Andreas Christ, Benjamin Brecht, Wolfgang Mauerer, Christine Silberhorn
Frequency conversion (FC) and parametric down-conversion (PDC) are among the most widely used nonlinear processes for the implementation of quantum optical experiments. Parametric down-conversion enables the efficient creation of quantum states ranging from photon-number states over squeezers to EPR-states. Frequency conversion gives rise to technologies enabling efficient atom-photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high gain regime, as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper we investigate these effects and put forward two models which enable a full description of FC and PDC in the high gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations which covers the complete dynamics of the process. And, as an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution which approximates the correct solution with high fidelity in a broad parameter range. The developed fundamental understanding of frequency conversion and parametric down-conversion gives valuable insights into the quantum properties of the processes, extends the current theoretical descriptions, and simplifies considerably the engineering process for future quantum information applications using FC and PDC.
View original:
http://arxiv.org/abs/1210.8342
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