text: As in nonlinear optics, four-wave mixing occurs in these substances, because the Hamiltonian of their wavefunctions includes a term for the wavefunction amplitude squared, times the wavefunction.
full_question: As in nonlinear optics, four-wave mixing occurs in these substances, because the Hamiltonian of their wavefunctions includes a term for the wavefunction amplitude squared, times the wavefunction. The critical density for these substances includes a constant factor of the zeta function of three-halves. The expected particle number is proportional to the exponential of non-dimensionalized energy, minus one, in these substances. They form if the de Broglie thermal wavelength becomes larger than the interatomic distance. NIST first produced one using rubidium atoms. For 10 points, name these collections of integer-spin particles that collapse into a single quantum state at very low temperatures, the so-called "fifth state" of matter.
first_sentence: As in nonlinear optics, four-wave mixing occurs in these substances, because the Hamiltonian of their wavefunctions includes a term for the wavefunction amplitude squared, times the wavefunction.
raw_answer: Bose-Einstein condensates [or BE condensates; or BECs]