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J. Raman Spectrosc. 2002;33:962-973 Publishedonline in Wiley InterScience (www.interscience.wiley.com). 10.1002/jrs.939 DOI:

JOURNAL OF RAMAN SPECTROSCOPY

I ];I~I
.

Laser coherent control of molecular chiral states via entanglement of the rotational and torsional degrees of freedom
Stanislav S. Bychkov,1 Boris A. Grishanin,1 Victor N. Zadkov1* and Hiroaki Takahashi2
, Faculty Physics International of end Laser Center, v, Lomonosov M. Moscow Stete University, Moscow 119899, Russia 2 Department Chemistry, of Waseda University, Tokyo169-8555, Japan
Received June 21 2002;Accepted15August 2002

A new mechanism tor controlling chiral states in simple chiral molecules with internal rotation, which employs the coherent quantum entanglement of the rotational-torsional states of the molecules, is proposed. It requires no preliminary spatial alignment of the molecules in a solution. A novel scenario tor the preferentiallaser synthesis of enantiomers flom a racemic solution of chiral molecules employing this new mechanism of inducing chirality is proposed and analyzed in detail and experimental scheme realizing this scenario is discussed. It is suggested that a non-linear optical activity coherent anti-Stokes Raman scattering (NOA.CARS) spectroscopic technique is used tor both inducing the gyration wave in the medium (vapor) of chiral molecules and detecting this photoinduced gyration wave in the medium by registering the NOA-CARS signal. All numerical estimates are made tor the hydrogen peroxide and deuterated hydrogen peroxide chiral molecules. Copyright @ 2002John Wiley & Sons,Ud.

INTRODUCTION Preliminary studies show that methods of laser physics can help in resolving ODe of the key issues of practical th fi Id f I cu! hirali h th l Importance In e e 0 mo e ar c ty-w e er aser ..., phYS1CS th and non-linear optics can be used tor preferential fr ti' Il f ' f 'd syn eS1S a reqwre type 0 enantiomers om an 1m a y 0 ti f I cu! ti' 1-8 A raceII\1CII\1Xture 0 mo e ar enan omers. pOS1ve t this I ti uld h .worth answer 0 cruc1a ques on wo open new onzons try di d b li ti' , h ~ 10r a num er app ca ons In c eII\1s ,me clne an h p armacy. aspectofchiralmolecule-laser fieldinteraction Aspecific lies in the fact that the electric field not only creates the responding rotation moment of the molecule, but also induces transitions between the chiral states, owing to the

..

. ..

..

.

.

.

.

.

them is based on preferentialselection ofleft- or right-handed enantiomers flom a racemic mixture with no change in the DUC I earconfigurationso fth emo Iecul es. Theo ther1s based on .., . a photolnduced synthes1sof a reqwred type of enantiomers . flom the others uslng methods of coherent control. Such th all d 1 d ' ' lla ' d h fir syn eS1S c e aser IStl tlon an ,as was s own 1S st in Ref.7, may be effic1ent tor practical applications 1t 15 . noting also that methods of coherent control of chiral ., states aIlow one to prepare the chiral states (left- and nghthanded) in a coherent superposition, which can be seen as ti f b ' t f inf an .Imp Iementation 0 a. quantum 1 0 , orma on (qub't ) 1; therefore,molecular chiral statescan be, In general, used tor the purpose of quantum infonnation processing,9 in contrast with the preferential selectionschemes that tumed out to be

.

.

..

.

.

interaction potential dependence on both the rotational degrees of freedom of the molecule in free space and the internal rotation degree of freedom, chiral or reaction coordinate. Keeping this in mind, one can suggest two basically different schemes tor preferential synthesis. One of 'Correspondence VictorN. Zadkov,FacultyofPhysicsend to: InternationalLaserCenter,M, V, Lomonosov MoscowStete University,Moscow 119899, Russia,
E-mail: zadkov@comsim1.ph>:s.msu.su,. Contract/ grant sponsor: Russlan Foundation

inefficient}-6 Although the methods of coh~ren~o~~~tro~ m~lec~ar of stateshave been known tor a long time, theu applications for controlling molecular chiral states are just at the development stage. So far, only a few scenarios of laser distillation flom a racemic mixture based on the coherent control of the corresponding ro-vibrational molecular states 7813-16 have been proposed ' , and none of them has been realized experimentally so far. This is partly due to
the intrinsic nature of the chiral transitions-their phase

