Gas Of Two-level Atoms Research Articles

Influence of Free Motion of Atoms on Atomic Density-Dependent Effects in Nonlinear Laser Spectroscopy of Resonant Gas Media

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.

Atomic-motion-induced spectroscopic effects that are nonlinear in atomic density in a gas

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.

Generalized uncertainty principle corrections on atomic excitation

In this paper, we investigate the effect of minimal length on Einstein model of a gas of two-level atoms in thermal equilibrium with blackbody radiation at temperature T. We reformulate the classical Hamiltonian describing the interaction of atomic electrons with the electromagnetic field of blackbody radiation by employing Kempf Algebra to obtain the Hamiltonian with a minimal length. In the electric dipole approximation, we obtain the modified transition rate relations, and modified Einstein coefficients for broadband excitation. We utilize the modified quantities to obtain the modified cross-section in the resonant laser excitation. We deduce the upper bounds for the deformation parameter and minimal length.

Hanbury Brown-Twiss Correlations for a Driven Superatom.

Hanbury Brown-Twiss interference and stimulated emission, two fundamental processes in atomic physics, have been studied in a wide range of applications in science and technology. We study interference effects that occur when a weak probe is sent through a gas of two-level atoms that are prepared in a singly excited collective (Dicke or "superatom") state and for atoms prepared in a factorized state. We measure the time-integrated second-order correlation function g^{(2)} of the output field as a function of the delay τ between the input probe field and radiation emitted by the atoms and find that, for the Dicke state, g^{(2)} is twice as large for τ=0 as it is for γ_{e}τ≫1 (γ_{e} is an excited state decay rate), while for the product state, this ratio is equal to 3/2. The results agree with those of a theoretical model in which any effects related to stimulated emission are totally neglected-the coincidence counts measured in our experiment arise from Hanbury Brown-Twiss interference between the input field and the field radiated by the atoms.

Dynamical Casimir Effect and Collective Excitation Effect at Finite Temperature Without the Rotating-Wave Approximation

The dynamical Casimir effect and the collective excitation effect are investigated in a resonantly vibrating cavity filled with a gas of two-level atoms without the rotating-wave approximation at finite temperature. Compared with the condition of the rotating-wave approximation, the created photons and the created excitons are more under the non-rotating wave approximation at different temperatures and different total coupling strengths. The numerical results show that the counter-rotating wave terms enhance the dynamical Casimir effect and the collective excitation effect at finite temperature.

Lasing and phase transition in atomic system with dressed states

The problem of phase transitions in the system of high-density gas of two-level atoms non-resonantly interacting with a pump field in the presence of optical collisions (OCs) and placed in the cavity is studied. The OCs are considered in the framework of thermalization of atomic dressed state (DS) population. For the case of a strong atom-field coupling condition we analyze the problem of thermodynamic equilibrium superradiant phase transition for the order parameter representing real amplitude of cavity mode and taking place as a result of the atomic DS thermalization process. At the same time such a transition can be connected with condensed (coherent) properties of low branch DS-polaritons occurring in the cavity. Various aspects of non-equilibrium phase transition to laser field generation by using atomic DS levels are studied in detail. It is important that for positive atom-light detuning DS lasing can be obtained in the presence of quasi-equilibrium DS population that corresponds to a true two-level atomic system with inversion in perturbative limit.

Nonlinear spectroscopic effects in quantum gases induced by atom-atom interactions

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.

Turbulence in a gas laser

We test a recent assertion [A. Muriel, Physica A 388 (4) (2009) 311] that a gas consisting of excited molecules is turbulent, in contrast to the laminar state of a gas of ground state molecules. Since a lasing gas is made up of excited molecules, we examine if a lasing gas system is indeed turbulent. Surprisingly, from a literature search, it appears that turbulence in a lasing gas medium has never been addressed. To test for turbulence, we use a recently proposed criterion for the existence of turbulence, the presence of multivalued steady-state velocity fields [P. Getreur, A. Albano, A. Muriel, Phys. Lett. A 366 (2007) 101]. To study this subject, we improve an old model of a gas of two-level atoms in a one-dimensional model [A. Muriel, M. Dresden, Physica D 94 (1996) 103] by including the effect of a radiation field with the use of Einstein A and B coefficients. A set of coupled equations for the velocity fields in one dimension are derived. The zeroth order implementation of an iterative solution establishes that the steady-state velocity fields are multivalued, given by the Lambert function. We obtain signature characteristics of turbulence such as velocity reversals, infinite gradients, and stagnation points.

