The mechanism of suppression of quantum transitions (quantum whirligig)
The mechanism allowing to stabilize of a state of quantum systems is considered. And, the initial condition can correspond both for excited state and for not excited, stationary state. The considered mechanism for the first time was offered for the excited states, and has received the name as quantu...
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| Cite this: | The mechanism of suppression of quantum transitions (quantum whirligig) / V.A. Buts // Вопросы атомной науки и техники. — 2010. — № 4. — С. 259-263. — Бібліогр.: 11 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-173432025-02-09T20:51:15Z The mechanism of suppression of quantum transitions (quantum whirligig) Механизм подавления квантовых переходов (квантовая юла) Механізм подавлення квантових переходів (квантова юла) Buts, V.A. Нелинейные процессы в плазменных средах The mechanism allowing to stabilize of a state of quantum systems is considered. And, the initial condition can correspond both for excited state and for not excited, stationary state. The considered mechanism for the first time was offered for the excited states, and has received the name as quantum whirligig (QWE). In this work the close connection of the considered mechanism with Zeno effect is shown. The considerations are stated, that many experimental results, which are interpreted as observation of Zeno effect, apparently, correspond to QWE. Рассматривается механизм, позволяющий стабилизировать состояния квантовых систем, причем начальные состояния могут соответствовать как возбужденному, так и невозбужденному стационарным состоянием. Рассматриваемый механизм впервые был предложен для возбужденных состояний и получил название квантовая юла. В работе показана тесная связь рассматриваемого механизма с эффектом Зенона. Высказаны соображения, что многие экспериментальные результаты, которые интерпретируются как наблюдение эффекта Зенона, повидимому, соответствуют эффекту квантовой юлы. Розглядається механізм, який дозволяє стабілізувати стан квантових систем. Причому, початковий стан може відповідати як збудженому, так і незбудженому стаціонарному стану. Механізм, який розглядався вперше, був запропонований для збуджених станів і одержав назву квантової юли. В роботі показано тісний зв'язок механізму, який розглядається, з ефектом Зенона. Виказані розуміння, що багато-які експериментальні результати, які інтерпретуються як спостереження ефекту Зенона, можливо, відповідають ефекту квантової юли. The author is gratefull Yu.L. Bolotin, S.V. Peletminsky, A.L. Sanin, K.N. Stepanov, and also N.F. Shulga and managed by him seminar for well-wishing and useful discussions, and also Yu.N. Ranyuk and V.I. Kirischuk for the given materials of yet not published results of experiments. 2010 Article The mechanism of suppression of quantum transitions (quantum whirligig) / V.A. Buts // Вопросы атомной науки и техники. — 2010. — № 4. — С. 259-263. — Бібліогр.: 11 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/17343 en application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Нелинейные процессы в плазменных средах Нелинейные процессы в плазменных средах Buts, V.A. The mechanism of suppression of quantum transitions (quantum whirligig) |
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The mechanism allowing to stabilize of a state of quantum systems is considered. And, the initial condition can correspond both for excited state and for not excited, stationary state. The considered mechanism for the first time was offered for the excited states, and has received the name as quantum whirligig (QWE). In this work the close connection of the considered mechanism with Zeno effect is shown. The considerations are stated, that many experimental results, which are interpreted as observation of Zeno effect, apparently, correspond to QWE. |
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Buts, V.A. |
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The mechanism of suppression of quantum transitions (quantum whirligig) |
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The mechanism of suppression of quantum transitions (quantum whirligig) |
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The mechanism of suppression of quantum transitions (quantum whirligig) |
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The mechanism of suppression of quantum transitions (quantum whirligig) |
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The mechanism of suppression of quantum transitions (quantum whirligig) |
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mechanism of suppression of quantum transitions (quantum whirligig) |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Нелинейные процессы в плазменных средах |
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The mechanism of suppression of quantum transitions (quantum whirligig) / V.A. Buts // Вопросы атомной науки и техники. — 2010. — № 4. — С. 259-263. — Бібліогр.: 11 назв. — англ. |
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| first_indexed |
2025-11-30T16:13:48Z |
| last_indexed |
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1850232517701926912 |
| fulltext |
THE MECHANISM OF SUPPRESSION OF QUANTUM TRANSITIONS
(QUANTUM WHIRLIGIG)
A.V. Buts
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: vbuts@kipt.kharkov.ua
The mechanism allowing to stabilize of a state of quantum systems is considered. And, the initial condition can
correspond both for excited state and for not excited, stationary state. The considered mechanism for the first time
was offered for the excited states, and has received the name as quantum whirligig (QWE). In this work the close
connection of the considered mechanism with Zeno effect is shown. The considerations are stated, that many ex-
perimental results, which are interpreted as observation of Zeno effect, apparently, correspond to QWE.
