Observed Interference Fringes Research Articles

Tailoring Photon Statistics with an Atom-Based Two-Photon Interferometer.

Controlling the photon statistics of light is paramount for quantum science and technologies. Recently, we demonstrated that transmitting resonant laser light past an ensemble of two-level emitters can result in a stream of single photons or excess photon pairs. This transformation is due to quantum interference between the transmitted laser light and the incoherently scattered photon pairs [Prasad etal., Nat. Photonics 14, 719 (2020)NPAHBY1749-488510.1038/s41566-020-0692-z]. Here, using the dispersion of the atomic medium, we actively control the relative quantum phase between these two components. We thereby realize a tunable two-photon interferometer and observe interference fringes in the normalized photon coincidence rate. When tuning the relative phase, the coincidence rate varies periodically, giving rise to a continuous modification of the photon statistics from antibunching to bunching. Beyond the fundamental insight that there exists a tunable quantum phase between incoherent and coherent light that dictates the photon statistics, our results lend themselves to the development of novel quantum light sources.

Haidinger–Michelson rings in white light

We use coherence theory to explain why it is necessary to modify the conventional setup of a Michelson interferometer to obtain Haidinger rings with an extended source of white light. The modification consists of introducing a glass slide into one of the two arms of the interferometer. This insertion circumvents the drastic restriction imposed by the low temporal coherence of white light, which prevents the observation of interference rings with the conventional setup. In order to understand this restriction, we developed and implemented a criterion for observing interference fringes. The modified setup also makes it possible to perform a spectral interferometry experiment to analyze the output of the interferometer and determine the refractive index of the glass slide over the whole visible spectrum. The fit of measured data using Sellmeier's law gives the extrapolated value of the refractive index to the IR nIR=1.5307±0.0003 and the value of the characteristic wavelength λ0=(164.5±0.4) nm of the oscillator responsible for the dispersion.

Diagnosing phase correlations in the joint spectrum of parametric downconversion using multi-photon emission

The development of new quantum light sources requires robust and convenient methods of characterizing their joint spectral properties. Measuring the joint spectral intensity between a photon pair ignores any correlations in spectral phase which may be responsible for degrading the quality of quantum interference. A fully phase-sensitive characterization tends to require significantly more experimental complexity. Here, we investigate the sensitivity of the frequency-resolved double-pair emission to spectral phase correlations, in particular to the presence of a simple form of correlated phase which can be generated by a chirped pump laser pulse. We observe interference fringes in the four photon coincidences which depend on the frequencies of all four photons, with a period which depends on the strength of their correlation. We also show that phase correlations in the JSA induce spectral intensity correlations between two signal photons, even when the corresponding idler photons are not detected, and link this correlation pattern to the purity of a single signal photon. These effects will be useful in assessing new photon-pair sources for quantum technologies, especially since we require little additional complexity compared to a joint spectral intensity measurement - essentially just the ability to detect at least two photons in each output port.

Matter-wave interference of a native polypeptide

The de Broglie wave nature of matter is a paradigmatic example of quantum physics and it has been exploited in precision measurements of forces and fundamental constants. However, matter-wave interferometry has remained an outstanding challenge for natural polypeptides, building blocks of life, which are fragile and difficult to handle. Here, we demonstrate the wave nature of gramicidin, a natural antibiotic composed of 15 amino acids. Its center of mass is delocalized over more than 20 times the molecular size in our time-domain Talbot-Lau interferometer. We compare the observed interference fringes with a model that includes both a rigorous treatment of the peptide’s quantum wave nature as well as a quantum chemical assessment of its optical properties to distinguish our result from classical predictions. The realization of quantum optics with this prototypical biomolecule paves the way for quantum-assisted measurements on a large class of biologically relevant molecules.

Quantitative Surface Plasmon Interferometry via Upconversion Photoluminescence Mapping.

