非共振性幫浦激發在週期位能勢下之一維和二維激子-極子凝聚

我們研究在一維和二維的週期位能勢下的非共振性幫浦激發之激子-極子凝聚現象。藉由分析在凝聚系統中的能帶結構，我們發現當使用均勻的幫浦激發激子-極子時，在布里淵區的邊緣（Brillouin zone boundary）將會產生所謂的「延伸能隙布拉格模態」(extended gap Bloch state)。這種凝聚態的凝聚極子分佈於整個空間，因此能帶結構中僅存在於能隙中的一個孤立態。在一維週期位能勢的激子-極子凝聚態下，固定非線性散射損失以及適當選取均勻幫浦強度與位能勢振幅的比例，可以得到延伸能隙布拉格狀態；若改採用週期性的幫浦激發時，我們無法產生延伸能隙布拉格狀態，但是我們使用相位為90度的幫浦激發時，我們可以在適當的幫浦振幅範圍內得到穩定的能帶結構。同樣地，我們用相同的方法探討在二維週期位能勢下，使用均勻幫浦激發時，對於不論是不同尺寸的正方形(如1:1和2:2) 晶格以及不同尺寸的長方形(如2:1、2:3和2:5)晶格都無法產生能隙布拉格狀態。因此我們改採用週期性幫浦激發，發現無論是使用不同尺寸的正方形(1:1和2:2)以及不同尺寸的長方形晶格(2:1、2:3和2:5)皆無法產生能隙布拉格狀態，但在尺寸較大的晶格中我們可以找到較大的週期性幫浦振幅範圍使其有穩定的能帶結構。我們發現在不同尺寸的二維晶格中皆無法產生穩定的能隙布拉格狀態的原因可能為波函數的基底取不夠多或者是二維晶格的流動性相對於一維晶格的流動性更佳而導致無法產生此現象。但總言之，使用均勻幫浦在一維晶格中的激發方式所產生的能隙布拉格狀態，並且可在特定的均勻幫浦強度與位能勢振幅的比例，藉由改變幫浦強度大小，來達成控制能隙布拉格狀態的躍遷。我們可利用上述的方式應用於光資訊之存取和傳輸。由這樣的理論計算模擬，可提供未來的實驗者選擇適當的激發方式在一維的晶格中產生能隙布拉格狀態。

關鍵字

激子-極子；凝聚；非共振性幫浦；週期位能勢

並列摘要

We study nonresonantly pumped exciton-polariton condensates in 1-D and 2-D periodic potentials. By analyzing the band structure of these systems, we found under the uniform pump the so-called the “extended gap Bloch-states” can be formed at the edges of the Brillouin zones. This state has its condensate density distributes over the whole system but it is only a single state within the bandgap in the band structure. In 1-D lattice system and under fixed nonlinear scattering loss and an appropriate ratio of the pumping strength to the amplitude of potential height, we obtain a so-called extended gap Bloch-states at the edges of the Brillouin zones. This state not only has its condensate density distributing over the whole system but also is an isolated state within the bandgap. But if we use periodic pump to excite the condensates in the potential valleys there is no gap Bloch state instead we acquire stable condensate band structures in certain range of periodic pump’s amplitude. On the other hand, in the 2-D periodic system with uniform pump, no matter what sizes are in square and rectangular lattices there are no gap Bloch states can be found. However, under the periodic pump to excite in the potential peaks or valleys, there are also no gap Bloch states can be found. Instead we find there will be a wider range of periodic pump’s amplitude which excites the condensate on larger sizes (square、rectangle) in the potential peaks or valleys can have stable condensate band structures. We have our explanation that there will have no any gap Bloch states might attribute to we don’t have our wavefunction’s basis enough to have stable gap Bloch states or the fluidity in 2-D lattice is better than 1-D lattice. However, we use the uniform pump to excite in 1-D lattice in order to have extended gap Bloch states. By changing the uniform pumping strength, we can control the transparency of the extended gap Bloch states in a specific range of the ratio (pumping strength)/(potential barrier) as nonlinear scattering loss is fixed. In conclusion, this study may provide the predictions for the future experiments and for further applications in informatics such as optical storage, processing, and transmission.

並列關鍵字

exciton-polariton ； condensate ； nonresonantly pumped ； periodic potential

參考文獻

[2] Szu-Cheng Cheng, “An Effective Theory for Bright Gap Solitons in Optical Lattices,” Chinese Journal of Physics 43(4), 835 (2005).

[4] A. Kavokin, “Exciton-polaritons in microcavities present and future”, Applied Physics A 89, 241-246 (2007).

[5] Jonathan Keeling and Natalia G.Berloff,“Spontaneous Rotating Vortex Lattices in a Pumped Decaying Condensate,”Physical Review Letters 100, 250401 (2008).

[8] Ting-Wei chen, Yu-Ling Chiang, Szu-Cheng Cheng, Wen-Feng Hsieh, “Stability and excitations of spontaneous vortices in polariton condensates,” Solid State Communications 165, 6-10 (2013).

[9] Ting-Wei Chen, Ming-Dar Wei, Szu-Cheng Cheng, Wen-Feng Hsieh, “Phase diagram of microcavity polariton condensates with a harmonic potential trap,” Solid State Communications 178, 23-27 (2014).

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非共振性幫浦激發在週期位能勢下之一維和二維激子-極子凝聚

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