Spontaneous decay of an atom excited in a dense and disordered atomic ensemble: quantum microscopic approach

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by  A. S. Kuraptsev

Spontaneous decay of an atom excited in a dense and disordered atomic
ensemble: quantum microscopic approach
A.S. Kuraptsev, I.M. Sokolov
St.-Petersburg State Polytechnic University, 195251, St.-Petersburg, Russia
(Dated: January 15, 2016)
On the basis of general theoretical results developed previously in [I. M. Sokolov et al., J. Exp.
6
Theor. Phys. 112, 246 (2011)], we analyze spontaneous decay of a single atom inside cold atomic
1
clouds under conditions when the averaged interatomic separation is less or comparable with the
0
wavelength of quasi resonant radiation. Beyond the decay dynamics we analyze shifts of resonance
2
as well as distortion of thespectral shape of theatomic transition.
n
a PACSnumbers: 34.50.Rk,34.80.Qb,42.50.Ct,03.67.Mn
J

4
1 I. INTRODUCTION problems in [35]-[37]. In addition, we do not use
a continuousmediaapproximation. It allowsus to

]
take into account correctly the discrete structure
h Influence of the environment on atomic spon-
p taneous decay has attracted considerable interest of atomicclouds andconsequentlythe interatomic
- correlations which play, in our case, an important
m both because of its fundamental importance and
role.
because of its significance in different applications
o One further unique feature of the present work
such as quantum metrology, quantum informa-
at tionscience,andlasingindisorderedmedia[1]-[8]. is that we calculate not only the decay constant,
. but also dynamics of decay and the spectrum of
s These influences are of special interest for realiza-
c tion of highly stable and accurate optical atomic the atomic transition, particularly the shifts of
i atomic lines caused by the dipole-dipole interac-
s clocks[9]-[14],particularlyneutral-atom-basedop-
y tical frequency standards [15]-[18]. tion. The question of density dependent spectral
h lineshiftsforcoldatomicgasesrecentlygaveriseto
There are a great number of works where the
p a wide discussion, [39]-[48] and this question is es-
environmental influence on the atomic decay con-
[
pecially important for opticalfrequency standards
stant is studied both theoretically and experimen-

1 [17], [49].
tally [19]-[37]. In the vast majority of these re-
v In the following paragraphs,we firstlay out our
searchs, the case of a transparent and continuous
7 basic assumptions and approach. This is followed
surroundingmediumisconsidered. Fortheoretical
5
by a presentation of our main results, and a dis-
5 descriptionofsuchsystems,bothmacroscopicand
cussion of them.
3 microscopic approaches are used. Depending on
0 the different assumptions about the local environ-
. ment of the embedded atom several models have
1
0 been proposed and studied. Among the most im- II. BASIC ASSUMPTIONS AND
6 portant,we note suchapproachesas a virtualcav- APPROACH
1 ity, a real cavity and so-called ”fully microscopic”
v: models. The calculation of spontaneous decay dynamics
i The main goal of the present work is to study in this paper will be made on the basis of a mi-
X
theoretically the case of disordered atomic ensem- croscopic quantum approach developed in [38]. A
r bles with averaged interatomic distances greater similarapproachwaspreviouslyusedforanalogous
a
than or comparable with the wavelength of the problemsin[30],[31]. Theauthorsofthesepapers
atomictransitionasitisheldintheopticalatomic searched for analytical solutions, in order to have
clock basedon coldatoms [15]-[18]. In such a case an opportunity to analyze the validity of real and
discretestructureofatomiccloudsshouldbetaken virtual cavity approximations. They succeeded in
into account. Besides that the atomic radiation finding an approximate expression for the decay
is quasi-resonant, and a model assuming quasi- constant up to the second order of the parame-
transparent non-absorbing media is not valid. ter nα, where n is the atomic density and α is
In this work we make numerical Monte-Carlo the polarizability of a free atom. Besides that, fi-
simulations based on a quantum microscopic ap- nal expressions in these papers were obtained for
proach [38]. Numerical simulation allows us to transparent and continuous medium.
