Quantum networks for single photon detection

Abstract

Single photon detection generally consists of several stages: the photon has to interact with one or more charged particles, its excitation energy will be converted into other forms of energy, and amplification to a macroscopic signal must occur, thus leading to a "click." We focus here on the part of the detection process before amplification (which we have studied in a separate publication). We discuss how networks consisting of coupled discrete quantum states and structured continua (e.g. band gaps) provide generic models for that first part of the detection process. The input to the network is a single continuum (a continuum of single-photon states), the output is again a single continuum describing the next irreversible step. The process of a single photon entering the network, its energy propagating through that network and finally exiting into another output continuum of modes can be described by a single dimensionless complex transmission amplitude, T (ω). We discuss how to obtain from T (ω) the photo detection efficiency, how to find sets of parameters that maximize this efficiency, as well as expressions for other input-independent quantities such as the frequencydependent group delay and spectral bandwidth. We then study a variety of networks and discuss how to engineer different transmission functions T (ω) amenable to photo detection.

Detecting two photons with one molecule

“…This bandwidth may be (much) larger than unity. For a fixed value of γ 1 + γ 2 the bandwidth is maximized by γ 1 = γ 2 , an optimal "impedance-matching" condition found before in the same context of designing an optimal single-photon detector [13,14,21]. The bandwidth is then approximately equal to the total time the detector has been on in units of 2/γ 1 .…”

“…Thus, a resonant photon with a narrow width in frequency space (much less than γ 1 ) and whose duration is, therefore, much longer than γ −1 1 , can be absorbed with near-unit efficiency, exactly as was found before in Refs. [13,14,21].…”

“…To construct the minimal absorber atom or molecule or multi-level system that can absorb two photons sequentially and produce classical outputs signaling the final state of the absorber, we consider the five level system of Figure 1 for efficient photon transduction. Some recent efforts for physically based fundamental models for photo detection assemble all parts of the process into a single fully coupled evolution problem [13,14,[18][19][20][21][22][23][24]. Minimal noise amplification of the absorbed photon signal has been shown to be optimally done with continuous quantum measurement [13,14,23].…”

“…[34,35]. The reflected quantum state is of no interest to us, and only the transmitted state ( [21]) which quantifies the probability of absorption is required for our purpose.…”

“…One motivation for this work comes from recent theory efforts to find fundamental (i.e., device-independent) limits to photo detection [13,14,[18][19][20][21][22][23][24]. For reasons fully explained in [23] we construct a Hamiltonian here for the full detection process, including the crucial amplification step.…”