Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Response of a two-level atom to a frequency-modulated optically coherent pulse train

James M. Supplee, Edward A. Whittaker, Keith Andrew

Published Jul 1, 1998• 2 citations
Publisher

Abstract

We present an analytical expression for the response of a two-level atom to a frequency-modulated optically coherent pulse train. The optical beam has sinusoidal frequency modulation and is chopped to have a square-wave envelope. We assume that the laser pulses are short compared with the atomic-decay time, the pulse-repetition time, and the modulation period. With this short-pulse assumption we are able to use a method similar to Temkin’s [J. Opt. Soc. Am. B10, 830–839 (1993)] and solve the optical Bloch equations in closed form.

DOI
10.1364/josab.15.001833

Related papers

Excitation of an atom by a train of short pulses

Richard J. Temkin

A general, analytic theory is presented of the excitation of a two-level atom by a series of short optical laser pulses. The atom is assumed to be isolated (collisionless) with radiative decay from upper to lower state at rate γ. The laser pulses are assumed to have a duration tp such that γtp ≪ 1 (the transient regime), and the spacing between pulses tr is such that tr ≫ tp. In this regime the atomic density matrix is calculated as a function of time during each optical pulse. An analytic expression for the atomic state (Bloch vector) after n optical pulses is also derived. For large n the atomic state converges to a repeating (steady state) cycle of pump excitation followed by radiative decay. The excited-state population in the steady state can be large but only if the spacing between pulses tr is small so that γtr ≲ 0.5. These results indicate that lasers that produce trains of pulses, such as mode-locked conventional lasers and free-electron lasers, can be effective in optical pumping of atoms.

Journal of the Optical Society of America B•May 1, 1993•33 citations

Frequency-modulated few-cycle optical-pulse-train-induced controllable ultrafast coherent population oscillations in two-level atomic systems

Parvendra Kumar, Amarendra K. Sarma

We report a study on the ultrafast coherent population oscillations (UCPOs) in two-level atoms induced by a frequency-modulated few-cycle optical pulse train. The phenomenon of UCPOs is investigated by numerically solving the optical Bloch equations beyond the rotating wave approximation. We demonstrate that the quantum state of the atoms and the frequency of the UCPOs may be controlled by controlling the number of pulses in the pulse trains and the pulse repetition time, respectively. Moreover, the robustness of the population inversion against the variation of the laser pulse parameters is also investigated. The proposed scheme may be useful for the creation of atoms in selected quantum states for desired time duration and may have potential applications in ultrafast optical switching. The scheme may also be used to measure pulse repetition rate.

arXiv:1207.6701•Physical Review A•Feb 1, 2013•13 citations

Atomic excitation by a pulse train I: two-level atoms

Lee C. Bradley

An assembly of ground-state two-level atoms with a Maxwellian velocity distribution is considered to be illuminated by a near-resonant train of Gaussian pulses whose pulse separation is of the same order of magnitude as the natural decay time of the upper state by spontaneous emission. The equations of motion of the density matrix, including spontaneous decay, are numerically integrated over the duration of one pulse and are analytically integrated between pulses. In this way, the transition matrix is derived. The time evolution of the system is then followed by successive multiplications of the state vector by the transition matrix. Steady state is attained after a few pulses. Because the pulse train has side bands separated by the pulse repetition frequency, corresponding velocity groups are preferentially excited. The response (defined as the time-average spontaneous emission of the assembly) is found to be a quasi-sinusoidal function of the number of Rabi flops per pulse. Frequency modulation of the pulse train leads to smaller variation in the response and, consequently, to considerably higher response.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Optical Bloch Equations for a Two-Level Atom Revisited: Analytical Solutions

Heung‐Ryoul Noh

We present a comprehensive analytical study of the optical Bloch equations for a closed two-level atom. We obtain a map in phase space of the Rabi frequency and the laser frequency detuning, discriminating the characteristics of solutions to the optical Bloch equations separated by a boundary in phase space. Outside the boundary, oscillatory behavior is shown, while simple decaying behavior is shown inside the boundary. The behavior of the solutions is also found to be dependent on the relative magnitude of the decay rates of the optical coherence and the excited state population.

Journal of the Physical Society of Japan•Aug 20, 2015•4 citations

Experimental observation of chirped continuous pulse-train soliton solutions to the Maxwell-Bloch equations

Shihadeh Saadeh, John L. Shultz, Gregory J. Salamo

A frequency chirped continuous wave laser beam incident upon a resonant, two-level atomic absorber is seen to evolve into a Jacobi elliptic pulse-train solution to the Maxwell-Bloch equations. Experimental pulse-train envelopes are found in good agreement with numerical and analytical predictions.