Surface optical solitons of self-induced transparency in indefinite media

The nonlinear surface TM-modes propagating along the interface separating an isotropic medium and an indefinite medium are investigated. A transition layer sandwiched between the connected media is described using a model of a two-dimensional gas of two-level atoms. Two cases of isotropic media, left-handed and metallic, are considered. It is shown that explicit analytical expressions for a surface optical soliton of self-induced transparency depends on the parameters of the two-level atoms and the connected media.

Refractive index of two-level gas in quantized field of counterpropagating waves

An expression for the refractive index of a gas of two-level atoms in the quantized single-mode field of counterpropagating waves is calculated. It is shown that in the limit of large numbers of photons the result reproduces the quasiclassical result in only the case of standing wave where intensities of both waves are equal. Explanation of this “strange” situation where the abilities of quantum field theory turn to be more restricted than those of classical theory is given.

Stability of coherent states of a Bose gas of two-level atoms in resonant laser field at zero temperature

It is shown that a Bose gas of two-level atoms in the intense resonant laser field at zero temperature is a mixture of two condensates with a definite ratio of the densities. The criteria of stability are found for the stationary states of such system against the increment of the amplitudes of quasi Bogoliubov elementary excitations. Besides the usual acoustic mode the gap mode is shown to exist and the magnitude of the gap is proportional to the laser field amplitude. The involvement of the gas nonideality under definite conditions results in an instability and decay of the condensates.

Effective photon-photon interaction in a two-dimensional “photon fluid”

We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional ``photon fluid'' confined in a Fabry-Perot resonator. With the atoms modelled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the ``bare'' strength of the anharmonic term. The resulting expression for the non-linear Kerr susceptibility, is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity.

Kinetic Theory of a Spin-1/2 Bose-Condensed Gas

We derive a kinetic theory for a spin-1/2 Bose-condensed gas of two-level atoms at finite temperatures. The condensate dynamics is described by a generalized Gross–Pitaevskii equation for the two-component spinor order parameter, which includes the interaction with the uncondensed fraction. The noncondensate atoms are described by a quantum kinetic equation, which is a generalization of the spin kinetic equation for spin-polarized quantum gases to include couplings to the condensate degree of freedom. The kinetic equation is used to derive hydrodynamic equations for the noncondensate spin density. The condensate and noncondensate spins are coupled directly through the exchange mean field. Collisions between the condensate and noncondensate atoms give rise to an additional contribution to the spin diffusion relaxation rate. In addition, they give rise to mutual relaxation of the condensate and noncondensate due to lack of local equilibrium between the two components.

Linear spin waves in a trapped Bose gas

An ultracold Bose gas of two-level atoms can be thought of as a spin-1/2 Bose gas. It supports spin-wave collective modes due to the exchange mean field. Such collective spin oscillations have been observed in recent experiments at JILA with ${}^{87}\mathrm{Rb}$ atoms confined in a harmonic trap. We present a theory of the spin-wave collective modes based on the moment method for trapped gases. In the collisionless and hydrodynamic limits, we derive analytic expressions for the frequencies and damping rates of modes with dipole and quadrupole symmetry. We find that the frequency for a given mode is given by a temperature-independent function of the peak density n, and falls off as $1/n.$ We also find that, to a very good approximation, excitations in the radial and axial directions are decoupled. We compare our model to the numerical integration of a one-dimensional version of the kinetic equation and find very good qualitative agreement. The damping rates, however, show the largest deviation for intermediate densities, where one expects Landau damping---which is unaccounted for in our moment approach---to play a significant role.

Effect of the pressure of light on the shape of saturated-absorption resonance in a gas

The effect of a force of resonance pressure of light on the amplitude and frequency properties of saturated-absorption resonance in a gas of two-level atoms was studied. On the basis of numerical solutions of the Liouville and Fokker-Planck equations, dynamics of changes in the velocity-distribution function of an ensemble of atomic particles, depending on the saturation parameter and time of their interaction with a strong field of light, was evaluated. The shape of a resonance line, related to saturated absorption, and its location relative to the frequency of the atomic transition were determined taking into account the dynamics of the distribution function. The results of the calculations are compared with the experimental data.

Longitudinal spin waves in a dilute bose gas.

We present a kinetic theory for a dilute noncondensed Bose gas of two-level atoms that predicts the transient spin segregation observed in a recent experiment. The underlying mechanism driving spin currents in the gas is due to a mean-field effect arising from the quantum interference between the direct and exchange scattering of atoms in different spin states. We numerically solve the spin Boltzmann equation, using a one-dimensional model, and find excellent agreement with experimental data.

