Under the introduction of any interface in its trajectory, an optical beam experiences polarization-dependent deflections in the longitudinal and transverse directions with respect to the plane of incidence. The physics of such optical beam shifts is connected to profound universal wave phenomena governed by the fine interference effects of wave packets and has opened up avenues towards metrological applications. Here, we reveal the inherent non-separability of the longitudinal and transverse beam shifts by considering a rather simple case of a partially reflecting Gaussian laser beam from a dielectric interface. This non-separability appears substantially in some particular regions in the corresponding parameter space. We further show that such non-separability manifests as a position-position classically entangled state of light. The tunability of the related experimental parameters offers control over the degree of entanglement. Uncovering of the inherent non-separability of the two types of beam shifts is expected to enrich the physical origin of this fundamental effect, impact the understanding of numerous analogous effects, and might find useful applications by exploiting the position-position-polarization classical entanglement in a fundamental Gaussian beam.
Under the introduction of any interface in its trajectory, an optical beam experiences polarization-dependent deflections in the longitudinal and transverse directions with respect to the plane of incidence. The physics of such optical beam shifts is connected to profound universal wave phenomena governed by the fine interference effects of wave packets and has opened up avenues towards metrological applications. Here, we reveal the inherent non-separability of the longitudinal and transverse beam shifts by considering a rather simple case of a partially reflecting Gaussian laser beam from a dielectric interface. This non-separability appears substantially in some particular regions in the corresponding parameter space. We further show that such non-separability manifests as a position-position classically entangled state of light. The tunability of the related experimental parameters offers control over the degree of entanglement. Uncovering of the inherent non-separability of the two types of beam shifts is expected to enrich the physical origin of this fundamental effect, impact the understanding of numerous analogous effects, and might find useful applications by exploiting the position-position-polarization classical entanglement in a fundamental Gaussian beam.
Abstract Under the introduction of any tilted interface in its trajectory, an optical beam experiences polarization‐dependent deflections in the longitudinal and transverse directions with respect to the plane of incidence. The physics of such optical beam shifts are connected to profound universal wave phenomena governed by the fine interference effects of wave packets and have opened up avenues toward metrological applications. Here, the inherent non‐separability of the longitudinal and transverse optical beam shifts is revealed by considering a rather simple case of a partially reflecting Gaussian laser beam from a dielectric interface. This non‐separability appears substantially at some particular regions in the corresponding experimental parameter space. This manifests as a position–position non‐separable state of classical light field. The tunability of the related experimental parameters offers control over the degree of non‐separability. These findings are expected to be a step forward in the exploration of optical beam shifts and a number of analogous universal phenomena. The initial observation also indicates its practical impact on metrology and generation of high‐quality tunable position–position non‐separable states of classical light fields.
Classically entangled light is used to refer to a class of structured beams with space-polarization, polarization-time, and space-time non-separable states akin to entangled states, which enable novel quantum-analog methods and applications in structured light. Here, we argue that classical entanglement is also available for pure scalar beams with multiple non-separable spatial degrees of freedom (DoFs). We theoretically and experimentally demonstrate a class of scalar ray-wave structured light with multiple controllable local DoFs to emulate multipartite entangled states, including the Greenberger-Horne-Zeilinger states. Our work unveils a rich parameter space for high-dimensional and multi-DoF control of structured light to extend applications in classical-quantum regimes.
Quantum weak measurements became extremely popular in classical optics to amplify small optical signals for fundamental interests and potential applications. Later, a more general extension, joint weak measurement has been proposed to extract weak value from a joint quantum measurement. However, the detection of joint weak value in the realm of classical optics remains less explored. Here, using the polarization-dependent longitudinal and transverse optical beam shift as a platform, we experimentally realize the quantum joint weak measurement in a classical optical setting. Polarization states are cleverly pre and post-selected, and different single and joint canonical position-momentum observables of the beam are experimentally extracted and subsequently analyzed for successful detection of complex joint weak value. We envision that this work will find usefulness for gaining fundamental insights on quantum measurements and to tackle analogous problems in optics.
Quantum weak measurements became extremely popular in classical optics to amplify small optical signals for fundamental interests and potential applications. Later, as a more general extension, joint weak measurement has been proposed to extract the weak value from a joint quantum measurement. However, unlike traditional weak measurements, the detection of a joint weak value in the realm of classical optics remains less explored. Here, using the polarization-dependent longitudinal and transverse optical beam shift as a platform, we experimentally realize a classical optical analog of the quantum joint weak measurement. Polarization states are cleverly pre- and postselected, and different single and joint canonical position-momentum observables of the beam are experimentally extracted and subsequently analyzed for successful detection of the complex joint weak value. We envision that this work will find usefulness for gaining fundamental insights on quantum measurements and to tackle analogous problems in optics.
Classical entanglement refers to non-separable correlations between the polarization direction and the polarization amplitude of a light field. The degree of entanglement is quantified by the Schmidt number, taking the value of unity for a separable state and two for a maximally entangled state. We propose two detection methods to determine this number based on the distinguishable patterns of interference between four light sources derived from the unknown laser beam to be detected. The second method, being a modification of the first one, has interference fringes with discernable angles uniquely related to the entangled state. The maximally entangled state corresponds to fringes symmetric about the diagonal axis at either a 45° or a 135° direction, while the separable state corresponds to fringes symmetric about either the X or Y axis, or both simultaneously. States with Schmidt number between unity and two have fringes of symmetric angles between these two extremes. We believe these detection methods would be beneficial in both computation and communications applications of the classically entangled states.
The insights offered by quantum mechanics to the field of optical metrology are many-fold, with non-classical states of light themselves used to make sensors that surpass the sensitivity of sensors using classical states of light. Unfortunately, this advantage, referred to often as "super-sensitivity" is notoriously fragile, and even the slightest experimental imperfections may greatly reduce the efficacy of the non-classical sensors, sometimes completely obviating their advantage. In my thesis I have shown that the performance of an otherwise ideal two-photon interferometer, which exploits entanglement between photons to make super-sensitive measurements of phase, is crippled by the slightest introduction of decoherence between modes of the interferometer. I have shown further that such drastic reduction in sensitivity can also appear in classical measurement problems, specifically that the recently developed methods of estimating the separation between a pair of point sources are rendered less effective when the ideal assumption of complete spatial incoherence is relaxed. Towards overcoming these and other issues, I have designed new configurations that use ancillary optical degrees of freedom, a tool-set that has recently garnered much interest in the field of quantum optics. In the context of two-photon interferometry, I have shown that by coupling polarization to the spatial-structure of the two photon state used to probe phase it is possible to obviate the need for a reference phase, even in the context of decoherence and imperfections in the interferometer. In the context of two-point resolution, I have developed an anisotropic imaging system that performs the function of an image-inversion interferometer and is inherently stable, offering an attractive implementation of recently developed methods of sub-Rayleigh imaging. I have further shown both theoretically and experimentally that the same anisotropic image-inversion interferometer is useful in measuring spatially encoded phases, both in the context of classical illumination as well as quantum-aided two-photon super-sensing. In both cases, the ability to perform interferometric measurements of the spatial structure of an electric field without splitting beam paths forms a bridge between conception and implementation of precision-sensing measurement strategies. Finally, I have shown that binary interferometric method based on the common-path anisotropic imaging system that I introduced, are able to measure both phase gradients and transverse beam tilts with a sensitivity beating conventional systems that are used both commercially and in research laboratories.