Domes and semi-capsules as model systems for infrared microspectroscopy of biological cells.

It is well known that infrared microscopy of micrometer sized samples suffers from strong scattering distortions, attributed to Mie scattering. The state-of-the-art preprocessing technique for modelling and removing Mie scattering features from infrared absorbance spectra of biological samples is built on a meta model for perfect spheres. However, non-spherical cell shapes are the norm rather than the exception, and it is therefore highly relevant to evaluate the validity of this preprocessing technique for deformed spherical systems. Addressing these cases, we investigate both numerically and experimentally the absorbance spectra of 3D-printed individual domes, rows of up to five domes, two domes with varying distance, and semi-capsules of varying lengths as model systems of deformed individual cells and small cell clusters. We find that coupling effects between individual domes are small, corroborating previous related literature results for spheres. Further, we point out and illustrate with examples that, while optical reciprocity guarantees the same extinction efficiency for top vs. bottom illumination, a scatterer's internal field may be vastly different in these two situations. Finally, we demonstrate that the ME-EMSC model for preprocessing infrared spectra from spherical biological systems is valid also for deformed spherical systems.

Space-resolved chemical information from infrared extinction spectra.

A new method is presented for the extraction of the complex index of refraction from the extinction efficiency, [Formula: see text], of homogeneous and layered dielectric spheres that simultaneously removes scattering effects and corrects measured extinction spectra for systematic experimental errors such as baseline shifts, tilts, curvature, and scaling. No reference spectrum is required and fit functions may be used that automatically satisfy the Kramers-Kronig relations. Thus, the method yields the complex refractive index of a sample for unambiguous interpretation of the chemical information of the sample. In the case of homogeneous spheres, the method also determines the radius of the sphere. In the case of layered spheres, the method determines the substances within each layer. Only a single-element detector is required. Using numerically computed [Formula: see text] data of polymethyl-methacrylate and polystyrene homogeneous and layered spheres, we show that the new reconstruction algorithm is accurate and reliable. Reconstructing the complex refractive index from a published, experimentally measured raw absorbance spectrum shows that the new method simultaneously corrects spectra for scattering effects and, given shape information, corrects raw spectra for systematic errors that result in spectral distortions such as baseline shifts, tilts, curvature, and scaling.

Effects of the coupling of dielectric spherical particles on signatures in infrared microspectroscopy.

Infrared microspectroscopy is a powerful tool in the analysis of biological samples. However, strong electromagnetic scattering may occur since the wavelength of the incident radiation and the samples may be of comparable size. Based on the Mie theory of single spheres, correction algorithms have been developed to retrieve pure absorbance spectra. Studies of the scattering characteristics of samples of different types, obtained by microspectroscopy, have been performed. However, the detailed, microscopic effects of the coupling of the samples on signatures in spectra, obtained by infrared microspectroscopy, are still not clear. The aim of this paper is to investigate how the coupling of spherical samples influences the spectra. Applying the surface integral equation (SIE) method, we simulate small dielectric spheres, arranged as double-spheres or small arrays of spheres. We find that the coupling of the spheres hardly influences the broad oscillations observed in infrared spectra (the Mie wiggles) unless the radii of the spheres are different or the angle between the direction of the incident radiation and the normal of the plane where the spheres are located is large. Sharp resonance features in the spectra (the Mie ripples) are affected by the coupling of the spheres and this effect depends on the polarization of the incident wave. Experiments are performed to verify our conclusions.

Efficient Stabilized Two-Qubit Gates on a Trapped-Ion Quantum Computer.

In order to scale up quantum processors and achieve a quantum advantage, it is crucial to economize on the power requirement of two-qubit gates, make them robust to drift in experimental parameters, and shorten the gate times. Applicable to all quantum computer architectures whose two-qubit gates rely on phase-space closure, we present here a new gate-optimizing principle according to which negligible amounts of gate fidelity are traded for substantial savings in power, which, in turn, can be traded for substantial increases in gate speed and/or qubit connectivity. As a concrete example, we illustrate the method by constructing optimal pulses for entangling gates on a pair of ions within a trapped-ion chain, one of the leading quantum computing architectures. Our method is direct, noniterative, and linear, and, in some parameter regimes, constructs gate-steering pulses requiring up to an order of magnitude less power than the standard method. Additionally, our method provides increased robustness to mode drift. We verify the new trade-off principle experimentally on our trapped-ion quantum computer.

The effect of deformation of absorbing scatterers on Mie-type signatures in infrared microspectroscopy.

Mie-type scattering features such as ripples (i.e., sharp shape-resonance peaks) and wiggles (i.e., broad oscillations), are frequently-observed scattering phenomena in infrared microspectroscopy of cells and tissues. They appear in general when the wavelength of electromagnetic radiation is of the same order as the size of the scatterer. By use of approximations to the Mie solutions for spheres, iterative algorithms have been developed to retrieve pure absorbance spectra. However, the question remains to what extent the Mie solutions, and approximations thereof, describe the extinction efficiency in practical situations where the shapes of scatterers deviate considerably from spheres. The aim of the current study is to investigate how deviations from a spherical scatterer can change the extinction properties of the scatterer in the context of chaos in wave systems. For this purpose, we investigate a chaotic scatterer and compare it with an elliptically shaped scatterer, which exhibits only regular scattering. We find that chaotic scattering has an accelerating effect on the disappearance of Mie ripples. We further show that the presence of absorption and the high numerical aperture of infrared microscopes does not explain the absence of ripples in most measurements of biological samples.

