated samples of cyclo(L ‐Met‐L ‐Met) are reported and discussed. The Raman and FT‐IR results show characteristic amide I vibrations (Raman: 1649 cm⁻¹, infrared: 1675 cm⁻¹) for molecules exhibiting a cis amide conformation. A Raman band, assigned to the cis amide II vibrational mode, is observed at ∼1493 cm⁻¹ but no IR band is observed in this region. Cyclo(L ‐Met‐L ‐Met) crystallises in the triclinic space group P1 with one molecule per unit cell. The overall shape of the diketopiperazine (DKP) ring displays a (slightly distorted) boat conformation. The crystal packing employs two strong hydrogen bonds, which traverse the entire crystal via translational repeats. B3‐LYP/cc‐pVDZ calculations of the structure of the molecule predict a boat conformation for the DKP ring, in agreement with the experimentally determined X‐ray structure. Copyright © 2009 John Wiley & Sons, Ltd.     

The validity of nonlinear geometric optics for weak solutions of conservation laws

The method of weakly nonlinear geometric optics is one of the main formal perturbation techniques used in analyzing nonlinear wave motion for hyperbolic systems. The tacit assumption in using such perturbation methods is that the corresponding solutions of the hyperbolic system remain smooth; since shock waves typically form in such solutions, these assumptions are rarely satisfied in practice. Nevertheless, in a variety of applied contexts, these methods give qualitatively reliable answers for discontinuous weak solutions. Here we give a rigorous proof for the validity of nonlinear geometric optics for general weak solutions of systems of hyperbolic conservation laws in a single space variable. The methods of proof do not mimic the formal construction of weakly nonlinear asymptotics but instead rely on structural symmetries of the approximating equations, stability estimates for intermediate asymptotic times, and the rapid decay in variation of weak solutions for large asymptotic times.Partially supported by NSF Grant No. DMS-8301135Partially supported by NSF Grant No. MCS-81-02360 and ARO Grant No. 483964-25530     

Dark matter and inflation

I demonstrate that dark matter consisting of any type or types of stable weakly interacting elementary particle is incompatible with the minimal predictions of inflation, based on present observation of galaxy clustering, and assuming galaxies are good tracers of mass in the universe. If we wish to resolve this problem by particle physics alone, we seem to be driven to the possibility that the initial dark matter was unstable.Research supported in part by the National Science Foundation under Grant No. PHY-82-15249 and also by the NSERC (Canada).This essay received the first award from the Gravity Research Foundation for the year 1984-Ed.