Contract/grantnumbers:01-02-16311; 02-03-32200, Contract/grantsponsor: INTAS; Contract/grantnumber:INFO OO-479./ C W d U .. ty Int ti I ontract grant sponsor: ase a ruversl erna ona Exchange Fund,

tor BasIc Research;

sensitivity to the molecule rotations in free space averaging over which cancelsthe distillation effect}4,16In other words, it reveals in complete suppression of the chiral asymmetry of the field-molecule interaction in the case of rotationally

Copyrighte 2002JolmWiley & Sans, Ltd.

'."

c Ccc

,",-


II;I~I
symmetric interaction, unless special efforts to break down this symmetry are undertaken (seethe next section). In this paper, we present a detailed analysis of coherent control methods tor molecular chiral states and suggesta new laser distillation scenario tor the preferential synthesis of enantiomers from a racemic solution. Most general features of a chiral molecule-laser field interaction and comparative analysis of possible laser distillation scenarios from a racemic solution are discussed in the next section. To elucidate key peculiarities of using coherent control tor manipulating molecular chiral states,we start with the hydrogen peroxide molecule (H2OV and its isotopomer (HOOD), the simplest chiral molecules. These molecules have, in addition to the internal rotational or chiral degree of freedom, rotational degrees of freedom corresponding to the molecule' s rotation in free space. A new laser distillation scenario tor H2O2 andHOODemployingquantumentanglementbetweenrotational and chiral molecular degreesof freedom is proposed in the section Laser Preferential Synthesis of Enantiomers from a Racemic Vapor of Molecules. In the fol1owing sections of the paper we discuss in detail the feasibility of an experimental scheme tor the proposed laser distillation scenario. It is shown that an experimental scheme employing a variance of coherent anti-Stokes Raman spectroscopy tor registration of non-linear optical activity (NOA-CARS) can be effectively used tor both laser distillation of a racemic solution and registration of the optical rotation in this solution. Polarization properties of the NOA-CARS signal produced by scattering of the probe pulse in the presence of gyration wave, due to the photoinduced non-racemicity in the solution, are analyzed and the intensity of the signal is estimated. MECHANISMS MOLECULAR OF LASER CONTROL CHIRAL STATES OF

Laser coherent ofmolecular states 963 control chiral
be effectively used tor applications in chemistry and pharmaceutics. The first scenario, tor example, yields only an excess of about 10-6% of a required type of enantiomers from a racemic solution. An experimental realization of the second scenario requires the use of laser intensities at least 10% higher than the allowable spectroscopic maximum of 1013 cm-2. W A different approach employs the dipole interaction, which, obviously, is much more intensive than quadrupole or magneto-dipole interactions used in the first approach. A few scenarios based on this approach have been proposed so far.3-7 They all are based on the dependence of laser field interaction with chiral molecular states, L and D, on the coherent laser field phases, by varying which one can control the excessof the enantiomers of a required type from a racemic solution. This interaction also has a rotationally symmetric dependence on the molecules' orientation (and this obstacle has not been previously laken into account by other authors), which cancels the effect of laser distillation of enantiomers from a racemic solution due to the averaging over rotations of molecules. In order to cope with this obstacle, one should therefore either align preliminarily the molecules in a solution or use the chiral-asymmetric spatial structure of the applied laser field (seethe next subsection). For example, the scenario suggested in Ref. 7 uses the dynamics of a chiral molecule in the excited electronic state. The potential of the excited electronic state is suggested to be a quasi-harmonic function of the reaction coordinate 9, with the minimum at 9 = O. Two of its first eigenstates 11), 12) are represented with symmetric and antisymmetric wavefunctions with respect to 9 = 0, respectively (the transition frequency between these states lies in the infrared region). Skipping averaging over the molecules' rotations, it can be shown that an appropriate scenario may be implemented with use of two subpicosecond pulses [Fig.1(a)].7 A laser

