Abstract
We study the photoelectric current generated by a driving light with nonclassical photon statistics. Due to the nonclassical input photon statistics, it is no longer enough to treat the driving light as a planar wave as in classical physics. We make a quantum approach to study such problems, and find that: when the driving light starts from a coherent state as the initial state, our quantum treatment well returns the quasi-classical driving description; when the the driving light is a generic state with a certain P function, the full system dynamics can be reduced as the P function average of many ‘branches’—in each dynamics branch, the driving light starts from a coherent state, thus again the system dynamics can be obtained in the above quasi-classical way. Based on this quantum approach, it turns out the different photon statistics does make differences to the photoelectric current. Among all the classical light states with the same light intensity, we prove that the input light with Poisson statistics generates the largest photoelectric current, while a nonclassical sub-Poisson light could exceed this classical upper bound.
Highlights
When considering a driving light shining on a quantum two-level system (TLS) (Hs = Ω|e e|, with |e/g as the excited/ground state), the interaction between the TLS and the light beam is usually described by the following quasi-classical driving [1,2,3],V = −d · E0 sin(ωkt − k · x − φ0). (1)where d = ℘ (σ− + σ+) is the dipole moment operator of the TLS, with ℘ := e|d|g as the transition dipole moment, and σ+ := |e g| = (σ−)†.In such an interaction, the driving light is modeled as a planar wave as in classical physics
The quantized EM field, if the driving mode starts from a coherent state |α as its initial state, it turns out the system dynamics can be described by a master equation, which just returns the above quasi-classical driving widely adopted in literature
“branches”: in each dynamics branch the driving mode starts from a coherent state, again it can be solved separately as the above quasi-classical driving situation, and their P function average gives the full dynamics
Summary
If the initial state of the driving mode isnot a coherent state, but a generic quantum state represented by a P function = d2α P (α)|α α|, it turns out the system dynamics can be rewritten as the P function average of many evolution “branches”: in each dynamics branch the driving mode starts from a coherent state, again it can be solved separately as the above quasi-classical driving situation, and their P function average gives the full dynamics Based on this approach, we study a photoelectric converter model [13,14,15,16,17,18,19], and calculate the photoelectric currents generated by the input light with different photon statistics (Poisson, sub-Poisson, thermal).
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