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Introduction
Published in David N. Klyshko, Yuri Sviridov, Photons and Nonlinear Optics, 2018
David N. Klyshko, Yuri Sviridov
As the frequency of the signal ω1 approaches the pump frequency ω3, the idler frequency ω2 approaches the natural frequencies of the crystal lattice ωμ, which lie within the range from 102 to 103 cm−1. In this process, parametric scattering continuously develops into scattering by polaritons (SP), while, in the case of an exact coincidence of ω2 with one of the frequencies ωμ, it changes into Raman scattering (RS) by optical phonons. A polariton is a quantum of mixed electromagnetic and mechanical waves that arises in ionic crystals when infrared light is incident upon them. Mixed excitations in the region of electronic frequencies are also often called “polaritons.” The electric field of a light wave with ω ~ ωμ causes the charged ions of the lattice to oscillate and thus irradiate light. As a result, the group velocity of the wave u drops sharply (almost to zero at an exact resonance), while its phase velocity becomes a nonmonotonic function of the frequency (the so-called anomalous dispersion). The functions u(ω) = dω/dk and n(ω) = kc/ω are unambiguously associated with the law of polariton dispersion, i.e., the dependence ω(k) (Figure 1.7). Under the law of the conservation of momentum during scattering, the link ω2(k2) determines the observed tuning curve ω1(θ1) by trigonometric formulas.
Nonlinear Dynamics in Quantum Photonic Structures
Published in Joachim Piprek, Handbook of Optoelectronic Device Modeling and Simulation, 2017
Gabriela Slavcheva, Mirella Koleva
Quantum coherent control represents a universal approach for predictable manipulation of the properties of quantum systems, such as atoms and molecules. This technique has most recently been applied to QD solid-state systems. Coherent control in semiconductor nanostructures allows for coherent manipulation of the carrier wavefunctions on a time scale shorter than typical dephasing times. This is a prerequisite for successful implementation of ultrafast optical switching and quantum information processing. Quantum coherent control requires use of ultrashort pulses considerably shorter than the characteristic relaxation times in matter (τ≪T1,T2). This is equivalent to the photon-dipole coupling rate exceeding all dissipative rates in the system, a general condition for achieving the strong-coupling regime. The ultrashort pulses are usually characterized by high field amplitudes and, consequently, lead to nonlinear optical effects, such as coherent pulse propagation and self-induced transparency (SIT) [17]. The phenomenon of SIT is observable above a critical power threshold for a given pulse width: a high-intensity, ultrashort pulse propagating through a medium composed of an ensemble of resonant quantum two-level absorbers, whose relaxation times greatly exceed the pulse duration, travels at a reduced speed and unchanged shape with anomalously low energy loss. The absorbers are driven into the excited state by absorbing ultrashort pulse energy; by reradiating this energy into the pulse, they return to the ground state. Thus, the optical energy is carried through the medium not by the electromagnetic field, but by a coupled light-matter polariton wave. The polariton is a mixed light-matter quasiparticle resulting from the strong coupling of the optical wave to the medium's polarization. As a result, the pulse travels as a solitary wave, known as a SIT-soliton. This soliton is localized both in space and time, in contrast with the well-known nonlinear optics solitons which result from the interplay between nonlinearity and the medium's dispersion and/or diffraction. The condition of SIT is predicted by the remarkable pulse-area theorem (PAT) [18] which establishes a general criterion for stable, ultrashort pulse propagation in attenuating or amplifying media based on an integral quantity—namely, the pulse area. This phenomenon can be preserved to a great extent in solid-state systems—e.g., semiconductors—and has been experimentally demonstrated by picosecond pulse propagation in QD waveguides [19].
Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers
Published in Journal of Modern Optics, 2018
Robert A. Nyman, Benjamin T. Walker
There is a large community working with light and solid-state matter which are strongly-coupled, in the cavity QED sense that the coherent coupling is faster than incoherent mechanisms like spontaneous emission or cavity loss, using microcavities. Strongly coupled light-matter systems are known as polaritons. Typically the light interacts with a quasiparticle made of a bound electron and hole pair known as an exciton, making an exciton–polariton. In near-planar microcavities, sufficient pump power leads polariton condensation [10]. Condensation is considered distinct from lasing in that the excitons interact with each other substantially (see Ref. [11], p. 362), approaching thermal equilibrium, even if imperfectly. The excitons associated with the condensed polaritons can be free to move (Wannier excitons, typical of inorganic semiconductors [12]) or bound to individual sites (Frenkel excitons, typical of organic fluorescent solids [13,14]). By contrast, thermalization and BEC of photons as described above is performed in the weak-coupling limit, and with liquid-state matter.
Implications of causality for quantum biology – I: topology change
Published in Molecular Physics, 2018
A discussion of ‘causality’ needed to develop CQB begins by analysing the propagation of signals limited to a finite maximum speed of light. Signalling processes involving electromagnetic radiation, naturally, have lower maximum speeds whenever the signal interacts with the quantum environment. The actual speed can be lower amounting to an introduction of an index of refraction. Other signalling processes involve coherent structures such as acoustic and transverse molecular vibration waves. Limiting the speed of excitations is the breakup of the quasiparticle excitations mediated by nonlinear processes, generally into pair-excitation modes, some of which may lead to other types of excitations. Of course, describing the physics of quasiparticle excitations in picture is only a convenience. There are more fundamental limits. For instance, in electrodynamics, one uses just the electron and photons where the maximum speed is the speed of light in vacuum c. In a solid, the interaction of an electromagnetic wave and bound electronic polarisations (excitons – electron-hole pairs) leads to a quasiparticle called an exciton-polariton. Coupling to the phonon field gives a phonon-polariton. In solids or liquids, the interaction of longitudinal and transverse sound leads to a separation of the excitation energy curves E(k) vs. k into an optical and a longitudinal branch near k = 0: the optical branch has a small speed for long wavelength, much smaller than that of the acoustic branch. The physics described in this range of small k-values is often large shear displacements such as shear waves in liquid metals found in the interior of the planet. The distinction has been useful in seismology where the acoustic waves are called p-waves and the transverse waves called s-waves. The analogue for waves propagating down a helical or coiled biomolecule is clear. These modes easily couple to the ambient acoustical and transverse modes of the ambient liquid surrounding the biomolecule. For shorter wavelengths, the optical branch asymptotes to a line E(k) = cmk whereas the acoustic branch asymptotes to a line parallel to the k-axis E(k) = const. The point is the conceptual framework of quasiparticles described using a formulation consistent with special relativity [24, Ch.1] for an asymptotic cm applies to the energetics of these slower processes as well to the more fundamental processes of quantum electrodynamics, even when the modes interact.