Complement 2C: The density matrix and the optical Bloch equations

2012 ◽  
pp. 140-166
Author(s):  
Gilbert Grynberg ◽  
Alain Aspect ◽  
Claude Fabre ◽  
Claude Cohen-Tannoudji
Keyword(s):  
Density Matrix ◽  
Bloch Equations ◽  
Optical Bloch Equations

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

2003 ◽  
Vol 17 (14) ◽  
pp. 2715-2733 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Electromagnetic Field ◽  
Density Matrix ◽  
Large Population ◽  
Matrix Elements ◽  
Level System ◽  
Bloch Equations ◽  
Optical Bloch Equations ◽  
Experimental Realization ◽  
Approximate Analytical Solutions ◽  
Field Dependent

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.

Quantum description of light–matter coupling

2017 ◽  
Author(s):  
Alexey V. Kavokin ◽  
Jeremy J. Baumberg ◽  
Guillaume Malpuech ◽  
Fabrice P. Laussy
Keyword(s):  
Cavity Mode ◽  
Optical Field ◽  
Level System ◽  
Bloch Equations ◽  
Optical Bloch Equations ◽  
Matter Coupling ◽  
Matter Interaction ◽  
Light Matter Interaction ◽  
Full Quantum ◽  
The Ideal

In this chapter we study with the tools developed in Chapter 3 the basic models that are the foundations of light–matter interaction. We start with Rabi dynamics, then consider the optical Bloch equations that add phenomenologically the lifetime of the populations. As decay and pumping are often important, we cover the Lindblad form, a correct, simple and powerful way to describe various dissipation mechanisms. Then we go to a full quantum picture, quantizing also the optical field. We first investigate the simpler coupling of bosons and then culminate with the Jaynes–Cummings model and its solution to the quantum interaction of a two-level system with a cavity mode. Finally, we investigate a broader family of models where the material excitation operators differ from the ideal limits of a Bose and a Fermi field.

Analytical solutions and expressions of the propagator for Bloch equations

2020 ◽  
Vol 34 (18) ◽  
pp. 2050158
Author(s):  
Heung-Ryoul Noh
Keyword(s):  
Analytical Solutions ◽  
Initial Conditions ◽  
Secular Equation ◽  
Magnetization Vector ◽  
Bloch Equations ◽  
Optical Bloch Equations ◽  
Parameter Spaces ◽  
Pulse Spectroscopy ◽  
Analytical Expressions ◽  
Composite Laser

In this paper, we present analytical solutions to the Bloch equations. After solving the secular equation for the eigenvalues, derived from the Bloch equations, analytical solutions for the temporal evolution of the magnetization vector are obtained at arbitrary initial conditions. Subsequently, explicit analytical expressions of the propagator for the Bloch equations and optical Bloch equations are obtained. Compared to the results of existing analytical studies, the present results are more succinct and rigorous, and they can predict the behavior of the propagator in different regions of parameter spaces. The analytical solutions to the propagator can be directly used in composite laser-pulse spectroscopy.

scholarly journals Time-domain violation of the optical Bloch equations for solids

1993 ◽  
Vol 48 (10) ◽  
pp. 6903-6907 ◽  
Author(s):  
R. N. Shakhmuratov ◽  
A. Szabo
Keyword(s):  
Time Domain ◽  
Bloch Equations ◽  
Optical Bloch Equations

Optical Bloch equations with multiply connected states

2008 ◽  
Vol 41 (8) ◽  
pp. 085502 ◽  
Author(s):  
D N Stacey ◽  
D M Lucas ◽  
D T C Allcock ◽  
D J Szwer ◽  
S C Webster
Keyword(s):  
Bloch Equations ◽  
Optical Bloch Equations ◽  
Multiply Connected
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