Photons rarely interact—which makes it challenging to build all-optical devices in which one light signal controls another. Even in nonlinear optical media, in which two beams can interact because of their influence on the medium’s refractive index, this interaction is weak at low light levels. Here, we propose a novel approach to realizing strong nonlinear interactions at the single-photon level, by exploiting the strong coupling between individual optical emitters and propagating surface plasmons confined to a conducting nanowire. We show that this system can act as a nonlinear two-photon switch for incident photons propagating along the nanowire, which can be coherently controlled using conventional quantum-optical techniques. Furthermore, we discuss how the interaction can be tailored to create a single-photon transistor, where the presence (or absence) of a single incident photon in a ‘gate’ field is sufficient to allow (or prevent) the propagation of subsequent ‘signal’ photons along the wire.

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A single-photon transistor using nanoscale surface plasmons

Multiphoton interference reveals strictly nonclassical phenomena. Its applications range from fundamental tests of quantum mechanics to photonic quantum information processing, where a significant fraction of key experiments achieved so far comes from multiphoton state manipulation. The progress, both theoretical and experimental, of this rapidly advancing research is reviewed. The emphasis is given to the creation of photonic entanglement of various forms, tests of the completeness of quantum mechanics (in particular, violations of local realism), quantum information protocols for quantum communication (e.g., quantum teleportation, entanglement purification, and quantum repeater), and quantum computation with linear optics. The scope of the review is limited to ``few-photon'' phenomena involving measurements of discrete observables.

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Multiphoton entanglement and interferometry

We present a wave-function approach to the study of the evolution of a small system when it is coupled to a large reservoir. Fluctuations and dissipation originate in this approach from quantum jumps that occur randomly during the time evolution of the system. This approach can be applied to a wide class of relaxation operators in the Markovian regime, and it is equivalent to the standard master-equation approach. For systems with a number of states N much larger than unity this Monte Carlo wave-function approach can be less expensive in terms of calculation time than the master-equation treatment. Indeed, a wave function involves only N components, whereas a density matrix is described by N2 terms. We evaluate the gain in computing time that may be expected from such a formalism, and we discuss its applicability to several examples, with particular emphasis on a quantum description of laser cooling.

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Monte Carlo wave-function method in quantum optics

The study of open quantum systems – microscopic systems exhibiting quantum coherence that are coupled to their environment – has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physic...

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Quantum trajectories and open many-body quantum systems

A dressed-atom approach to resonance fluorescence in intense laser fields is presented. Simple and general results are derived which include the now well known predictions concerning two-level atoms but are not restricted to such simple cases. The positions of the various components of the fluorescence and absorption spectra are given by the allowed Bohr frequencies of the total system: atom+laser mode (dressed atom). The master equation, describing spontaneous emission from the dressed atom is solved in the limit of high intensities. Simple expressions, taking into account the effect of cascades, are derived for the widths of the components.

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Dressed-atom description of resonance fluorescence and absorption spectra of a multi-level atom in an intense laser beam

A fully quantum-mechanical treatment of resonant light scattering is presented. The incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation. Complete solutions are obtained for the correlated atom-field pure state vector, including multiphoton contributions of arbitrary order. The frequency spectrum of the scattered field is evaluated and is found to agree exactly with the result previously obtained by means of the quantum fluctuation-regression theorem. A derivation of the fluctuation-regression theorem and of the optical Bloch equations is given which is fully quantum mechanical and which relies upon no assumption of statistical factorization of atom and field states. The accuracy of the result found for the scattered - field spectrum is thus shown to be limited only by the assumption of the smallness of the saturated linewidth compared to the (optical) atomic resonance frequency. The one-photon approximation is analyzed in some detail. The method of adding an imaginary term to the upper-atomic-state energy is clarified, and it is shown how the vacuum and one-photon amplitudes thereby obtained may be used, within a simple and plausible iteration scheme, to construct the complete multiphoton spectrum. A variety of commonly used injection schemes and methods of representing atomic relaxation are discussed, and comparisons are made with results found by other authors. The entire analysis is performed with the aid of a canonical transformation which replaces the applied field by a $c$ number. It is thus proved quite rigorously and generally that the use of a $c$-number applied field is a fully quantum-mechanical procedure, provided only that radiation-reaction terms are retained.

Pure-state analysis of resonant light scattering: Radiative damping, saturation, and multiphoton effects

Correlation effects in parametric photon-pair production are studied within the framework of a physically realistic model. The analysis, which is fully quantum mechanical, takes into account the finite sizes of the target and the beam cross section, and allows for dispersion and anisotropy in the linear susceptibility. The correlations in position and time at which the two members of a parametrically generated pair may be detected are carefully evaluated. These correlations, which have been measured experimentally, are intrinsically quantum mechanical; i.e., they can be explained by no theory in which the subharmonic fields are described purely by $c$-number functions. A complete solution, from which field correlation functions of arbitrarily high order may be evaluated, is obtained by a method which at the same time allows for an arbitrary degree of parametric gain. The solution is expressed entirely in terms of a particular two-point field-correlation-function, as evaluated in lowest order in the incident field strength, at points distant from the target. The function in question is found by directly examining the fluctuating currents in the material medium, rather than by eliminating the matter variables at the outset through the introduction of a nonlinear electomagnetic susceptibility.

Photon Correlations in the Parametric Frequency Splitting of Light

The power spectrum of the radiation emitted by a driven collision-damped two-level system is evaluated. The driving field, which is treated classically, is assumed to oscillate harmonically near the atomic resonance frequency, and its intensity is allowed to assume arbitrary values. The collisions are assumed to be strong, i.e., to instantaneously thermalize the state of the atom. The limiting forms of the power spectrum of the radiated field are discussed for the cases of low and high excitation of the atomic system.

B. R. Mollow

Papers

Pure-state analysis of resonant light scattering: Radiative damping, saturation, and multiphoton effects

Photon Correlations in the Parametric Frequency Splitting of Light

Resonant Scattering of Radiation from Collision-Damped Two-Level Systems