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Chinese Physics B

Enhanced second harmonic generation in a two-dimensional optical micro-cavity

Jian-Jun Zhang, Hui-Fang Wang, Junhua Hou

Published Mar 1, 2018• 0 citations
Publisher

Abstract

We introduce a two-dimensional Bose–Einstein condensation model consisting of massive photon and photon-pair. Based on the new nonlinear model, the traditional process of second harmonics generation is reinvestigated. In order to describe the process, a new quantum phase, the harmonic phase, is introduced. The order parameter of the new physical phase is also given in this paper.

DOI
10.1088/1674-1056/27/3/034207

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We introduce a two-dimensional Bose–Einstein condensation model consisting of massive photon and photon-pair. Based on the new nonlinear model, the traditional process of second harmonics generation is reinvestigated. In order to describe the process, a new quantum phase, the harmonic phase, is introduced. The order parameter of the new physical phase is also given in this paper.
We investigate the Bose-Einstein condensation of photons and photon pairs in a two-dimension optical microcavity. We find that in the paraxial approximation, the mixed gas of photons and photon pairs is formally equivalent to a two dimension system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phase. We also discuss the quantum phase transition of the system and obtain the critical point analytically. Moreover, we find that the quantum phase transition of the system can be interpreted as second harmonic generation.
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The effect of Bose-Einstein condensation, achieved recently for alkaline gases in magnetic traps, should lead to a strong enhancement of non-linear harmonic generation. A nearly resonant light imposed on the gas of two-level atoms excites the intra-atomic transitions and causes generation of various harmonics. Normally, in the thermal state of the gas, a contribution of the inter-atomic interaction to the non-linear harmonic generation is negligible. However, if a Bose-Einstein condensate (BEC) is present, the inter-particle interaction cannot be ignored. Considering second harmonic generation, we show that, in the presence of the BEC, the intensity of the second harmonic is proportional to (aN n)/sup 2/, where N and n are the total number and the effective density of the condensed atoms, respectively, and a stands for the scattering length describing the process of scattering of two excited atoms by each other so that, after the collision, one excited atom enters the condensate. We consider the interaction between light, represented by the electric field E, and the atomic Bose field /spl Psi/ as well as the two body interaction treated within the scattering length approximation.
Bose-Einstein condensation (BEC) is the transition to a macroscopic occupation of the ground state of a system of bosonic particles. In 1995 the first experimental realization of BEC was achieved by condensing a dilute atomic gas [1,2]. It was long thought only massive particles could undergo BEC. However, in 2010 it was shown that photon BEC was achieved in an optical dye-filled microcavity [3]. In 2015, we became the second group to successfully repeat these experiments.\n\nBEC is a phase transition and thus it occurs at thermal equilibrium. To achieve a thermal photon gas the cavity is filled with a fluorescent dye solution. The dye molecules thermalize the photons by means of repeated absorption-emission cycles. We optically pump the cavity. With the pump we determine the number of photons absorbed by the dye, consequently defining a nonvanishing chemical potential. This ensures a conserved photon number. The photons are trapped by the harmonic potential induced by the concave cavity mirrors. Due to the cutoff energy determined by the cavity length, the trapped photons have a dispersion similar to that of a massive particle in a quantum harmonic oscillator. The cavity length is tuned such that the free spectral range is larger than the bandwidth of the dye. Therefore, only one longitudinal mode fits inside the cavity, making the photon gas effectively two-dimensional. We end up with a thermalized two-dimensional photon gas that has the eigenenergies of a quantum harmonic oscillator. The Bose-Einstein distribution function predicts a critical photon number. Pumping the thermal photon gas beyond this critical number will lead to photon BEC.\n\nWe measure the spectral- and spatial distributions of our two-dimensional photon gas. In both distributions we observe photon BEC. Results show the characteristics of a phase transition: the appearance of a sharp peak on top of the thermal cloud that coincides with a converging chemical potential to zero. Both the spectral- and spatial distribution are in agreement with the theoretical distribution of photons with an effective mass in a quantum harmonic oscillator. Expansion of the condensate has been measured. This could indicate nonlinear optical effects such as thermal lensing or repulsive photon-photon interactions.
Light propagation in the medium is light-matter interaction process. For such a dynamic process, the process can be viewed as consisting of two sub-components: radiative processes and media response process medium light. This paper describes a two-dimensional nonlinear optical microcavities coupling of changing circumstances, to study the two-dimensional photon - photon mixed gas condensation, quantum phase transition, the post also pointed out that the mixed gas of quantum phase transitions and non-traditional linear optics and frequency generation relationship.
We consider a possible second harmonic generation (SHG) of propagating collective excitations in a two-component Bose–Einstein condensate (BEC) with repulsive atom–atom interactions. We show that the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of the excitations are chosen adequately from different dispersion branches. We solve the nonlinear amplitude equations for the SHG derived using a method of multiple-scales and provide SHG solutions similar to those obtained for a SHG in nonlinear optical media. A possible experimental realization of the SHG for the propagating collective modes in a cigar-shaped two-component BEC is also discussed.