A molecular system having two energy levels separated by\hbar\Omegaand coupled to an electromagnetic field by a transition dipole moment will resonantly absorb energy at all odd sub-harmonics of the energy level separation\omega =\Omega,\Omega/3,\Omega/5.... These correspond to 1, 3, 5,... quantum absorption processes. Part of this absorbed energy is emitted back into the field at harmonics of\omegaand part is dissipated into the lattice degrees of freedom. It is therefore possible to drive the molecular system with a field of frequency\omega \approx \Omega/m(n odd), and obtain radiation at a frequencym\omega \approx \Omega. Here we present results of a theoretical study of these resonant multi-quantum conversion processes. Two characteristic regions of operation are predicted: one previously discussed by Fontana, Pantell and Smith3in which the molecular efficiency\varepsilon= (power converted ton \omega)/ (power abosrbed at\omega) =\frac{1}{2}under conditions of maximum power converted per unit volume; and another region (not previously reported) in which maximum power conversion per unit volume can occur with molecular efficiencies approaching unity.
In 1959, E. T. Jaynes suggested that resonant, multiquantum processes could provide an efficient method of frequency conversion at high frequency and high powers. This conversion is mediated by a gas or solid composed of molecules having a strong electric-dipole absorption at a frequency /spl Omega/. Such a system can resonantly absorb energy from an electromagnetic field at all odd subharmonic of /spl Omega/. The /spl omega/ /spl ap/ /spl Omega/ /(2n + 1) subharmonic absorption is said to correspond to a 2n + 1 quantum process. The excited (driven) molecular system has electric dipole moments at all odd harmonics of the drive /spl omega/. The resonant dipole moment at a frequency (2n + 1)/spl omega/ /spl ap/ /spl Omega/ generates an electromagnetic field resulting in the frequency conversion process proposed by Jaynes. Here we report theoretical calculations and experimental observation of this multiquantum frequency conversion in a traveling-wave structure.
The interaction between radiation and a two-level molecular system in the presence of permanent dipole moments is analyzed. It is found that the nonzero difference between permanent dipoles induces a polarization that oscillates at frequencies /spl omega/, 2/spl omega/, 3/spl omega/, etc., where /spl omega/ is the frequency of the electromagnetic field resonant with the two-level system. An analysis of the propagation equation of the harmonics shows that even harmonics are amplified while odd harmonics are absorbed.
The rate of absorption and emission of radiation is calculated for two laser fields interacting with a homogeneously broadened, three-level molecular system. The time-dependent Schrödinger equation is used in the density matrix formalism and the laser fields are treated classically. The laser fields, at frequencies ωpand ωs, are off resonance by δpand δs, respectively, such that|\delta_{p}|, |\delta_{s}| \ll \omega_{p}, \omega_{s}. Analytic expressions are derived for the imaginary part of the electric susceptibility,\chi"(\omega_{p})and\chi"(\omega_{s}). The present work differs from previous calculations in that the laser fields may have arbitrary values of field strength and each field may be on or off resonance. A discussion is presented of the properties of the solutions for\chi"(\omega_{p})and\chi"(\omega_{s}), for both strong and weak laser fields, based on computer evaluation of the general analytic expressions. It is shown that the solutions may be divided into single-photon and two-photon, or Raman, contributions. Conditions for optimizingdI(\omega_{s})/dzand the photon conversion efficiency are derived. These results may be applied to analyzing the pulsed, optically pumped submillimeter laser and to studying two-photon absorption in a gas.
The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by
TrN, where
N is the total number of atoms,
T is the average time of coherent interaction of atoms and the radiation field, and
r is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.
The influence of nonlinear interference processes and of changes in populations in strong electromagnetic fields, and also of the Doppler broadening on resonant four-wave frequency mixing is investigated for a system of Raman-type transitions. The case in which a quantum system interacts with one weak field and two strong fields is considered. Each of the energy levels is assumed to be perturbed by just one strong field. It is shown that the Doppler broadening alters drastically the contributions of the populations of the various levels to the investigated process and that this can alter by several orders of magnitude and nonlinear susceptibilities averaged over the velocities and influence significantly the selection of optimal configurations of the transitions and of the experimental conditions for effective resonant four-wave conversion of the radiation frequencies. A numerical analysis of the derived expressions is used to account for the experimentally observed considerable differences between the spectral dependences of the output power and the conclusions drawn from perturbation theory.
Within the Rabi quantum model, it has been shown theoretically that a two-level atom ultrastrongly coupled to an electromagnetic field generates or absorbs photons. Photons can be generated if the field is initially in the vacuum state. Under certain initial states of the atom + field system, the absorption of photons is possible in the field mode in the ultrastrong atom–field coupling regime. If the atom is initially in the ground (unexcited) state and the field is in the vacuum state, photons can be generated under resonance condition ωa ≈ ωf or ξ ≡ ωa/ωf ≈ 1, where ωa and ωf are the atomic transition and field frequencies, respectively, in the ultrastrong coupling regime. At the negative detuning when ξ
≪ 1 or ωa
≪ ωf, Rabi oscillations of the average number of photons
⟨n^⟩t with
0⩽⟨n^⟩t⩽nmax≫1 are observed in the case of the ultrastrong coupling with the atom–field coupling constant
g~≡|g|/ωf∼1 ; in this case, the population of the excited atomic state is Pe(t) ≈ 0.5. At a large positive detuning when ξ
≫ 1, photons are not generated, i.e.,
⟨n^⟩≈0 , and the atom remains in the initial state, i.e., Pe(t) ≈ 0. The statistics of photons in the generation regime is nearly chaotic: the variance of photons is much larger than the level of the coherent field state (i.e., is super-Poisson). Field photons are absorbed without the excitation of the atom in the ultrastrong coupling regime in the case of the coherent initial state of the field
(⟨n^(t=0⟩>0) for certain positive detuning values. In this case, the field becomes sub-Poisson.