Spontaneous Emission of a Dressed Atomic System

in a Strong Light Field

A. V. Bogatskaya and A. M. Popov

D. V. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991, Russia

Keywords: Quantum Description of Interaction of Light and Matter, Photoionization of Atoms, Rydberg States,

Interference Stabilization.

Abstract: New approach to the study of the spontaneous emission of an atomic system driven by a strong light field is

developed. This approach is based on the accurate consideration of quantum system interaction with

vacuum quantized field modes in the first order of perturbation theory, while the strong light field is

considered classically. The proposed approach is applied to study the dynamics of field-driven atomic

systems. Among them are Rabi oscillations in two-level system, resonant and nonresonant Raman and

Rayleigh scattering, interference stabilization of Rydberg atoms. It is demonstrated that analyzing the

spontaneous emission allows to study the specific features of quantum systems dressed by the field.

1 INTRODUCTION

Study of the nonperturbative atomic dynamics in

strong laser fields is the core problem of nonlinear

optics (Akhmanov and Nikitin, 1997). Typically this

dynamics is studied in the semiclassical approach

(Agostini and Di Mauro, 2004; Couairon and

Mysyrowicz, 2007; Krausz and Ivanov, 2009; Chin,

2010). It means that while the atomic system is

analyzed from quantum-mechanical point of view

the electromagnetic field is considered still classical-

ly. In (Bogatskaya et al, 2016) the possibility to use

semiclassical approach for analyzing radiative

processes in high intensity fields was questioned. It

was demonstrated that the application of the semi-

classical approach to study emission of the quantum

system driven by high intensity laser field is

generally in contradiction with quantum electro-

dynamical calculations. Also it means that

spontaneous emission from the quantum system is

neglected. If laser field is strong enough the

probability of spontaneous transitions is negligibly

small in comparison with stimulated transitions.

Nevertheless, any stimulated emission starts from a

spontaneous background radiation. It means that in

order to study initial stage of any nonlinear process

one need to take into account spontaneous processes

as well. On the other hand it is known atomic

spectrum can be dramatically reconstructed by the

strong external laser field (Delone and Krainov,

1994; Fedorov, 1997). New quantum object with

essentially different spectrum than the field-free

atomic spectrum, (so called the dressed atom),

appears to exist. The simplest example of such

reconstruction is the AC Stark shift of energy levels

in relatively weak laser field. Another example of

the dressed atom is the so called Kramers -

Henneberger atom that appears to exist in

superatomic fields (Fedorov, 1997). The sponta-

neous emission from

this dressed by the laser field

atomic system can provide the unique information

about its energy spectrum. To study the structure of

dressed atom one needs to take into account the

interaction with the electromagnetic vacuum. The

interaction with vacuum modes also should be taken

into account for analyzing a lot of nonlinear

processes. A lot of practical applications of theory

including interaction of the atomic system with both

classical and vacuum field modes can be found in

quantum optics (Scally and Zubairy, 1997).

The aim of this paper is to develop the approach

for studying first-order spontaneous radiative

processes in a quantum system driven by a strong

classical laser field. This approach is based on the

first order perturbation theory applied to the

interaction of the atomic system dressed by the

strong laser field with a lot of quantized field modes

in the assumption that initially all the modes are in a

vacuum state. The proposed approach is applied for

Bogatskaya A. and Popov A.

Spontaneous Emission of a Dressed Atomic System in a Strong Light Field.

DOI: 10.5220/0006099301290136

In Proceedings of the 5th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2017), pages 129-136

ISBN: 978-989-758-223-3

Copyright

c

2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

129

study of a number of quantum systems such as

quantum dots, quantum wires, clusters in the

presence of the intense laser field.

2 ATOM DYNAMICS IN A

STRONG LASER FIELD IN

THE PRESENCE OF

QUANTIZED

ELECTROMAGNETIC FIELD

We analyse the atomic system using the following

Hamiltonian

),()(),(

0

ε

ε

rVHtrHH

f

++= ,

(1)

where

),()(

0

trWrHH

at

+=

;

)(rH

at

is the atomic

Hamiltonian,

)(tEdW

⋅−=

represents the interaction

of atom with classical laser field in the dipole

approximation,

f

H - Hamiltonian of the set of field

modes excluding laser field mode,

),(

ε

rV

stands for

the interaction of the atom with the quantized

electromagnetic field,

red

= is the dipole moment,

r

is the electron radius-vector and

ε

is the set of

quantized field mode coordinates.

