Radiative Higgs mode in photoinduced η pairs

We demonstrate that the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>η</a:mi></a:math> symmetry of the pump-induced <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>η</b:mi></b:math>-pairing state in the Hubbard chain can be transiently broken by an additionally applied probe pulse. This leads to characteristic dynamic Higgs oscillations of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>η</c:mi></c:math>-pair correlations during the probe pulse and a sharp dynamic negative optical conductivity <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>σ</d:mi><d:mo>(</d:mo><d:mi>ω</d:mi><d:mo>;</d:mo><d:mi>t</d:mi><d:mo>)</d:mo></d:mrow></d:math>, which appears above the equilibrium Mott gap <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>ω</e:mi><e:mo>></e:mo><e:msub><e:mi mathvariant="normal">Δ</e:mi><e:mi mathvariant="normal">c</e:mi></e:msub></e:mrow></e:math>, long after the pump pulse is finished. This negative peak in the real part of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>σ</h:mi><h:mo>(</h:mo><h:mi>ω</h:mi><h:mo>;</h:mo><h:mi>t</h:mi><h:mo>)</h:mo></h:mrow></h:math> is a distinctive hallmark of the photoinduced <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>η</i:mi></i:math>-pairing state, distinguishing it from parameter regimes dominated by incoherent doublon formation, which do not exhibit this feature. Remarkably, the broadband probe pulse then leads to the emission of photons with the Higgs frequency.