We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for nonlinear photon-number amplification schemes with optimistic implications for singlephoton detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification takes place, in general, at a different frequency ω than the frequency ω of the input photons. This can be exploited to suppress thermal noise even further up to a fundamental limit imposed by amplification into a single bosonic mode. A practical example that fits our description very well is electron-shelving.
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.
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