We are going to deal with the quantized field

using perturbation theory. In the case when there is

no interaction with quantized field modes one can

write the well-known equation

),()(

),(

0

trtH

t

tr

i

ψ

ψ

=

∂

∂

,

(2)

which describes the atomic dynamics in a classical

laser field. Initial condition can be written as

)()0,( rtr

φ

ψ

==

,

(3)

where

)(r

φ

is some stationary or unstationary state

of the atomic discrete spectrum or continuum. We

will suppose also that at the initial instant of time all

field modes are in the vacuum state

{}

0

. Provided

that we know the solution of equation (2), the

solution of the general equation with the

Hamiltonian (1)

()

),,()(

),,(

0

trVHtH

t

tr

i

f

ε

ε

Ψ++=

∂

Ψ∂

,

(4)

and initial condition

{}

0)()0,,( ×==Ψ rtr

φε

can be

found by means of the perturbation theory.

Wave function of zero-order approximation

excluding interaction with the quantum field modes

reads

}0{),(),,(

)0(

×=Ψ trtr

ψε

,

(5)

We are going to find the solution of (4) in the form:

),,(),,(),,(

)0(

trtrtr

εδεε

Ψ+Ψ=Ψ

,

(6)

with

)0(

Ψ<<Ψ

δ

.

Substituting (6) in (4) in the first order of

smallness one obtains:

()

),,(),,()(

),,(

)0(

0

trVtrHtH

t

tr

i

f

εεδ

εδ

Ψ+Ψ+

=

∂

Ψ∂

(7)

with the initial condition

0)0,,( ==Ψ tr

ε

δ

.

In fact (7) can be formulated as Schroedinger

equation for the

Ψ

δ

with the source in the right

hand. For further analysis of eq. (7) let us remind

that initially we have vacuum in all field modes.

Therefore in the first order of perturbation theory

Ψ

δ

contains only one-photon excitations in a some

field mode:

{}

×=Ψ

λ

λλ

δψεδ

,

0,0,...0,1,....0,0),(),,(

k

kk

trtr

,

(8)

Here

),( tr

k

λ

δ

ψ

is the electron wave function

provided that one photon with wave vector

k

and

polarization

λ

has appeared.

As the interaction of the atom with quantized field

can be written in a form

λ

λ

λ

λ

λ

εε

k

k

k

k

k

edVrV

−== )(),(

,

,

(9)

(

λ

ε

k

is the field operator of mode

{}

λ

,k

and

λ

k

e

is

the polarization vector) for a given mode with one-

photon excitation one can write:

()

()

.0),(,),()(

,23),(,

),(

)(

0

trVktrhtH

ktrk

t

tr

i

kk

f

k

kk

k

ψλδψ

λωδψλ

δ

ψ

λλ

λ

λλ

λ

++=

×+

∂

∂

(10)

Here

)( f

k

h

λ

is the Hamiltonian of the field mode

λ

,k

. Provided that

λωλ

λ

λ

,23,

,

)(

kkh

k

f

k

⋅= , and

λ

ε

ε

λ

,

2

0 k

norm

k

= , (

3

4 L

knorm

λ

ωπε

=

is the

auxiliary normalizing constant,

3

L

is the

normalization volume), the final form of the eq. (10)

can be written as

PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology

130

)exp(),(

2

)(

),()(

),(

0

titred

trtH

t

tr

i

k

norm

k

k

k

λλ

λ

λ

ωψ

ε

δψ

δψ

×××−

=

∂

∂

(11)

with the initial condition

0)0,( ==tr

k

λ

δ

ψ

.

It is obvious that the expression

= rdtrtW

kk

3

2

),()(

λλ

δψ

(12)

represents the probability to find a photon in the

mode

λ

,k

as a function of time. Then the total

probability to emit the photon of any frequency and

polarization during the transition

if →

is

=

λ

λ

,

)()(

k

kfi

tWtW

(13)

As the spectrum of field modes is dense, we can

replace the sum in eq. 13 by the integral:

Ω= dd

c

Lkd

L

kk

λλ

ωω

ππ

2

33

3

3

3

3

8

2

)2(

2

(14)

After the integration over angular distribution of

photons and summation over possible polarizations

the probability of the spontaneous decay in the

spectral interval

),(

ω

ω

ω

d+

can be expressed in the

form

λωω

ωω

π

ω

,/

2

32

3

3

ck

Wd

c

L

dW

=

×=

(15)

where

λ

,k

W is given by (12). One should note, that

the expression (14) does not depend on the

normalization volume, as

3

,

1~ LW

k

λ

.