Possible scenarios tor preferentiallaser synthesis of enantiomers flom a racemic solution There are two different approaches to construct scenarios of preferentiallaser synthesis of a required enantiomer from a racemic solution of chiral molecules. One of them employs an asymmetry of the non-local polarized laser field-molecule interaction. Quadrupole or magneto-dipole interaction with a chiral molecule results in breaking down the symmetry of the D ~ L transitions (throughout the paper we will use notations D and L to designate right- and left-handed molecular chiral states, respectively) and therefore an excess of a re quired enantiomer can be achieved. So far, only two scenarios employing this idea have been proposed -one on non-resonant interaction of continuous-wave (cw) circularpolarized light with the electronic subsystem of a chiral molecule1 and the other based on resonant interaction of the pulsed circular-polarized light with the nuclear subsystem of a chiral molecule.2 However, even a qualitative analysis shows that both scenarios based on the relatively weak quadrupole or magneto-dipole interaction cannot

a)

>

b)

>

'
-1t

"
0 1t

e

'
-1t

"
0
1t

e

Figure 1. (a) Laser synthesis scenario from a racemic mixture of spatiallyaligned enantiomerswith the use of.two lase~pulses with frequenciesW1and W2.7(b) Laser synthesls scenario from a racemic mixture of isotropically distributed enantiomers with use of three laser pulses with frequenciesW1 W2and W3and , non-coplanar polarizationvectors.16 Reactioncoo:dinate e is responsibletor the chirality of the ground electronlc state.

Copyright@2002John Wiley & Sons, Ltd.

J. Raman Spectrosc. 33: 962-973 2002;

",""

0'

,",


964 S. Bychkov S. et al.
pulse sition of two ultraviolet L- and i2 with of the laser frequency 11) and pulses iI W2 prepares 12) states. and i2 Then, the coherent simultaneous WI lies population superpoaction in the into of the As a next the preferential from a racemic the is a step, we will synthesis solution. properties of qualitatively of a required To do this,

l]il~1
analyze type we scenarios of

of enantiomers will start with

(the frequency transfers coherent

region) D-states

asymmetrically owing to the

analyzing which

of a free

molecule's rotational and

dynamics, internat dynamics as a whole in optical detunings. is coupled complicated a molecule's state of

interference

sum

translational, dynamics.

corresponding Symmetry interaction Previously

wavefunctions. analysis of laser field-chiral molecule

electronic-vibrational are and decoupled its interna! only rotation from rotation

Translational molecule and results Doppler as a whole in a very models and of

rotation

of the

dynamics

spectroscopy suggested from scenarios a racemic for the preferential solutionl-7 of an optical leaving synthesis on By contrast, with war.

in the corresponding of the molecule dynamics simplest

of enantiomers simple molecular questions intermolecular along known the models

are all based field with

its interna! However,

rotation in the

of interaction coordinate, other

a single

reaction of how

out of the discussion coordinates molecule's same time, and

dynamics,

one can neglect can then Euler matrix

this coupling be written

the steady product

intramolecular affect At the the

of a free molecule the corresponding rotations density

as a tensor depend

interactions reaction coordinate.

dynamics it is weil

angles p~) and

æ, which

on the free

the chirality

operator:

that

molecular

degrees

of freedom

are entangled {Ja = p~o>@ (nf>IL) 0 where D-states, nio> and which (LI + ng>ID) (DI) (2)

and can essentially the selected reaction rote of molecular will show

affect the molecule's dynamics along coordinate. Here we will clarify the rotational later, degrees of affect freedom, the which,

n~> are the initial are equal

populations

of the L- and mixture,

as we dynamics.

