It is the aim of the present work to show some departures from the well-known optical Bloch equations usually obtained when the damping of a two-level system driven by a Glauber coherent mode of the radiation field is treated in the Markovian approximation. In particular, we show that for an arbitrary intensity we have a set of 4 n optical Bloch equations which can be reduced to the usual optical Bloch equations when the population of the mode becomes important. A criterion for the quasi-classical evolution can be deduced. Obviously, in both limits of an arbitrarily weak or strong excitation intensity the Mollow's results are obtained. In addition, we do not need here the introduction of a particular form like the plane wave used by Mollow for the corresponding classical field--as the problem is solved explicitly.It is the aim of the present work to show some departures from the well-known optical Bloch equations usually obtained when the damping of a two-level system driven by a Glauber coherent mode of the radiation field is treated in the Markovian approximation. In particular, we show that for an arbitrary intensity we have a set of 4 n optical Bloch equations which can be reduced to the usual optical Bloch equations when the population of the mode becomes important. A criterion for the quasi-classical evolution can be deduced. Obviously, in both limits of an arbitrarily weak or strong excitation intensity the Mollow's results are obtained. In addition, we do not need here the introduction of a particular form like the plane wave used by Mollow for the corresponding classical field--as the problem is solved explicitly.

Optical EngineeringJun 1, 19830 citations

Dynamical aspects in the optical bloch equations

Smail B. Bougouffa, S. Al‐Awfi

The European Physical Journal Special TopicsJun 17, 20084 citations

On the relaxation of a two-level system driven by a strong electromagnetic field

Eitan Geva, Ronnie Kosloff, James L. Skinner

A detailed and unified account of the theory of the generalized Bloch equations is presented. The equations apply to a two-level system weakly coupled to a heat bath and subject to a monochromatic rotating field of arbitrary intensity. The relaxation tensor obtained is explicitly field-dependent. The derivation is valid for general coupling to a quantum heat bath. The generalized Bloch equations are shown to be thermodynamically consistent, as opposed to the standard Bloch equations. Different limits of the generalized Bloch equations are examined and related to previous studies. The potential use of the generalized Bloch equations as a probe of the bath spectral density is demonstrated for the case of a two-level system embedded in a Debye solid.A detailed and unified account of the theory of the generalized Bloch equations is presented. The equations apply to a two-level system weakly coupled to a heat bath and subject to a monochromatic rotating field of arbitrary intensity. The relaxation tensor obtained is explicitly field-dependent. The derivation is valid for general coupling to a quantum heat bath. The generalized Bloch equations are shown to be thermodynamically consistent, as opposed to the standard Bloch equations. Different limits of the generalized Bloch equations are examined and related to previous studies. The potential use of the generalized Bloch equations as a probe of the bath spectral density is demonstrated for the case of a two-level system embedded in a Debye solid.

The Journal of Chemical PhysicsJun 1, 1995132 citations

Experimental Test of the Optical Bloch Equations for Solids

Ralph G. DeVoe, Richard G. Brewer

This paper provides the first experimental test of the Bloch equations for an optical transition in a low-temperature impurity-ion solid, ${\mathrm{Pr}}^{3+}$ : La ${\mathrm{F}}_{3}$ , where the condition ${T}_{1}\ensuremath{\gg}{T}_{2}$ applies. Intensity-dependent optical free-induction-decay measurements are performed by use of an ultrastable cw dye laser (linewidth, 300 Hz) and reveal an $\mathrm{exp}(\ensuremath{-}\frac{2t}{{T}_{2}})$ decay law at low Rabi frequency ($\ensuremath{\chi}$), as predicted by the Bloch equations, and an $\mathrm{exp}(\ensuremath{-}\ensuremath{\chi}t)$ decay at high $\ensuremath{\chi}$, which violates the Bloch prediction but agrees with Redfield's characterization of NMR saturation in solids.This paper provides the first experimental test of the Bloch equations for an optical transition in a low-temperature impurity-ion solid, ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$, where the condition ${T}_{1}\ensuremath{\gg}{T}_{2}$ applies. Intensity-dependent optical free-induction-decay measurements are performed by use of an ultrastable cw dye laser (linewidth, 300 Hz) and reveal an $\mathrm{exp}(\ensuremath{-}\frac{2t}{{T}_{2}})$ decay law at low Rabi frequency ($\ensuremath{\chi}$), as predicted by the Bloch equations, and an $\mathrm{exp}(\ensuremath{-}\ensuremath{\chi}t)$ decay at high $\ensuremath{\chi}$, which violates the Bloch prediction but agrees with Redfield's characterization of NMR saturation in solids.

Physical Review LettersApr 25, 1983197 citations

Analytic solutions of the optical Bloch equations

Heung‐Ryoul Noh, Wonho Jhe

Optics CommunicationsFeb 12, 201029 citations

This paper provides the first experimental test of the Bloch equations for an optical transition in a low-temperature impurity-ion solid,

{\mathrm{Pr}}^{3+}

: La

{\mathrm{F}}_{3}

, where the condition ${T}_{1}\ensuremath{\gg}{T}_{2}$ applies. Intensity-dependent optical free-induction-decay measurements are performed by use of an ultrastable cw dye laser (linewidth, 300 Hz) and reveal an $\mathrm{exp}(\ensuremath{-}\frac{2t}{{T}_{2}})$ decay law at low Rabi frequency ($\ensuremath{\chi}$), as predicted by the Bloch equations, and an $\mathrm{exp}(\ensuremath{-}\ensuremath{\chi}t)$ decay at high $\ensuremath{\chi}$, which violates the Bloch prediction but agrees with Redfield's characterization of NMR saturation in solids.