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Optics and Spectroscopy

Quantum dynamics of interaction of elementary detector with single-mode multiphoton states of electromagnetic field

Alexandr Ignatenko, S. Ya. Kilin

Published Mar 1, 2010• 0 citations
Publisher

Abstract

The dynamics of the elementary photoelectric conversion in the interaction of a single-mode electromagnetic field with an arbitrary photon number distribution and a bound electron in a 1D rectangular potential well is considered. It is shown that if the frequency of the coherent field exceeds the frequency corresponding to the electron work function, the photoexcitation of this electron is incomplete.

DOI
10.1134/s0030400x1003015x

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The dynamics of the elementary photoelectric conversion in the interaction of a single-mode electromagnetic field with an arbitrary photon number distribution and a bound electron in a 1D rectangular potential well is considered. It is shown that if the frequency of the coherent field exceeds the frequency corresponding to the electron work function, the photoexcitation of this electron is incomplete.
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The photon quantum dynamics in a damped single-mode quantized cavity field coupled with a resonantly driven two-level system possessing nonzero permanent dipoles is investigated here. The interacting subsystems are very different frequencies (microwave and optical domains) and, in this highly dispersive regime, the emitter couples to the resonator mode via its diagonal dipole moments only. As a result, this interaction regime is responsible for the cavity multiphoton quantum dynamics and photon conversion from optical to terahertz ranges, for instance. Furthermore, enhanced terahertz photon correlations occur as well.
The possibility of the electron oscillations in a two-well potential is investigated in the article. The Hamiltonian of the system is calculated taking into account the formulas of the James-Cummings model. The unitary dynamics is carried out using a general solution of the Schrodinger equation. The conditions for the parameters of the problem under which the oscillation takes place are shown. These conditions for the exact formulation are discrete. However, it is valuable to find out at what parameters of the problem there occur approximate oscillations, at which an incomplete transition of a particle from one well to another is observed. In the standard manuals on the quantum theory of a single particle, the Hamiltonian was considered from the very beginning without photons, so it was assumed that complete oscillations always take place. This approximate consideration corresponds to reality only with a high potential between the wells. If the potential is low, the wells actually merge into one well, so that the spectrum and eigenvalues of the Hamiltonian become similar to the spectrum and eigenvalues of a one-dimensional potential – a radically different case. Such a discrepancy occurs due to ignoring the interaction of the electron with the electromagnetic field. If such an interaction is taken into account we get the dynamics described by the Jaynes-Cummings Hamiltonian. At a low potential, the energy gap between the ground and excited energy states of the electron grows. Since the probability of photon emission is proportional to this value, the interaction with the field cannot be ignored.
The probabilities of transitions between the Fock states of two electromagnetic field modes under the influence of coupling between modes of finite duration are investigated. It is shown that the transition probability is a strongly oscillating function of the mode numbers of the photons. Under conditions in which the coupling frequency exceeds the geometric mean of the mode frequencies (strong coupling), large numbers of photons are excited in the mode with the lower frequency. The excitation of a two-dimensional radiation field oscillator and the “red” asymmetry of the transition probabilities can be attributed to instability of the classical two-dimensional oscillator with strong mode coupling.