Search results for "Bloch equations"
showing 8 items of 18 documents
Generalized bloch equations for optical interactions in confined geometries
2005
By combining the field-susceptibility technique with the optical Bloch equations, a general formalism is developed for the investigation of molecular photophysical phenomena triggered by nanometer scale optical fields in the presence of complex environments. This formalism illustrate the influence of the illumination regime on the fluorescence signal emitted by a single molecule in a complex environment. In the saturated case, this signal is proportional to the optical local density of states, while it is proportional to the near-field intensity in the non-saturated case. (C) 2005 Elsevier B.V. All rights reserved.
Nonlinear magneto-optical resonances atD1excitation ofR85bandR87bfor partially resolved hyperfineFlevels
2009
Experimental signals of nonlinear magneto-optical resonances at ${D}_{1}$ excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The ${D}_{1}$ transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. The experimental signals wer…
Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation
2004
In this paper we, to our knowledge, for the first time obtain the rate equations for Zeeman coherences in the broad line approximation and steady-state balance equations directly from optical Bloch equations without the use of the perturbation theory. The broad line approximation allows us to use the adiabatic elimination procedure in order to eliminate the optical coherences from the optical Bloch equations, but the steady-state condition allows us to derive the balance equations straightforward. We compare our approach with the perturbation theory approach as given previously and show that our approach is more flexible in analyzing various experiments. Meanwhile we also show the validity …
Electric field induced hyperfine level-crossings in (nD)Cs at two-step laser excitation: experiment and theory
2005
The pure electric field level-crossing of m_F Zeeman sublevels of hyperfine F levels at two-step laser excitation was described theoretically and studied experimentally for the nD_3/2 states in Cs with n = 7,9, and 10, by applying a diode laser in the first 6S_1/2 to 6P_3/2 step and a diode or dye laser for the second 6P_3/2 to nD_3/2 step. Level-crossing resonance signals were observed in the nD_3/2 to 6P_1/2 fluorescence. A theoretical model was developed to describe quantitatively the resonance signals by correlation analysis of the optical Bloch equations in the case when an atom simultaneously interacts with two laser fields in the presence of an external dc electric field. The simulat…
Stimulated nutation echo: application to the driven decoherence study
2003
We study experimentally the dynamical and decay properties of the stimulated nutation echo (SNE) in a two-level spin system, the signal of which allows the observation timescale of the driven coherence relaxation to be extended. This signal appears in the transient response of the system to the second pulse at time τ1 from its start and coinciding with the duration of the first pulse. The information about the first pulse duration is imprinted into the population difference of the inhomogeneously broadened ensemble of the two-level absorbers. The decay of the SNE signal has two contributions. One originates from the population decay during the time τ between the two pulses. Another is cause…
Optimal control of an ensemble of Bloch equations with applications in MRI
2016
International audience; The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal control and the dynamics is analyzed in the framework of geometric optimal control. This lead to numerical implementations or suboptimal controls using averaging principle.
Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to…
2017
The aim of this article is to classify the singular trajectories associated with the optimal control problems of a pair of controlled Bloch equations. The motivation is to analyze the robustness of the optimal solutions to the contrast and the time-minimal saturation problem, in magnetic resonance imaging, with respect to the parameters and B1-inhomogeneity. For this purpose, we use various computer algebra algorithms and methods to study solutions of polynomial systems of equations and inequalities which are used for classification issues: Gröbner basis, cylindrical algebraic decomposition of semi-algebraic sets, Thom's isotopy lemma.
Double-quantum nutations in a two-level spin system
1986
The transient oscillatory behavior of the nonlinear response of a two-level electron-spin system is experimentally investigated in a sample of glassy silica with ${E}_{1}^{\mathcal{'}}$ centers (S=(1/2)) at microwave frequency at T=4.2 K. The transient regime, excited by an intense step-modulated radiation tuned to double-quantum (DQ) resonance, is monitored by revealing the second-harmonic (SH) wave radiated by the spins undergoing DQ transitions. Time- and frequency-domain results show that the emitted SH wave has two components: the former, which vanishes at the DQ resonance, exhibits an overdamped transient regime, the latter consists of damped oscillations at a frequency which depends …