Lasers without inversion (LWI) in Space: A possible explanation for intense, narrow-band, emissions that dominate the visible and/or far-UV (FUV) spectra of certain astronomical objects

The optical or far-UV (FUV) spectra of certain objects in Space are completely dominated by one or two spectrally narrow emission lines, strongly suggesting that laser action of some kind occurs in these objects. However, the electronic level structures of the atoms/ions producing these emissions preclude the possibility of maintaining population inversions on the electronic transitions involved. In lasers, gain is normally produced on an optical transition that is inverted, i.e. one that has more atoms maintained in the upper than in the lower state, so that stimulated emission can exceed stimulated absorption. However, as a result of discoveries made in quantum electronics over the past 30 years or so, one now knows that there are several ways to make stimulated emission occur on a transition that is not inverted, i.e. to realize a \laser without inversion (LWI). This requires rst making the atoms non-absorbing at the lasing frequency, i.e. setting up a condition of \electromagnetically induced transparency (EIT). Some recently developed EIT techniques for three-level atoms are rst reviewed. A simple model for a space LWI based upon a gas of two-level atoms is then proposed. In this model, transparency results from a form of EIT induced by the presence of an intense, monochromatic, continuous-wave, laser beam tuned to the frequency !o of the two-level-atom transition. Amplication of light at this same frequency occurs via resonant stimulated hyper-Raman scattering (SHRS) and four-wave mixing (FWM), with pumping energy provided by continuum starlight spectrally overlapping the two outer absorption sidebands (\Mollow bands) induced by the presence of the beam at !o. Two specic examples of superintense line emission from Space are here considered. These are (a) the H() emission line appearing as a dominant singularity in certain reddened, early-type stars, and (b) the powerful O VI (1032 A, 1038 A) emission doublet that dominates the FUV emission spectra of symbiotic stars such as RR Tel.

Iterative Methods for the Non‐LTE Transfer of Polarized Radiation: Resonance Line Polarization in One‐dimensional Atmospheres

This paper shows how to generalize to non-LTE polarization transfer some operator splitting methods that were originally developed for solving unpolarized transfer problems. These are the Jacobi-based accelerated Λ-iteration (ALI) method of Olson, Auer, & Buchler and the iterative schemes based on Gauss-Seidel and successive overrelaxation (SOR) iteration of Trujillo Bueno and Fabiani Bendicho. The theoretical framework chosen for the formulation of polarization transfer problems is the quantum electrodynamics (QED) theory of Landi Degl'Innocenti, which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. This first paper establishes the grounds of our numerical approach to non-LTE polarization transfer by concentrating on the standard case of scattering line polarization in a gas of two-level atoms, including the Hanle effect due to a weak microturbulent and isotropic magnetic field. We begin demonstrating that the well-known Λ-iteration method leads to the self-consistent solution of this type of problem if one initializes using the exact solution corresponding to the unpolarized case. We show then how the above-mentioned splitting methods can be easily derived from this simple Λ-iteration scheme. We show that our SOR method is 10 times faster than the Jacobi-based ALI method, while our implementation of the Gauss-Seidel method is 4 times faster. These iterative schemes lead to the self-consistent solution independently of the chosen initialization. The convergence rate of these iterative methods is very high; they do not require either the construction or the inversion of any matrix, and the computing time per iteration is similar to that of the Λ-iteration method.

Electromagnetic bubbles: subcycle near-femtosecond and subfemtosecond field solitons

We demonstrate the feasibility of strong (up to atomic fields) and supershort (few-femtosecond or even subfemtosecond) subcycle (nonoscillating) electromagnetic solitons [EM bubbles (EMB’s)] in a gas of two-level atoms as well as EMB’s and preionization shock waves in classically nonlinear atoms. We show that EMB’s can be generated by existing sources of radiation, including subpicosecond half-cycle pulses and short laser pulses. We investigate how EMB characteristics are controlled by those of originating pulses. Our most recent results are focused on related transient phenomena, including EMB formation length, multibubble generation, and shocklike waves.

Sub-Doppler structure in the spectrum of resonance fluorescence excited by an evanescent wave at a gas-solid interface

We consider the resonance fluorescence from the gas of two-level atoms excited by an evanescent wave under the conditions of “hole burning”. We predict the sub-Doppler structure in the fluorescence spectrum due to the optical nutations of the atoms desorbing from the surface.