Direct far-field visualization and characterization of surface plasmon polaritons (SPPs) are of great importance for fundamental studies and technological applications. To probe the evanescently confined plasmon fields, one usually requires advanced near-field techniques, which is typically not applicable for real-time, high-throughput detecting or mapping of SPPs in complicated environments. Here, we report the utilization of rare-earth-doped nanoparticles to quantitatively upconvert invisible, evanescently confined SPPs into visible photoluminescence emissions for direct far-field visualization of SPPs in a complicated environment. The observed interference fringes between the SPPs and the coherent incident light at the metal surface provide a quantitative measurement of the SPP wavelength and the SPP propagating length and the local dielectric environments. It thus creates a new signaling pathway to sensitively transduce the local dielectric environment change into interference periodicity variation, enabling a new design of directly measurable, spectrometer-free optical rulers for rapid, ultrasensitive label-free detection of various biomolecules, including streptavidin and prostate-specific antigen, down to the femtomolar level.

A tunable path-separated electron interferometer with an amplitude-dividing grating beamsplitter

We demonstrate a tunable path-separated electron interferometer using a single amplitude-dividing beamsplitter to prepare multiple spatially isolated, coherent electron probe beams. We place four electrostatic bi-prisms in the optical column of a scanning transmission electron microscope (STEM) to achieve path separations of up to 25 μm, the largest demonstrated within amplitude-division electron interferometers while maintaining fringe visibility of the directly observed interference fringes at the detector. We characterize the fringe visibility of this setup over a range of path separations and perform STEM holography to reconstruct the full object wave of a fabricated Si ramp test phase object. We report a quantitative object-wave measurement in this configuration and confirm with an independent off-axis electron holography measurement. This experimental design can potentially be applied to high-resolution phase imaging and fundamental physics experiments, such as an exploration of the electron wave packet coherence length and the Aharonov-Bohm effect.

Generation of mechanical interference fringes by multi-photon counting

Exploring the quantum behaviour of macroscopic objects provides an intriguing avenue to study the foundations of physics and to develop a suite of quantum-enhanced technologies. One prominent path of study is provided by quantum optomechanics which utilizes the tools of quantum optics to control the motion of macroscopic mechanical resonators. Despite excellent recent progress, the preparation of mechanical quantum superposition states remains outstanding due to weak coupling and thermal decoherence. Here we present a novel optomechanical scheme that significantly relaxes these requirements allowing the preparation of quantum superposition states of motion of a mechanical resonator by exploiting the nonlinearity of multi-photon quantum measurements. Our method is capable of generating non-classical mechanical states without the need for strong single-photon coupling, is resilient against optical loss, and offers more favourable scaling against initial mechanical thermal occupation than existing schemes. Moreover, our approach allows the generation of larger superposition states by projecting the optical field onto NOON states. We experimentally demonstrate this multi-photon-counting technique on a mechanical thermal state in the classical limit and observe interference fringes in the mechanical position distribution that show phase super-resolution. This opens a feasible route to explore and exploit quantum phenomena at a macroscopic scale.

Three Phase-Grating Moiré Neutron Interferometer for Large Interferometer Area Applications.

We demonstrate a three phase-grating moiré neutron interferometer in a highly intense neutron beam as a robust candidate for large area interferometry applications and for the characterization of materials. This novel far-field moiré technique allows for broad wavelength acceptance and relaxed requirements related to fabrication and alignment, thus circumventing the main obstacles associated with perfect crystal neutron interferometry. We observed interference fringes with an interferometer length of 4 m and examined the effects of an aluminum 6061 alloy sample on the coherence of the system. Experiments to measure the autocorrelation length of samples and the universal gravitational constant are proposed and discussed.

