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In quantum optics, a superradiant phase transition is a phase transition that occurs in a collection of fluorescent emitters (such as atoms), between a state containing few electromagnetic excitations (as in the electromagnetic vacuum), and a superradiant state with many electromagnetic excitations trapped inside the emitters. The superradiant state is made thermodynamically favourable by having strong, coherent interactions between the emitters. The superradiant phase transition was originally predicted in so called Dicke model of superradiance when it is assumed that atoms have only two energetic levels and they are interacting only with one mode of the electromagnetic field . The phase transition occurs when the strength of the interaction between the atoms and the field is larger than the energy of the non-interacting part of the system which similarly to the case of superconductivity and ferromagnetism leads to the effective dynamical interactions between atoms of the ferromagnetic type and the spontaneous ordering of excitations below the critical temperature. It means that the collective Lamb shift in the system of atoms interacting with the vacuum fluctuations becomes comparable with the energies of atoms alone and the vacuum fluctuations cause the spontaneous self-excitation of matter. The transition can be readily understood with the use of Holstein-Primakoff transformation applied to two level atom. As the result of this transformation the atoms become the Lorentz harmonic oscillators with the frequency equal to the difference between the energy levels and the whole system becomes the system of the interacting harmonic oscillators of atoms and the field known as Hopfield dielectric which further predicts in the normal state polarons for photons or polaritons. If now the interaction with the field is so strong that the system collapses in the harmonic approximation and complex polariton frequencies (soft modes) appear then the physical system with nonlinear terms of the higher order becomes the system with the Mexican hat-like potential and will undergo ferroelectric-like phase transition. In this model the system is mathematically equivalent for one mode of excitation to the Trojan wave packet when the circularly polarized field intensity corresponds to the electromagnetic coupling constant and above the critical value it changes to the unstable motion of the ionization. The superradiant phase transition was the subject of a wide discussion if it is only a result of the simplified model of the matter-field interaction and if it can occur for the real physical parameters of physical systems (no-go theorem) . However both the original derivation and the later corrections leading to nonexistence of the transition due to Thomas–Reiche–Kuhn sum rule canceling for the harmonic oscillator the needed inequality to impossible negativity of the interaction were based on the assumption that the quantum field operators are commuting numbers and the atoms do not interact with the static Coulomb forces which generally is not true. It currently can be observed in model systems like Bose–Einstein condensates and artificial atoms . ==Theory== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「superradiant phase transition」の詳細全文を読む スポンサード リンク
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