PACS: 03.65.Wj; 03.65.Yz
1. INTRODUCTION
The name of effect "Quantum Zeno effect" (QZE)
for the first time has appeared in the work of George
Sudarshan and Baidyanat Missra [1] in 1977. In this
work they have shown, that if to spend often, better con-
tinuously observation at excited (unstable) quantum
systems, such unstable systems can be saved indefi-
nitely long time. This name has appeared so successful,
that despite of that fact, that as it has appeared later, the
similar physical phenomena in the quantum mechanics
were considered earlier by many other authors (see, for
example, such works: Alan Turing [2], John von Neu-
mann [3], Degasperis at all [4] and others) the QZE now
is strongly connected to names Sudarshan and Missra.
The mechanism of suppression of quantum transi-
tions considered in the present work is similar to QZE.
Therefore, to see clearly the difference between of the
offered mechanism and QZE, we shall briefly describe
this mechanism. Let we have a two-level quantum sys-
tem. The zero level is corresponds to the stationary, not
excited state. The first level is corresponds to the ex-
cited state. Let now under action of resonant perturba-
tion the considered quantum system passes from a zero
level to first and back. As it is known, such process is
described by the following simple system of the differ-
ential equations:
_______________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2010. № 4. 259
1 00 01i A V A⋅ ⋅ =&h ; , (1) 1 10i A V A⋅ ⋅ =&h
where iA − complex amplitudes of wave functions.
We shall consider that matrix elements of interaction
are equal, constant and real. Let at the initial moment of
time the quantum system finds in the excited condition.
Then the solutions of the equations (1) will be func-
tions:
( )1 cosA t= Ω⋅ , ( )0 sinA t= Ω⋅ , (2)
where − Rabi frequency. /VΩ = h
It is convenient for further all interval of time
2 /T π= Ω to break on small time intervals /t T nΔ = .
Now we shall enter a new element − measurement of a
state of investigated system. Let at the moment of time
we somehow can estimate a situation of our system.
The probability of that fact that she during the time
tΔ
tΔ
will not pass from the excited state to the basic state will
be equal:
( 2( ) 1w t tΔ = − Ω⋅Δ
This result in the theory of QZE is named as nonex-
ponential law of disintegration (see, for example, [8]).
After expiration of the following interval of time we
again include process of measurement. The probability
of detection of the originally excited system in the ini-
tial state will determined by formula:
( )( )22(2 ) 1w t t⋅ Δ = − Ω⋅Δ . (4)
Such formula reflects the fact of independence of
quantum transitions in each interval of time. At the end,
after the large number of measurements the probability
of a presence of system in the excited state will be ex-
pressed by the formula:
( )( )2( ) 1
n
w n t t⋅ Δ = − Ω⋅Δ . (5)
Within the limits of a large number of the measure-
ments during the period of time , the probability of
detection of system in its initial excited state approach
to unit:
T
( )2 2( ) exp / 1nw T T n →∞= −Ω ⎯⎯⎯→ . (6)
This fact makes the contents of QZE.
Now it is easy to explain the basic contents of the
work. It consists in the following:
1 - we refuse procedure of measurement;
2 - we take into consideration some third level;
3 - we enter stabilizing external perturbation which
frequency is resonant for transitions between one of the
basic levels and additional level (see Fig.1). Will be
shown, that the Rabi frequency of transitions, called by
stabilizing perturbation, will be higher, the probability
of transition of system from the initial state will be
smaller.
