Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “quantum coherence & coherence measures”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26

Preventing native oxide formation in niobium thin films through platinum encapsulation

Superconducting transmon qubits are a key technology in quantum computing, with niobium (Nb) widely used due to its favorable superconducting properties and compatibility with scalable fabrication. However, the performance of Nb-based qubits is hindered by two-level systems (TLS), which arise predominantly from native oxide layers at surfaces and interfaces. These oxides and suboxides form rapidly in air and contribute significantly to decoherence by introducing dielectric losses. While various mitigation strategies, including thermal-annealing, chemical-etching, and nitrogen plasma treatment, have been explored, many are challenging to integrate into large-scale manufacturing due to complexity and instability in ambient conditions. In this study, we investigate the structural, chemical, and superconducting properties of room-temperature sputtered Nb thin films grown on sapphire substrates. We focus on a surface protection strategy using noble metal encapsulation with platinum (Pt) to suppress oxides and reduce TLS-related losses. Structural and chemical characterization were performed using X-ray diffraction, X-ray photoelectron spectroscopy, and transmission electron microscopy. Superconducting properties were measured using a physical property measurement system. Results demonstrate that Pt encapsulation effectively suppresses surface oxidation and mitigates its detrimental impact on superconducting performance. In conclusion, this approach offers a promising path toward enhancing the coherence of Nb-based qubits while remaining compatible with scalable-fabrication processes.

36 MATERIALS SCIENCE↗

Measurement accuracy and spatial resolution of a distributed temperature sensor based on a two-pulse differential coherent reflectometer

We present a model and numerical simulation of a distributed temperature sensor based on a two-pulse differential coherent optical time-domain reflectometer (COTDR). The differential phase measured using a phase-sensitive Rayleigh reflectometer is shown to have a regular component, which is a linear function of temperature, and a random component, which is related to a random distribution of scattering centres in the fibre and restricts the accuracy of measurements of variations in temperature. Measurement accuracy can be improved by reducing the relative contribution of the random component via a decrease in pulse duration and/or an increase in the time delay between pulses. The spatial resolution of a differential two-pulse phase-sensitive reflectometer is shown to be determined by the time delay between pulses and to vary little with pulse duration. At a typical pulse duration (200 ns) and delay time (300 ns), the accuracy in measurements of variations in temperature in the 0.1-K range is 2 % and the spatial resolution is about 30 m. (fibre-optic sensors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Observation of the molecular response to light upon photoexcitation

Abstract When a molecule interacts with light, its electrons can absorb energy from the electromagnetic field by rapidly rearranging their positions. This constitutes the first step of photochemical and photophysical processes that include primary events in human vision and photosynthesis. Here, we report the direct measurement of the initial redistribution of electron density when the molecule 1,3-cyclohexadiene (CHD) is optically excited. Our experiments exploit the intense, ultrashort hard x-ray pulses of the Linac Coherent Light Source (LCLS) to map the change in electron density using ultrafast x-ray scattering. The nature of the excited electronic state is identified with excellent spatial resolution and in good agreement with theoretical predictions. The excited state electron density distributions are thus amenable to direct experimental observation.

74 ATOMIC AND MOLECULAR PHYSICS↗

Non-Markovian relaxation spectroscopy of fluxonium qubits

Recent studies have shown that parasitic two-level systems (TLS) in superconducting qubits, which are a leading source of decoherence, can have relaxation times longer than the qubits themselves. However, the standard techniques used to characterize qubit relaxation is only valid for measuring T 1 under the Born-Markov approximation and could mask environmental memory effects in practice. Here, we introduce two-timescale relaxometry, a technique to probe the qubit and environment relaxation simultaneously and efficiently. We apply it to high-coherence fluxonium qubits over a frequency range of 0.1-0.4 GHz, and reveal a discrete spectrum of TLS with millisecond lifetimes. Our analysis of the spectrum is consistent with a random distribution of TLS in the aluminum oxide tunnel barrier of the Josephson junction chain of the fluxonium, with a spectral and volumetric density and average electric dipole similar to previous TLS studies at much higher frequencies. Our study suggests that investigating and mitigating TLS in the junction chain is crucial to the development of various types of noise-protected qubits in circuit QED.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multidimensional coherent spectroscopy of light-driven states and their collective modes in multiband superconductors

