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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Can self-focusing of intense photon beams cause Bose-Einstein condensation into a superfluid state?

Friedwardt Winterberg

Published Apr 1, 1990• 0 citations
Publisher

Abstract

The cause of the phenomenon of self-focusing of intense laser beams is the nonlinear intensity dependent refractive index of optical materials. This property which leads to the self-focusing can be interpreted as an attractive force in between the photons thereby increasing the photon density. For large enough densities the photon gas may undergo Bose-Einstein condensation and if the attractive force is strong enough may even become a superfluid through a second order phase transition. This mechanism not possible for free photons is possible inside optical materials with a large refractive index because there the photons can be viewed as massive quasiparticles having a velocity less than the velocity of light. With the large dielectric constants of certain ferroelectric substances valid in the range of microwave frequencies the envisioned process might even work with microwave photons. This would make possible the generation of very intense highly coherent microwave beams. I .

DOI
10.1117/12.18568

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The cause of the phenomenon of self-focusing of intense laser beams is the nonlinear intensity dependent refractive index of optical materials. This property which leads to the self-focusing can be interpreted as an attractive force in between the photons thereby increasing the photon density. For large enough densities the photon gas may undergo Bose-Einstein condensation and if the attractive force is strong enough may even become a superfluid through a second order phase transition. This mechanism not possible for free photons is possible inside optical materials with a large refractive index because there the photons can be viewed as massive quasiparticles having a velocity less than the velocity of light. With the large dielectric constants of certain ferroelectric substances valid in the range of microwave frequencies the envisioned process might even work with microwave photons. This would make possible the generation of very intense highly coherent microwave beams. I .
For a nonlinear optical material with the adequate dependence of the refractive index with light intensity, a condensation phenomenon takes place for a laser beam. This process can be interpreted as a phase transition from a photon gas to a liquid of light. The physical properties of the resulting state, like surface tension, are similar to those of quantum liquids. Here we report a numerical exploration of the dynamics of these light condensates. We show that, as in the case of superfluids, eternal whirpools can be generated in light droplets. We also stress the deep connections and analogies between this new state of matter and Bose-Einstein condensates. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Summary form only given. Bose-Einstein condensed atomic gases are a new class of quantum fluids with many novel properties. We have studied collective modes and dissipation by perturbing the condensate with focused laser beams. The scattering of photons imparts momentum to the condensate and creates excitations. Consequently, the coherence and collective behavior of the condensate can strongly affect optical properties. We used light scattering to demonstrate that the coherence length of a condensate is equal to its physical size, and obtained dramatic evidence for the presence of correlated momentum excitations in the many-body condensate wavefunction. At higher laser intensity, a new form of superradiance was found which provided a gain mechanism for the generation of directed beams of atoms and light. This process amplified matter waves in a phase coherent way.
Starting from the first principles of nonrelativistic QED we have derived the system of Maxwell-Schrödinger equations, which can be used for theoretical description of atom optical phenomena at high densities of atoms and high intensities of the laser radiation. The role of multiple atomic transitions between ground and excited states in atom optics has been investigated. Nonlinear optical properties of interacting Bose gas are studied: formula for the refractive index has been derived and the polariton spectrum of a condensate interacting with an intense laser field has been investigated.
We study the thermodynamic properties of coherent photons in self-focusing nonlinear waveguides. The equation of the superfluid state of photons has been derived. There is a transition temperature [Formula: see text], above which the photon gas is in the coherent state, but below which the photon gas is in the superfluid state. At [Formula: see text], the photon system undergoes a first-order phase transition from the coherent to the superfluid state. To determine the fugacity [Formula: see text] and the transition temperature [Formula: see text] of the photon gas, we numerically solve the equation of the superfluid state of photons. The fugacity [Formula: see text] is a monotonically decreasing function of temperature [Formula: see text] and light intensity [Formula: see text]. The transition temperature [Formula: see text] is a monotonically decreasing function of light intensity [Formula: see text].
We study dynamical phases of a driven Bose-Einstein condensate coupled to the light field of a high-Q optical cavity. For high field seeking atoms at red detuning the system is known to show a transition from a spatially homogeneous steady state to a self-ordered regular lattice exhibiting superradiant scattering into the cavity. For blue atom pump detuning the particles are repelled from the maxima of the light-induced optical potential suppressing scattering. We show that this generates a new dynamical instability of the self-ordered phase, leading to the appearance of self-ordered stable limit cycles characterized by large amplitude self-sustained oscillations of both the condensate density and cavity field. The limit cycles evolve into chaotic behavior by period doubling. Large amplitude oscillations of the condensate are accompanied by phase slippage through soliton nucleation at a rate that increases in the chaotic regime. Different from a superfluid in a closed setup, this driven dissipative superfluid is not destroyed by the proliferation of solitons since kinetic energy is removed through cavity losses.
A scheme of an intense coherent gamma-ray source based on the spontaneous radiation of positronium atoms in a Bose-Einstein condensate (BEC) due to two-photon collective annihilation decay is investigated analytically arising from the second quantized formalism. It is shown that because of the intrinsic instability of annihilation decay of BEC, the spontaneously emitted entangled photon pairs are amplified, leading to an exponential buildup of a macroscopic population into end-fire modes at a certain shape of the elongated condensate. The considered scheme may also be applied to a BEC of atoms or quasiparticles as a laser mechanism with double coherence to create entangled photonic beams with a macroscopic number of photons.