2. STATEMENT OF A TASK AND BASIC
EQUATIONS
Let's consider quantum system, which is described
by Hamiltonian:
0 1
ˆ ˆ ˆ ( )H H H t= + . (7)
Second summand in the right part describes pertur-
bation. The wave function of system (7) satisfies
Schrödinger equation which solution we shall search as
a row of own functions of the not perturbed system:
( ) ( ) exp( )n n n
n
t A t i tψ ϕ ω= ⋅ ⋅∑ , (8)
where /n nEω = h ; 0
ˆn
n n ni H E
t
ϕ
ϕ ϕ
∂
= = ⋅
∂
h . ) . (3)
Серия: Плазменная электроника и новые методы ускорения (7), с.259-263.
mailto:vbuts@kipt.kharkov.ua
Let's substitute (8) in the equation Shrodinger and by
usual way we shall get system of the connected equa-
tions for a finding of complex amplitudes:
260
m
t i t E E dqϕ ϕ∗= ⋅ ⋅ ⋅ ⋅ ⋅ − ⋅∫ h
1
( )n n m
m
i A U t A⋅ = ⋅∑&h , (9)
where U H . 1
ˆ ( ) exp[ ( ) / ]n m m n n m
Let's consider the most simple case − the case of
garmonic perturbation
1 0 0 1
ˆ ˆ ˆ( ) exp( ) exp( )H t U i t U i tω ω= +
Ω
.
Then the matrix elements of interaction get the fol-
lowing expression:
exp{ [( ) / ]}nm nm n mU V i t E E= ⋅ ⋅ − +h ,
( ) ˆk
n m n k mV U dqϕ ϕ∗= ⋅ ⋅∫ {, },0 1ω ωΩ = (10)
Let's consider dynamics of three-level system
( 0 , 1 , 2 ). Let's take into consideration that fre-
quency of external perturbation and the own meanings
of energy of these levels satisfy to such relations:
1, 0m n= = , 0 1 0E Eω = − 2, 0m n= =
( ) E E
h ; ;
0 2 0ω δ+ = −h , 0δ ω<<
1
;
1 2E Eω = −h , 1~δ ω . (11)
These relations point out that fact, that the frequency
0ω of external perturbation is resonant for transitions
between zero and first levels, and the frequency 1ω is
resonant for transitions between the first and second
levels. Using these relations in system (9), it is possible
to be limited by three equations:
0 01 1 02 2 exp( )i A V A V A i tδ⋅ ⋅ = + ⋅ ⋅ ⋅&h ;
; 1 10 0 12i A V A V A⋅ ⋅ = +&h 2
2 21 1 20 0 exp( )i A V A V A i tδ⋅ ⋅ = + ⋅ − ⋅ ⋅&h . (12)
The system of the equations (12) is that system,
which we shall analyze. The scheme of energy levels for
system (12) is represented in Fig.1.
Fig.1. Energy levels.
1ω − the frequency of stabilizing perturbation
3. SOLUTIONS OF SYSTEM (12)
Let's consider, first of all, the case, when detuning is
large enough. In this case it is possible to neglect those
members in system (12), which contain this detuning.
Besides we shall consider that the matrix elements of
direct and return transitions are equal (V V12 21= ,
). Let's consider also, that the matrix elements
of transitions between the first and second levels are
much more, than matrix elements of transitions between
zero and first levels (V V
10 01V V=
12 10/ 1μ≡ >> ). It is convenient
to enter dimensionless time 10 /V tτ = ⋅ h . In view of
these reasons the system of the equations (12) becomes
elementary simple:
0 1iA A=& , iA1 0 2A Aμ= +&
2 1iA A, μ=& . (13)
Let at the initial moment of time ( ) the consid-
ered quantum system is on first, excited level. Then, as
it is easy to see, the solution of system (13) will be func-
tions:
0t =
( )0
1 sinA t
i
μ
μ
= ⋅
⋅
, ( )1 cosA tμ= ⋅ , ( )2 sinA i tμ= − ⋅ .(14)
Fig.2. Energy levels of Be ions
Fig.3. Energy levels of atoms rubidium
Fig.4. Energy levels of Hf-178 isomer
02ω
01ω
02ω
01ω
From the solution (14) follows, that than the large
parameter μ, the less will be probability that the system
from the excited state will pass in nonexcited, stationary
state. It is necessary to say some words about parameter
μ. Physically this parameter defines the ratio of number
of quanta of low-frequency perturbation which is re-
sponsible for transitions between the first and second
levels to number of quanta of high-frequency perturba-
tion, which determines transitions between the first and
zero levels.