We present a comprehensive theory of light-controlled multiband superconductivity, and apply it to predict distinctive signatures of light-driven superconducting (SC) states in terahertz multidimensional coherent spectroscopy (THz-MDCS) experiments. We first derive gauge-invariant Maxwell-Bloch equations for multiband BCS superconductors with spatial fluctuations. We consider driving electromagnetic fields determined self-consistently by Maxwell's equations. By calculating the THz-MDCS spectra measured experimentally in the clean SC limit, we identify unique signatures of finite-momentum Cooper-pairing states that live longer than the laser pulse. They are controlled by a pair of THz laser pulses with well-defined relative phase (pulse pair). The pseudospin oscillators that describe the properties of these SC states are parametrically driven by both finite-momentum Cooper pairing and by time oscillations of the order-parameter relative phase. We show that such strong parametric driving leads to drastic changes in the THz-MDCS spectral shape from the predictions of third-order nonlinear susceptibility calculations. These spectral changes strongly depend on the interband-to-intraband interaction ratio and on the collective modes of the light-driven state. For negligible interband interaction, the spectra show a transition with increasing field, from traditional pump-probe, four-wave-mixing, and third-harmonic generation peaks determined by the laser frequency to sidebands determined by the excitations of the driven system. These sidebands emerge from difference-frequency Raman processes in the nonequilibrium SC state. For interband couplings weaker than the intraband pairing, we show that the Leggett phase collective mode leads to harmonic sidebands around the traditional pump-probe peaks. Additional Higgs collective mode peaks result from light-induced inversion-symmetry breaking in a thin-film geometry. For strong interband coupling, we find a transition from a nonequilibrium finite Cooper-pair momentum state characterized by hybrid-Higgs amplitude mode peaks in THz-MDCS spectra to a driven state identified experimentally by the emergence of Floquet-type sidebands at bi-Higgs frequencies. Those dominant bi-Higgs-frequency satellites are manifestations of a new order parameter relative phase collective mode that characterizes the nonequilibrium SC state. The predicted interaction- and field-dependent transitions in the spectral profile allow us to propose THz-MDCS experiments for quantum tomography of light-driven superconductivity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Classical and quantum evolution in a simple coherent neutrino problem

The extraordinary neutrino flux produced in extreme astrophysical environments like the early Universe, core-collapse supernovae and neutron star mergers may produce coherent quantum neutrino oscillations on macroscopic length scales. The Hamiltonian describing this evolution can be mapped into quantum spin models with all-to-all couplings arising from neutrino-neutrino forward scattering. To date many studies of these oscillations have been performed in a mean-field limit where the neutrinos time evolve in a product state. In this paper we examine a simple two-beam model evolving from an initial product state and compare the mean-field and many-body evolution. The symmetries in this model allow us to solve the real-time evolution for the quantum many-body system for hundreds or thousands of spins, far beyond what would be possible in a more general case with an exponential number (2 N ) of quantum states. We compare mean-field and many-body solutions for different initial product states and ratios of one- and two-body couplings, and find that in all cases in the limit of infinite spins the mean-field (product state) and many-body solutions coincide for simple observables. This agreement can be understood as a consequence of the fact that the typical initial condition represents a very local but dense distribution about a mean energy in the spectrum of the Hamiltonian. We explore quantum information measures like entanglement entropy and purity of the many-body solutions, finding intriguing relationships between the quantum information measures and the dynamical behavior of simple physical observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Field-induced spin level crossings within a quasi-$XY$ antiferromagnetic state in $Ba$ 2 $FeSi$ 2 $O$ 7

