Summary of Doctoral Thesis in Physics: Influence of spontaneously generated coherence and relative phase between laser fields on optical properties of three-level atomic medium

Research purpose: to build an analytical model describing the dependence of the optical properties (absorption, dispersion, group velocity and group delay) of the three configuration energy level system Λ, Ξ and V according to the following parameters: control parameters (intensity, frequency, polarization and relative phase) of the laser fields.

LE NGUYEN MAI ANH

INFLUENCE OF SPONTANEROUSLY GENERATED

THREE-LEVEL ATOMIC MEDIUM

Specialization: OPTICS Code No: 9 44 01 10

SUMMARY OF DOCTORAL THESIS IN PHYSICS

NGHE AN, 2020

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The work is accomplished at Vinh University

Supervisors: 1 Prof Dr Nguyen Huy Bang

2 Dr Le Van Doai

Reviewer 1:

Reviewer 2:

Reviewer 3:

The thesis is defended before the doctoral evaluation board of Vinh University at … … , …… , …… , 2020

The thesis can be found at:

- Nguyen Thuc Hao Information Centre - Library of Vinh University

- Viet Nam National Library

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PREFACE Reason to choice the investigation subject

Absorption and dispersion are two basic parameters that characterize the optical properties of the atomic medium These two parameters are related

in real and imaginary parts of the susceptibility In addition to the linear susceptibility, atoms also have nonlinear inductances but they are usually of very small value, so only light sources of high intensity can observe optical nonlinear phenomena Therefore, the advent of lasers has opened up many new research directions and related applications One of the most interesting research is to control the optical properties of an atom based on the quantum interference effects of the shifting probability amplitudes in the atom

Among quantum interference effects, EIT (Electromagnetically Induced Transparency) is the earliest studied Accordingly, a probe and a pump laser field simultaneously excite two atomic shifts in common according to lambda (), ladder () and V (V) configurations Based on quantum theory, the above stimulation of the atomic system will lead to a superposition of the shifting probability amplitudes in the atom system, thus producing quantum interference between the shifting channels As a result, the amplitude of the total shifting probability can be either destructive (EIT)

or enhanced, known as the electromagnetically Induced Absorption (EIA)

So far, the EIT effect (related to absorption and dispersion) has been widely studied both theoretically and experimentally in the three configurable energy level -, - and V-type systems These studies show, as the intensity

of the pump laser beam increases, the depth and width of the EIT windows also increase, while the height of the dispersion lines usually increases but the slope decreases In addition, the position of the EIT windows is also shifted to the short wavelength or to the long wavelength by varying the frequency of the pump laser beam accordingly Besides the studies of EIT effects in separate three-level configurations, the study comparing the absorption and dispersion properties in the presence of the EIT effect has also been of interest

to the researchers Comparative research shows that, due to the arrangement

of different energy levels between excitation configurations (,  and V), the efficiency of the quantum interference is very different and therefore the EIT efficiency is also different Specifically, the EIT effect occurs more easily for

-type than for - and V-type systems

In addition to the EIT and EIA effects described above, another quantum interference effect occurs between the spontaneous emission channels due to the non-orthogonal orientation of the electric dipole moments induced by the between probe and pump laser field Non-orthogonal

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orientation of atomic dipole moments can be achieved by polarization between laser fields The result of this interference producing atomic coherence is called the coherence created by Spontaneously Generated Coherence (SGC)

The SGC effect can occur with the EIT effect in atomic systems with three configurable energy levels , , and V-type systems For the EIT effect, the intensity of the quantum interference depends on the intensity of the pump laser beam For SGC effect, the intensity of quantum interference depends on the polarization between the probe laser beam and pump laser beam In the presence of polarization between laser beams, both EIT and SGC effects can occur simultaneously in the medium Interestingly, the SGC effect also significantly changes the optical properties of the medium The studies show that the SGC effect makes the medium more transparent, but the transparent spectral width is narrowed, so the dispersion curve becomes steeper In addition, the influence of SGC makes the atomic medium asymmetric, so the response of the medium is very sensitive to the relative phase of the probe and pump laser fields Up to now, the effects of SGC and the relative phase on group velocity, lasing without population inversion, enhancement Kerr nonlinear, controlling optical bistability, controlling pulse propagation, have been widely studied

