Interference effects in the resonance fluorescence of a three-level atom at high proton densities

1980 ◽  
Vol 58 (7) ◽  
pp. 957-963 ◽  
Author(s):  
Constantine Mavroyannis
Keyword(s):  
Excitation Spectrum ◽  
Beat Frequency ◽  
Low Frequency ◽  
Delta Function ◽  
Resonance Fluorescence ◽  
Interference Effects ◽  
Lorentzian Line ◽  
Level Atom ◽  
Upper Level ◽  
The Stability

A theory on interference effects at high photon densities has been developed for two types of a single three-level atom for which transitions occur: (i) from two different upper levels to a common lower one and (ii) from a common upper level to two different lower levels. The excitation spectrum for the interference effects for the two types of atoms results from the symmetric and antisymmetric interference between the two electronic transitions of the system, respectively. The spectral function for the symmetric modes consists of three Lorentzian lines peaked at the frequencies ω = Δ and ω = Δ ± Ω and having spectral widths of the order of γ0 and 3γ0/4, respectively, where Δ is the beat frequency, Ω is the Rabi frequency, and γ0/2 is equal to the natural linewidth for a photon spontaneously emitted from an isolated atom. The antisy mmetric spectrum consists of the peak of ω = Δ, which has a delta-function distribution indicating the stability of the mode in question, and two Lorentzian lines peaked at ω = Δ ± Ω with radiative widths of the order of γ0/2. The excitation spectrum of each type of atom contains also a Lorentzian line describing the very low frequency mode of the system, respectively.

Resonance fluorescence spectra from a three-level atom interacting with a strong bichromatic field

1980 ◽  
Vol 58 (11) ◽  
pp. 1570-1579 ◽  
Author(s):  
M. P. Sharma ◽  
A. Balbin Villaverde ◽  
Constantine Mavroyannis
Keyword(s):  
Closed Form ◽  
Spectral Function ◽  
Excitation Spectrum ◽  
Electromagnetic Fields ◽  
Fluorescence Spectra ◽  
Central Peak ◽  
Relative Strength ◽  
Resonance Fluorescence ◽  
Level Atom ◽  
Bichromatic Field

We have studied the fluorescence spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes are equal to the two atomic transition frequencies, respectively. The Green's function formalism has been used to calculate the excitation spectrum of the system. An expression for the spectral function describing the excitation spectrum of the system has been derived in a closed form in the limit of high photon densities. Numerical computation of the expression for the spectral function indicates that at each transition frequency there may exist either one pair or two pairs or three pairs of sidebands, in addition to the central peak, depending upon the relative strength of the Rabi frequencies involved.

Optical mixing of frequencies of a strong bichromatic field interacting with a three-level atom

1981 ◽  
Vol 59 (12) ◽  
pp. 1917-1929 ◽  
Author(s):  
Constantine Mavroyannis
Keyword(s):  
Spectral Function ◽  
Excitation Spectrum ◽  
Graphical Representation ◽  
Single Band ◽  
Laser Fields ◽  
Optical Amplification ◽  
Lorentzian Line ◽  
Level Atom ◽  
Bichromatic Field ◽  
Optical Mixing

