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 Modern Optics

Coherent control on absorption and dispersion in closely spaced transitions for a four-level system with three closely-spaced upper levels

Saswata Ghosh, Swapan Mandal

Published Jun 16, 2010• 3 citations
Publisher

Abstract

Under the Doppler free condition, a four-level system with three coherently prepared closely spaced upper levels coupled to a single electromagnetic field is being investigated for the absorptive and dispersive lineshapes. By using a perturbation method, the optical Bloch equations for the present four-level system are solved analytically to obtain the induced polarization and hence the spectral lineshapes. The field induced and field independent coherences appear automatically in the analytical expressions of the imaginary and real parts of the complex polarization. These field independent and field dependent coherences are the outcome of the quantum interference between the probability amplitudes of finding the atom in those energy levels. The phase sensitive field induced polarizations are extensively studied for two special conditions of the ground level populations. The influence of the closely spaced transitions on the quantum coherence and hence the subsequent effects on absorption despite inversion, electromagnetically induced transparency and on the ultrahigh index of refraction are discussed.

DOI
10.1080/09500340.2010.486484

Related papers

Effects of field-induced quantum coherence on the absorptive line shape of a four-level system with three closely spaced upper levels

Saswata Ghosh, Swapan Mandal

The optical Bloch equations of a four-level atomic system with three closely spaced upper levels irradiated by a single mode of the electromagnetic radiation field are constructed. Under the rotating wave approximation and by using the slowly varying envelope approximation, we obtain the analytical solution to these optical Bloch equations. These solutions, which are obtained perturbatively, are used to calculate the polarization and hence the absorptive line shape. In particular, we examine the effects of the field-induced coherence arising from the interference between the probability amplitudes of the levels participating in dipole-allowed transitions. We obtain the shifts of the resonance peak positions due to two different reasons. The first is due to the nonlinear effects arising from the closely spaced nature of the peaks. The second is attributed to the field-induced coherence alone. It is found that the shifts of the positions of the resonance peaks due to field-induced coherence may be in the blue or in the red region.

Physical Review A•Aug 19, 2004•16 citations

Effects of field induced quantum coherence on the absorptive lineshape of a V-type three-level system

Swapan Mandal

A single electromagnetic field interacting with a V-type three-level system having two closely spaced upper levels is studied for the Doppler-free absorptive lineshape. The usual optical Bloch equations are constructed. Quantum interference between the probability amplitudes of the levels participating in a dipole allowed transition is taken into consideration. The quantum interference is manifested through the phase angle. It appears that these phases are significant only if the applied electromagnetic field is strong. The absorptive lineshape calculations are revisited in the light of such field induced coherence. The lineshape exhibits pushing between two spectral lines in addition to the usual pulling between them. It is found that the pushing of the spectral lines depends solely on the coherence induced by the strong field. The complete cancellation of field dependent shifts for the resonance peaks is possible by the suitable adjustment of the phase angles arising from the strong field induced coherence.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 6, 2000•7 citations

Effects of Field-Induced Coherence on Laser Without Population Inversion and on Absorptionless Dispersion for a V-Type Three Level System

Swapan Mandal

A V-type three level system with two closely spaced upper levels interacting with a single mode of the electromagnetic field is studied for the absorptive and dispersive lineshapes. A semiclassical description for the atom-field interaction is being adopted to obtain the usual optical Bloch equations. The approximate analytical solutions for the density matrix elements are obtained by solving coupled optical Bloch equations. Through the off-diagonal density matrix elements, the introduction of phase angles between the levels participating in dipole allowed transitions are automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. These field dependent phases (coherence) are responsible for the reduction of the inversionless gain and the absorptionless dispersion. For large decay constants, it is found that the energy gap between the upper two levels has no role to play on the laser without inversion and on the absorptionless dispersion. However, for large population per unit decay, a significant increase of the absorptionless dispersion and the inversionless gain is obtained. The condition for large population decay and a possible experimental realization of the field dependent phases are discussed.

