2024/12/27 by Gianluca Degli Esposti, Greger Torgrimsson, Esposti, Gianluca Degli +1 · 1 voice · 5 citations
Physics and Astronomy · #Laser-Plasma Interactions and Diagnostics #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.1103/3143-w4w3
We use a worldline-instanton formalism to study the momentum spectrum of Schwinger pair production in spacetime fields with multiple stationary points. We show that the interference structure changes fundamentally when going from purely time-dependent to space-time-dependent fields. For example, it was known that two time-dependent pulses give interference if they are antiparallel, i.e., <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>E</a:mi> <a:mi>z</a:mi> </a:msub> <a:mo stretchy="false">(</a:mo> <a:mi>t</a:mi> <a:mo stretchy="false">)</a:mo> <a:mo>−</a:mo> <a:msub> <a:mi>E</a:mi> <a:mi>z</a:mi> </a:msub> <a:mo stretchy="false">(</a:mo> <a:mi>t</a:mi> <a:mo>−</a:mo> <a:mi mathvariant="normal">Δ</a:mi> <a:mi>t</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> , but here we show that two spacetime pulses will typically give interference if they instead are parallel, i.e., <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>E</h:mi> <h:mi>z</h:mi> </h:msub> <h:mo stretchy="false">(</h:mo> <h:mi>t</h:mi> <h:mo>,</h:mo> <h:mi>z</h:mi> <h:mo stretchy="false">)</h:mo> <h:mo>+</h:mo> <h:msub> <h:mi>E</h:mi> <h:mi>z</h:mi> </h:msub> <h:mo stretchy="false">(</h:mo> <h:mi>t</h:mi> <h:mo>−</h:mo> <h:mi mathvariant="normal">Δ</h:mi> <h:mi>t</h:mi> <h:mo>,</h:mo> <h:mi>z</h:mi> <h:mo>−</h:mo> <h:mi mathvariant="normal">Δ</h:mi> <h:mi>z</h:mi> <h:mo stretchy="false">)</h:mo> </h:math> . We take into account the fact that the momenta of the electron, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>p</p:mi> <p:mi>z</p:mi> </p:msub> </p:math> , and of the positron, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msubsup> <r:mi>p</r:mi> <r:mi>z</r:mi> <r:mo>′</r:mo> </r:msubsup> </r:math> , are independent for <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:msub> <t:mi>E</t:mi> <t:mi>z</t:mi> </t:msub> <t:mo stretchy="false">(</t:mo> <t:mi>t</t:mi> <t:mo>,</t:mo> <t:mi>z</t:mi> <t:mo stretchy="false">)</t:mo> </t:math> [it would be <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>p</x:mi> <x:mi>z</x:mi> </x:msub> <x:mo>+</x:mo> <x:msubsup> <x:mi>p</x:mi> <x:mi>z</x:mi> <x:mo>′</x:mo> </x:msubsup> <x:mo>=</x:mo> <x:mn>0</x:mn> </x:math> for <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>E</z:mi> <z:mo stretchy="false">(</z:mo> <z:mi>t</z:mi> <z:mo stretchy="false">)</z:mo> </z:math> ], and find a type of fields which give moiré patterns in the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:msub> <db:mi>p</db:mi> <db:mi>z</db:mi> </db:msub> <db:mo>−</db:mo> <db:msubsup> <db:mi>p</db:mi> <db:mi>z</db:mi> <db:mo>′</db:mo> </db:msubsup> </db:math> plane. Depending on the separation of the two pulses, we also find an Aharonov-Bohm phase. We also study complex momentum saddle points in order to obtain the integrated probability from the spectrum. Finally, we calculate an asymptotic expansion for the eigenvalues of the Sturm-Liouville equation that corresponds to the saddle-point approximation of the worldline path integral, use that expansion to compute the product of the eigenvalues, and compare this with the result obtained with the Gelfand-Yaglom method.