Slow Group Velocity and Cherenkov Radiation

Abstract

We study theoretically the effect of ultraslow group velocities on the emission of Vavilov-Cherenkov radiation in a coherently driven medium. We show that in this case the aperture of the group cone on which the intensity of the radiation peaks is much smaller than that of the usual wave cone associated with the Cherenkov coherence condition. As a specific example, we consider a coherently driven ultracold atomic gas where such singular behavior may be observed.

Quantum Čerenkov Radiation: Spectral Cutoffs and the Role of Spin and Orbital Angular Momentum

“…Namely, it can also occur for classical charge distributions having a well-defined spread angle θ i , as well as in analogs of the Čerenkov effect in other areas of physics (for example, see Refs. [13,14]; similar conditions could be designed in other systems analogous to ČR [8][9][10][11][12][13][14][15][16][17][18][19]21,22]). In either case, the cone splitting we show here is uniquely tied to the shape of the incoming electron wave packet (or the charge distribution in a classical electron beam), and it is independent of material properties that can cause other kinds of cone splittings [50].…”

“…Because of the fundamental nature of ČR, it is found in many different physical systems, such as in nonlinear optics [8][9][10][11], it is used in the design of quantum cascade lasers [12], and it is predicted to yield the generation of entangled photon pairs [13,14]. Other kinds of ČR were found in photonic crystals [15,16], tunable light sources [17], coherently driven ultracold atomic gas [18], and recently even in active gain medium [19]. Many more novel ČR effects are still being found in new settings, such as surface polaritons [20] and metamaterials [21], where recent findings suggest revolutionizing Čerenkov detectors [22].…”

The C̆erenkov Effect Revisited: From Swimming Ducks to Zero Modes in Gravitational Analogues

“…Its aperture φ depends on the group velocity of light v gr as sin φ = v gr /v. The distinction between the phase and group cones has been anticipated in [18] to be most striking in the case of ultra-slow light media where v gr is reduced to the m/s range while v ph remains of the order of the speed of light in vacuo c 0 ≃ 3 · 10 8 m/s [33].…”

Bogoliubov-Čerenkov Radiation in a Bose-Einstein Condensate Flowing against an Obstacle

“…Electromagnetic waves in a nondispersive medium of refractive index n have a linear dispersion law relation ω em (k) = ck/n: theCerenkov condition is then satisfied on a conical surface in k-space of aperture cos φ = c/(nv), which corresponds to a conical wavefront of aperture θ = π/2 − φ behind the particle. Thanks to the interplay of interference and propagation, much richer features appear in the spatial and k-space pattern ofCerenkov radiation in dispersive media [3,4] and photonic crystals [5].The concept ofCerenkov radiation can be generalized to any system where a source is uniformly moving through a homogeneous medium at a speed larger than the phase velocity of some elementary excitation to which the source couples. Many systems have been investigated in this perspective, ranging from e.m. waves emitted by the localized nonlinear polarization induced by a strong light pulse travelling in a nonlinear medium [6,7], to the sonic waves generated by an airplane moving at supersonic velocities, to phonons in a polaritonic superfluid [8], and in a broader sense, to the surface waves emitted by a boat moving on the quiet surface of a lake [9].…”