analyze the process of single atom excitation de- Inthepresentworkwesearchfornumericalsolu-
cay, taking into account resonant multiple inco- tionstothisproblem. Itallowsustoobtainresults
herent scattering of the light inside atomic cloud, in all order of nα and for arbitrary parameters of
withoutintroductionofanyadjustableparameters, the excited atom. The approach used is depicted
as opposed to approaches used earlier for similar indetailin[38]andwewillnotdiscussithere. We
2
will mention only the main approximations used Inour calculationwe will assume thatallatoms
hereafterandwillshowtheprincipalanalyticalex- are motionless. To take into account residual
pressions utilized for numerical calculations. atomic motion and the random spatial inhomo-
Note also, that a similar microscopic approach geneity of the atomic ensemble, we will consider
combinedwithnumericalcalculationhasbeenused the statistical ensemble of clouds with a random
in [50] for determination of averaged decay rate distributionofatoms. Theresultspresentedbelow
and for discussion the influence of local density of areobtainedbyaveragingoverthisensembleusing
collective states on spontaneous decay of impurity the Monte Carlo method.
atoms. However the authors did not analyze the The microscopic approach enables us to con-
explicittimedependenceofatomicpopulationand siderthecloudsofarbitraryformwithanarbitrary
did not consider the spectrum of the atomic tran- nonuniformspatialdistribution ofatoms. The ini-
sition. tially excited atom can also be located at an arbi-
traryposition. Further,wewillassumethatatoms
We consider an ensemble consisting ofN atoms.
All atoms have a ground state with J = 0 and surrounding the emitting atom are randomly dis-
tributed in a cubic volume. The random distri-
an excited level with J = 1. In the present pa-
per we analyze two different cases. In the first, all bution is uniform. The initially excited atom it-
atoms including the initially exited one are identi- selfis in the center of the cube. For the chosen
cal. The physical properties of clouds considered geometry the system is isotopic on average, so we
in this part of the paper correspond to the situ- canconsiderthespontaneousdecayofanyZeeman
ation realized in atomic clocks [15]-[18]. Namely, sublevel. For determinacy we will assume that at
interatomic separations are relatively big and the initial time t = 0 only one substate m = 1 of
−
discrete structure of the clouds is important. The thecentralatomispopulated. Alltheotheratoms
identityoftheatomsmeansthatradiationemitted of the ensemble are in their ground state having
J =0, m=0.
byoneofthemisquasiresonantfortheother. The
main goal of this part of the paper is to study the All approximations described above allow us to
avail ourselves of the results of the general theory
single atom decay under such conditions. By now
single atom spectral response has not been stud- developed in [38]. This theory was then mainly
used for description of the interaction between
iedin experiment. Intypicalexperiments external
radiation interacts with whole (or essential part light and dense atomic clouds in steady-state con-
ditions [46], [53]-[55]. Here weanalyzethe dynam-
of) atomic clouds. However in our opinion such a
problemstatementisinterestingfromatheoretical ics of the dense atomic ensemble.
According to [38], the time dependent ampli-
point of view. Beside that it is not completely ab-
stract. Local excitation of atoms inside optically tudes of the collective atomic states with one ex-
depthanddensecloudscanbeperformedbymeans cited atom bema (t) can be found as follows
of method suggested earlier by M. D. Havey [51].
∞
For such excitation one has to illuminate the
dω
colnoauldlywpirtohpatgwaotendarlirgohwt baneadmosff. rEeasochnabnetamortdhooegs- bema (t)=−Z∞ 2πexp(−iωt)Xemb′ Remaemb′(ω)b0emb′.
not cause single photon excitation; but their si- (2.1)
multaneous interaction with atoms in the crossing Here,theindexem containsinformationaboutthe
a
region can cause two-photon excitation from the number a of atom excited in any considered state.
ground S to excited D state if conditions of two- It also indicates the specific Zeeman sublevel m
photon resonance are satisfied. The subsequent which is populated.
spontaneous transition from D to P state leads to The vector b0 is determined by the initial ex-
population of the studied P state. Thereby de- emb′
citation of the entire ensemble. In the considered
scribed method allows obtaining small cluster of
casethisvectorcontainsonlyonenon-zeroelement
excitedatoms in the middle ofthe cloud. Forsim- ′
corresponding to the Zeeman sublevel m = 1 of
plicity thereafter in the paper we will consider the −
the central atom.
case of only one atom excited. Note that possi-
bilities of two-photon excitation 5s S 2(1/2) The matrix Remaemb′(ω) in Eq. (2.1) takes into
′ − → account the possible excitation of the atoms by
5pP 2(j) 5dD 2(j) ofrubidiumatomshave
− → − the reradiated light. As it was shown in [56],
been already studied in experiment [52].