International Journal of Modern Physics B•Jun 10, 2003•3 citations

Atomic coherence effects in four-level systems: Doppler-free absorption within an electromagnetically-induced-transparency window

S. N. Sandhya, K. K. Sharma

We report here an effect in a four-level ladderlike system, which is in contrast to the usual quantum interference effects such as electromagnetically induced transperency (EIT) or coherent population trapping: we predict the occurrence of a narrow absorption peak within the EIT window when an EIT atomic system interacts with an additional driving rf field. The Doppler-free-central absorption appears when the three-photon resonance condition is satisfied. In the limit of the rf field strength ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{rf}}$\ensuremath{\rightarrow}0, the usual EIT profile is recovered.

Physical Review A•Mar 1, 1997•49 citations

Formation of field induced absorption in the probe response signal of a four-level V type atomic system a theoretical study

Khairul Islam, Ghosh, Arindam, Dipankar Bhattacharyya +1 more

A density matrix based analytical model is developed to study the coherent probe field propagation through a four-level V type system in presence of a coherent control field. The model allows coupling of the probe field from the upper ground level to both of the excited levels keeping the control field locked to a particular transition. The addition of an extra ground level to a conventional three-level V type system creates extra decay paths to the ground levels for the upper level population. A set of sixteen density matrix based equations are formed and then solved analytically under rotating wave approximation to study the probe response under steady state condition. The simulated probe absorption spectra shows absorption dip at the centre of a transparency window only under Doppler broadened condition although the conventional EIT window appears under Doppler free condition. The dependence of the field induced absorption signal on the Rabi frequency of the control field, population transfer rate among the ground levels and temperature of the vapour medium has been studied in details.

arXiv:1603.01686•Mar 5, 2016•0 citations

FORMATION OF FIELD INDUCED ABSORPTION IN THE PROBE RESPONSE SIGNAL OF A FOUR-LEVEL ‘V’ TYPE ATOMIC SYSTEM: A THEORETICAL STUDY

A density matrix based analytical model is developed to study the coherent probe field propagation through a four-level V type system in presence of a coherent control field. The model allows coupling of the probe field from the upper ground level to both of the excited levels keeping the control field locked to a particular transition. The addition of an extra ground level to a conventional three-level V type system creates extra decay paths to the ground levels for the upper level population. A set of sixteen density matrix based equations are formed and then solved analytically under rotating wave approximation to study the probe response under steady state condition. The simulated probe absorption spectra shows absorption dip at the centre of a transparency window only under Doppler broadened condition although the conventional EIT window appears under Doppler free condition. The dependence of the field induced absorption signal on the Rabi frequency of the control field, population transfer rate among the ground levels and temperature of the vapour medium has been studied in details.

