Shock-wave generation and propagation in dissipative and nonlocal nonlinear Rydberg media

We investigate the generation of optical shock waves in strongly interacting Rydberg atomic gases with a spatially homogeneous dissipative potential. The Rydberg atom interaction induces an optical nonlocal nonlinearity. We focus on local nonlinear <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>(</a:mo><a:msub><a:mi>R</a:mi><a:mi>b</a:mi></a:msub><a:mo>≪</a:mo><a:msub><a:mi>R</a:mi><a:mn>0</a:mn></a:msub><a:mo>)</a:mo></a:mrow></a:math> and nonlocal nonlinear <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>(</b:mo><b:msub><b:mi>R</b:mi><b:mi>b</b:mi></b:msub><b:mo>∼</b:mo><b:msub><b:mi>R</b:mi><b:mn>0</b:mn></b:msub><b:mo>)</b:mo></b:mrow></b:math> regimes, where <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>R</c:mi><c:mi>b</c:mi></c:msub></c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>R</d:mi><d:mn>0</d:mn></d:msub></d:math> are the characteristic length of the Rydberg nonlinearity and beam width, respectively. In the local regime, we show spatial width and contrast of the shock wave change monotonically when increasing strength of the dissipative potential and optical intensity. In the nonlocal regime, the characteristic quantity of the shock wave depends on <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>R</e:mi><e:mi>b</e:mi></e:msub><e:mo>/</e:mo><e:msub><e:mi>R</e:mi><e:mn>0</e:mn></e:msub></e:mrow></e:math> and dissipative potential nontrivially and on the intensity monotonically. We find that formation of shock waves dominantly takes place when <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>R</f:mi><f:mi>b</f:mi></f:msub></f:math> is smaller than <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>R</g:mi><g:mn>0</g:mn></g:msub></g:math>, while the propagation dynamics is largely linear when <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>R</h:mi><h:mi>b</h:mi></h:msub></h:math> is comparable to or larger than <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>R</i:mi><i:mn>0</i:mn></i:msub></i:math>. Our results reveal nontrivial roles played by dissipation and nonlocality in the generation of shock waves, and provide a route to manipulate their profiles and stability. Our study furthermore opens new avenues to explore non-Hermitian physics and nonlinear wave generation and propagation by controlling dissipation and nonlocality in the Rydberg media. Published by the American Physical Society 2024