Here, we present a high-field study of the strongly anisotropic easy-plane square lattice $S$ = 2 quantum magnet $Ba$ 2 $FeSi$ 2 $O$ 7 . This compound is a rare high-spin antiferromagnetic system with very strong easy-plane anisotropy, such that the interplay between spin level crossings and antiferromagnetic order can be studied. We observe a magnetic field-induced spin level crossing occurring within an ordered state. This spin level crossing appears to preserve the magnetic symmetry while producing a nonmonotonic dependence of the order parameter magnitude. The resulting temperature–magnetic field phase diagram exhibits two dome-shaped regions of magnetic order overlapping around 30 T. The ground state of the lower-field dome is predominantly a linear combination of |$S^z$ = 0$\rangle$ and |$S^z$ = 1$\rangle$ states, while the ground state of the higher-field dome can be approximated by a linear combination of |$S^z$ = 1$\rangle$ and |$S^z$ = 2$\rangle$ states. At 30 T, where the spin levels cross, the magnetization exhibits a slanted plateau, the magnetocaloric effect shows a broad hump, and the electric polarization shows a weak slope change. We determined the detailed magnetic phase boundaries and the spin level crossings using measurements of magnetization, electric polarization, and the magnetocaloric effect in pulsed magnetic fields to 60 T. Furthermore, we calculate these properties using a mean-field theory based on direct products of SU(5) coherent states and find good agreement. Finally, we measure and calculate the magnetically induced electric polarization that reflects magnetic ordering and spin level crossings. This multiferroic behavior provides another avenue for detecting phase boundaries and symmetry changes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fluid structure interaction of a subaqueous pendulum: Analyzing the effect of wake correction via large eddy simulations

The dynamic behavior of a subaqueous cylindrical pendulum and corresponding flow dynamics are investigated. The objectives were twofold: (i) to examine whether the two-dimensional model equations sufficiently capture the three-dimensional dynamics and (ii) to investigate the emerging three-dimensional vortical flow structures. Large eddy simulations with two-way coupling fluid structure interaction were carried out using the immersed boundary method to simulate the motion of the pendulum and its interactions with the initially stagnant water. The resulting pendulum motion is compared against measured data obtained in a series of experimental tests to validate the simulation results and the model equations with and without wake corrections. An analysis of the flow vorticity revealed the development of a vortex ring during the first swing and the formation of tip vortices. The evolution of the vortex rings emerging from the motion of the subaqueous cylindrical pendulum was visualized using Q-criteria showing a reasonable agreement with vortical structures observed in the experiment using particle imaging velocimetry. The hydrodynamic moments acting on the simulated pendulum and the moments calculated from the model equations are analyzed. Using the insights from these numerical simulations, a modification of the wake correction is proposed to enhance the accuracy of the rate of decay and period. The transient effect of coherent flow on pendulum dynamics, especially the added mass effect, is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Extreme high-field superconductivity in thin Re films

We report the high-field superconducting properties of thin, disordered Re films via magnetotransport and tunneling density of states measurements. Films with thicknesses in the range of 9 to 3 nm had normal-state sheet resistances of ~0.2 kΩ to ~1 kΩ and corresponding transition temperatures in the range of 6 to 3 K. Tunneling spectra were consistent with those of a moderate coupling BCS superconductor. Notwithstanding these unremarkable superconducting properties, the films exhibited an extraordinarily high upper critical field. Here, we estimate their zero temperature H c2 to be more than twice the Pauli limit. Indeed, in 6-nm samples the estimated reduced critical field H c2 /T c ~ 5.6T/K is among the highest reported for any elemental superconductor. Although the sheet resistances of the films were well below the quantum resistance R Q = h/4e 2 , their H c2 's approached the theoretical upper limit of a strongly disordered superconductor for which k F ℓ ~ 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Energy dependence of coherent photonuclear production of J/ψ mesons in ultra-peripheral Pb-Pb collisions at $\sqrt{{\textrm{s}}_{\textrm{NN}}}$ = 5.02 TeV