The second case we will consider in the pa- Remaemb′(ω) is a resolvent operator of the consid-
ered system projected on the states consisting of
per correspondsto spontaneousdecay of an impu-
singleatomexcitation,distributedovertheensem-
rity atomembedded in homogeneousensemble. In
ble, and the vacuum state for all the field modes
this casethe transitionfrequencyofthe embedded
atomωemb andthe naturallinewidthofitsexcited −1
state γemb differ from the corresponding values ω0 Remaemb′(ω)=h(ω−ωa)δemaemb′ −Σemaemb′i ,
and γ of surrounding atoms. (2.2)
0
3
Here ω is equal to ω for the embedded atom
a emb
and ω for surrounding atoms.
0
If a 6= b, the matrix Σemaemb′ describes the exci-
tation exchange between atoms a and b inside the
cloud. In this case its matrix elements are
dµ dν
Σemaemb′ = ema;g¯har3gb;emb′ × (2.3)
Xµ,ν
ω r ω r 2 ω r
a a a
δ 1 i exp i
µν
(cid:20) (cid:18) − c −(cid:16) c (cid:17) (cid:19) (cid:16) c (cid:17) −
r r ω r ω r 2 ω r
µ ν a a a
3 3i exp i .
− r2 (cid:18) − c −(cid:16) c (cid:17) (cid:19) (cid:16) c (cid:17)(cid:21)
Here r is the projection of the vector r=r
µ a
r on the axis µ of the chosen coordinate fram−e
b
and r = r is the interatomic distance. Note that
| |
the expression(2.3)iswrittenintheso-calledpole
approximation. This approximation is based on
the fact that (2.3) depends very slowly on ω , so
a
in calculating (2.3) we can consider that for all a
ω =ω .
a 0
Ifaandbarethesameato′mthenΣemaemb′ differs
from zero only for m = m. In this case Σemaema
determines the Lambshift and the decay constant
ofthecorrespondingexcitedstate. IncludingLamb
shifts in the transition frequency ω we get
a
Σemaema′ =−iδmm′γa/2. (2.4)
In the next section, we use relations (2.1)-(2.4)
to calculate both the time dependence of the ex- FIG. 1: (Color online) Spontaneous decay dynamics
cited state population and the spectrum of the (a); time dependence of the effective spontaneous de-
atomic transition. cay rate (b);n=0.05, γemb =γ0, ∆=0
III. RESULTS AND DISCUSSION
1 dP (t)
A. Spontaneous decay dynamics γ(t)= 0 . (3.2)
−P (t) dt
0
Relations (2.1)-(2.4) allow calculating the time- Figure1showsthespontaneousdecaydynamics
dependent population of any Zeeman sublevel of of an excited atom in the case when the initially
any atom in an ensemble. Here we will ana- excited atom coincides with all other atoms in the
lyze the decay of an initially populated sublevel cloud, i.e. in the case when γ = γ and ∆ =
emb 0
J = 1, m = 1 of central atom. For brevity we ω ω =0. The calculations were made for an
emb 0
− −
denote the amplitude of this state as b (t). The atomic density n = 0.05 and for three different N
0
corresponding population P (t) can be found as – N =300; N =1000and N =2000. Hereafter in
0
follows this paper we use the inverse wave number of the
resonance probe radiation in vacuum k−1 = c/ω
0 0
as a unit of length.
P (t)=< b (t)2 >. (3.1) Figure1ademonstratesthattheprocessofspon-
0 0
| |
taneous decay in a dense atomic ensemble is de-
Hereanglebracketsdenoteaveragingoverauni- scribed by a multi-exponential law. Initial state
form random atomic distribution of surrounding with only one excited atom can be expanded as
atoms. As was mentioned previously, this averag- a series over set of nonorthogonal eigenvectors of
ing is performed by a Monte Carlo method. Green matrix for each random spatial configura-
Besides P (t) we will calculate the time depen- tion of the system. Among different collective
0
dent decay rate γ(t) quantum states in the considered ensemble there
4
are both super- and sub-radiant ones. The former
influences the spontaneous decay dynamics pre-
dominantly in the earlystages; anatominside the
ensemble decays faster than a free atom. Even in
the case of relatively small densities like n = 0.05
the increasing in decay rate is important. With
time the role of sub-radiant states increases, re-
sulting ina decreaseindecayrate. Fort>1/γ
emb
thisratebecomeslessthanthatforfreeatoms(see
Fig. 1b).
