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arXiv:2108.00498 · Physical Review A

Detecting two photons with one molecule

Saumya Biswas, S. J. van Enk

Published Oct 11, 2021• 3 citations
arXivHTMLPDF

Abstract

Taking inspiration from the human eye, the authors propose using a five-level molecule to detect up to two photons of different frequency that arrive sequentially. They use two formalisms to develop this model: a density-matrix method to achieve analytical results and characterize the proposed detector, and a Hamiltonian method that they show is well suited for numerical calculations.

DOI
10.1103/physreva.104.043703

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Taking inspiration from the human eye, the authors propose using a five-level molecule to detect up to two photons of different frequency that arrive sequentially. They use two formalisms to develop this model: a density-matrix method to achieve analytical results and characterize the proposed detector, and a Hamiltonian method that they show is well suited for numerical calculations.
We develop a comprehensive model for the effective two-photon density matrix produced by a parametric source of entangled-photon pairs under a variety of detector configurations commonly seen in a laboratory setting: two and four photon-number-resolving (PNR) and threshold detectors. We derive the probability of obtaining a single coincidence assuming Poisson-distributed photon pairs, nonunit detection efficiency, and dark counts; obtain the effective density matrix; and use this quantity to compute the fidelity of this state with respect to the maximally entangled ideal. The four-detector PNR case admits an analytic result valid for any combination of parameters, while all other cases leverage low-efficiency approximations to arrive at closed-form expressions. Interestingly, our model reveals appreciable fidelity improvements from four detectors as opposed to two but minimal advantages for PNR over threshold detectors in the regimes explored. Overall, our work provides a valuable tool for the quantitative design of two-photon experiments under realistic nonidealities.
The human eye can detect optical signals containing only a few photons. We investigate the possibility to demonstrate entanglement with such biological detectors. While one person could not detect entanglement by simply observing photons, we discuss the possibility for several observers to demonstrate entanglement in a Bell-type experiment, in which standard detectors are replaced by human eyes. Using a toy model for biological detectors that captures their main characteristic, namely, a detection threshold, we show that Bell inequalities can be violated, thus demonstrating entanglement. Remarkably, when the response function of the detector is close to a step function, quantum nonlocality can be demonstrated without any further assumptions. For smoother response functions, as for the human eye, postselection is required.
The method of stochastic recurrent relation is used for simulating a random sequence (trajectory) of the counts of a detector of atomic states at the output of a single-atom micromaser. A random sequence of the relative frequencies of counts of a detector during a fixed time interval is calculated. The frequencies of counts vary randomly near the average time-independent level. It is assumed that these average levels are reproducible observables for each random trajectory. A micromaser can jumpwise transfer from one average level of the relative frequencies of counts to another. It is assumed that a certain subensemble of the states of a field mode corresponds to each measured average level of the frequencies of counts. A method is proposed for calculating possible average relative frequencies of counts and corresponding (mean) reduced density matrices of the mode ρ st . The matrix ρ st characterizes a micromaser during its development along a specified periodic trajectory. It is found by solving the eigenvalue problem for the evolution operator on the period. An analytic method for solving this problem is developed. The matrix ρ st is the solution to the inverse problem of the reconstruction of the statistics of a field mode from the statistics of a random trajectory. The procedure of selecting the parameters of the evolution operator on the period is discussed through a numerical example.