The cross section for coherent photonuclear production of J/ψ is presented as a function of the electromagnetic dissociation (EMD) of Pb. The measurement is performed with the ALICE detector in ultra-peripheral Pb-Pb collisions at a centre-of-mass energy per nucleon pair of $\sqrt{{\textrm{s}}_{\textrm{NN}}}$ = 5.02 TeV. Cross sections are presented in five different J/ψ rapidity ranges within |y| < 4, with the J/ψ reconstructed via its dilepton decay channels. In some events the J/ψ is not accompanied by EMD, while other events do produce neutrons from EMD at beam rapidities either in one or the other beam direction, or in both. The cross sections in a given rapidity range and for different configurations of neutrons from EMD allow for the extraction of the energy dependence of this process in the range 17 < W γ Pb,n < 920 GeV, where W γ Pb,n is the centre-of-mass energy per nucleon of the γPb system. This range corresponds to a Bjorken-x interval spanning about three orders of magnitude: 1.1 × 10 —5 < x < 3.3 × 10 —2 . In addition to the ultra-peripheral and photonuclear cross sections, the nuclear suppression factor is obtained. These measurements point to a strong depletion of the gluon distribution in Pb nuclei over a broad, previously unexplored, energy range. These results, together with previous ALICE measurements, provide unprecedented information to probe quantum chromodynamics at high energies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-efficiency, high-fidelity charge initialization of shallow nitrogen-vacancy centers in diamond

Nitrogen-vacancy (N-𝑉) centers in diamond exhibit long spin-coherence times, optical initialization, and optical-spin readout under ambient conditions, making them excellent quantum sensors. However, the conventional scheme for charge-state initialization based on off-resonant green excitation results in significant state-preparation errors, typically around 30%. One method for improving charge-state initialization fidelity is to use multicolor excitation, which has been demonstrated to achieve a near-unity preparation fidelity for bulk N-𝑉 centers by using a few milliseconds of near-infrared (NIR) (5-mW) and green (10-μ⁢W) excitation. The translation of such schemes to N-𝑉 centers near the diamond surface with higher-efficiency optical pumping would enable new applications in nanoscale sensing. Here, we demonstrate a protocol for efficient charge initialization of shallow N-𝑉 centers between 5 nm and 15 nm from the diamond surface. By carefully studying the charge dynamics of shallow N-𝑉 centers, we identify a region of parameter space that allows for near-unity (95%) charge initialization within 300 μ⁢s of NIR (905-nm, 1-mW) and green (520-nm, 10-μ⁢W) excitation. The time to 90% charge initialization can be as fast as 10 μ⁢s for 4 mW of NIR and 39 μ⁢W of green illumination. This fast, efficient charge initialization protocol will especially benefit nanoscale sensing applications in which state-preparation errors currently prohibit scaling, such as measuring higher-order multipoint correlators.

infrared techniques↗

Exploring Excited State Proton Transfer Dynamics upon Ultraviolet Excitation

Excited state intramolecular proton transfer (ESIPT) has been investigated in two prototypical systems─salicylaldehyde azine (SAA) and 1,5-dihydroxyanthraquinone (DHAQ)─using transient absorption spectroscopy upon ultraviolet excitation into the less studied higher excited (S n ) manifold. Excitation with sub-30 fs pulses and broadband visible probing has allowed for direct measurement of the ESIPT rate. In conjunction with steady-state measurements and TD-DFT calculations, a complete delineation of the ultrafast photophysics has been carried out. In SAA, ESIPT remains ultrafast (∼30 fs), consistent with previous S 1 excitation studies. Coherent vibrational beats maps reveal significant wavelength dependence, however. Theoretical analysis suggests that the observed modes and their intensities in coherent vibrational spectra are modulated by the nature of the electronically excited state. In DHAQ, the first direct observation of ESIPT presents a time-constant of ∼85 fs, and a slower component of 9 ps, akin to previous reports on double-proton transfer systems. Collectively, the results suggest that while the ultrafast ESIPT rate remains largely invariant vis-à-vis the excitation energy, the product yield, as well as accompanying coherent oscillations, may be substantively altered, owing to the existence of alternative decay pathways.