The accounting of influence of the members contain-
ing detuning can be made by numerical methods. Such
analysis was carried out. He has shown that presence
even enough large detuning only slightly influences on
result. And, the more value of parameter μ, the smaller
appears this influence.
Above we have considered quantum system, which
is in the excited state and on which the external stabiliz-
ing perturbation acts. It is interesting to consider other
physical situation, when considered quantum system at
the initial moment of time is at a zero stationary level.
Under influence of external perturbation on resonant
frequency ω0 the examined quantum system can pass to
the first excited level. There is a question: whether can
the external additional perturbation on resonant fre-
quency for transitions from the first level on second
suppress transitions from the zero level on the first lev-
el? Let's show, that really such opportunity is realized.
Let's note, that in this case we act on quantum system
by perturbation, which is not resonant for an initial state
of quantum system. Moreover, on the first sight the con-
sidered quantum system should not feel this perturba-
tion. The paradox consists that such seems neutral per-
turbation can considerably change property of consid-
ered quantum system. This change consists that she be-
comes practically tolerant to external resonant perturba-
tion. She doesn’t feel it. The system of the equations,
which describes the given physical situation, coincides
with system of the equations (13). The difference con-
sists only that in this case we should change initial con-
ditions. At the initial moment of time the considered
system is at a zero stationary level. For the solution of
system (13) it is convenient to pass to new variables:
261
0 0 2A x ix= + 1 1 3; A x ix= + 5; 2 4A x ix= + .
Let's note, that the system (13) has following integral:
2 5
2 2
0 0
1k k
k k
A x
= =
= =∑ ∑ . (15)
Integral (15) corresponds to usual normalization of
wave functions. Now we should solve system (13) with the
following initial conditions: ; 0 (0) 1x = (0) 0, 0ix i= > . It
is easy enough to show, that the examined system at
these initial conditions has the following solution:
( )( )0 2
11 1 cosx t= + − Ω⋅
Ω
; ; 1 2 5 0x x x= = =
( )3
1 sinx t= − Ω⋅
Ω
; ( )( )4 2 1 cosx tμ
= − Ω⋅
Ω
, (16)
where 21 μΩ = + .
From the solution (16) follows, that if parameter μ is
great enough, the probability to pass into excited state
will be small. Thus, by selection of frequency and inten-
sity of external perturbation it is possible to forbid quan-
tum transitions. This inhibition is true as for the excited
states, and for basic stationary states.
4. SOME GENERALIZATIONS
Above we have considered general enough quantum
systems. However they were limited by induced transi-
tions. In many cases the determining role are played the
spontaneous transitions. To generalize the received re-
sults on this case it is possible by make using the Fok-
Krilov theorem [9]. This theorem can be formulated as
follows: the probability to save to quantum system in
her initial state (L(t)) is equal to a square of the module
of characteristic function:
2( ) ( )L t p t= , (17)
where ; − dif-
ferential function of distribution of an initial state. At
this, the value
( ) ( ) exp( / )p t w E i E t dE= ⋅ − ⋅ ⋅ ⋅∫ h ( )w E
( )w E dE⋅ defines a spectrum of energy
of an initial state. The formula (17) allows to get the
important enough information about quantum system,
taking into account only some properties of function
w(E). So, for example, let the all her special features in
a complex plane E represents only by poles (mero-
moephic function) and let these poles are situated in
points nE E i n= ± Γ . In this case characteristic function
will represent the sum of residuals on these poles. At the
large enough time the basic role will be played only the
pole, which will have minimal imaginary part. In this
case expression for characteristic function gets a kind:
( ) ( )min( ) exp / /p t i E t t≈ − ⋅ ⋅ − Γ ⋅⎡ ⎤⎣ ⎦h h , (18)
and the probability for system at the moment of time t
((Γmin⋅t)>>1) remain in an initial state to be defined by
the well known law of exponential disintegration:
( )min~ exp /L t−Γ ⋅ h .
The law of disintegration essentially varies on small
intervals of time (t<<1). To show it it is convenient to
enter centered characteristic function:
[ ]1 0( ) ( ) exp( / ) exp / ( )p t p t i E t i E t w E dE= ⋅ ⋅ ⋅ = ⋅Δ ⋅ ⋅∫h h , (19)
where 0E E EΔ = − ; − average meaning of energy
of system at the initial moment of time.