3 RABI OSCILLATIONS IN A

TWO-LEVEL SYSTEM AND

TRIPLET MOLLOW

Let us restrict ourselves to the consideration of two-

level system (energy levels and stationary state wave

functions

1

E

and

i

ϕ

,

2,1=i

respectively) inter-

acting with near resonant field of frequency

)(

1221

EE −=≈

ω

ω

and initially (

)0=t

being in

the state

1

.

Figure 1: Dressing of two-level system in a resonant

electromagnetic field.

In the case of exact resonance

0

21

≡−=Δ

ω

ω

ω

wave function of the system governed by the

classical field with electric field

t

ω

ε

ε

cos

0

=

can be

represented in a form

)exp()()(),(

2,1

tE

i

rtCtr

n

n

nn

=

−=

ϕψ

(16)

with

tC Ω= cos

1

and

tiC Ω−= sin

2

, where

2

021

ε

d=Ω

is the Rabi frequency. One can easily

see that in our case dressing means splitting of each

level into two quasienergy states with energies

Ω±→

ii

EE

. The structure of this splitting for the

case

21

ω

<<Ω

is performed at fig.1. It means that

the line of spontaneous emission corresponding to

the transition

)(

12

EE

k

−==

ω

ω

λ

should split up

into three lines

Ω±= 2,

ω

ω

ω

λ

k

, so-called triplet

Mollow (Mollow, 1969). To confirm this statement

we will find the solution of general equation (11) in

a form

)exp()()(),(

2,1

)(

tE

i

rtCtr

n

n

n

k

nk

=

−=

ϕδψ

λ

λ

.

(17)

Then the equations for amplitudes

)(

λ

k

n

C

reads

()

,))(exp())(exp(

2121

*

)(

2

)(

1

titi

CCi

kk

kk

Ω+−+Ω−−

×Ω−Ω−=

ωωωω

λλ

λλ

()

.))(exp())(exp(

2121

*

)(

1

)(

2

titi

CCi

kk

kk

Ω+++Ω−+−

×Ω−Ω−=

ωωωω

λλ

λλ

(18)

Here

22

21

*

norm

d

ε

=Ω is the coupling constant of the

quantum system with quantized field. First terms in

(18) mean the transitions between two atomic states

of the system under the resonant laser field while

second terms stand for the emission of photons

2

Spontaneous Emission of a Dressed Atomic System in a Strong Light Field

131

{}

λ

,k

. General analytical solution of eq. (18) with

initial conditions

0)0(

)(

2,1

==tC

k

λ

we can write as

Ω±−

Ω±−

+

Ω

−

−

×Ω=

Ω±−

Ω±−

+

Ω

−

−

×Ω=

4/)2(

)2/)2(sin

sin4

4/)(

)2/)(sin

)()(

4/)2(

)2/)2(sin

cos4

4/)(

)2/)(sin

)

()(

2

21

21

2

2

2

21

21

2

2*

2

)(

2

2

21

21

2

2

2

21

21

2

2*

2

)(

1

ωω

ωω

ωω

ωω

ωω

ωω

ωω

ωω

λ

λ

λ

λ

λ

λ

λ

λ

λ

λ

k

k

k

k

k

k

k

k

k

k

t

t

t

tC

t

t

t

tC

(19)

It represents emission of photons near the

frequencies

Ω±= 2,

ω

ω

ω

λ

k

and subsequent Rabi

oscillations of the atomic population probabilities.

The probability to emit photon

{}

λ

,k

is

2

)(

2

2

)(

1

)(

λλ

λ

kk

k

CCtW += and is given at fig.2 for

two different laser pulse durations. As we supposed

earlier, the initial line splits into three lines that are

known as triplet Mollow. The intensity of the central

line is twice larger in comparison with satellites at

frequencies

Ω±= 2

ω

ω

λ

k

. As the duration of the

pulse increases the splitting of the initial line into the

triplet Mollow becomes more and more pronounced

(see solid and dashed curves at fig.2).

Figure 2: Triplet Mollow for short (solid) and long (dash)

laser pulses. Pulse durations are 10

4

and 2 10

4

at.un.

