We consider nonlinear spectroscopic effects—interaction-enhanced double resonance and spectrum instability—that appear in ultracold quantum gases owing to collisional frequency shift of atomic transitions and, consequently, due to the dependence of the frequencies on the population of various internal states of the particles. Special emphasis is put to two simplest cases, (a) the gas of two-level atoms and (b) double resonance in a gas of three-level bosons, in which the probe transition frequency remains constant.
We consider nonlinear spectroscopic effects—interaction-enhanced double resonance and spectrum instability—that appear in ultracold quantum gases owing to collisional frequency shift of atomic transitions and, consequently, due to the dependence of the frequencies on the population of various internal states of the particles. Special emphasis is put to two simplest cases, (a) the gas of two-level atoms and (b) double resonance in a gas of three-level bosons, in which the probe transition frequency remains constant.
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.
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.
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.
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.
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.