0E
At small intervals of time the expression (19) can be
decomposed into a Taylor line. At this, take into ac-
count meaning of functions and its derivative at the ini-
tial moment of time:
( )( )2
1 1 1(0) 1, (0) 0, (0) /p p p E t′ ′′= = = Δ ⋅ h ,
we turn out the following expression for probability of a
finding system in an initial state:
( )( )
22
1 /L E t⎡ ⎤≈ − Δ ⋅⎢ ⎥⎣ ⎦
h . (20)
The formula (20) coincides with the formula (3), if
as Rabi frequency we shall take value . Thus, the
nonexponential law of disintegration on small interval
of times is a general characteristic of disintegration
process.
/EΔ h
If at the initial moment of time in quantum system
for some any reasons two energy levels were selected,
the differential function of distribution can be presented
as: . Then the probability to find
system in an initial state is equal:
2
1
( ) ( )n
n
w E E Eδ
=
≈ −∑
( )( ) (1 cos ) / 2L t E t→ + Δ ⋅ , (21)
where 2 1E E EΔ = − .
From this formula follows, that two initial states will
disappear periodically and periodically to appear. This
result reminds the result which was got above. And, as
the selected states it is possible to consider the induced
processes of transition between two levels on a back-
ground of spontaneous transitions. Thus, it is possible to
say, that the principle of QWE can be used both for in-
duced, and for spontaneous transitions. As an example
of possible stabilization of the excited states it is possi-
ble to bring an example of synchrotron radiation sup-
pression, which was considered in works [10-11]. Let's
note that the arguments concerning suppression of syn-
chrotron radiation in these works were others. The re-
sults, received in this section, give additional arguments
for an opportunity of suppression of such radiation.
5. DISCUSSION OF SOME
EXPERIMENTAL RESULTS
262
Now th n experi-
mental re
Be
sup
ere are many works devoted to a
search of QZE. Their quantity quickly grows.
low we briefly shall describe most important, in our
opinion, results. The first experimental work, directly
devoted to research of QZE, was the work [5]. The im-
portance of this work, first of all, consists in such fact:
before this work QZE was considered as some kind of
speculative paradox revealed incompleteness of our
understanding of quantum processes. After this work the
attitude to QZE qualitatively has changed. After this
work a plenty others (theoretical and experimental (for
example [6])) works devoted to this effect at once has
appeared. In experiments of work [5] the ions beryllium
were used. Three energy states of this ion (see Fig.2)
were used. Distance between a zero level and first level
corresponds to energy of microwave quantum. The tran-
sitions between zero and second levels could be carried
out by influencing on system by optical radiation. The
transitions between the first and second levels were for-
bidden. In experiment the transitions between zero and
first levels were studied firstly. For this purpose the ions
of beryllium were exposed by high-frequency radiation.
The traditional picture of quantum transitions was ob-
served. Then, the ions of beryllium were exposed to
influence of short pulses of laser radiation. The laser
radiation could transfer the ions from a zero level on the
second level. It is necessary to note, that the time of life
of the second level was significant smaller, than period
of Rabi frequency for transitions between zero and first
energy levels occurring under influence of microwave
radiation. It was the shortest characteristic interval of
time in this task. If the number of pulses of laser radia-
tion falling in an interval of time, which is equal to the
Rabi period, was great enough, the authors observed
appreciable increase of life-time of the basic, not ex-
cited states of ions.
In described above experiment the fact of suppres-
sion of quantum transitions was only authentically es-
tablished. The real suppression was insignificant. In this
relation other experiment [7] deserves the attention.
