Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of
stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary selector vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a weighted readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.
Photonic circuits in which stateful components are coupled via guided electromagnetic fields are natural candidates for native implementation of iterative stochastic algorithms based on propagation of information around a graph. Conversely, such mess
age passing algorithms suggest novel circuit architectures for signal processing and computation that are well matched to nanophotonic device physics. Here we construct and analyze a quantum optical model of a photonic circuit for iterative decoding of a class of low-density parity-check (LDPC) codes called expander codes. Our circuit can be understood as an open quantum system whose autonomous dynamics map straightforwardly onto the subroutines of an LDPC decoding scheme, with several attractive features: it can operate in the ultra-low power regime of photonics in which quantum fluctuations become significant, is robust to noise and component imperfections, achieves comparable performance to known iterative algorithms for this class of codes, and provides an instructive example of how nanophotonic cavity quantum electrodynamic components can enable useful new information technology even if the solid-state qubits on which they are based are heavily dephased and cannot support large-scale entanglement.
Quantum error correction provides a fertile context for exploring the interplay of feedback control, microscopic physics and noncommutative probability. In this paper we deepen our understanding of this nexus through high-level analysis of a class of
quantum memory models that we have previously proposed, which implement continuous-ti
Contemporary experiments in cavity quantum electrodynamics (cavity QED) with gas-phase neutral atoms rely increasingly on laser cooling and optical, magneto-optical or magnetostatic trapping methods to provide atomic localization with sub-micron unce
rtainty. Difficult to achieve in free space, this goal is further frustrated by atom-surface interactions if the desired atomic placement approaches within several hundred nanometers of a solid surface, as can be the case in setups incorporating monolithic dielectric optical resonators such as microspheres, microtoroids, microdisks or photonic crystal defect cavities. Typically in such scenarios, the smallest atom-surface separation at which the van der Waals interaction can be neglected is taken to be the optimal localization point for associated trapping schemes, but this sort of conservative strategy generally compromises the achievable cavity QED coupling strength. Here we suggest a new approach to the design of optical dipole traps for atom confinement near surfaces that exploits strong surface interactions, rather than avoiding them, and present the results of a numerical study based on $^{39}$K atoms and indium tin oxide (ITO). Our theoretical framework points to the possibility of utilizing nanopatterning methods to engineer novel modifications of atom-surface interactions.
Our 2005 Physical Review Letter entitled Suppression of Spin-Projection Noise in Broadband Atomic Magnetometry (volume 94, 203002) relied heavily in its claims of experimental quantum-limited performance on the results of a prior publication from our
group [1]. In subsequent work we have determined that the results of [1] were incorrect and must therefore retract this Physical Review Letter as well. The authors would like to emphasize that the broadband magnetometry approach taken in our work remains valid, as described in the theoretical paper [2], but we have lost confidence in the calibration procedures employed at the time to establish sensitivity relative to the spin-projection noise level. [1] JM Geremia, John K. Stockton and Hideo Mabuchi, Real-Time Quantum Feedback Control of Atomic Spin-Squeezing, Science 304, 270, (2004). [2] John K. Stockton, JM Geremia, Andrew C. Doherty and Hideo Mabuchi, Robust quantum parameter estimation: Coherent magnetometry with feedback, Phys. Rev. A 69, 032109, (2004).
We report high time-resolution measurements of photon statistics from pairs of dye molecules coupled by fluorescence resonance energy transfer (FRET). In addition to quantum-optical photon antibunching, we observe photon bunching on a timescale of se
veral nanoseconds. We show by numerical simulation that configuration fluctuations in the coupled fluorophore system could account for minor deviations of our data from predictions of basic Forster theory. With further characterization we believe that FRET photon statistics could provide a unique tool for studying DNA mechanics on timescales from 10^-9 to 10^-3 s.
