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Free-induction-decay (FID) magnetometers have evolved as simple magnetic sensors for sensitive detection of unknown magnetic fields. However, these magnetometers suffer from a fundamental problem known as a "dead zone," making them insensitive to certain magnetic field directions. Here, we demonstrate a simple experimental scheme for the dead-zone-free operation of a FID atomic magnetometer. Using a single laser beam containing equal strength of linear- and circular-polarization components and amplitude-modulation at a low-duty cycle, we have synchronously pumped the rubidium-87 atoms with both first- and second-order frequency harmonics. Such a novel pumping scheme has enabled us to observe the free Larmor precession of atomic spins at a frequency of $\Omega_L$ (orientation) and/or 2$\Omega_L$ (alignment) in a single FID signal, depending on the direction of the external magnetic field. We observed that the amplitude of the FID signal does not go to zero for any magnetic field direction, proving the absence of dead zones in the magnetometer. The magnetometer has a sensitivity in the range of 3.5 - 7.8 pT/$\sqrt{Hz}$ in all directions. Such a generic experimental scheme can play a crucial role in developing miniaturized atomic magnetometers for various practical applications, including geomagnetic applications., Comment: 5 pages, 4 figures

The spontaneous parametric down-conversion (SPDC), an inherently random quantum process, produces a non-deterministic photon-pair with strong temporal and spatial correlations owing to both energy and momentum conservation. Therefore, the SPDC-based photon pairs are used for quantum random number generation (QRNG). Typically, temporal correlation in association with an ideal unbiased beam splitter is used for QRNG without fully exploring the spatial correction. As a result, SPDC-based QRNG has a low bit rate. On the other hand, due to the spatial correlation, the photon pairs in non-collinear phase-matched geometry are generated randomly in diametrically opposite points over an annular ring spatial distribution. Therefore, exploring the temporal correlation between photon pairs from different sections of the annual ring can lead to multi-bit QRNG at a high rate, avoiding the need for a beam splitter. As a proof-of-concept, we report on high-bit-rate QRNG by using spatial correlation of photon-pairs by sectioning the SPDC ring of a non-collinear, degenerate, high-brightness source and temporal correlation between the diametrically opposite sections. Dividing the annular ring of the high-brightness photon-pair source based on a 20 mm long, type-0 phase-matched, periodically-poled KTP crystal into four sections, recording the timestamp of the coincidences (widow of 1 ns) between photons from diametrically opposite sections and assigning bits (0 and 1), we extracted 90 million raw bits over 27.7 s at a pump power of 17 mW. We determined the extraction ratio using the minimum entropy evaluation of more than 95% in our case. Using Toeplitz matrix-based post-processing, we achieved a QRNG with a bit-rate of 3 Mbps, passing all NIST 800-22 and TestU01 test suites. The generic scheme shows the possibility of further enhancement of the bit rate through more sectioning of the SPDC ring.

Talbot length, the distance between two consecutive self-image planes along the propagation axis for a periodic diffraction object (grating) illuminated by a plane wave, depends on the period of the object and the wavelength of illumination. This property makes the Talbot effect a straightforward technique for measuring the period of a periodic object (grating) by accurately determining the Talbot length for a given illumination wavelength. However, since the Talbot length scale is proportional to the square of the grating period, traditional Talbot techniques face challenges when dealing with smaller grating periods and minor changes in the grating period. Recently, we demonstrated a Fourier transform technique-based Talbot imaging method that allows for controlled Talbot lengths of a periodic object with a constant period and illumination wavelength. Using this method, we successfully measured periods as small as a few micrometers and detected sub-micrometer changes in the periodic object. Furthermore, by measuring the Talbot length of gratings with varying periods imaged through the combination of a thick lens of short focal length and a thin lens of long focal length and large aperture, we determined the effective focal length of the thick lens in close agreement with the theoretical effective focal length of a thick lens in the presence of spherical aberration. These findings establish the Talbot effect as an effective and simple technique for various sensing applications in optics and photonics through the measurement of any physical parameter influencing the Talbot length of a periodic object.

Hong-Ou-Mandel (HOM) interferometry has emerged as a valuable tool for quantum sensing applications, particularly in measuring physical parameters that influence the relative optical delay between pair photons. Unlike classical techniques, HOM-based quantum sensors offer higher resolution due to their intrinsic dispersion cancellation property. Despite this advantage, achieving precise measurements of optical delay crucial for practical applications often involves time-consuming integration and post-processing with traditional statistical methods. To address this challenge, our recent work focused on optimizing optical delay measurements in a time-efficient manner. By carefully selecting the length of a 1 mm periodically-poled KTP (PPKTP) crystal for pair photon generation, we achieved a remarkable group index measurement precision of $\sim 6.75\times 10^{-6}$ per centimeter of sample length, surpassing the previous maximum precision by over 400$\%$. These current measurements maintain fast detection and high photon counts, which are essential for practical quantum sensing applications. The HOM-based method, while limiting the measurement range, can be extended by compensating for photon delay using an optical delay stage. As a proof-of-principle, we measured the group index variation of PPKTP over a temperature range up to 200$^{\circ}$C with a precision in the range of one part per million ($\sim$10$^{-6}$). This advancement not only contributes to quantum sensing but also holds promising implications for high-precision and long-range measurements in quantum optical coherence tomography.

