Photon echoes using atomic frequency combs in Pr:YSO - experiment and semiclassical theory.

Photon echoes in rare-earth-doped crystals are studied to understand the challenges of making broadband quantum memories using the atomic frequency comb (AFC) protocol in systems with hyperfine structure. The hyperfine structure of Pr3+ poses an obstacle to this goal because frequencies associated with the hyperfine transitions change the simple picture of modulation at an externally imposed frequency. The current work focuses on the intermediate case where the hyperfine spacing is comparable to the comb spacing, a challenging regime that has recently been considered. Operating in this regime may facilitate storing quantum information over a larger spectral range in such systems. In this work, we prepare broadband AFCs using optical combs with tooth spacings ranging from 1 MHz to 16 MHz in fine steps, and measure transmission spectra and photon echoes for each. We predict the spectra and echoes theoretically using the optical combs as input to either a rate equation code or a density matrix code, which calculates the redistribution of populations. We then use the redistributed populations as input to a semiclassical theory using the frequency-dependent dielectric function. The two sets of predictions each give a good, but different account of the photon echoes.

Single-photon three-qubit quantum logic using spatial light modulators.

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.Photons are essential for quantum information processing, but to date only two-qubit single-photon operations have been realized. Here the authors demonstrate experimentally a three-qubit single-photon linear deterministic quantum gate by exploiting polarization along with spatial-parity symmetry.

Optical coherency matrix tomography.

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.

Two-point optical coherency matrix tomography.

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.