We develop a nonlinear theory of propagation of a monochromatic light wave in a gas of two-level atoms under the condition of inhomogeneous Doppler lineshape broadening, while considering a self-consistent solution of the Maxwell–Bloch equations in the mean-field approximation using a single atom density matrix formalism. Our approach shows a significant deformation of the Doppler resonant lineshape (shift, asymmetry), which depends on the atomic density. These effects are a consequence of only the free motion of atoms in a gas and is not associated with interatomic interaction. In particular, the frequency shift of the field-linear contribution to the transmission signal is more than an order of magnitude greater than the shift due to the interatomic dipole–dipole interaction, and the first nonlinear correction has an even stronger deformation, which exceeds the effect of the interatomic interaction by three orders of magnitude. The found effects caused by the free motion of atoms require a significant revision of the existing picture of spectroscopic effects, which depend on the atomic density in a gas.
We develop a nonlinear theory of propagation of a monochromatic light wave in a gas of two-level atoms under the condition of inhomogeneous Doppler lineshape broadening, while considering a self-consistent solution of the Maxwell–Bloch equations in the mean-field approximation using a single atom density matrix formalism. Our approach shows a significant deformation of the Doppler resonant lineshape (shift, asymmetry), which depends on the atomic density. These effects are a consequence of only the free motion of atoms in a gas and is not associated with interatomic interaction. In particular, the frequency shift of the field-linear contribution to the transmission signal is more than an order of magnitude greater than the shift due to the interatomic dipole–dipole interaction, and the first nonlinear correction has an even stronger deformation, which exceeds the effect of the interatomic interaction by three orders of magnitude. The found effects caused by the free motion of atoms require a significant revision of the existing picture of spectroscopic effects, which depend on the atomic density in a gas.
We develop a nonlinear theory of propagation of a monochromatic light wave in a gas of two-level atoms under the condition of inhomogeneous Doppler lineshape broadening, while considering a self-consistent solution of the Maxwell–Bloch equations in the mean-field approximation using a single atom density matrix formalism. Our approach shows a significant deformation of the Doppler resonant lineshape (shift, asymmetry), which depends on the atomic density. These effects are a consequence of only the free motion of atoms in a gas and is not associated with interatomic interaction. In particular, the frequency shift of the field-linear contribution to the transmission signal is more than an order of magnitude greater than the shift due to the interatomic dipole–dipole interaction, and the first nonlinear correction has an even stronger deformation, which exceeds the effect of the interatomic interaction by three orders of magnitude. The found effects caused by the free motion of atoms require a significant revision of the existing picture of spectroscopic effects, which depend on the atomic density in a gas.
We develop a field-nonlinear theory of sub-Doppler spectroscopy in a gas of two-level atoms, based on a self-consistent solution of the Maxwell-Bloch equations in the mean field and single-atom density matrix approximations. This makes it possible to correctly take into account the effects caused by the free motion of atoms in a gas, which lead to a nonlinear dependence of the spectroscopic signal on the atomic density even in the absent of a direct interatomic interaction (e.g., dipole-dipole interaction). Within the framework of this approach, analytical expressions for the light field were obtained for an arbitrary number of resonant waves and arbitrary optical thickness of a gas medium. Sub-Doppler spectroscopy in the transmission signal for two counterpropagating and co-propagating waves has been studied in detail. A previously unknown red shift of a narrow sub-Doppler resonance is predicted in a counterpropagating waves scheme, when the frequency of one wave is fixed and the frequency of the other wave is varied. The magnitude of this shift depends on the atomic density and can be more than an order of magnitude greater than the known shift from the interatomic dipole-dipole interaction (Lorentz-Lorenz shift). The found effects, caused by the free motion of atoms, require a significant revision of the existing picture of spectroscopic effects depending on the density of atoms in a gas. Apart of fundamental aspect, obtained results are important for precision laser spectroscopy and optical atomic clocks.