Determination of Optical Properties of Undoped Amorphous Selenium (a-Se) Films by Dielectric Modeling of Their Normal-Incidence Transmittance Spectra

Normal-incidence specular transmittance T_exp (?) of undoped amorphous selenium ( a -Se) films of several thicknesses (0.25-1 ?m) thermally evaporated on thick microscopic glass-slide substrates upheld at temperatures near 30 o C (below glass transition temperature of undoped Se) has been measured at room temperature in the spectral wavelength?range 300-1100 nm. Above a threshold wavelength ?_c (~ 600 nm), their as-measured T_exp (?)-? curves display transmittance values near that of glass substrates and exhibit well-resolved interference-fringe maxima and minima, signifying good uniformity of fabricated a -Se films. Below?_c, the T_exp (?)-? curves decline progressively to zero transmittance, preceded by a tailing-like trend of possible structural disorder origin. The spectral dependencies of optical constants n(?) and?(?) of the studied a -Se films on ? were retrieved from iterative curve-fitting of their T_exp (?)-? data to theoretical T_theor (?)-formulations of an air-supported {thin film/thick substrate}-stack using the O’Leary-Johnson-Lim (OJL) interband-transition dielectric model, combined with a dielectric constant , representing the dielectric background at very high photon energies (at spectral wavelengths much smaller than measured). Regardless of the number of observed interference fringes, reliable simulation to the as-measured normal-incidence T_exp (?)-? spectra has been achieved, but were remarkably curve-fitted if we presume that a thin roughness layer (<5 nm) of selenium was formed on top of the fabricated undoped a -Se films. The retrieved n(?)-? spectra display a broad peak around??0.52 ?m, below which n(?) was found to vary with wavelength in accordance with a Sellmeier-like (Wemple-DiDominco) single-oscillator (normal) dispersion formula, with a static index of refraction n(E=0)=?(?_s )?2.42, where ?_s is the static dielectric constant of the material at zero photon energy , and an oscillator “average” bandgap energy of E_o?3.93 eV?2 E_g^opt, the optical (Tauc) bandgap energy. The values of E_g^opt of studied undoped a -Se films deduced from Tauc-like plots were around 1.92 eV (± 0.02 eV) and the retrieved values of OJL band-tailing energy parameter ? (Urbach-tail parameter ?_U) was found to be in the range 40-50 meV, slightly dependent on film thickness.

Surface modification of indium phosphide by 100 MeV iron ions

Surface modification of indium phosphide (InP) irradiated with 100 MeV 56Fe7+ ions for various ion fluences ranging from 5×1012 to 2×1014 cm−2was studied using Raman scattering, Fourier transform infrared (FTIR) and atomic force microscopy. The shift in the Raman peak revealed the presence of stress in the irradiated samples. The average crystallite size obtained by analyzing Raman spectra with the phonon-confinement model decreased with ion fluence. The observed interference fringes in the Fourier transform reflectance spectra of irradiated InP indicate the presence of disorder and defects in the surface region of irradiated InP. The power spectral density obtained from Atomic Force Microscopy (AFM) measurements showed the surface evolution due to diffusion process up to ion fluence 5×1013 cm−2; however, surface diffusion process was less dominant at higher ion fluences.

Optical thickness measurement of mask blank glass plate by the excess fraction method using a wavelength-tuning interferometer

The absolute optical thickness of a 140-mm2 mask blank glass plate 3.1mm thickness was measured by three-surface interferometry using a wavelength-tuning Fizeau interferometer. The interference order was determined by the excess fraction method. The wavelength of a tunable laser diode was scanned linearly from 632 to 642nm, and a CCD detector recorded 2000 interference images. Two kinds of optical thicknesses measured by discrete Fourier analysis and phase-shifting were synthesized to obtain the optical thickness with respect to the ordinary refractive index. The optical thickness defined by the group refractive index at the 637nm central wavelength was measured by wavelength scanning. The optical thickness deviation defined by the ordinary refractive index was measured using tunable phase-shifting. The systematic errors caused by nonlinearity in the wavelength tuning were corrected through correlation analysis between the theoretical and observed interference fringes.

Reconstructing interference fringes in slit experiments by complex quantum trajectories

AbstractThere are external and internal representations for a quantum state Ψ. External representation is commonly adopted in the standard quantum mechanics by exploiting probability density function Ψ*Ψ to explain the observed interference fringes in slit experiments. On the other hand, in quantum Hamilton mechanics, the quantum state Ψ has a dynamical representation that reveals the internal mechanism underlying the externally observed interference fringes. The internal representation of Ψ is described by a set of Hamilton equations of motion, by which quantum trajectories of a particle moving in Ψ can be solved. In this article, millions of complex quantum trajectory connecting slits to a screen are solved from the Hamilton equations, and the statistical distribution of their arrivals on the screen is shown to reproduce the observed interference fringes. This appears to be the first quantitative verification of the equivalence between the trajectory‐based statistics and the wavefunction‐based statistics on slit experiments. © 2012 Wiley Periodicals, Inc.

