Statistical Properties Of A Kerr Nonlinear Blackbody

The characteristics of quantum field have attracted much attention in the area ofquantum optics. The statistical properties of radiation thermal field in a Kerr nonlinearblackbody have been investigated, and some significative and new results have obtained.There are five parts in this thesis.First, the photon field in a Kerr-nonlinear blackbody is in an amplitude-squaredsqueezed state. The amplitude-squared squeezing effect enhances with increasingtemperature T and parameterγ. As frequencyω_k increases, the amplitude-squaredsqueezing effect firstly enhances as frequencyω_k increases. Atω_m=6.7×10¹³s^-1, theamplitude-squared squeezing effect is strongest, then the squeezing effect weakens as asfrequencyω_k increases. The amount of the amplitude-squared squeezing in aKerr-nonlinear blackbody is much larger than the corresponding squeezing in normalblackbody, and the degree of amplitude-squared squeezing is much larger than theamplitude squeezing for the same range of parameters in a Kerr-nonlinear blackbody.Second, the phase symmetry breaking is investigated in a Kerr-nonlinear blackbodyin terms of the quasiprobability distribution. The quasiprobability (Q function)distribution is discussed in detail in the different ranges of temperature T. It is foundthat the distribution of Q function strongly depends on the temperature T and couplingparameterγ. Non-classical effects of quadrature squeezing have been observed. In thetransition from the normal to the squeezed thermal radiation state, the phase symmetry ofthe photon system in a Kerr-nonlinear blackbody is spontaneously broken.Third, we study the statistical properties of thermal radiation in a Kerr nonlinearblackbody. The second-order correlation function, the phase space distribution function and the photon number distribution are considered. It is found that blow a transitiontemperature T-c, the second-order correlation function g² (0)≥2, which shows that thephoton system is classical bunching, and the statistical behavior always super-Poissonianin the Kerr-nonlinear blackbody, and the super-Poissonian statistics are stronglydependent on the temperature T and the coupling parameterγ; the photon numberdistribution P(n) presents nonclassical oscillations, while the oscillatory behaviorsonly occur at very low number of photons, which shows the photon filed in a Kerrnonlinear blackbody is in a squeezed state; the phase distribution P(θ) has a doubletstructure and the peaks are at±π/2, but with broader width and more significantamplitude as the temperature T and the coupling parameterγincrease.Fourth, the degree of nonclassicality of a photon field is considered in a Kerrnonlinear blackbody. The space-phase and distance-type measures are employed,respectively. It is shown that blow a transition temperature T_c, the photon field becomesless nonclassical in the Kerr-nonlinear blackbody as temperature T, Kerr nonlinearcoefficientγand frequencyω_k increase. Furthermore, the degree of nonclassicality of aKerr nonlinear blackbody is always higher than that of a normal blackbody.Fifth, we derive a quantum Langevin equation for the macroscopic description of acharged oscillator in a harmonic potential well interacting with a Kerr nonlinearblackbody radiation field via dipole coupling. It is shown that below a transitiontemperature T_c, the memory function in our quantum Langevin equation is a decreasingfunction of temperature T and Kerr nonlinear coefficientγ. In the large-cutoff limit, theobserved mass and free energy shift of a charged oscillator in a Kerr nonlinear blackbodyare larger than those in a normal blackbody. The free energy shift is a complex functionof temperature which is no longer a simply T²-dependent function. The energy level shift of an oscillator in a normal blackbody is a negative, while in our Kerr nonlinearblackbody, only near zero temperature the corresponding energy level shift is a negative.As the temperature increases to transition temperature T, the corresponding energy levelshift becomes a large positive value. Above T_c, our results are the same as those in anormal blackbody.