Optics Express•Jan 15, 2001•2 citations

Resonance fluorescence of a two-level atom driven by phase-modulated laser light

Maciej Janowicz

The spectral distribution of light scattered by a two-level atom in a laser beam with phase modulation has been calculated. The spectrum has been obtained via numerical solution of the optical Bloch equations using the algorithm of Wilkens and Rza\ifmmode \mbox{\c{}}\else \c{}\fi{}\ifmmode \dot{z}\else \.{z}\fi{}ewski [Phys. Rev. A 40, 3164 (1989)]. The modulation produces additional sidebands in both coherent and incoherent parts of the spectrum; the location of the added components depends on the modulation depth. In the case of two-frequency phase modulation with incommensurate frequencies, wild, ``chaotic'' behavior of the spectrum has been observed, similar to the case of bichromatic amplitude modulation. The intensity distribution is practically insensitive to the chosen constant value of the phase of modulation.

Physical Review A•Sep 1, 1991•11 citations
We present an analytical expression for the response of a two-level atom to a frequency-modulated optically coherent pulse train. The optical beam has sinusoidal frequency modulation and is chopped to have a square-wave envelope. We assume that the laser pulses are short compared with the atomic-decay time, the pulse-repetition time, and the modulation period. With this short-pulse assumption we are able to use a method similar to Temkin’s [J. Opt. Soc. Am. B10, 830–839 (1993)] and solve the optical Bloch equations in closed form.
A general, analytic theory is presented of the excitation of a two-level atom by a series of short optical laser pulses. The atom is assumed to be isolated (collisionless) with radiative decay from upper to lower state at rate γ. The laser pulses are assumed to have a duration tp such that γtp ≪ 1 (the transient regime), and the spacing between pulses tr is such that tr ≫ tp. In this regime the atomic density matrix is calculated as a function of time during each optical pulse. An analytic expression for the atomic state (Bloch vector) after n optical pulses is also derived. For large n the atomic state converges to a repeating (steady state) cycle of pump excitation followed by radiative decay. The excited-state population in the steady state can be large but only if the spacing between pulses tr is small so that γtr ≲ 0.5. These results indicate that lasers that produce trains of pulses, such as mode-locked conventional lasers and free-electron lasers, can be effective in optical pumping of atoms.
We report a study on the ultrafast coherent population oscillations (UCPOs) in two-level atoms induced by a frequency-modulated few-cycle optical pulse train. The phenomenon of UCPOs is investigated by numerically solving the optical Bloch equations beyond the rotating wave approximation. We demonstrate that the quantum state of the atoms and the frequency of the UCPOs may be controlled by controlling the number of pulses in the pulse trains and the pulse repetition time, respectively. Moreover, the robustness of the population inversion against the variation of the laser pulse parameters is also investigated. The proposed scheme may be useful for the creation of atoms in selected quantum states for desired time duration and may have potential applications in ultrafast optical switching. The scheme may also be used to measure pulse repetition rate.
An assembly of ground-state two-level atoms with a Maxwellian velocity distribution is considered to be illuminated by a near-resonant train of Gaussian pulses whose pulse separation is of the same order of magnitude as the natural decay time of the upper state by spontaneous emission. The equations of motion of the density matrix, including spontaneous decay, are numerically integrated over the duration of one pulse and are analytically integrated between pulses. In this way, the transition matrix is derived. The time evolution of the system is then followed by successive multiplications of the state vector by the transition matrix. Steady state is attained after a few pulses. Because the pulse train has side bands separated by the pulse repetition frequency, corresponding velocity groups are preferentially excited. The response (defined as the time-average spontaneous emission of the assembly) is found to be a quasi-sinusoidal function of the number of Rabi flops per pulse. Frequency modulation of the pulse train leads to smaller variation in the response and, consequently, to considerably higher response.
We present a comprehensive analytical study of the optical Bloch equations for a closed two-level atom. We obtain a map in phase space of the Rabi frequency and the laser frequency detuning, discriminating the characteristics of solutions to the optical Bloch equations separated by a boundary in phase space. Outside the boundary, oscillatory behavior is shown, while simple decaying behavior is shown inside the boundary. The behavior of the solutions is also found to be dependent on the relative magnitude of the decay rates of the optical coherence and the excited state population.
The spectral distribution of light scattered by a two-level atom in a laser beam with phase modulation has been calculated. The spectrum has been obtained via numerical solution of the optical Bloch equations using the algorithm of Wilkens and Rza\ifmmode \mbox{\c{}}\else \c{}\fi{}\ifmmode \dot{z}\else \.{z}\fi{}ewski [Phys. Rev. A 40, 3164 (1989)]. The modulation produces additional sidebands in both coherent and incoherent parts of the spectrum; the location of the added components depends on the modulation depth. In the case of two-frequency phase modulation with incommensurate frequencies, wild, ``chaotic'' behavior of the spectrum has been observed, similar to the case of bichromatic amplitude modulation. The intensity distribution is practically insensitive to the chosen constant value of the phase of modulation.