Along with the studies on the influence of SGC on absorption and dispersion, there have been many studies on controlling light group velocity From there, we can shift between superluminar to subluninar and vice versa Besides, the group velocity can be reduced differently in each configuration leading to increased group delay (plays an important role in reducing the distortion of light pulses) This exciting feature could create breakthrough applications in optical communication and information processing technology

Although, the effects of SGC and the relative phase between laser fields

on the optical properties of the three energy atomic medium in three excitation configurations have been studied However, firstly, most of the current studies mainly use the numerical method (although there are some studies on the influence of SGC on optical properties by analytical methods, they must use using a incoherent pump laser and approximate), so investigations of the dependence of optical atomic properties on laser parameters are limited and have not shown continuous changes in properties optical according to the control parameters Furthermore, numerical studies will not favor the optimal selection of experimental parameters Second, up to now, there have been no studies to evaluate and compare the effects in the presence of SGC and without SGC in weak and strong probe fields on the

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optical properties of three-level -, Ξ- and V-type This comparison will be essential to see the advantages and disadvantages of each configuration and to have the appropriate selection for application purposes and experimental At the same time, we found extremely small group velocities in the ultraslow light with extremely large delays in each of the three energy configurations

Facing the unresolved problems of the research field and the results

achieved by the group, we chose the topic "Influence of spontaneously

generated coherence and relative phase between laser fields on optical properties of three-level atomic medium” do graduate thesis

Chapter 1 Basics of control of optical properties by laser

1.1 Introduction

1.2 Theoretical basis of light propagation in the medium

1.2.2 Absorption and dispersion

The refractive index of the medium is determined by:

With is the imaginary part of linear susceptibility Accordingly, when

 > 0, the electromagnetic wave is absorbed exponentially while when  < 0, the light wave is amplified when propagating in the medium

1.3 Group and phase velocities

c



= is the wave constant

We have phase velocity: vp = z

g

c v

d d

1.5 Group delay of pulses

Group delay of pulses propagating in the medium compared with delay when light pulses propagate in vacuum according to the formula:

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Chapter 2 Influences of polarization and relative phase between laser

fields on absorption and dispersion 2.1 Atomic stimulation according to a -type configuration

2.1.1 Equations of density matrix

Consider three energy levels excited by two laser fields according to lambda configurations shown in Figure 2.1 (a)

Figure 2.1 (a) Schematics of the three-level -type atomic system and (b) - the polarization is chosen such that one field only drives one transition

2.1.3 The influence of the relative phase between laser fields

When taking into account the interference between spontaneous and phase emissions between laser fields, we have the following system of density matrix equations:

where 31 = 3 - 1 is the frequency difference between level |3 and level

|1 If levels |1 and |3 lie so closely that the SGC effect has to be taken into account, then η = 1, otherwise η = 0

Remark: From the equations above, we see that equations of 31 and 13 appear term 2 2122 related to the interference of the relative phase and spontaneous emissions between the laser fields This term is called the

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coherence produced by spontaneously Generated Coherence Spontaneously Generated Coherence), where  is characteristic of the phase dependence of laser fields If the energy levels |3 and the |1 level are distributed far apart, the terms of the oscillation i 31t

(SGC-e rotate very quickly, possibly approaching 0 and  = 0 (that is, the coherence of spontaneous emission or difference SCG application will not occur) So to study the interference enhancement of the optimal spontaneous emission in the configurations, we have to assume |3 and |1 two lower closely spaced levels, near the degeneration level then 31  0 (or the energy between |3 and |1 is quite small), so = e it

2.2 Atomic stimulation in a -type configuration

Schematic diagram of atomic system excitation of three energy levels in a ladder configuration is described in Figure 2.2(a)

Figure 2.2 (a) Schematics of the three-level -type atomic system (b) The polarization is

chosen such that one field only drives one transition

Similar to the above, we calculate the following equations:

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2.3 Atomic stimulation in a V-type configuration

Excitation of three energy-level atomic systems in a V-type configuration is shown in Figure 2.3 (a)

