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arXiv:1412.0017 · Physical Review A

First-order decomposition of thermal light in terms of a statistical mixture of single pulses

Aurélia Chenu, Agata M. Brańczyk, John E. Sipe

Published Jun 15, 2015• 9 citations
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Abstract

We investigate the connection between thermal light and coherent pulses, constructing mixtures of single pulses that yield the same first-order, equal-space-point correlation function as thermal light. We present mixtures involving (i) pulses with a Gaussian line shape and narrow bandwidths and (ii) pulses with a coherence time that matches that of thermal light. We characterize the properties of the mixtures and pulses. Our results introduce an alternative description of thermal light in terms of multifrequency coherent states, valid for the description of broadband linear light-matter interactions. We anticipate our results will be relevant to time-resolved measurements that aim to probe the dynamics of systems as if they were excited by natural thermal light.

DOI
10.1103/physreva.91.063813

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We ask whether or not thermal light can be represented as a mixture of single broadband coherent pulses. We find that it cannot. Such a mixture is simply not rich enough to mimic thermal light; indeed, it cannot even reproduce the first-order correlation function. We show that it is possible to construct a modified mixture of single coherent pulses that does yield the correct first-order correlation function at equal space points. However, as we then demonstrate, such a mixture cannot reproduce the second-order correlation function.
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The theoretical description of broadband, multimode quantum pulses undergoing a second-order χ(2)χ^{(2)}χ(2)-nonlinear interaction can be quite intricate, due to the large dimensionality of the underlying phase space. However, in many cases only a few broadband (temporal) modes are relevant before and after the nonlinear interaction. Here we present an efficient framework to calculate the relation between the quantum states at the input and output of a nonlinear element in their respective relevant modes. Since the number of relevant input and output modes may differ, resulting in an open quantum system, we introduce the generalized Bloch-Messiah decomposition (GBMD), reducing the description to an equal number of input and output modes. The GBMD enables us to calculate the multimode Wigner function of the output state by convolving the rescaled Wigner function of the reduced input quantum pulse with a multivariate Gaussian phase-space function. We expand on this result by considering two examples input states: A Fock state in a single broadband mode and a two-mode squeezed vacuum, both in the THz-frequency regime, up-converted to a single output broadband mode of optical frequencies. We investigate the effect, the convolution and thermalization due to entanglement breakage have on the output Wigner function by calculating the von Neumann entropy of the output Wigner function. The methods presented here can be used to optimize the amplification or frequency conversion of broadband quantum states, opening an avenue to the generation and characterization of optical quantum states on ultrafast time scales.
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