This experiment was fulfilled with participation of the
Nobel winner Wolfgang Katterle. These experiments
succeeded in suppressing the quantum transitions (more
than 98% atoms left in their initial states). In the unique
experiments of these group researchers the Bose-
Einstein condensate of rubidium was used. As well as in
experiments described above, the authors used three
working energy levels (see Fig.3). And, the transitions
between zero and first levels lay, as well as in the previ-
ous experiments, in a microwave range and occurred
with participation fourth, virtual level. The choice of
such transitions (with participation of a virtual level),
apparently, was caused by that the Rabi period of these
microwave transitions (between zero and first levels)
was great enough (16 mc). During this time it was pos-
sible to organize a large number of laser pulses, the en-
ergy of which corresponds to transitions from the first
energy level on second. When the number of laser
pulses during the Rabi period of microwave transitions
exceeded 300, the practically complete suppression of
quantum transitions was observed. Let's note the follow-
ing essential difference of these experiments from pre-
vious. First of all, it, certainly, high degree of stabiliza-
tion of a quantum states (more than 98%). Further, the
most impressing and essential is fact that "observation"
was made at the first (excited) energy level. These lev-
els are not populated and as a result of "observation" its
remained not populated. It is most typical feature of
QZE. Besides in these experiments the process of "ob-
servation" was most full appear. Really, the exited at-
oms of rubidium (the atoms which are taking place at
the first, excited level) under action of laser radiation
were moved away from a magnetic trap. Thus, the "ex-
treme" variant of process of observation was carried out.
In all cases at discussion about opportunities of QZE
for using there was done statement, that such processes
can not be realized at a nuclear level, for example, for
pression or acceleration of radioactive disintegration.
Below we briefly shall describe some results of experi-
ments, which were spent in the Kharkov Physic-
Technical institute under manage of the professor
Yu.N. Ranyuk and in the Kiev institute of Nuclear Re-
searches under manage of V.I. Kirischuk, in which,
probably, the process of braking of disintegration Hf-
178 isomer was observed. The essence of experiment
was in the following. The sample of a material, which
contained Hf-178, was acted by electron flows with
energy from 10 кeV up to 50 кeV. On a sample, as on a
target, the energy of electrons was converted in energy
of x-ray radiation. The authors supposed that a little bit
above basic metastable level of Hf-178 should be short-
living trigger level (see Fig.4). The purpose of experi-
ments was in transferring the metastable state of Hf-178
on unstable short-living trigger level. In many experi-
ments the quite distinct acceleration of process disinte-
gration was observed. The authors however are even
more often observed opposite effect, when the process
of radioactive disintegration was broken at influence of
a beam on a target. These last experiments can be easily
explained by the mechanism QWE. Really, in consid-
ered nuclear system except for a trigger level there are
large number others long-living of energy levels. At
influence of an electron beam on a target the wide spec-
trum of x-ray radiation is appeared. Such radiation will
transfer nuclear system not only on certain energy level
(desirable on the trigger level) but also on many others
long-living levels. The system of the equations, which
will describe such transitions, is possible to present as:
0 1iA A=& , 1 0
2
N
k k
k
iA A Aμ
=
= +∑& ; 2 2 1iA Aμ=& , 3 3 1iA Aμ=& ;
iA Aμ=& . (22… )
This system describe the connection a transition
of considered system from first (A1) m
the basic level (A ) du f spontane
on
1N N
nd s
etastable level on
e o ous transferring and 0
other levels, which are close − located to metastable
level. The last transitions are induced transitions. The
system (22) is easily solved in a general analytical kind:
( )1 cosA t= Ω⋅ ; ( )0
1 sinA t
i
= Ω ⋅
⋅Ω
;
( )sink
kA t
i
μ
= Ω⋅ ; 2,3,...k N= , (23)
⋅Ω
where 2
2
1
N
k
k
μ
=
Ω = +∑ .
263
From these solutions follows, that the large number
gy levels will , the less will be probability for
spon
g rec-
ommendations fo excited quantum
syste
st
rateful Yu.L. Bolotin,
S.V
ES
1. E.C.G. Sudarsh eno’s paradox in
2. ofstadter, A. Turing. Life and
3. f
4. . Fonda & G.C. Ghirardi. Does the
5. n, J.J. Bokkinger, D.J Wine-
6. rrez-Medina, and M.G. Rai-
7. . Boyd, K. Gretchen,
y, K
8. s.
9. -
10. ect –
11. b-
.05.2010 г.
ВЫХ ПЕРЕХОДОВ (КВАНТОВАЯ ЮЛА)
Рассматр ем, на-
чальные состояния могут соответствовать как возбужденному, так и невозбужденному стационарным со-
сто
Розглядає ковий стан
може відповідати як збудженому, так і незбудж аціонарному стану. Механізм, який розглядався
of ener be
taneous transferring and the probability for transi-
tion on trigger short-living level. From the formulated
picture of transitions it is possible to formulate the basic
recommendation for updating experiments. She consists
that the conversion of energy of electron beams in x-ray
radiation is necessary to spent on independent target
with following separation of necessary spectral compo-
nent. Only with this narrow spectral component should
act on a sample with Hf-178. Such scheme of experi-
ment will allow to remove from dynamics of transitions
all useless (harmful) energy levels. It is necessary to
say, that these results are, apparently, first experimental
results, in which the opportunity to affect on nuclear
disintegration by external influences was shown.