The specific type of decay dynamics for given
density depends on the size of the atomic ensem-
ble, i.e. on the number of atoms N in it. It is typ-
ical situation when sub and super radiant states
manifest themselves in collective decay (for more
detail see [57]-[59]). We have analyzed how the
function P (t) changes with N and found that for
0
small clouds when mean free path of photon less
or comparable with linear size of atomic ensemble
these changes are very essential. As N and lin-
earsizeincreasethechangesinP (t)becomemore
0
and more weak. This dependence has evident ten-
dency to saturation. Our calculation shows that
for studied geometry for n = 0.05 the curve P (t)
0
does not practically changes as N becomes more
than 300. So results obtained for N > 300 can
be usedfordescriptionofsingleatomspontaneous
decay inside any macroscopic ensemble with rea-
sonable accuracy.
FIG. 2: (Color online) Spontaneous decay dynamics
It is illustrated by the fig. 1a where we show (a); time dependence of the effective spontaneous de-
timedependenceofP0(t)forthreedifferentN. For cay rate (b);n=1, γemb =γ0, ∆=0, N =2000
times less or comparable with 3/γ all three curves
coincide with accuracy of calculations. Such be-
haviorconnects with specific initial condition con-
sidered in this paper (contrary to the cases stud- Asdensityincreasesthesizeofmesoscopiccloud
ied in [57]-[59]). Modification of decay rate of ini- for which we can neglect dependence P0(t) on N
tially excited central atom is caused by radiation is also increase. For n=1 we observed saturation
of this atom which is scattered back by atoms of for N 2000.
≈
environment. Results displayed in the fig.1a show Figures 1 and 2 describe one atom excitation
that atoms of the cloud located far from central decay in completely homogeneous clouds. In this
atom influence on decay faintly at this time inter- case, the frequency of emitted photon lies in the
val. Slight discrepancy at bigger times when pop- absorption band of the surrounding atoms. Con-
ulation P (t) is already small, connects with the sider now the case of spontaneous emission of a
0
fact that lifetimes of the most long-livedcollective foreign atom embedded in a dense ensemble when
states are very sensitive to specific spatial config- this atom and atoms of the medium have essen-
uration of the cloud and for accurate averaging of tially different transition frequencies.
corresponding dates volume of calculation has to We will choose parameters of the cloud’s atoms
be increased immensely. insuchawaythatthedielectricconstantwouldbe
Increasing the density of surrounding atoms realwithagoodaccuracy. Itgivesuspossibilityto
causes enhancement of collective effects and con- compare our results obtained in the framework of
sequently more considerable modification of spon- our quantum microscopic approach with different
taneous decay. This effect is illustrated by Fig. models suggested earlier.
2 which shows the dynamics of single atom exci- We canneglectimaginarypartofdielectric con-
tation decay inside an ensemble with the atomic stantifIm(ε(ω)) Re(ε(ω)) 1forallfrequencies
≪ −
density n=1. emitted by the impurity atoms. It is known that
At short times the decay constant is several for large detuning from resonance Re(ε(ω)) 1 is
−
timesgreaterthanforfreeatoms. Onthecontrary, inversely proportional to ∆ whereas Im(ε(ω)) is
for t > 1/γ the decay process shown in Fig. 2 inversely proportional to ∆2. So to have the pos-
emb
goes noticeably slower than in case of n=0.05. sibilitytosatisfycorrespondinginequalitywehave
5
decay constant depends on time. There is an es-
sential difference between predictions of our quan-
tum approach and the different models suggested
earlier. In our opinion the main reason for such
a discrepancy lies in using a continuous medium
approach. This approach does not allow one to
take into account inter-atomic correlations quite
correctly.
B. Atomic transition spectrum
Interaction of a radiating atom with its sur-
roundings causes not only modification of the de-
cay constant but also a shift of the atomic tran-
sition. Moreover, this interaction can be the rea-
son of fundamental distortion of the spectral line.
