Recovery of polarization entanglement in partially coherent photonic qubits.

Partially coherent photonic qubits, owing to their robustness in propagation through random media compared to fully coherent qubits, find applications in free-space communication, quantum imaging, and quantum sensing. However, the reduction of spatial coherence degrades entanglement in qubits, adversely affecting entanglement-based applications. We report the recovery of entanglement in the partially coherent photonic qubits generated using a spontaneous parametric downconversion process despite retaining their multimode nature. This study utilizes an electron multiplying charge-coupled device (EMCCD) to perform coincidence measurements, eliminating the need for raster scanning of single-pixel detectors, which simplifies optical alignment, enhances precision, and reduces time consumption. We demonstrate that the size of apertures used to select biphotons substantially impacts the visibility and S-parameter of polarization-entangled partially coherent qubits. The entanglement is recovered with partial spatial coherence properties by choosing small sizes of the apertures in the captured image plane. This study could help in the advancement of free-space quantum communication, quantum imaging, and quantum metrology.

Phase encoded quantum key distribution up to 380 km in standard telecom grade fiber enabled by baseline error optimization.

Phase encoding in quantum key distribution (QKD) enables long-distance information-theoretic secure communication in optical fibers. We present a novel theoretical model characterizing errors from various sources in practical phase encoding-based QKD systems, namely the laser linewidth, detector dark counts, and channel dispersion. This model provides optimized optical pulse parameters and less distortion in pulses, which eliminates system imperfections and leads to a reduced quantum bit error rate (QBER) for practical QKD scenario. This analysis is applicable to various fiber-based phase and time encoding protocols. In particular, we implement this to a differential phase shift (DPS) QKD scheme operating at a 2.5 GHz clock, which produces a secure key rate of 193 bits/s at a fiber length of 265 km and an unprecedented QBER < 1[Formula: see text] up to 225 km length with standard telecom components. We show that by adjusting the quantum efficiency and dark count rates of detectors, proposed system can establish secure keys up to 380 km distance using standard telecom grade fiber with a QBER of 1.48%. Moreover, the system is compatible with existing optical fiber networks and capable of establishing a secure key exchange between two cities 432 km apart using ultra-low-loss (ULL) specialty fiber.

Generation of cross-spectrally pure electromagnetic fields using a pair of moving diffusers.

In this paper, we demonstrate that the vector light field is cross-spectrally pure if it passes through two diffusers (having similar correlation properties) moving with identical linear speeds in opposite directions. To determine the spatio-temporal coherence function of cross-spectrally pure light, a double slit is placed just after the second diffuser. We show that the normalized space-time coherence Stokes parameters of emerging light can be described in the form of a reduction formula, whereas the absolute values of the normalized space-frequency coherence Stokes parameters are the same for every frequency component of the light field. These are the conditions of cross-spectral purity of Stokes parameters. We further prove that at zero time delay, the condition of strict cross-spectral purity is validated. Furthermore, we establish the conditions for cross-spectral purity for a vector light field passing through the aforesaid diffusers, when they rotate with identical angular speeds in opposite directions, offering a possibility to optimize the scheme using only a single diffuser. For the first time, to our knowledge, an additional condition for equality of the degree of cross-polarization in space-time and space-frequency domains for strict cross-spectrally pure light beams is also introduced.

Hong-Ou-Mandel interference of longitudinal spatially coherent beams.

The Hong-Ou-Mandel (HOM) interference of two light beams having different longitudinal spatial coherence properties is investigated theoretically and experimentally. The normalized second-order correlation function (g (2)) is determined for the interfering photons from two sources of different angular widths using Feynman's path integral theory. We find that the difference in angular width of the sources has an explicit impact on the HOM interference pattern, which can be quantified through the visibility and full width at half maxima of the HOM dip. The effect of distinguishability of the interfering longitudinally spatially coherent beams on the HOM dip is verified experimentally and is analogous to non-classical HOM interference. The magnitude of the angular width of beams manifested through the difference in angular width has a significant impact. Along with the difference of two sources, this HOM scheme is sensitive to the angular spectrum width of each source. The enhanced sensitivity can be useful in the remote sensing of objects and beams in metrological applications. This work can play a significant role in fundamental and applied physics.

Experimental investigation of degree of cross-polarization for an electromagnetic Gaussian-Schell model beam.