As a vector version of scalar Bessel beams, Poincar\'{e}-Bessel beams (PBBs) have attracted a great deal of attention due to the presence of polarization singularities and their nondiffraction and self-healing properties. Previous studies of PBBs have been restricted primarily to understanding the disinclination patterns in the spatially variable polarization, and many of the properties of PBBs remain unexplored. Here, we present a theoretical and experimental study of the polarization characteristics of PBBs, investigating a variety of their features. Using a mode transformation of a full Poincar\'{e} (FP) beam in a rectangular basis, ideally carrying 100$\%$ polarization coverage of polarization states represented on the surface of the Poincar\'{e} sphere, we observe the PBB as the superposition of an infinite number of FP beams, as each ring of PBB has polarization coverage >75$\%$. We also observe the resilience of a PBB's degree of polarization to perturbation. The polarization-ellipse orientation map of PBBs shows the presence of infinite series of C-point singularity pairs. The number of such series pairs is decided by the number of C-point singularity pairs of the FP beam. The dynamics of C-point singularity pairs in the self-healing process show a non-trivial creation of new singularities and recombination of existing singularities. Such dynamics provide insight into ``Hilbert Hotel'' style evolution of singularities in light beams. The present study can be useful for imaging in the presence of depolarizing surroundings, studying turbulent atmospheric channels, and exploring the rich mathematical concepts of transfinite numbers., Comment: 9 pages,11 figures

Hong-Ou-Mandel (HOM) interference, the bunching of two indistinguishable photons on a balanced beam-splitter, has emerged as a promising tool for quantum sensing. There is a need for wide spectral-bandwidth photon pairs (for high-resolution sensing) with high brightness (for fast sensing). Here we show the generation of photon-pairs with flexible spectral-bandwidth even using single-frequency, continuous-wave diode laser enabling high-precision, real-time sensing. Using 1-mm-long periodically-poled KTP crystal, we produced degenerate, photon-pairs with spectral-bandwidth of 163.42$\pm$1.68 nm resulting in a HOM-dip width of 4.01$\pm$0.04 $\mu$m to measure a displacement of 60 nm, and sufficiently high brightness to enable the measurement of vibrations with amplitude of $205\pm0.75$ nm and frequency of 8 Hz. Fisher-information and maximum likelihood estimation enables optical delay measurements as small as 4.97 nm with precision (Cram\'er-Rao bound) and accuracy of 0.89 and 0.54 nm, respectively, therefore showing HOM sensing capability for real-time, precision-augmented, in-field quantum sensing applications.

Historically, infinity was long considered a vague concept - boundless, endless, larger than the largest - without any quantifiable mathematical foundation. This view changed in the 1800s through the pioneering work of Georg Cantor showing that infinite sets follow their own seemingly paradoxical mathematical rules. In 1924, David Hilbert highlighted the strangeness of infinity through a thought experiment now referred to as the Hilbert Hotel paradox, or simply Hilbert's Hotel. The paradox describes an "fully" occupied imaginary hotel having infinite number of single-occupancy rooms, the manager can always find a room for new guest by simply shifting current guests to the next highest room, leaving first room vacant. The investigation of wavefield singularities has uncovered the existence of a direct optical analogy to Hilbert's thought experiment. Since then, efforts have been made to investigate the properties of Hilbert's Hotel by controlling the dynamics of phase singularities in``fractional'' order optical vortex beams. Here, we have taken such proposals to the next level and experimentally demonstrated Hilbert's Hotel using both phase and polarization singularities of optical fields. Using a multi-ramped spiral-phase-plate and a supercontinuum source, we generated and controlled fractional order vortex beams for the practical implementation of Hilbert's Hotel in scalar and vector vortex beams. Using a multi-ramped spiral-phase-plate, we show the possibility for complicated transitions of the generalized Hilbert's Hotel. The generic experimental scheme illustrates the usefulness of structured beams in visualizing unusual mathematical concepts and also for fractional vector beams driven fundamental and applied research., Comment: 9 pages, 5 figures

Full Poincar\'e (FP) beams, a special class of fully correlated beams generated through the coaxial superposition of a Laguerre-Gauss and fundamental Gaussian modes of orthogonal polarizations, contain all possible polarization states on the surface of the Poincar\'e sphere in a single beam. While the presence of all unconventional polarization states makes the FP beams useful for various applications, the dependence of the refractive index on the polarization restricts the efficient generation of FP beams across the electromagnetic spectrum through nonlinear frequency processes. To avoid such difficulty, we use two contiguous BIBO crystals with orthogonal optic axes and generate an ultrafast FP beam at 405 nm with average power as high as 18.3 mW at a single-pass conversion efficiency of 2.19%. Using Stokes parameters and Stokes phases, we observed the doubling of C-points and L-lines singularities and the orbital angular momentum in the SHG process. We have also devised a new technique to estimate the polarization coverage of the pump and SHG FP beams and observed the variation in polarization coverage with the intensity weightage of the constituting beams. Interestingly, the SHG beam has the highest polarization coverage for the FP beam of equal intensity weightage of the superposed beams. We validated our experimental results in close agreement with the theoretical results.

We report on an imaging-inspired measurement of orbital angular momentum (OAM) using only a simple tilted lens and an Intensified Charged Coupled Device (ICCD) camera, allowing us to monitor the propagation of OAM structured photons over distance, crucial for free-space quantum communication networks. We demonstrate measurement of OAM orders as high as 14 in a heralded single-photon source (HSPS) and show, for the first time, the imaged self-interference of photons carrying OAM in a modified Mach-Zehnder Interferometer (MZI). The described methods reveal both the charge and order of a photons OAM, and provide a proof of concept for the interference of a single OAM photon with itself. Using these tools, we are able to study the propagation characteristics of OAM photons over distance, important for estimating transport in free-space quantum links. By translating these classical tools into the quantum domain, we offer a robust and direct approach for the complete characterization of a twisted single-photon source, an important building block of a quantum network.