excited states↗

Experimental determination of energy-level structures of diamond silicon-vacancy centers in off-axis magnetic fields

Here, we report the development of an experimental approach to efficiently determine the energy level structure of an individual silicon vacancy (SiV) center in a magnetic field along an arbitrary direction. This approach uses two coupling rates (one each for the ground and the excited states) to characterize the combined effects of static strain and dynamic Jahn-Teller coupling and exploits the fact that orbital Zeeman effects vanish when the magnetic field is normal to the SiV axis. With an analytical expression for the energy level structure of the SiV under a transverse magnetic field, the two coupling rates can be directly derived from two measurements: one on the frequency separation between two spin-conserved transitions and the other on the coherent population trapping resonance of the SiV ground spin states. A detailed comparison between the numerical calculation and the experimental result on the dependence of the spin-conserved splitting on both the amplitude and direction of the magnetic field further reveals unequal orbital magnetic coupling for the ground and excited states, indicating that unequal orbital quenching factors are needed for an accurate description of the SiV energy level structure in a magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nonadiabatic coupling of the dynamical structure to the superconductivity in YSr 2 Cu 2.75 Mo 0.25 O 7.54 and Sr 2 CuO 3.3

A crucial issue in cuprates is the extent and mechanism of the coupling of the lattice to the electrons and the superconductivity. Here we report Cu K edge extended X-ray absorption fine structure measurements elucidating the internal quantum tunneling polaron (iqtp) component of the dynamical structure in two heavily overdoped superconducting cuprate compounds, tetragonal YSr 2 Cu 2.75 Mo 0.25 O 7.54 with superconducting critical temperature, T c = 84 K and hole density p = 0.3 to 0.5 per planar Cu, and the tetragonal phase of Sr 2 CuO 3.3 with T c = 95 K and p = 0.6. In YSr 2 Cu 2.75 Mo 0.25 O 7.54 changes in the Cu-apical O two-site distribution reflect a sequential renormalization of the double-well potential of this site beginning at T c , with the energy difference between the two minima increasing by ~6 meV between T c and 52 K. Sr 2 CuO 3.3 undergoes a radically larger transformation at T c , >1-Å displacements of the apical O atoms. The principal feature of the dynamical structure underlying these transformations is the strongly anharmonic oscillation of the apical O atoms in a double-well potential that results in the observation of two distinct O sites whose Cu–O distances indicate different bonding modes and valence-charge distributions. The coupling of the superconductivity to the iqtp that originates in this nonadiabatic coupling between the electrons and lattice demonstrates an important role for the dynamical structure whereby pairing occurs even in a system where displacements of the atoms that are part of the transition are sufficiently large to alter the Fermi surface. The synchronization and dynamic coherence of the iqtps resulting from the strong interactions within a crystal would be expected to influence this process.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Efficient prediction of attosecond two-colour pulses from an X-ray free-electron laser with machine learning

Abstract X-ray free-electron lasers are sources of coherent, high-intensity X-rays with numerous applications in ultra-fast measurements and dynamic structural imaging. Due to the stochastic nature of the self-amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two-coloured X-ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networks and decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high-repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X-ray spectroscopy using XFELs, such as in time-resolved X-ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Search for 3D topological superconductors using laser-based spectroscopy (Final Technical Report)