At present there is a whole number of theoretical
works devoted to analysis of spectral properties of
cold atomic clouds. Theory predicts that different
observables have different spectral dependence for
densecloudsandthesedependenciestransformdif-
ferently as density increases. Thus, the spectrum
of the dielectric permittivity of cold and dense
atomic clouds has a blue shift [46], [60]. The max-
imal probability to excite the dense ensemble is
observed for a negative detuning of exciting radi-
ation [53]. The calculation of the total scattering
cross section shows that the corresponding spec-
FIG.3: (Coloronline)Timedependenceoftheeffective trum has several resonances [38]. Two of them
spontaneous decay rate (a): n = 0.05, γemb = 0.1γ0, are red shifted, and the third is in the blue re-
∆=4γ0; (b): n=1, γemb =2γ0, ∆=70γ0 gion. Spectral dependence of fluorescence also has
complicated behavior. It depends both on direc-
tion of fluorescence and its polarization [38]. By
now density dependence of spectral properties of
to choose ω ω severaltimes greater than γ .
emb− 0 0 coldcloudshasbeenstudiedinseveralexperiments
Thewidthofemittedradiationshouldberelatively
[17], [61],[62]. In these experiments laser induced
small so that necessary inequality would be satis-
fluorescence of atomic ensemble was studied. Ex-
fied not only at ω but at all the spectral area
emb periments showed red shift and some distortion of
of the radiation.
excitation spectrum.
The detailed analysis performed on the basis of
In experiment external laser radiation excites
known dielectric permittivity of cold atomic en-
whole atomic ensemble. Different atoms in the
sembles [46], [55] shows that the requirements for-
cloud excite with different probabilities. Observed
mulated above are satisfied particularly for ∆ =
fluorescence is result of averagingof secondary ra-
4γ and γ = 0.1γ for the atomic density
0 emb 0 diationofallatoms. Anditdepends essentiallyon
n = 0.05; and for ∆ = 70γ and γ = 2γ for
0 emb 0 specifictypeofexcitation. Fortypicalspatiallyin-
the atomic density n=1.
homogeneouscloudsmaincontributioncomesfrom
Figure 3 shows the spontaneous decay dynam-
relatively dilute external regions. In such a case
ics ofanatomembeddedinanensemble ofatomic
observedcollective effects are weak and spatial in-
density n=0.05 andn=1 obtained in the frame-
homogeneitymakesinterpretationofexperimental
work of the quantum microscopic approach. For
result more difficult.
comparison we included results predicted for the
In this paper we analyze decay of local excita-
same parameters by a real cavity model (γ =
rc tion inside dense atomic ensemble. The transi-
2
√ε(3ε/(2ε+1)) γemb), a virtual cavity (γvc = tion spectrum can be described by inverse Fourier
2
√ε((ε+2)/3) γemb) and a so-called”fully micro- transformation of b0(t) (2.1). It is completely de-
scopic” model (γfm =((ε+2)/3)γemb) termined by Fourier components of the resolvent
It is clear for both considered cases that spon- matrix (3.2).
taneous decay of the foreign atom is described by Figure4showsthespectrumofanatomictransi-
a multi-exponential law. The current value of the tion in the case when the excited atomis identical
6
FIG.5: (Coloronline)Atomictransitionspectrum: ab-
FIG. 4: (Color online) Atomic transition spectrum
sorbtion curve(a); dispersion curve(b);γemb =0.1γ0;
for different densities of atomic ensemble: absorbtion
1 – n=0.05, ∆=+4γ0; 2 – n=0.2, ∆ =+4γ0; 3 –
curve(a); dispersion curve(b)
n=0.05, ∆=−4γ0; 4 – n=0.2, ∆=−4γ0
to the surrounding ones. It demonstrates that the
InFig. 5weshowthe transitionlineshapes ofa
absorption curve (Fig. 4.a) as well as the disper-
foreign atom embedded in a homogeneous atomic
sion one (Fig. 4.b) are significantly modified in
ensemble. Distortion of the line shape here is no-
comparison with the classical Lorenz and disper-
ticeably weaker than in the case shown in Fig. 4.
sion curves typical for a free atom. The contours
Suchaneffectisdirectlyconnectedwithweakening
have relativelynarrowpeaks andwide wings. The
ofdipole-dipoleinteractionbetweentheembedded
maximumofthespectrallineisshiftedinlowerfre-
atomandatomsofthesurroundingensembleasthe
quency as compared with a free atom. The value
difference in resonance frequencies of these atoms
of the shift and average width of the contour in-
increases.
creases with density.
