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

International Journal of Modern Physics B

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

Swapan Mandal

Published Jun 10, 2003• 3 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979203018363

Related papers

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

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

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.

Journal of Modern Optics•Jun 16, 2010•3 citations

Gain without inversion in three-level V-type system: a dressed-state analysis

Doron Braunstein, R. Shuker

Summary form only given.A three-level atom in the V-configuration is treated under two coherent laser fields at resonance with the two allowed transitions. The master equation for the system and full quantum mechanical Hamiltonian are derived, and equations of motion for the elements of the density matrix are obtained by projecting into the bare- and dressed-states schemes. Analysis of light amplification without population inversion in this V-type system is accomplished within the framework of the dressed-state basis. The physical content of the equations of motion for the density matrix elements, namely the coherences and the populations is provided by identifying effective decay and relaxation rates and gain/absorption constants with the appropriate composite coefficients. These depend on the Rabi frequencies of both the drive and probe coherent fields. Time-dependent solutions for both the coherences and the populations are obtained both numerically and analytically under the secular approximation. We have shown how to construct these analytical approximate time-dependent solutions for dressed-state populations and coherences. These approximate solutions, as well as the full numerical calculation quantities, exhibit oscillations at the generalized Rabi frequency.

Conference on Lasers and Electro-Optics•Jan 1, 1998•0 citations

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

Analytical studies on pump-induced optical resonances in anM-typesix-level system

Saswata Ghosh, Swapan Mandal

In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 1, 2010•8 citations

Doppler-free absorptive signal lineshape of a four-level double λ-type system: Rabi splitting and two-photon effects

Saswata Ghosh, Swapan Mandal

Two electromagnetic fields (the stronger called the pump and the weaker called the signal) are allowed to interact with a four-level double λ-type system with two pairs of closely spaced levels. The present four-level system could also be viewed as an example of a double resonant system. Under the Doppler-free condition and using a semiclassical formulation of atom–field interaction, we derive the optical Bloch equations involving the said four-level system coupled to two external fields. These coupled optical Bloch equations are unsolvable in closed analytical form. In order to obtain the absorptive lineshapes, we use the usual perturbation method for getting the approximate analytical solution to the coupled optical Bloch equations for the density matrix elements. Through the off-diagonal complex density matrix elements, the introduction of phase angles between the levels participating in dipole-allowed transitions is automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. For on-resonance pump conditions, we obtain the usual Rabi splitting. The effects of two-photon resonances are clearly shown for off-resonance pump conditions.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 24, 2009•4 citations
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.
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.
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.
Summary form only given.A three-level atom in the V-configuration is treated under two coherent laser fields at resonance with the two allowed transitions. The master equation for the system and full quantum mechanical Hamiltonian are derived, and equations of motion for the elements of the density matrix are obtained by projecting into the bare- and dressed-states schemes. Analysis of light amplification without population inversion in this V-type system is accomplished within the framework of the dressed-state basis. The physical content of the equations of motion for the density matrix elements, namely the coherences and the populations is provided by identifying effective decay and relaxation rates and gain/absorption constants with the appropriate composite coefficients. These depend on the Rabi frequencies of both the drive and probe coherent fields. Time-dependent solutions for both the coherences and the populations are obtained both numerically and analytically under the secular approximation. We have shown how to construct these analytical approximate time-dependent solutions for dressed-state populations and coherences. These approximate solutions, as well as the full numerical calculation quantities, exhibit oscillations at the generalized Rabi frequency.
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.
In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.
Two electromagnetic fields (the stronger called the pump and the weaker called the signal) are allowed to interact with a four-level double λ-type system with two pairs of closely spaced levels. The present four-level system could also be viewed as an example of a double resonant system. Under the Doppler-free condition and using a semiclassical formulation of atom–field interaction, we derive the optical Bloch equations involving the said four-level system coupled to two external fields. These coupled optical Bloch equations are unsolvable in closed analytical form. In order to obtain the absorptive lineshapes, we use the usual perturbation method for getting the approximate analytical solution to the coupled optical Bloch equations for the density matrix elements. Through the off-diagonal complex density matrix elements, the introduction of phase angles between the levels participating in dipole-allowed transitions is automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. For on-resonance pump conditions, we obtain the usual Rabi splitting. The effects of two-photon resonances are clearly shown for off-resonance pump conditions.