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Journal of Experimental and Theoretical Physics

Features of the photon statistics of two coupled electromagnetic field modes under the conditions of strong mode coupling

M. E. Veĭsman, S. Kalmykov

Published Jul 1, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1134/1.558317

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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.
Squeezing the quantum fluctuations of the two-mode light due to the nonstationary coupling between the quadrature components q1{q}_{1}q1​ and q2{q}_{2}q2​ is examined. The \ensuremath{\delta}- and step-function mode couplings are considered. The conditions of weak and strong step-function coupling are distinguished, the latter being the condition of the instability for the classical counterpart of the quantum system under study. Under the conditions of weak coupling the quadrature squeezing is established in both a two-mode electromagnetic noise in thermal equilibrium (the thermal state) and a two-mode correlated coherent state (CCS). Squeezing in the thermal state is suppressed at a high temperature. The photon distribution function (PDF) in the thermal state reveals oscillatory behavior for both high and low temperature, the oscillations decrease while the temperature increases. The PDF in the CCS can be either oscillatory or smooth, whereas the photon statistics is essentially non-Poissonian. The nonclassical intermode photon-number correlations in the CCS are briefly studied.
The dynamics of interaction of an electromagnetic field with a two-level atom uniformly moving in an open resonator is analysed. The probability of the radiative transition of an excited atom to a lower state is studied as a function of the slope of its trajectory relative to the resonator axis and of the detuning of the atomic transition frequency from the resonator mode frequency. The study was performed in the case of strong coupling by the method of dressed states. The complicated dependences of the transition probability on the detuning and the slope of the atomic trajectory are analysed for small angles (~1°) for typical experimental conditions. It is shown that under certain conditions, a field can be efficiently excited in the resonator by atoms whose transition frequency considerably differs from the field-mode frequency when the detuning is not close to the Doppler shift.
Abstract One of the greatest successes in quantum theory, and certainly one of the more important parts for application to devices and applications is the prediction of the emission of light through the quantization of an electromagnetic field. Broadly, this is the field of quantum electrodynamics. In this chapter, we develop the Hamiltonian for the classical electromagnetic field. It is seen that the Hamiltonian for each mode (identified by the k-vector and polarization of the field) of the plane wave electromagnetic field is identical to that of the harmonic oscillator. One unit of energy, ℏω, in a mode is a called a photon. The eigenkets for the system are number states (Fock states). We then consider a two-level system described by a Hamiltonian which couples the two-level quantum system to the quantized electromagnetic field. Using the Weisskopf–Wigner formalism developed in Chapter 14, we solve the equations of motion for the time dependent Schrödinger equation assuming the system starts in the excited state with no radiation present in the vacuum field. The results show the creation of one unit of energy in an electromagnetic mode corresponding to the emission of a photon. The excited state probability decays exponentially with the emission of this photon. We consider the important and special case of such a two-level system but in a cavity restricting the radiation field to a single mode. The Jaynes–Cummings Hamiltonian shows that this system, if started in the excited state, Rabi oscillates with no radiation incident on the system.
The statistic properties of photon in the system of a two-mode entangled coherent state interacting with a Ξ-type three-level atom are investigated by solving Schrdinger equation and using numerical calculations. The effects on the statistic properties of photon induced by the degree of entanglement of the two-mode entangled coherent state, the ground state probability amplitude of the atomic initial state, the detuning, the atom-field coupling constant and the mean photon number are analyzed. The results indicate that the influence of the degree of entanglement of the two-mode entangled coherent state on the statistic properties of photon is small. The increasing of the ground state probability amplitude of the atomic initial state causes the center of the time evolution curve to move up distinctly. The increasing of the detuning results in the decrease of the oscillating frequency of the time evolution curve. The influences of the atom-field coupling constant and the mean photon number on the statistic properties of photon are noticeable. The correlation of the two modes of light is non-classical all the time.
We have studied the excitation spectrum arising from the interaction of a two-level atom with two strong electromagnetic fields whose initially populated modes ω a and ω b are near resonance with the atomic transition frequency In the limit of high photon densities the Green's function of the system describing the electronic transition in question has been derived in a closed form and includes processes arising from the interaction of seven photon modes of both laser fields. The spectral function of the system is calculated when the frequency ω a of the one laser field is in resonance with the atomic transition frequency while the frequency ω b of the other field is varied. The excitation spectrum is found to consist, apart from the central peak at the excitation frequency ω a , of several lorentzian lines which are peaked in the neighbourhood of the frequencies ω a ± Δ, ω a ± 2Δ, ω a ± 3Δ and ω a ± 4Δ, where Δ = ω a - ω b and describe the type of optical mixing of light modes which is of the third, fifth, seventh and ninth order, respectively. Additional peaks appear in the spectra, which result from the interaction between the frequency modes in question. The probability amplitudes describing the relative intensities of the peaks in question are expressed as functions of the parameters η a = Ω a /Δ and η b = Ω b /Δ, where Ω a and Ω b are the Rabi Frequencies of the two laser fields, respectively. It is found that when η a ⩾ 1 and η b ⩾ 1 the expression for the relative intensities of the bands in question are remarkably enhanced and take extremely large positive or negative values. Results of numerical calculations for a wide range of values of η a and η b when η a = η b ⩾ 1 are presented graphically and the complete excitation spectrum is discussed in detail. The method may be useful to investigate the behaviour of excited states as well as those close to the limit of ionization.
Spectral properties of an atom interacting with two modes of quantized field are described-Two types of spectra are investigated-Fluorescent and Output spectra. It is shown that both the spectra are sensitive to coupling strengths, which affect the two-photon transition probability. In case of equal coupling strength ratio (r=1), the fluorescent spectra exhibit a transition from asymmetric to symmetric two-peak structure and the output spectra demonstrate a single peak. The single peak of output spectrum resembles with a two-photon signal of linearly polarized light.