Efficient arbitrary simultaneously entangling gates on a trapped-ion quantum computer.

Efficiently entangling pairs of qubits is essential to fully harness the power of quantum computing. Here, we devise an exact protocol that simultaneously entangles arbitrary pairs of qubits on a trapped-ion quantum computer. The protocol requires classical computational resources polynomial in the system size, and very little overhead in the quantum control compared to a single-pair case. We demonstrate an exponential improvement in both classical and quantum resources over the current state of the art. We implement the protocol on a software-defined trapped-ion quantum computer, where we reconfigure the quantum computer architecture on demand. Our protocol may also be extended to a wide variety of other quantum computing platforms.

Extracting pure absorbance spectra in infrared microspectroscopy by modeling absorption bands as Fano resonances.

Midinfrared absorbance spectra obtained from spatially inhomogeneous and finite samples often contain scattering effects characterized by derivative-like bands with shifted peak positions. Such features may be interpreted and accurately modeled by Fano theory when the imaginary part of the complex dielectric function is small and Lorentzian in nature-as is the case for many biological media. Furthermore, by fitting Fano line shapes to isolated absorbance bands, recovery of the peak position and pure absorption strength can be obtained with high accuracy. Additionally, for small and optically soft spherical scatterers, recovery of one or the other of constant refractive index or radius (given approximate knowledge of the other) is possible.

Star Atoms.

We define star atoms as dressed quantum star graphs with Coulomb potentials on their edges. Focusing on star-lithium (star-Li), we study its classical and quantum mechanics. We find that, classically, star-Li is completely chaotic. Quantum mechanically, we identify an energy regime in which star-Li shows Wigner statistics, a hallmark of quantum chaos. Our results are relevant for identifying energy regimes and conditions under which quantum chaos may be identified in lithium and other multiply excited many-electron atoms.

Mie scatter corrections in single cell infrared microspectroscopy.

Strong Mie scattering signatures hamper the chemical interpretation and multivariate analysis of the infrared microscopy spectra of single cells and tissues. During recent years, several numerical Mie scatter correction algorithms for the infrared spectroscopy of single cells have been published. In the paper at hand, we critically reviewed existing algorithms for the correction of Mie scattering and suggest improvements. We developed an iterative algorithm based on Extended Multiplicative Scatter Correction (EMSC), for the retrieval of pure absorbance spectra from highly distorted infrared spectra of single cells. The new algorithm uses the van de Hulst approximation formula for the extinction efficiency employing a complex refractive index. The iterative algorithm involves the establishment of an EMSC meta-model. While existing iterative algorithms for the correction of resonant Mie scattering employ three independent parameters for establishing a meta-model, we could decrease the number of parameters from three to two independent parameters, which reduced the calculation time for the Mie scattering curves for the iterative EMSC meta-model by a factor of 10. Moreover, by employing the Hilbert transform for evaluating the Kramers-Kronig relations based on a FFT algorithm in Matlab, we further improved the speed of the algorithm by a factor of 100. For testing the algorithm we simulate distorted apparent absorbance spectra by utilizing the exact theory for the scattering of infrared light at absorbing spheres, taking into account the high numerical aperture of infrared microscopes employed for the analysis of single cells and tissues. In addition, the algorithm was applied to measured absorbance spectra of single lung cancer cells.

Fringes in FTIR spectroscopy revisited: understanding and modelling fringes in infrared spectroscopy of thin films.

The appearance of fringes in the infrared spectroscopy of thin films seriously hinders the interpretation of chemical bands because fringes change the relative peak heights of chemical spectral bands. Thus, for the correct interpretation of chemical absorption bands, physical properties need to be separated from chemical characteristics. In the paper at hand we revisit the theory of the scattering of infrared radiation at thin absorbing films. Although, in general, scattering and absorption are connected by a complex refractive index, we show that for the scattering of infrared radiation at thin biological films, fringes and chemical absorbance can in good approximation be treated as additive. We further introduce a model-based pre-processing technique for separating fringes from chemical absorbance by extended multiplicative signal correction (EMSC). The technique is validated by simulated and experimental FTIR spectra. It is further shown that EMSC, as opposed to other suggested filtering methods for the removal of fringes, does not remove information related to chemical absorption.

Ray-splitting correction to the Weyl formula: experiment versus theory.

An abrupt change in the dielectric constant of media filling a microwave cavity was predicted by Prange et al. [Phys. Rev. E 53, 207 (1996)]] to produce a ray splitting correction to the Weyl formula for the mean staircase function of resonances. We present the first experimental confirmation of this effect. Our results with a quasi-two-dimensional cavity are directly relevant to the ray-splitting correction in two-dimensional quantal ray-splitting billiards.