Cold-atom gravimetry with a Bose-Einstein condensate

We present a cold atom gravimeter operating with a sample of Bose-condensed Rubidium-87 atoms. Using a Mach-Zehnder configuration with the two arms separated by a two-photon Bragg transition, we observe interference fringes with a visibility of 83% at T=3 ms. We exploit large momentum transfer (LMT) beam splitting to increase the enclosed space-time area of the interferometer using higher-order Bragg transitions and Bloch oscillations. We also compare fringes from condensed and thermal sources, and observe a reduced visibility of 58% for the thermal source. We suspect the loss in visibility is caused partly by wavefront aberrations, to which the thermal source is more susceptible due to its larger transverse momentum spread. Finally, we discuss briefly the potential advantages of using a coherent atomic source for LMT, and present a simple mean-field model to demonstrate that with currently available experimental parameters, interaction-induced dephasing will not limit the sensitivity of inertial measurements using freely-falling, coherent atomic sources.

Raman scattering and FTIR studies of 100 MeV Fe9+ ion-irradiated gallium phosphide

Gallium phosphide samples have been irradiated with 100 MeV 56Fe9+ ions for various ion fluences varying from 1×1011 to 1×1014 cm−2 at room temperature. Irradiated samples were characterized by Raman scattering and Fourier transform infrared techniques. The stress estimated from the Raman peak shift for the ion fluences of 1×1012, 5×1012, 1×1013, 5×1013 and 1×1014 cm−2 were found to be 222, 280, 290, 355 and 522 MPa, respectively. The average crystallite size obtained by analyzing Raman spectra with phonon confinement model was decreased with the increase in the ion fluence. The electron–phonon coupling strength estimated from the first- and second-order longitudinal optical modes of Raman spectra was found to decrease as the crystallite size became smaller in the irradiated samples. The observed interference fringes in the Fourier transform reflectance spectra of irradiated gallium phosphide indicate the presence of disorder and defects in the surface region of irradiated gallium phosphide.

Polarization-resolved Second Harmonic microscopy in anisotropic thick tissues

We thoroughly analyze the linear propagation effects that affect polarization-resolved Second Harmonic Generation imaging of thick anisotropic tissues such as collagenous tissues. We develop a theoretical model that fully accounts for birefringence and diattenuation along the excitation propagation, and polarization scrambling upon scattering of the harmonic signal. We obtain an excellent agreement with polarizationresolved SHG images at increasing depth within a rat-tail tendon for both polarizations of the forward SHG signal. Most notably, we observe interference fringes due to birefringence in the SHG depth profile when excited at π/4 angle from the tendon axis. We also measure artifactual decrease of ρ = Χxxx/Χxyy with depth due to diattenuation of the excitation. We therefore derive a method that proves reliable to determine both ρ and the tendon birefringence and diattenuation.

Continuous-wave light modulation at molecular frequencies

By using continuous-wave (CW)--stimulated Raman scattering inside a high-finesse cavity, we generate three CW spectral components covering about one octave of optical bandwidth. We investigate the mutual coherence of these three beams by studying phase-dependent second harmonic generation. From the high contrast of the observed interference fringes, we infer very good phase coherence across the spectrum and thereby infer the synthesis of a near single-cycle optical wave form.

