The statistical description of optical fields in classical coherence theory is the foundation for many applications in metrology, microscopy, lithography and astronomy. Partial coherence is commonly attributed to underlying fluctuations originating at the source or arising upon passage through a random medium. A less acknowledged source of uncertainty (partial coherence) stems from the act of ignoring a degree of freedom of a beam when observing another degree of freedom coupled to (or classically entangled with) it. We demonstrate here that Bell’s measure, which is commonly used in tests of quantum non-locality, may be used as a quantitative tool in classical optical coherence to delineate native incoherence associated with statistical fluctuations from correlation- (or, entanglement-) based incoherence. Our results demonstrate the applicability of the concepts recently developed in quantum information science to classical optical coherence theory and optical signal processing
The two-point coherence of an electromagnetic field is represented completely by a 4×4 coherency matrix G that encodes the joint polarization-spatial-field correlations. Here, we describe a systematic sequence of cascaded spatial and polarization projective measurements that are sufficient to tomographically reconstruct G--a task that, to the best of our knowledge, has not yet been realized. Our approach benefits from the correspondence between this reconstruction problem in classical optics and that of quantum state tomography for two-photon states in quantum optics. Identifying G uniquely determines all the measurable correlation characteristics of the field and, thus, lifts ambiguities that arise from reliance on traditional scalar descriptors, especially when the field's degrees of freedom are correlated or classically entangled.
The information-carrying capacity of a single photon can be vastly expanded by exploiting its multiple degrees of freedom: spatial, temporal, and polarization. Although multiple qubits can be encoded per photon, to date only two-qubit single-photon quantum operations have been realized. Here, we report an experimental demonstration of three-qubit single-photon, linear, deterministic quantum gates that exploit photon polarization and the two-dimensional spatial-parity-symmetry of the transverse single-photon field. These gates are implemented using a polarization-sensitive spatial light modulator that provides a robust, non-interferometric, versatile platform for implementing controlled unitary gates. Polarization here represents the control qubit for either separable or entangling unitary operations on the two spatial-parity target qubits. Such gates help generate maximally entangled three-qubit Greenberger–Horne–Zeilinger and W states, which is confirmed by tomographical reconstruction of single-photon density matrices. This strategy provides access to a wide range of three-qubit states and operations for use in few-qubit quantum information processing protocols.
The coherence of an optical beam having multiple degrees of freedom (DoFs) is described by a coherency matrix G spanning these DoFs. This optical coherency matrix has not been measured in its entirety to date—even in the simplest case of two binary DoFs where G is a 4 × 4 matrix. We establish a methodical yet versatile approach—optical coherency matrix tomography—for reconstructing G that exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Here G is reconstructed from a minimal set of linearly independent measurements, each a cascade of projective measurements for each DoF. We report the first experimental measurements of the 4 × 4 coherency matrix G associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young’s double slit to spatial parity and orbital angular momentum modes.
We study, theoretically and experimentally, electromagnetically induced transparency (EIT) in two different solid-state systems. Unlike many implementations in homogeneously broadened media, these systems exhibit inhomogeneous broadening of their optical and spin transitions typical of solidstate materials. We observe EIT lineshapes typical of atomic gases, including a crossover into the regime of Autler-Townes splitting, but with the substitution of the inhomogeneous widths for the homogeneous widths. We obtain quantitative agreement between experiment and theory for the width of the transparency feature over a range of optical powers and inhomogeneous linewidths. We discuss regimes over which analytical and numerical treatments capture the behavior. As solid-state systems become increasingly important for scalable and integratable quantum optical and photonic devices, it is vital to understand the effects of the inhomogeneous broadening that is ubiquitous in these systems. The treatment presented here can be applied to a variety of systems, as exemplified by the common scaling of experimental results from two different systems.
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