4 NONRESONANT

SPONTANEOUS RAMAN AND

RAYLEIGH SCATTERING

In this chapter we will study Raman and Raylegh

scattering of laser radiation by atomic system. To

obtain the general expression for probabilities of

Raman and Raylegh scattering let us consider the

atomic dynamics in classical laser field also in the

first order of perturbation theory. Then

,exp)()(

exp)(),(

)1(

≠

−+

−=

in

nnn

ii

tE

i

rtC

tE

i

rtr

ϕ

ϕψ

(20)

where

+

+

+

−

−

=

)(

))(exp(

)(

))(exp(

2

)(

0

)1(

ωω

ωω

ωω

ωω

ni

ni

ni

nini

n

titiEd

tC

(21)

Substituting (20) and (21) into (11) and assuming

that

i

is the initial atomic state one derives the

equation for probability amplitude to find the atom

in

f

and the photon in the mode

{}

λ

,k

:

).)(exp()(

2

)exp())((

)1(

)(

)(

tideC

titEdCCi

kfnfnk

in

n

norm

n

fnfn

k

n

k

f

λλ

λ

λ

ωω

ε

ω

+−

−=

≠

(22)

Second term in the right part of (22) stands for the

emission of photon

{}

λ

,k

while the first one

describes the evolution of atomic wave function in

the classical field after the emission of photon and

here we will neglect such evolution. From (22) one

derives:

.)(2

1

22

))((

)(

2

0

2

2

)(

tEE

ded

tC

kif

in

ni

nikfn

norm

k

f

×+−−×

−

=∞→

≠

λ

λ

λ

ωωπδ

ωω

ε

ε

(23)

This is the probability of Stoks component of the

spontaneous Raman scattering corresponding to the

final state

f

and emission of a photon

)(

ifk

EE −−=

ω

ω

λ

(24)

If the final state coincides with the initial one

if =

we derive the expression for the Rayleigh

scattering

,)(2

1

22

))((

)(

2

0

2

2

)(

t

ded

tC

k

in

ni

nikin

norm

k

i

×−×

−

=∞→

≠

ωωπδ

ωω

ε

ε

λ

λ

λ

(25)

when the frequency of spontaneous photon is the

same as for laser radiation. Not far from resonanse

when laser frequency is

ni

ω

ω

≈

with definite value

PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology

132

of

n

, the transition takes place through the only

intermediate state and summation over all

intermediate states in expressions (23) and (25)

should be omitted:

.)(2

1

22

))((

)(

)(

2

0)(

2

2

)(

)(

tEE

ded

tC

kiif

ni

niknif

norm

k

if

×+−−×

−

=∞→

λ

λ

λ

ωωπδ

ωω

ε

ε

(26)

5 FOUR-LEVEL SYSTEM

DYNAMICS IN A PRESENCE

OF QUANTIZED

ELECTROMAGNETIC FIELD

To provide more insight into atomic dynamics in

discrete spectrum we will study the spontaneous

emission in four-level system

3,2,1,0

with

even parities for

2,0

and odd ones for

3,1

. The

wave function of the system

=

−=

3

0

)exp()()(),(

n

nnn

tE

i

rtCtr

ϕψ

(27)

is obtained from the set of equations

)exp(cos)(

0

titdCCi

fn

n

fnnf

ωωε

−=

(28)

with initial condition

0)0(,1)0(

3,2,10

====

=

tCtC

i

.

Then the equation (11) is also equivalent to a set of

equations for amplitudes

)(

)(

tC

k

f

λ

for different

{}

λ

,k

modes:

).exp()exp()()(

2

)(

)exp(cos)(

3

0

0

)(

)(

titE

i

rtCed

titdCCi

k

n

nnn

norm

k

fn

n

fn

k

n

k

f

λλ

λ

λ

ωϕ

ε

ωωε

=

−−

−−=

(29)