We investigate the properties of the degree of cross-polarization (DOCP) for an electromagnetic Gaussian-Schell model (EMGSM) beam in the radial direction of the cross section of the beam. The coherence and polarization features of a partially coherent light beam are engineered to construct the isotropic and non-isotropic EMGSM beams, and the resulting changes in the DOCP are examined. For experimental realization, a double-slit interferometer is utilized at the output to probe the coherence properties for different polarization components across the beam diameter of an electromagnetic source. Experimental observations infer that variation in DOCP does not become apparent for isotropic coherence widths in the orthogonal polarization directions, whereas the variation can be apparent only once both the coherence widths are distinct. Furthermore, experimentally, a special case is also investigated for which the value of DOCP goes beyond unity. The DOCP finds application in areas such as second-order intensity interference, imaging, and characterization of non-homogeneously polarized beams.

Investigation of partially coherent vector vortex beams with non-isotropic states of spatial correlation.

In this work, the far-field properties of non-isotropic partially coherent vector vortex beams (PCVVBs) are investigated both theoretically and experimentally. The term non-isotropic signifies that the spatial correlations between the parallel and orthogonal electric field components are distinguishable. It is found that self-orientation and shaping of intensity profile, correlation-induced polarization and depolarization are highly dependent on both the non-isotropic correlation parameters and Poincaré-Hopf index (PHI) of the beam. The simultaneous depolarization and polarization effects are due to the difference in the input correlation parameters that alter the state of polarization (SOP) and degree of polarization (DOP) distributions. The experimental results are in good agreement with the theoretical predictions. The distinguishability of correlation parameters at the source plane leads to significant changes on its intensity profile, DOP, and SOP distributions on far-field propagation, which may found potential applications in beam shaping, detecting and imaging atmospheric lidar, optical imaging and directional transportation where the self-rotation characteristic of beam plays an important role.

Statistical features of an electromagnetic Gaussian-Schell model beam propagating through a smoke aerosol environment.

In this paper, we investigate both theoretically and experimentally the statistical properties of an electromagnetic Gaussian-Schell model (EMGSM) beam propagating through polluted atmosphere specifically containing smoke aerosol medium. Experimentally, a glass chamber of 1 m length is constructed to mimic the smoky atmosphere inside the laboratory, in which incense sticks are used for smoke aerosol production inside the chamber in a time-controlled manner. An input EMGSM beam having a variable degree of coherence and degree of polarization (DOP) propagates through the aerosol medium, and its coherence and polarization features after propagation are probed. The results show that the coherence features of the vectorial beam are modified significantly by the smoke aerosol medium, while, for the given propagation length of 1 m, the polarization features remain unaffected. We also investigate the coherence features of the EMGSM beam through smoke aerosols in a particular condition when the DOP of the beam is kept zero. These results are expected to provide insights into atmospheric effects on free-space optical communication in real situations when the medium contains air pollution.

Cross-spectral purity of nonstationary vector fields in space-time and space-frequency domains.

We establish the concept of cross-spectral purity for nonstationary electromagnetic fields having any degree of coherence or polarization. The conditions of cross-spectral purity in all Stokes parameters are derived for both space-time and space-frequency domains, which demonstrate that the normalized two-point coherence properties of such fields can be expressed as products of a spatial and a time (or frequency) dependent function. We further determine the condition of strict cross-spectral purity for nonstationary fields, which establishes the equivalence of normalized two-point Stokes parameters governing the spatial factors of the space-frequency and space-time domains. This study may provide interesting aspects of statistical properties of beams obtained from practically available sources such as pulsed lasers, modulated and fluctuating light sources, etc.

Coherence-induced polarization effects in vector vortex beams.

We demonstrate theoretically and experimentally coherence-induced polarization changes in higher-order vector vortex beams (VVBs) with polarization singularity. The prominent depolarization on decreasing the transverse correlation width in a focused partially coherent VVB provides a means to shape the intensity profile and degree of polarization (DOP) while preserving the polarization distribution. The intensity variation and DOP dip are found to be dependent on the polarization singularity index of the beam. Our results may provide an additional degree of freedom in myriad applications presently projected with VVBs.

Investigation of longitudinal spatial coherence for electromagnetic optical fields.

For light fields, the coherence in longitudinal direction is governed by both the frequency spectra and angular spectra they possess. In this work, we develop and report a theoretical formulation to demonstrate the effect of the angular spectra of electromagnetic light fields in quantifying their longitudinal spatial coherence. The experimental results obtained by measuring the electromagnetic longitudinal spatial coherence and degree of cross-polarization of uniformly polarized light fields for different angular spectra validate the theoretical findings.

High production rate of single-photon and two-photon Fock states for quantum state engineering.