We have studied the excitation spectrum arising from the optical mixing of the frequencies of a strong bichromatic field interacting with a three-level atom, where the two initially populated modes ωa and ωb are equal to the two atomic transition frequencies, respectively. In the limit of high photon densities, the excitation spectrum near the frequency ω = ωa – 2ωb has been calculated as a function of the parameter η = Ωa2/Ωb2, where Ωa and Ωb are the Rabi frequencies of the two laser fields, respectively. For [Formula: see text] and for weak fields for which [Formula: see text], the spectral function describes a Lorentzian line peaked at the frequency ω = ωa – 2ωb and has a width of the order of γ0, where γ0/2 is the natural width for a two-level atom. When Ωb2 > γ02 and [Formula: see text], the band at ω = ωa – 2ωb splits into two bands described by two Lorentzian lines peaked at ω = ωa – 2ωb ± Ωb/√2 and have spectral widths of the order of 3γ0/4. The ratio of the height of the band ω = ωa – 2ωb to the height ω = ωa – 2ωb ± Ωb/2 is 3:2. The probability amplitudes for both bands take large negative values indicating that optical amplification of the signal field may be expected to occur at these frequencies. When Ωa = Ωb = Ω, η = 1, and for Ω2 < γ02, the spectral function describes a single band at ω = ωa – 2ωb while for Ω2 > γ02, the single band splits into five pairs of bands which are separated from the frequency ω = ωa – 2ωb by frequency shifts which are equal to: ± Ω/√2, [Formula: see text], ± Ω, ± Ω√2, and ± Ω√3, respectively, and have spectral widths of the order of 3γ0/4. For [Formula: see text] and for laser fields for which Ωa2 > γ02 and Ωb2 > γ02, the spectral function consists of three pairs of bands. The probability amplitudes for these bands vary linearly with η and may take large values for [Formula: see text]. A complete discussion of the excitation spectrum as well as a graphical representation of the derived results has been given.

Resonance in a mathematical model of baroreflex control: arterial blood pressure waves accompanying postural stress

2005 ◽  
Vol 288 (6) ◽  
pp. R1637-R1648 ◽  
Author(s):  
Peter E. Hammer ◽  
J. Philip Saul
Keyword(s):  
Blood Pressure ◽  
Mathematical Model ◽  
Blood Volume ◽  
Low Frequency ◽  
Pressure Waves ◽  
Central Blood Volume ◽  
Arterial Baroreflex ◽  
Arterial Blood ◽  
Gain Margin ◽  
The Stability

A mathematical model of the arterial baroreflex was developed and used to assess the stability of the reflex and its potential role in producing the low-frequency arterial blood pressure oscillations called Mayer waves that are commonly seen in humans and animals in response to decreased central blood volume. The model consists of an arrangement of discrete-time filters derived from published physiological studies, which is reduced to a numerical expression for the baroreflex open-loop frequency response. Model stability was assessed for two states: normal and decreased central blood volume. The state of decreased central blood volume was simulated by decreasing baroreflex parasympathetic heart rate gain and by increasing baroreflex sympathetic vaso/venomotor gains as occurs with the unloading of cardiopulmonary baroreceptors. For the normal state, the feedback system was stable by the Nyquist criterion (gain margin = 0.6), but in the hypovolemic state, the gain margin was small (0.07), and the closed-loop frequency response exhibited a sharp peak (gain of 11) at 0.07 Hz, the same frequency as that observed for arterial pressure fluctuations in a group of healthy standing subjects. These findings support the theory that stresses affecting central blood volume, including upright posture, can reduce the stability of the normally stable arterial baroreflex feedback, leading to resonance and low-frequency blood pressure waves.

scholarly journals Evolution of a narrow-band spectrum of random surface gravity waves

2003 ◽  
Vol 478 ◽  
pp. 1-10 ◽  
Author(s):  
KRISTIAN B. DYSTHE ◽  
KARSTEN TRULSEN ◽  
HARALD E. KROGSTAD ◽  
HERVÉ SOCQUET-JUGLARD
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Band Spectrum ◽  
Nls Equation ◽  
Random Surface ◽  
Narrow Bandwidth ◽  
Quasi Stationary State ◽  
The Stability ◽  
Three Dimensional Simulations

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

FABRICATION OF NANOPOROUS CHITOSAN MEMBRANES

NANO ◽  
2010 ◽  
Vol 05 (01) ◽  
pp. 53-60 ◽  
Author(s):  
XIAOLIANG WANG ◽  
XIANG LI ◽  
ELEANOR STRIDE ◽  
MOHAN EDIRISINGHE
Keyword(s):  
Low Frequency ◽  
Drug Carriers ◽  
Structural Features ◽  
Wound Dressings ◽  
Ftir Analysis ◽  
Tissue Engineering Scaffolds ◽  
Nanoscale Structures ◽  
Low Frequency Ultrasound ◽  
Chitosan Membranes ◽  
The Stability