Figure 2.3 (a) Schematics of the three-level V-type atomic system and (b) - the polarization is chosen such that one field only drives one transition

Call  =p p −21and  =p p −21, respectively, the frequency offset

of the probe and control beam We calculate the following system of equations:

2.4 Absorption and dispersion coefficients

After simpliflcation the expression for the dielectric susceptibility related to 21 for the given atom-fleld system can be written as

2 21 21 0

2

p

N G

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According to the Kramer-Kronig relation, the real and imaginary parts

of susceptibility are directly related to the linear dispersion coefficient and the linear absorption coefficient by:

2.5 Controlling absorption and dispersion coefficients

To study absorption and dispersion controls according to laser parameters such as intensity, frequency, polarization and relative phase We replace the expressions for 21 found in the three configurations above and apply the calculation results to the 85Rb gas atomic medium and ignore the effects of Doppler broadening

Figure 2.4 Schematics of the 85Rb atom system give a three-energy excitation configuration: (a) lambda, (b) ladder, (c) V-type configuration

For the -type configuration, the energy levels |1, |2 và |3 corresponding to the states 52S1/2 F = , 3 52P F = và 1/2 3 52S1/2 F = For the 2V-type configuration , energy levels |1, |2 và |3 corresponding to the states

-10

2.5.1 Influence of the SGC

In this section, we examine the effect of SGC (generated by light polarization and characterized by interference parameter p) on the absorption and dispersion of the medium by fixing the intensity, the frequency and relative phase of the laser fields at Gp = 5, Gc = 10, c = 0 và  = 0,, are depicted in Figures 2.5 and 2.6 respectively

In general, in all three configurations, the influence of SGC on absorption in the V-configuration is more effective This can be explained by the larger spontaneous emission rate in V-configuration due to the stronger coherence created by spontaneous emission (ie term 12 * 12) Furthermore, comparing the density matrix equations of the three configurations, we see the term "coherence generated by spontaneous emission" appearing in all density matrix equations in the configuration, but in the lambda and ladder configurations this term appears only in the equation for 21

Figure 2.5 Variations of absorption coefficient versus probe field detuning for different values of p = 0.9 (solid line), p = 0.7 (dotted-dash line), p = 0 (dash line): (a) , (b)  and (c) V-type

Figure 2.5 Variations of dispersion coefficient versus probe field detuning for different values of p = 0.9 (solid line), p = 0.7 (dotted-dash line), p = 0 (dash line): (a) , (b)  and (c) V-type

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This phenomenon can be explained as follows: EIT effect is a result of destructive interference of probability amplitudes induced by laser fields or enhanced interference resulting in EIA - Electromagnetically Induced Absorption Besides, there is also the appearance of the term " Spontaneously Generated Coherence - SGC" which is a newly generated oscillating source (corresponding to a spontaneous emission shift probability) Thus, when the effects of EIT and SGC are present at the same time, inside the atom, interference of inductive probability amplitude and spontaneous emission probability will occur Interference of many such "coherent sources" will reduce the "interference pattern", ie, the spectral EIT (destructive interference) and EIA (enhanced interference) as shown in Figure 2.5 Increasing the interference parameter p is increasing the intensity of the spontaneous emission source

Figure 2.7 Variations of absorption (a) and dispersion (b) coefficient versus p in Λ-type system (solid line), ladder-type system (dot-dashed line) and (c) V-type system (dashed line)

To see this difference more intuitively, we compare the variation of the absorption and dispersion coefficients of the three configurations according to the interference parameter p as described in Figure 2.7 The parameters selected are  = 0, ∆c = 0, Gp = 5γ, Gc = 10γ and ∆p = 4γ corresponding to an EIT window near point

From Figure 2.7 (b), the dispersion coefficient significantly changes the dispersion properties of the medium when the interference parameter p changes from 0.7 to 1 Along with the absorption change from EIT to EIA, the dispersion was also changed from conventional to anomalous dispersion

In particular, the variation of the dispersion curve with parameter p in the configuration is opposite to the lambda and ladder configuration Therefore, the light propagation properties can be changed from fast light to slow light