In our opinion one atom spectral response ana- The influence of the dipole-dipole interaction is
lyzed above can be the foundation of new practi- determined not only by the difference in absolute
calmethodofstudyingofcollectiveeffectsindense valueoftheirresonancefrequenciesbutalsobythe
media. Fewatomexcitationscanberealizedinex- sign of the difference. For comparison in Fig. 5
perimentasitdescribedinsec.II.Itgivesopportu- we show two pairs of curves. The first one corre-
nitytocreatelocalexcitationindeeppartofdense sponds to the case when the resonance frequency
ensemble and study directly single atom polariz- of the embedded atom is greater than that of the
ability modified by resonant dipole-dipole interac- surrounding atoms ∆ = 4γ0. The second group
tion. Itwillgiveadditionalinformationforfurther ofcurvesiscalculatedforthe sameabsolutevalue,
analysisofcomplicateinfluenceofcollectiveeffects but a negative detuning of ∆= 4γ0. As the sign
−
on the spectral properties of cold clouds. Rela- of the detuning changes, the sign of the line shift
tivelystrongmodificationofspectrumallowsusto changes as well.
hope that this method will be sensitive. Such behavior of the level shift of an embedded
7
atomcanbeillustratedbytheexampleofdiatomic Our calculation confirmed expected results con-
system where the eigenstate problem is solved an- sistinginincreasingenvironmentalinfluenceaspa-
alytically [19]. For a system consisting of two dif- rameters of emitting atom approach those of sur-
ferent atoms the function b (ω) can be written as rounding atoms. Most significantly this influence
0
follows manifests itself when the initially excited atom is
identical to the other ones. Particularly, in this
casethe distortionofthetransitionismostpromi-
1
b (ω)= nent and the shift of resonance is maximal. The
0 f2(r12)/(ω+∆+iγ0/2) (ω+iγemb/2) latter becomes comparable with the half-width of
−
(3.3) atomic transition even for relatively small density
In this formula f(r12) is a function depending on n=0.05.
the interatomic separation r12. Inouropinionresultsobtainedinthis paper are
veryimportantforfutureimprovementinquantum
3 1 ik r (k r )2
0 12 0 12 frequencystandardsbasedonopticaltransitionsin
f(r12)= 4√γ0γemb − (k0r−12)3 exp(ik0r12) coldatomicensembles. Insuchstandardsallatoms
(3.4) are identical to each other and for optimization of
The solution (3.3)-(3.4) is written in a coordi- these devices the density dependence of the main
nate frame with the Z-axis oriented along the in- characteristics have to be taken into account.
teratomic axis and under the assumption that ini-
tially only one Zeeman sublevel m = 1 of the
−
embedded atom is excited. V. ACKNOWLEDGEMENTS
Itcanbe seenfromeqs. (3.3)-(3.4)thatfortyp-
icalparametersofthe consideredsystemsthe level We thank M. D. Havey for useful discussions.
shift decreases inversely with ∆ for ∆ >> γ0/2 We acknowledge financial support from Ministry
| |
and its sign changes as the sign of ∆ does. of Education and Science of Russian Federation
(State Assignment 3.1446.2014)and Russian Sci-
ence Support Foundation. ASK appreciate the fi-
IV. CONCLUSION nancial support from the Russian Foundation for
Basic Research (Grant No. RFBR-14-02-31422),
Russian President Grant for Young Candidates
In this paper, we analyze the influence of the
of Sciences (project MK-5318.2010.2), the Gov-
dipole-dipole interatomic interaction on the pro-
ernment of Saint-Petersburg, and the company
cess of spontaneous decayof atoms inside the cold
”British Petroleum”.
atomiccloudsunderconditionswhenthe averaged
interatomic separation is less than, or comparable
with, the wavelengthof quasi resonanceradiation.
Besides decay dynamics, we analyze shifts of res-
onance as well as distortion of spectral shape of
atomic transition. Two maincases areconsidered.
First we study decay of atom identical to the sur-
rounding ones. In addition we consider the case
of an impurity atom, one with different properties
than atoms of the surroundings.
The calculations were made on the basis of a
quantum approach taking into account the vec-
tor nature of the electromagnetic field and Zee-
man structure of atomic sublevels. A continuous
mediumapproximationwasnotused. Itallowedus
to take into consideration random inhomogeneity
oftheatomicsystemandconsequentlytheexisting
interatomic correlations.
It was shown that under the considered condi-
tions, decaydynamics canbe describedby a multi
exponentiallaw. Instantaneousdecayratedepends
ontime. Atthebeginningofthedecayitisgreater
thandecayconstantofafreeatomγ. Induecourse
the rate decreases and becomes less than γ. We
also found a noticeable distortion of the spectral
shapeoftransitionincomparisonwiththeLorentz
profile typical for motionless free atoms.
8
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