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Laser Physics

From microsecond spin echo to femtosecond photon echo

Игорь Сергеевич Осадько

Published Nov 4, 2019• 3 citations
Publisher

Abstract

Abstract For more than 70 years spin and photon echo excited by micro- and nanosecond pulses have been the subject of research by various scientific groups. Bloch equations are the mathematical basis in these studies. However, Bloch equations cannot describe echo signals if excitation of the electron-vibrational system is realized by short femtosecond pulses. Only theory for density matrix, which is more general than the Bloch equation approach, is able to describe femtosecond relaxation of polarization and decay of femtosecond echo signals. This work gives an overview of the resent results obtained in developing such a general theoretical formalism.

DOI
10.1088/1555-6611/ab4dad

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Abstract For more than 70 years spin and photon echo excited by micro- and nanosecond pulses have been the subject of research by various scientific groups. Bloch equations are the mathematical basis in these studies. However, Bloch equations cannot describe echo signals if excitation of the electron-vibrational system is realized by short femtosecond pulses. Only theory for density matrix, which is more general than the Bloch equation approach, is able to describe femtosecond relaxation of polarization and decay of femtosecond echo signals. This work gives an overview of the resent results obtained in developing such a general theoretical formalism.
The semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.
The availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.
The excitation of the primary and stimulated photon echoes by pulses modulated in phase with Barker codes is modeled. The shape of the complex envelopes of the primary and stimulated echoes is found by solving the optical Bloch equations. Linear and nonlinear excitation modes are considered. In linear modes, it is possible to realize a time delay and form the correlation function of modulated pulses. The results obtained can be used in modeling and analyzing the corresponding algorithms of the photon echo excitation and in calculating the characteristics of signal processors based on the phenomena of photon and spin echoes.
Femtosecond photon echos in semiconductors are studied on the basis of a stochastic description of the polarization decay. A satisfactory agreement with experimental results [ Phys. Rev. Lett.61, 1647 ( 1988)] is found with respect to the nonexponential decay of the echo energy as a function of the time delay between the laser pulses. Moreover, the shape of the echo is studied, and the detuning of the laser frequency with respect to the band edge is found to depend significantly on the shape of the light pulses.