Naturally derived biopolymers have been widely used for biomedical applications such as drug carriers, wound dressings, and tissue engineering scaffolds. Chitosan is a typical polysaccharide of great interest due to its biocompatibility and film-formability. Chitosan membranes with controllable porous structures also have significant potential in membrane chromatography. Thus, the processing of membranes with porous nanoscale structures is of great importance, but it is also challenging and this has limited the application of these membranes to date. In this study, with the aid of a carefully selected surfactant, polyethyleneglycol stearate-40, chitosan membranes with a well controlled nanoscale structure were successfully prepared. Additional control over the membrane structure was obtained by exposing the suspension to high intensity, low frequency ultrasound. It was found that the concentration of chitosan/surfactant ratio and the ultrasound exposure conditions affect the structural features of the membranes. The stability of nanopores in the membrane was improved by intensive ultrasonication. Furthermore, the stability of the blended suspensions and the intermolecular interactions between chitosan and the surfactant were investigated using scanning electron microscope and Fourier transform infrared spectroscopy (FTIR) analysis, respectively. Hydrogen bonds and possible reaction sites for molecular interactions in the two polymers were also confirmed by FTIR analysis.

Effect of imposed head vibration on the stability and waveform of flagellar beating in sea urchin spermatozoa

1991 ◽  
Vol 156 (1) ◽  
pp. 63-80 ◽  
Author(s):  
C. Shingyoji ◽  
I. R. Gibbons ◽  
A. Murakami ◽  
K. Takahashi
Keyword(s):  
Sea Urchin ◽  
Beat Frequency ◽  
Distal Region ◽  
Proximal Region ◽  
Bend Angle ◽  
Vibration Frequencies ◽  
Sliding Velocity ◽  
Additional Energy ◽  
The Stability ◽  
Cyclic Changes

The heads of live spermatozoa of the sea urchin Hemicentrotus pulcherrimus were held by suction in the tip of a micropipette mounted on a piezoelectric device and vibrated either laterally or axially with respect to the head axis. Within certain ranges of frequency and amplitude, lateral vibration of the pipette brought about a stable rhythmic beating of the flagella in the plane of vibration, with the beat frequency synchronized to the frequency of vibration [Gibbons et al. (1987), Nature 325, 351–352]. The sperm flagella, with an average natural beat frequency of 48 Hz, showed stable beating synchronized to the pipette vibration over a range of 35–90 Hz when the amplitude of vibration was about 20 microns or greater. Vibration frequencies below this range caused instability of the beat plane, often associated with irregularities in beat frequency. Frequencies above about 90 Hz caused irregular asymmetrical flagellar beating with a marked decrease in amplitude of the propagated bends and a skewing of the flagellar axis towards one side; the flagella often stopped in a cane shape. In flagella that were beating stably under imposed vibration, the wavelength was reduced at higher frequencies and increased at lower frequencies. When the beat frequency was equal to or lower than the natural beat frequency, the apparent time-averaged sliding velocity of axonemal microtubules, obtained as twice the product of frequency and bend angle, decreased with beat frequency in both the proximal and distal regions of the flagella. However, at vibration frequencies above the natural beat frequency, the sliding velocity increased with frequency only in the proximal region of the flagellum and remained essentially unchanged in more distal regions. This apparent limit to the velocity of sliding in the distal region may represent an inherent limit in the intrinsic velocity of active sliding, while the faster sliding observed in the proximal region may be a result of passive sliding or elastic distortion of the microtubules induced by the additional energy supplied by the vibrating pipette. Axial vibration with frequencies either close to or twice the natural beat frequency induced cyclic changes in the waveform, compressing and expanding the bends in the proximal region, but did not affect bends in the distal region or alter the beat frequency.

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