We report the implementation of a high-rate source of single- and two-photon states. By combining the advantages of short pulses and cavities, heralding rates as high as 200 kHz have been obtained for the single photons, as well as 250 Hz for the two-photon states. In this setup, homodyne measurements are conditioned by the heralding of the quantum states thanks to the introduction of a low-loss optical delay line in the heralded states path. This enables the detection of most of the heralded events, and fidelities reaching 68.5% (91% with correction for detection efficiency) and 50.4% (85% with correction) were obtained for the single- and two-photon states, respectively. Such high rates and fidelities in the generation of elementary Fock states may open the path for the production of complex quantum states.

Experimental observation of the polarization coherence theorem.

For light fields, the manifestation of correlations between fluctuating electric field components at different space-time points is referred to as coherence, whereas these correlations appearing between orthogonal electric field components at a single space-time point are referred to as polarization. In this context, a natural question is as follows: how are coherence and polarization interconnected? Very recently, a tight equality P2=V2+D2, namely, the "polarization coherence theorem" (PCT) connecting polarization P with interference visibility V (measure of coherence) and distinguishability D (measure of which-path information) has been proposed [Optica4, 1113 (2017)OPTIC82334-253610.1364/OPTICA.4.001113]. We here report a direct observation of the PCT for classical light fields using a Mach-Zehnder interferometer along with a synthesized source producing a complete gamut of degrees of polarizations. Our experimental demonstration could motivate ongoing experimental efforts toward probing the hidden coherences and complementarity features.

Experimental generation of squeezed cat States with an operation allowing iterative growth.

We present what is, to our knowledge, the first implementation of a "cat breeding" operation, which allows an iterative growth of cat states. We thus report the experimental generation of a squeezed cat state from two single photon Fock states, which can be seen as cat states with zero amplitude. These Fock states are mixed on a symmetrical beam splitter, and the generation is heralded by a homodyne measurement in one of the two output arms. The output state has a fidelity of 61% with an even squeezed cat state of amplitude α=1.63. This hybrid operation opens up new prospects in quantum optics, as the protocol depicted here can be iterated in order to produce new kinds of mesoscopic states.

Iterative tailoring of optical quantum states with homodyne measurements.

As they can travel long distances, free space optical quantum states are good candidates for carrying information in quantum information technology protocols. These states, however, are often complex to produce and require protocols whose success probability drops quickly with an increase of the mean photon number. Here we propose a new protocol for the generation and growth of arbitrary states, based on one by one coherent adjunctions of the simple state superposition α|0〉 + ß|1〉. Due to the nature of the protocol, which allows for the use of quantum memories, it can lead to high performances.

Experimental observation of invariance of spectral degree of coherence with change in bandwidth of light.

An experimental study is conducted to show the effect of the change in bandwidth of light on the spectral degree of coherence at a pair of points in the cross section of a beam. For this purpose a polychromatic source and a monochromator with variable entrance and exit slits were used to produce a variable bandwidth source. The classic Young's interferometer was used to produce an interference pattern. The spectral measurements of the visibility of the interference fringes show that the spectral degree of coherence remains unaffected by the change in the frequency passband of the light.

Experimental study of the relation between the degrees of coherence in space-time and space-frequency domain.

We present an experimental study showing the effect of the change in the bandwidth of light on the magnitude of both the complex degree of coherence and the spectral degree of coherence at a pair of points in the cross-section of a beam. A variable bandwidth source with a Young's interferometer is utilized to produce the interference fringes. We also report for the first time that if the field is quasi-monochromatic or sufficiently narrowband, the elements of both the beam coherence polarization matrix and the cross-spectral density matrix, normalized to intensities (spectral densities) at the two points possess identical values.

Direct determination of the generalized Stokes parameters from the usual Stokes parameters.

We report an experimental method to determine the generalized Stokes parameters for a pair of points in the cross section of an electromagnetic beam, e.g., an expanded laser beam, with the help of a Young's interferometer and a set of polarizers and quarter-wave plates. The method is investigated theoretically using the electromagnetic spectral interference law. The generalized Stokes parameters, owing to their two-point nature, determine the behavior of the single-point polarization properties of the electromagnetic beam at a field point. The present method offers a unique means to determine the two-point parameters (correlation functions) by measuring the usual Stokes parameters (intensities) and the contrast parameters (visibilities) of the beam. The method might be applicable to determine the polarization dependent changes in various optical measurements.

Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam.

We report an experimental method to determine the elements of the electric cross-spectral density matrix for laser light. For this purpose an additional setup consisting of mirrors and reflecting prisms is utilized with the conventional Young's interferometer to overcome existing experimental limitations. The generalized Stokes parameters, which are the characteristics of two spatial points of the electromagnetic field, are also obtained for a pair of points. The knowledge of these two quantities might be useful in determining the change in polarization properties of light in propagation and their effects in optical measurements.