Optical properties of an epitaxial Na0.5Bi0.5TiO3 thin film grown by laser ablation: Experimental approach and density functional theory calculations

This study reports on the determination of the optical constants of a lead-free ferroelectric material, Na0.5Bi0.5TiO3. The optical transmission measurements were carried out in the 300–3000 nm wavelength range, on a (100)-oriented Na0.5Bi0.5TiO3 thin film, epitaxially grown by laser ablation on a (100)MgO single crystal substrate. Applying the “method of the envelopes,” developed by Manifacier et al. [J. Phys. E 9, 1002 (1976)] and by Swanepoel [J. Phys. E 16, 1214 (1983)], the analysis of the observed interference fringes allowed extracting some optical data for Na0.5Bi0.5TiO3, namely the linear refractive and extinction indices n and k, the absorption coefficient α, and as well the nature (direct or indirect transition) and value of the optical band gap. It was found that n∞=2.321 and the transmission data suggested a 3.30 eV indirect transition. Our experimental results are thus in opposition to the few data reported so far for Na0.5Bi0.5TiO3, where a direct transition was evoked. Therefore, we have confronted the optical transmission data to supplementary diffuse reflectance and ellipsometry measurements, and finally, to first principles calculations. The diffuse reflectance data, collected for Na0.5Bi0.5TiO3 powders, indicate a 3.26 eV optical band gap. In addition, the ellipsometry measurements reveal a refractive index of 2.346 at 2.066 μm, an energy gap of ∼3.20 eV, and also confirm the thickness of the layer. These additional data are then in very good agreement with the data derived from the optical transmission measurements. Finally, first principles calculations were carried out in the framework of the density functional theory for the three Na0.5Bi0.5TiO3 polymorphs (i.e., rhombohedral, tetragonal, and cubic). For each polymorph, in order to consider the Na/Bi disorder on the perovskite A-site, three different Na/Bi distributions within the unit cell were investigated, leading to nine atomic configurations. The electronic structure of these nine configurations was then calculated after geometry optimization and only one of them did not converge. These calculations complete the above experimental data, as six electronic structures over eight presented an indirect band gap, with a band gap energy Eg falling in the 3.90–4.60 eV energy range. The latter value is higher than the experimental ones but is definitely more compatible with the energy band gap expected for ferroelectric oxide materials.

Manipulation of multiphoton entanglement in waveguide quantum circuits

On-chip integrated photonic circuits are crucial to further progress towards quantum technologies and in the science of quantum optics. Here we report precise control of single photon states and multiphoton entanglement directly on-chip. We manipulate the state of path-encoded qubits using integrated optical phase control based on resistive elements, observing an interference contrast of 98.2 ± 0.3%. We demonstrate integrated quantum metrology by observing interference fringes with two- and four-photon entangled states generated in a waveguide circuit, with respective interference contrasts of 97.2 ± 0.4% and 92 ± 4%, sufficient to beat the standard quantum limit. Finally, we demonstrate a reconfigurable circuit that continuously and accurately tunes the degree of quantum interference, yielding a maximum visibility of 98.2 ± 0.9%. These results open up adaptive and fully reconfigurable photonic quantum circuits not just for single photons, but for all quantum states of light. Precise control of single-photon states and multiphoton entanglement is demonstrated on-chip. Two- and four-photon entangled states have now been generated in a waveguide circuit and their interference tuned. These results open up adaptive and reconfigurable photonic quantum circuits not just for single photons, but for all quantum states of light.

Characteristics of total reflection at interface between left-handed and right-handed materials

Characteristics of total reflection at the interface between left-handed and right-handed materials are derived from electromagnetic theory, and the phase is researched. The experimental idea of observing interference fringes of evanescent waves, when total reflection takes place at the interface is discussed, and the distribution of interference fringes is calculated from electromagnetic theory.

Infrared dielectric function of wurtzite aluminum nitride

The infrared dielectric function of wurtzite AlN has been determined by fitting an analytic Lorentzian dielectric function to experimentally observed interference fringes in infrared transmission. The analytic model is scaled to agree with recent measurements of the visible refractive index, and the experiment and model extend to the submillimeter range of the infrared. A complete, experimentally verified dielectric function is found from the visible to the submillimeter spectral region for radiation with E⊥c axis, and an analytic model is produced for E‖c axis. Refractive indices and extinction coefficients from the visible to zero frequency are presented.