On nonlinear amplification: improved quantum limits for photon counting

Abstract

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.

Phase-Preserving Linear Amplifiers Not Simulable by the Parametric Amplifier

“…Because of advances in quantum optics and quantum information, linear amplifiers are now also seen as a facilitating component of many useful tasks such as state discrimination [3], quantum feedback [4], metrology [5], and entanglement distillation [6,7]. New paradigms of amplification such as heralded probabilistic amplification [3,6,8,9] and photon number amplification [10] are being actively researched for these and other applications.…”

Detecting two photons with one molecule

“…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].…”

“…The absence of a signal and the two different signals from the two levels |F 2 and |F 4 help the observer distinguish the number of photons (0, 1, or 2) absorbed by the molecule. Since the frequency of the amplified signal is independent of the input photon frequency [22], we can have different shelving states (classically) driving different oscillators of different frequencies [23]; and hence we can have distinguishable classical output signals for one or two detected photons.…”

“…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.…”

Quantum simulation of weak-field light-matter interactions

“…This is especially true in regimes of light-matter interaction where the electromagnetic field and the material system it interacts with must both be treated quantum mechanically -i.e., where semiclassical approximations break down. Two examples of recent results in this area are the revelation that a single photon can be jointly absorbed by two atoms given the right conditions [5], and the establishment of the fundamental limits and trade-offs present in building detectors for single or few photons [6][7][8][9]. Other settings where the interaction of weak fields with complex material systems must be captured accurately are in the modeling of recently developed entanglement-assisted spectroscopies that have the potential to provide unprecedented resolution of electronic, molecular, and condensed phase dynamics [10,11], and the modeling of light absorption by photosynthetic organisms [12,13].…”