SummaryWe have found new effects nonlinear in the atomic density caused by the free motion of atoms, considering the self-consistent solution of the Maxwell-Bloch equations in the mean-field approximation and for one-atomic density matrix in a gas of two-level atoms. These effects distort the Doppler lineshape (shift, asymmetry, broadening), but are not associated with an atom-atom interaction. In particular, in the case of dominating Doppler broadening of the linewidth (in respect with collisional broadening), founded atomic-motion-induced effects significantly exceed the well-known influence of the dipole-dipole interatomic interaction (e.g., Lorentz-Lorenz shift) by more than one order of magnitude.
We develop the theory of propagation of laser wave in a gas of two-level atoms (with an optical transition frequency ω0) under the condition of inhomogeneous Doppler broadening, considering the self-consistent solution of the Maxwell-Bloch equations in the mean-field approximation and for one-atomic density matrix. The nonlinear effects in the atomic density n, caused by the free motion of atoms, are found. These effects distort the lineshape (shift, asymmetry, broadening), but are not associated with atom-atom interaction. Moreover, in the case nk0−3<1 (where k0=ω0/c) and temperatures T≳300~K, these quasi-collective effects exceed the well-known influence of the dipole-dipole interatomic interaction (e.g., Lorentz-Lorenz shift) by more than one order of magnitude. It was also found that for some area of parameters, the frequency interval appears, within which the non-trivial self-consistent solution of the Maxwell-Bloch equations is absent at all. Thus, the physical picture of collective effects in a gas medium should be substantially revised.
We develop a field-nonlinear theory of sub-Doppler spectroscopy in a gas of two-level atoms, based on a self-consistent solution of the Maxwell-Bloch equations in the mean-field and single-atom density-matrix approximations. This makes it possible to correctly take into account the effects caused by the free motion of atoms in a gas, which lead to a nonlinear dependence of the spectroscopic signal on the atomic density even in the absence of a direct interatomic interaction (e.g., dipole-dipole interaction). Within the framework of this approach, analytical expressions for the light field were obtained for an arbitrary number of resonant waves and arbitrary optical thickness of a gas medium. Sub-Doppler spectroscopy in the transmission signal for two counterpropagating and copropagating waves has been studied in detail. A previously unknown redshift of a narrow sub-Doppler resonance is predicted in a counterpropagating waves scheme, when the frequency of one wave is fixed and the frequency of the other wave is varied. The magnitude of this shift depends on the atomic density and can be more than an order of magnitude greater than the known shift from the interatomic dipole-dipole interaction (Lorentz-Lorenz shift). The found effects, caused by the free motion of atoms, require a significant revision of the existing picture of spectroscopic effects depending on the density of atoms in a gas. Apart from the fundamental aspect, obtained results are important for precision laser spectroscopy and optical atomic clocks.
The interatomic dipole–dipole interaction is commonly thought to be the main physical reason for spectroscopic effects, which are nonlinear in atomic density. However, we have found that the free motion of atoms can lead to other effects that are nonlinear in atomic density n , using a previously unknown self-consistent solution of the Maxwell–Bloch equations in the mean-field approximation for a gas of two-level atoms with an optical transition at unperturbed frequency ω 0 . These effects distort the Doppler lineshape (shift, asymmetry, broadening), but are not associated with an atom–atom interaction. In particular, in the case of n k 0 − 3 < 1 (where k 0 = ω 0 / c ) and significant Doppler broadening (with respect to collisional broadening), atomic-motion-induced nonlinear effects significantly exceed the well-known influence of the dipole–dipole interatomic interaction (e.g., Lorentz–Lorenz shift) by more than one order of magnitude. Moreover, under some conditions, a frequency interval appears in which a non-trivial self-consistent solution of the Maxwell–Bloch equations is absent due to atomic motion effects. Thus, the existing physical picture of spectroscopic effects that are nonlinear in atomic density in a gas medium should be substantially revised.