The positions of energy levels were chosen as

follows

1.0,2.0,25.0

322110

===

ω

ω

ω

and hence

55.0

30

=

ω

. Hereafter all values will be given in

atomic units. Nonzero values of the dipole matrix

elements were chosen equal to each other

1

21323010

==== dddd

. The duration of laser pulse

was

4

104 ×=

τ

, laser intensity was 10

-3

, that means

the Rabi frequency is

4

105

−

×=Ω . The spectrum of

spontaneous emission for various spectral intervals

and different detuning of the laser frequency from

the frequency of transition

30 →

(

)55.0

30

=

ω

are presented at fig.3. First we should mention that

in the laser frequency range

005.0

30

>−

ω

ω

for

definite laser pulse parameters both Raman and

Raleigh processes

230 →→

and

030 →→

correspondingly have nonresonant

character and can be studied using the expression

(23). Near the resonance the situation is changing

dramatically due to dressing of the upper

3

and

ground

0

levels by external laser field. As far as

levels

0

and

3

split into two sublevels the lines of

Raman also splits into two lines (fig.3a) while the

Rayleigh scattering line is divided into three lines,

that corresponds to the Mollow triplet. In the case of

exact resonance the value of this splitting is equal to

Ω2

(сurves 1). For the near-resonance case

001.0

30

=−=

ω

ω

δ

the splitting of states becomes

asymmetrical and the position of doublet Raman and

triplet Rayleigh lines changes (curves 2). Further

increment of the detuning (curves 3) results in the

formation the ordinary Raman and Rayleigh lines

with frequencies

30

ω

ω

−

and

ω

respectively.

Figure 3: Spectral lines of Raman (a) and Rayleigh (b)

processes in dependence on laser frequency detuning

(

30

ω

ω

δ

−=

) from the atomic transition frequency (1 -

0=

δ

, 2 - 001.0=

δ

, 3 - 005.0=

δ

). Pulse duration is

40000, Rabi frequency

4

105

−

×=Ω .

Spontaneous Emission of a Dressed Atomic System in a Strong Light Field

133

Rest lines with frequency

32

ω

and

30

ω

can be

interpreted as spontaneous transitions

23 →

and

03 →

resulting from the nonresonant excitation

of level

3

by laser radiation.

6 STABILIZATION IN A

PRESENCE OF QUANTIZED

ELECTROMAGNETIC FIELD

The interference stabilization (IS) of Rydberg atoms

was first predicted in (Fedorov and Movsesian,

1988), analyzed in detail in subsequent works

(Fedorov et al, 1996; Fedorov and Tikhonova,

1998), as well as in (Fedorov, 1997). According to

(Fedorov, 1988), IS occurs due to destructive

interference of the amplitudes of transitions to a

continuum from excited Rydberg states coherently

repopulated by Raman Λ-type transitions during

laser excitation. It is known that the widths of these

transitions are determined by Fermi’s golden rule

2

0

22

επ

nE

d=Γ

(30)

Here,

nE

d

is the matrix element of the dipole

moment operator for the

ω

+=→

nn

EEE

transition and

0

ε

is the electromagnetic field

strength amplitude of the wave. According to

(Fedorov, 1997), the IS threshold is determined by

the overlap of ionization widths of Rydberg states

and can be written in the atomic system of units in

the form:

1

35

0

>

ωε

(31)

or by passing to intensities:

310*

ω

≈> II

. For

example, for the emission frequency of a Ti:Sa laser,

we obtain from (31) the threshold intensity I* ≈ 2.5

× 10

12

W/cm

2

.

The general expression for the quasi-energy

spectrum of a field-dressed atom in the simplest

model of two close nondegenerate levels and a

nondegenerate continuum (1D) was obtained in

(Fedorov, 1988):

Γ−−±Γ−+=

±

22

1221

)(

2

1

EEiEE

γ

(32)

Here,

2,1

E are unperturbed energy levels and Γ is the

ionization width calculated from (30) and assumed

the same for both levels. The imaginary part of (32)

determines the ionization width of shifted levels. A

structure of broadened quasienergy levels is seen to

change drastically at

12

EEГ −=

, which confirms

the threshold character of the IS. In the region

12

EEГ −>

the shift results in a form of a narrowing

quasienergy level located approximately at

2/)(

21

EE +

embedded into a widening one. In terms

of the time evolution of populations this means that

the decay (ionization) has a two-exponential

character. I.e., there are short- and long-living parts

of populations. Existence of the latter is a clear

manifestation of stabilization.

It follows from (32) that in the strong-field limit

12

EEГ −>

the decay rate of the long living

stabilized part of population decrease with

increasing intensity as:

I

EE

strong

1~

2

)(

Im2

2

12

Γ

−

=−=Γ

+

γ

(33)

In this chapter we are going to embed spontaneous

radiation in the stabilization phenomenon. We

employ with three-level system where there is a

ground state

0

and levels

2,1

which are

supposed to be Rydberg levels of the opposite parity

with respect to the ground state. The energies of

levels are chosen

5.0

0

−=E

for

0

,

3

1

105

−

×−=E

and

3

2

104

−

×−=E

for levels

2,1

respectively (we

are working within the atomic system of units).