International Journal of Advance Engineering and Research Development•Jun 30, 2016•0 citations
Under the Doppler free condition, a four-level system with three coherently prepared closely spaced upper levels coupled to a single electromagnetic field is being investigated for the absorptive and dispersive lineshapes. By using a perturbation method, the optical Bloch equations for the present four-level system are solved analytically to obtain the induced polarization and hence the spectral lineshapes. The field induced and field independent coherences appear automatically in the analytical expressions of the imaginary and real parts of the complex polarization. These field independent and field dependent coherences are the outcome of the quantum interference between the probability amplitudes of finding the atom in those energy levels. The phase sensitive field induced polarizations are extensively studied for two special conditions of the ground level populations. The influence of the closely spaced transitions on the quantum coherence and hence the subsequent effects on absorption despite inversion, electromagnetically induced transparency and on the ultrahigh index of refraction are discussed.
The optical Bloch equations of a four-level atomic system with three closely spaced upper levels irradiated by a single mode of the electromagnetic radiation field are constructed. Under the rotating wave approximation and by using the slowly varying envelope approximation, we obtain the analytical solution to these optical Bloch equations. These solutions, which are obtained perturbatively, are used to calculate the polarization and hence the absorptive line shape. In particular, we examine the effects of the field-induced coherence arising from the interference between the probability amplitudes of the levels participating in dipole-allowed transitions. We obtain the shifts of the resonance peak positions due to two different reasons. The first is due to the nonlinear effects arising from the closely spaced nature of the peaks. The second is attributed to the field-induced coherence alone. It is found that the shifts of the positions of the resonance peaks due to field-induced coherence may be in the blue or in the red region.
A single electromagnetic field interacting with a V-type three-level system having two closely spaced upper levels is studied for the Doppler-free absorptive lineshape. The usual optical Bloch equations are constructed. Quantum interference between the probability amplitudes of the levels participating in a dipole allowed transition is taken into consideration. The quantum interference is manifested through the phase angle. It appears that these phases are significant only if the applied electromagnetic field is strong. The absorptive lineshape calculations are revisited in the light of such field induced coherence. The lineshape exhibits pushing between two spectral lines in addition to the usual pulling between them. It is found that the pushing of the spectral lines depends solely on the coherence induced by the strong field. The complete cancellation of field dependent shifts for the resonance peaks is possible by the suitable adjustment of the phase angles arising from the strong field induced coherence.
A V-type three level system with two closely spaced upper levels interacting with a single mode of the electromagnetic field is studied for the absorptive and dispersive lineshapes. A semiclassical description for the atom-field interaction is being adopted to obtain the usual optical Bloch equations. The approximate analytical solutions for the density matrix elements are obtained by solving coupled optical Bloch equations. Through the off-diagonal density matrix elements, the introduction of phase angles between the levels participating in dipole allowed transitions are automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. These field dependent phases (coherence) are responsible for the reduction of the inversionless gain and the absorptionless dispersion. For large decay constants, it is found that the energy gap between the upper two levels has no role to play on the laser without inversion and on the absorptionless dispersion. However, for large population per unit decay, a significant increase of the absorptionless dispersion and the inversionless gain is obtained. The condition for large population decay and a possible experimental realization of the field dependent phases are discussed.
We report here an effect in a four-level ladderlike system, which is in contrast to the usual quantum interference effects such as electromagnetically induced transperency (EIT) or coherent population trapping: we predict the occurrence of a narrow absorption peak within the EIT window when an EIT atomic system interacts with an additional driving rf field. The Doppler-free-central absorption appears when the three-photon resonance condition is satisfied. In the limit of the rf field strength ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{rf}}$\ensuremath{\rightarrow}0, the usual EIT profile is recovered.
A density matrix based analytical model is developed to study the coherent probe field propagation through a four-level V type system in presence of a coherent control field. The model allows coupling of the probe field from the upper ground level to both of the excited levels keeping the control field locked to a particular transition. The addition of an extra ground level to a conventional three-level V type system creates extra decay paths to the ground levels for the upper level population. A set of sixteen density matrix based equations are formed and then solved analytically under rotating wave approximation to study the probe response under steady state condition. The simulated probe absorption spectra shows absorption dip at the centre of a transparency window only under Doppler broadened condition although the conventional EIT window appears under Doppler free condition. The dependence of the field induced absorption signal on the Rabi frequency of the control field, population transfer rate among the ground levels and temperature of the vapour medium has been studied in details.
A density matrix based analytical model is developed to study the coherent probe field propagation through a four-level V type system in presence of a coherent control field. The model allows coupling of the probe field from the upper ground level to both of the excited levels keeping the control field locked to a particular transition. The addition of an extra ground level to a conventional three-level V type system creates extra decay paths to the ground levels for the upper level population. A set of sixteen density matrix based equations are formed and then solved analytically under rotating wave approximation to study the probe response under steady state condition. The simulated probe absorption spectra shows absorption dip at the centre of a transparency window only under Doppler broadened condition although the conventional EIT window appears under Doppler free condition. The dependence of the field induced absorption signal on the Rabi frequency of the control field, population transfer rate among the ground levels and temperature of the vapour medium has been studied in details.