Abstract
We introduce a three-parameter family of single-mode optical states whose density operator is a weighted difference of two thermal states, the thermal-difference states. We identify the parameter values for which these states have a negative non-singular P-function, implying they are nonclassical. We show that the states of the “heralded photons” generated via spontaneous parametric downconversion belong to this family, with the three parameters corresponding to the nonlinear gain and the losses in the signal and the idler channels. The thermal-difference states yield new benchmark states for the analysis of nonclassicality and quantum macroscopicity criteria.
Highlights
In the last decades much attention is attracted to the photon heralding technique [1,2,3,4,5,6,7,8,9], which consists in generating a photon pair in two modes and detecting a photon of one mode, preparing the other mode in a single-photon state
In this work we consider spontaneous parametric downconversion (SPDC) as a source of photon pairs and find the density matrix of the signal mode conditioned by a photon detection in the idler one
We show that the conditional state of the signal mode is a weighted difference of two thermal states
Summary
In the last decades much attention is attracted to the photon heralding technique [1,2,3,4,5,6,7,8,9], which consists in generating a photon pair in two modes and detecting a photon of one (idler) mode, preparing the other (signal) mode in a single-photon state. In the ideal case, where exactly one photon pair is generated in a given time window and there is no loss, the conditional state of the signal field is a one-photon Fock state. In realistic experimental conditions two and more pairs can be generated by the source at a time and the light collection and detection is accompanied by loss and non-unit quantum efficiency of the photodetector. These factors lead to appearance of multiphoton and vacuum components in the state of the signal field. We call such states thermal-difference states and study some of their properties below
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