In frames of previous consideration we solve

numerically the following system of equations:

=

′

′′′

Γ−=

2

1

)exp(

2

n

nnnnnn

tiC

i

Ci

ω

,

0

0

=Ci

,

),)(exp()(

2

)(

00

0

)(

titC

edCi

kn

norm

kn

k

n

λ

λ

λ

ωω

ε

+××

×−=

,))(exp()()(

2

2

1

00

)(

0

=

′

′′′

−

×−=

n

nknkn

norm

k

titCed

Ci

ωω

ε

λλ

λ

(34)

where

2

0

4

0

2

2

42

ε

π

επ

nE

n

nEnEnn

d

dd

==Γ

′

′′

.

The first equation is obtained using the method of

adiabatic elimination of the continuum (Fedorov,

1997), as well as the approximation of equal

PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology

134

Rydberg-continuum dipole matrix elements for all

Rydberg levels efficiently involved in the process of

ionization. In our simulations we assume matrix

elements to be calculated in quasiclassical

approximation

)(1

3/55.1

ω

nd

nE

=

, where principal

quantum number n is supposed to be 10 and

ω

equals 0.057 that corresponds to the radiation of Ti-

Sa laser pulse. Fig. 4 shows the spectrum of

spontaneous emission to the ground state for

different values of laser intensity. The situation

described at fig. 6a corresponds to the initial

population amplitudes of Rydberg levels

21)0(,21)0(

21

−== СС

(antisymmetrized

combination). In the absence of laser pulse one can

see two independent emission profiles from Rydberg

levels, but with the increase of radiation intensity

due to the interference of amplitudes of Raman

Λ -

type transitions Rydberg levels reconstructed

significantly. As a result emission lines gradually

merge forming new transition with the energy

)2/)((

210

EEE +−−

(curve 3 fig. 4a). Such initial

condition provides pretty resistant atomic system

with respect to ionization process. The fraction of

Figure 4: Reconstruction of the spectrum of the

spontaneous emission of an atom in the regime of

interference stabilization. Amplitudes of initially

populated Rydberg states are opposite (a) and the same

(b). Intensities of Ti:Sa laser ( 057.0=

ω

) are (1 - 0 , 2 -

5

105.2

−

× , 3 -

4

105.2

−

× ). Pulse duration is 40000.

population trapped in Rydberg states in this case is

very close to unity (fig. 5). Another situation is

developing for the symmetrized combination of

population amplitudes

21)0(,21)0(

21

== СС

. In

this case for rather high intensity of laser field when

12

EEГ −>>

we can clearly observe a two-

exponential dynamics of population decay (fig. 5)

showing short- and long-living parts of populations.

Such type of temporal dynamics is pronounced

in spontaneous emission spectra. Indeed, blue curve

on fig 4b represents the wide line of emission from a

rapidly disintegrating background, while the narrow

depletion in the center of this line results from long-

time decay of the small stable fraction of population.

The life times of these long- and short-living

fractions can be estimated as

2

12

)(2 EE −Γ

and

Γ

/1

correspondingly.

Figure 5: Temporal dependensies of the trapped

population for the initially populated simmetrized (1) and

antisimmetrized (2) states (see the text). Laser intenisity is

4

2.5 10 .

−

×

7 CONCLUSIONS

To conclude, general approach to analyze the

spontaneous emission of an atomic system driven by

a strong laser field is developed. It based on the first

order of perturbation theory for the interaction with

quantized vacuum field modes while the interaction

with the intense classical laser field is considered

numerically or analytically beyond the perturbation

theory. Several problems (Rabi oscillations and

formation of the Mollow triplet, spontaneous Raman

and Rayleigh scattering, ionization suppression in

the regime of interference stabilization) were

studied. It was demonstrated that the spontaneous

emission can be effectively used to study the

reconstruction of the energy spectrum by the laser

field, and different types of dressing were analyzed.

Spontaneous Emission of a Dressed Atomic System in a Strong Light Field

135

We would like to mention that our approach can

be used to study the spectrum and dynamics under

external fluence of artificial atoms, such as quantum

dots or quantum wires, and the coupling of these

atoms with photons (Michler et al, 2000; Santori et

al 2002; Faraon et al, 2008) or with crystalline

lattice via phonons (Förstner et al, 2003;

Machnikowski and Jacak, 2004; Ahn, et al, 2005).

Developed approach can be of significant interest for

the study of relaxation processes in a lot of modern

nanoelectronic devices devoted for information

receiving and processing (

Hoang et al, 2012; Jöns et

al, 2015)

.

ACKNOWLEDGEMENTS

This work was supported by the Russian Foundation

for Basic Research (projects no. 15-02-00373, 16-

32-00123).

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