The three-dimensional topological superconductor (3D TSC) is a novel quantum phase of matter that is predicted to exhibit exotic thermal and electrical properties, which may serve applications ranging from precision thermal management and sensing technologies to fault-tolerant quantum information processing. Over the past decade, there has been an intensive effort to realize 1D and 2D TSCs by artificially engineering them from combinations of already existing materials. For example, coupling conventional superconductors to spin-orbit coupled 1D nanowires or to 2D topological insulator surfaces by the proximity effect provides a route to realizing 1D and 2D TSCs respectively. However no artificial engineering strategy is available for a 3D TSC. Therefore, current searches are limited to intrinsically superconducting compounds whose topological properties are difficult to predict. The overarching goal of this project was to realize and to identify 3D TSCs in bulk single crystals using novel laser-based spectroscopic techniques. One major thrust was to develop ultralow temperature and ultra-high-resolution angle-resolved photoemission spectroscopy (ARPES) to directly measure the dispersion of Majorana excitations that are predicted to exist on the surfaces of 3D TSCs. Another major thrust was to develop a rational route to realize 3D TSCs by identifying their precursor phases. It is theoretically proposed that the critical fluctuations of certain ordered electronic phases can mediate Cooper pairing in odd-parity channels and lead to topological superconductivity. Therefore, 3D TSCs may potentially emerge upon suppressing these inversion symmetry broken precursor phases to a critical point with external perturbations such as pressure, strain or even light. To test this hypothesis, we studied candidate materials using a suite of symmetry-sensitive optical probes including rotational anisotropy optical second harmonic generation (RA-SHG) and time-resolved coherent phonon spectroscopy, all operable under high-pressure and low temperature environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Optical Phase Recovery and Locking in a PPM Laser Communication Link

Free-space optical communication holds great promise for future space missions requiring high data rates. For data communication in deep space, the current architecture employs pulse position modulation (PPM). In this scheme, the light is transmitted and detected as pulses within an array of time slots. While the PPM method is efficient for data transmission, the phase of the laser light is not utilized. The phase coherence of a PPM optical signal has been investigated with the goal of developing a new laser communication and ranging scheme that utilizes optical coherence within the established PPM architecture and photon-counting detection (PCD). Experimental measurements of a PPM modulated optical signal were conducted, and modeling code was developed to generate random PPM signals and simulate spectra via FFT (Fast Fourier Transform) analysis. The experimental results show very good agreement with the simulations and confirm that coherence is preserved despite modulation with high extinction ratios and very low duty cycles. A real-time technique has been developed to recover the phase information through the mixing of a PPM signal with a frequency-shifted local oscillator (LO). This mixed signal is amplified, filtered, and integrated to generate a voltage proportional to the phase of the modulated signal. By choosing an appropriate time constant for integration, one can maintain a phase lock despite long dark times between consecutive pulses with low duty cycle. A proof-of-principle demonstration was first achieved with an RF-based PPM signal and test setup. With the same principle method, an optical carrier within a PPM modulated laser beam could also be tracked and recovered. A reference laser was phase-locked to an independent pulsed laser signal with low-duty-cycle pseudo-random PPM codes. In this way, the drifting carrier frequency in the primary laser source is tracked via its phase change in the mixed beat note, while the corresponding voltage feedback maintains the phase lock between the two laser sources. The novelty and key significance of this work is that the carrier phase information can be harnessed within an optical communication link based on PPM-PCD architecture. This technology development could lead to quantum-limited efficient performance within the communication link itself, as well as enable high-resolution optical tracking capabilities for planetary science and spacecraft navigation.

Aveline, David C.↗

Small-angle scattering interferometry with neutron orbital angular momentum states

Methods to prepare and characterize neutron helical waves carrying orbital angular momentum (OAM) were recently demonstrated at small-angle neutron scattering (SANS) facilities. These methods enable access to the neutron orbital degree of freedom which provides new avenues of exploration in fundamental science experiments as well as in material characterization applications. However, it remains a challenge to recover phase profiles from SANS measurements. We introduce and demonstrate a novel neutron interferometry technique for extracting phase information that is typically lost in SANS measurements. An array of reference beams, with complementary structured phase profiles, are put into a coherent superposition with the array of object beams, thereby manifesting the phase information in the far-field intensity profile. We demonstrate this by resolving petal-structure signatures of helical wave interference for the first time: an implementation of the long-sought recovery of phase information from small-angle scattering measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