CONCLUSIONS
Thus, it is possible to formulate the followin
r stabilization of the
all, it is necessary to knms. First of ow time of life
of these excited states. Further it is necessary to pick up
the appropriate energy levels located not too far from an
excited state. Further, it is necessary to pick up perturba-
tion which frequency will correspond to transitions be-
tween the excited state and this additional level. The in-
tensity of this perturbation should be such, that the appro-
priate Rabi frequency was as it is possible greater in
comparison with return lifetime of the excited system.
The special interest represents an opportunity to sta-
bilize such states, with which the stabilizing perturba-
tion, on the first sight, does not interact. The simple
example can be served the opportunity to suppress a
photocurrent at realization of a photoeffect. At this the
states of internal electrons in a solid can be stabilized by
external microwave radiation. For observation of sup-
pression effect it is necessary, that the Rabi frequency
for transitions under action of an external microwave
field was as it is possible greater in comparison with
return lifetime of photoelectrons. If we shall not be in-
terested in change in a condition of a field (resulting in a
photoeffect), the formulas, received in section 2, are
completely applied for this case. It is necessary to note,
that the analysis of the experimental results, which had
been gotten to the present time, shows, that they more
naturally and easier can be explained by the QWE.
Moreover, this mechanism can be used for considerably
wider schemes of physical systems. The explanation of
this mechanism does not leave of framework of the tra-
ditional quantum mechanics.
The author is g
МЕХАНИЗМ ПОДАВЛЕНИЯ КВАНТО
. Peletminsky, A.L. Sanin, K.N. Stepanov, and also
N.F. Shulga and managed by him seminar for well-
wishing and useful discussions, and also Yu.N. Ranyuk
and V.I. Kirischuk for the given materials of yet not
published results of experiments.
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Статья поступила в редакцию 28
В.A. Буц
ивается механизм, позволяющий стабилизировать состояния квантовых систем. Прич
яниям. Рассматриваемый механизм впервые был предложен для возбужденных состояний и получил на-
звание квантовая юла. В работе показана тесная связь рассматриваемого механизма с эффектом Зенона. Вы-
сказаны соображения, что многие экспериментальные результаты, которые интерпретируются как наблюде-
ние эффекта Зенона, по-видимому, соответствуют эффекту квантовой юлы.
МЕХАНІЗМ ПОДАВЛЕННЯ КВАНТОВИХ ПЕРЕХОДІВ (КВАНТОВА ЮЛА)
В.О.Буц
ться механізм, який дозволяє стабілізувати стан квантових систем. Причому, почат
еному ст
вперше, був запропонований для збуджених станів і одержав назву квантової юли. В роботі показано тісний
зв'язок механізму, який розглядається, з ефектом Зенона. Виказані розуміння, що багато-які експеримента-
льні результати, які інтерпретуються як спостереження ефекту Зенона, можливо, відповідають ефекту кван-
тової юли.
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000018000004000756000001&idtype=cvips&gifs=yes
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000018000004000756000001&idtype=cvips&gifs=yes
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000018000004000756000001&idtype=cvips&gifs=yes
http://books.google.com/books?id=th0_ipQKmGMC&pg=PA54&dq=%22Turing+paradox%22&lr=&as_brr=0&sig=ACfU3U0aOoVPNlecFf9n-bOQymEyGFKA5g
http://books.google.com/books?id=th0_ipQKmGMC&pg=PA54&dq=%22Turing+paradox%22&lr=&as_brr=0&sig=ACfU3U0aOoVPNlecFf9n-bOQymEyGFKA5g
http://www.springerlink.com/content/4064h6xv57162038/
http://www.springerlink.com/content/4064h6xv57162038/
http://www.springerlink.com/content/4064h6xv57162038/
http://www.boulder.nist.gov/timefreq/general/pdf/858.pdf
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