20 / 25
Crystallography 2018
Structural Chemistry & Crystallography Communication
ISSN: 2470-9905
Page 45
June 04-05, 2018
London, UK
3
rd
Edition of International Conference on
Advanced Spectroscopy,
Crystallography and Applications
in Modern Chemistry
T
he present study is devoted to investigation of radiative
properties of N-level quantum systems driven by external
semi-classical monochromatic high-frequency electromagnetic
field and interacting with a heat bath simultaneously. In essence,
one-electron multi-level atom model with violated symmetry was
studied under the assumption that its transition dipole operator
possesses permanent diagonal matrix elements and not all of
them are equal to each other, which assumption amounts to the
violation of the spatial inversion symmetry. A general formula for
the intensity of the electromagnetic field radiated from such a
system in the far-distant zone was derivedwhich does not contain
contributions stemming from these non-zero permanent diagonal
matrix elements of the transition dipole moments explicitly [1].
Hence, it can be concluded that the dynamics of these diagonal
matrixelementsmayaffectthesystemfluorescenceonlyindirectly
through the alteration of the time dependence of the non-diagonal
matrix elements due to quantum processes of higher orders. As
an example, radiative properties of a monochromatically driven
two-level quantum system with permanent non-equal dipole
moment diagonal matrix elements were thoroughly analyzed.
The time evolution of the atomic subsystem of the whole
quantum system (i.e. the atom + heat bath) was described by
the approximate master equation for the atomic reduced density
operator. On its basis, a closed set of evolution equations for the
time-dependent averages of some selected relevant subsystem
variables and their correlation functions was deduced. The so
obtained set of equations was analyzed and solved by means
of the well-established technique [e.g. 4, 5]. Equations derived
were solved numerically in the steady-state limit. Finally, the
steady-state fluorescence spectrum was calculated and it was
found that the radiative properties (spectrum) of this two-level
atomwith violated spatial inversion symmetry can be significantly
modified compared to those of atoms without such violation. In
particular, it was found that the system in question can radiate
at essentially lower frequencies than the frequency of the driving
field [2]. It is important to note that the system dynamics itself
was studied not only numerically but also analytically, and the
existence of a small parameter governing this phenomenon of
the low-frequency radiation was revealed explicitly as a result.
The central part of this work results are the (plausible) conditions
under which a simple two-level quantumsystemdrivenby external
semi-classical monochromatic high-frequency electromagnetic
(laser) field can radiate continuously at much lower frequency.
It was shown that this can be possible under certain conditions
and was also discussed how such a system could be realized
in practice. The absorption-amplification response to the weak
probe field in a simple two-level quantum system with non-equal
permanent diagonal transitional dipole moment matrix elements
driven by semi-classical monochromatic field at resonant
frequency was studied too [3]. It was found that this system is
able to amplify low-frequency EM radiation for a broad enough
range of frequencies. It is reasonable to assume that all the
results mentioned above may be of use in various fields of nano-
electronics and can be employed in development of practically
useful devices dedicated for generation and amplification of
relatively low-frequency (terahertz) EM radiation.
Recent Publications
1. Bogolubov N.N. (Jr.), Soldatov A.V. (2018)
Fluorescence in a quantum system with violated
symmetry. Moscow University Physics Bulletin, 2018,
No.2 (to appear).
2. SoldatovA.V. (2016) Laser frequency down-conversion
by means of a monochromatically driven two-level
system. Mod. Phys. Lett. B, 30:27, 1650331, 1-11.
3. Soldatov A.V. (2017) Broadband EM radiation
amplification by means of a monochromatically driven
two-level system. Mod.Phys.Lett.B, 31:4, 1750027,1-
11.
4. Z. Ficek Z., Seke J., Soldatov A.V., Adam G. (2001)
Fluorescence spectrum of a two-level atom driven by
a multiple modulated field. Phys.Rev. A, 64, 013813,
1-10.
5. Ficek Z., Seke J., Soldatov A.V, Adam G., Bogolubov
N.N. (Jr.) (2002) Absorption and dispersion by a
multiple driven two-level atom. Eur. Phys. J. D, 19,
411–419.
FLUORESCENCE IN QUANTUM SYSTEMS WITH VIOLATED SYMMETRY
Nikolai N. Bogolubov
1
and
Andrey V.Soldatov
Mathematical Institute of the RAS, Russia
Nikolai N. Bogolubov et al., Struct Chem Crystallogr Commun 2018, Volume 4
DOI: 10.21767/2470-9905-C1-005