essentially we will

molecule's

to each other

for a racemic

For simplicity,

neglect

the intermolecular during

nio> = ng> = 1/2. The degree density matrix: . in where Sr(E) 15 the X = Tr (X @ lrot)Sr(E){Ja transItion or dynam1cs which superoperator (3) m of chirality is determined by the transformed

interactions the excitation. We istic will

and intramolecular

energy

redistribution

start

with

introducing

a quantitative

characterx, which

of a chiral

medium,

the degree of chirality can be written

chirality of operator: terms quantum

mechanics

as an averaged

the interaction X = IL) (LI -ID) where states
O

representation, optical fields,

depends

on the Euler operator

(DI

(1)

angles

and applied

and [rot is the unity

IL) and of the

...in ID) denote the ground electroruc-vIbrational ...space. L- and D-enan~omers, respectively.. non-zero eI genvalues

the quantum-mechanical This p(LIE) e res and p(DIE)

Th

ultin chirality d '

representation

g epen 5 on of photoinduced transitions

d

tw

of the rotational

0 pro a es to the IL)- and

b bill' ti'

p erator

has onl y two

X = :1:1 WIth the eigenvalues therefore

ID) -5 t a t es, respec ti ve 1 y:

.

corresponding are equal to

eigenstates zero in the

IL) and residue

ID); all other subspace

and

X = p(LIE) p(LIE) p(DIE) = SU(E)nL

-p(DIE) (°> + SW(E)nD + SDL(E)nf> (°> (4)

are not involved The corresponding matrix The 0-3. chirality

in the chiral properties non-zero submatrix

of the final state. is simply the Pauli

= SDD(E)ng>

operator function

as given

in

Eqn

(1) is

also

a Here matrix elements Sa~ = Trla)(al . With
probabillties

pseudo-scalar

of the nuclei

coordinates

of a chiral symmetry operator

molecule17.18 and relation f{-1 xf{ = performing inversion of all the f nucleichiral th and
center 0 e

therefore -X, where

must satisfy the f{ is the inversion

.° @ I(Sr(E)Iú)(úI

@ p~ » d
ú

(5) d
"

operation r -+ -r for the coordinates electrons tiWlth respect to the mverSion nfi

.

a .,ú

=

LD
of the

an

d

0

< -a

5

~<

1

escri
for

.

b

e con
fixed

Ition al
lllitial

F co gura ons. or

th e

. Slffip

1 es

t

chiral

resulted

chiral

states

the

molecules 5

H2O2 e.

and

HOOD e f
and

the

chirality (~
operators which 1b f 0

operator

takes ])
.ties urut to

states a. To
spec of ify

. further
the .

imil .

1 aryto
vectors

R f 17 th
~ noo, the an ~ naH,

ormx=slgnnoo'
~ nOD ., are the

..

r~

~ noDxnoH,
of the

proceed

and
applied superoperator

elucIdate .,
laser

the

general

properto .m t 0

where

Sa~ versus th e d ynamlCS

fields, S r (E) fir

we need 5 t .g Takin ..

vectors along b th .h e eng td IL) an -states,

corresponding bonds, 1 ft h d d rth e -an e 0 ogona ti 1 In t respec ve y. erms d

are f or 1

chosen th

ases . t m erna

mo

ID) e 1 cul e

account -., laser e

dipole field-matter ..

and

quadrupole/magnetodlpole interaction and relaxation

terms . mteractions,

m

.the coordinates,

these

vectors

depend

on the bond

angles,

but

transition Sr(E)

superoperator = Texp

t ak es th e f Olm (rUÆIHrUo, ° 0] + L:r) d-r

the chirality between two operator O-H O-H (for the HOOD

depends only on the (for the H2O2 molecule) torsionalO-D angle (J or and molecule) bonds.

{

-~ .t1

}

(6)

copyright

@ 2002 John Wiley & Sons, Ltd.

J. RamanSpectrosc. 2002; 33: 962-973


!

I]:;I~I
where T is the time ordering symbol, which meaps ~t operator, 0,is the substitution expression [A,0] represents a invariant

Laser coherent control molecular of chiralstates 965
with respect to inversion, one can readily gel flom to

Eqn (7) on account of Eqn (5) the transition the chiral states:

probabilities

commutator with A, Uo is the free evolution operator, , 'v .'.0 'v !;, Hr = Hr +t1I' Hr = -E.d-E.11 is the dipole term of the Hamiltonian of the molecule interaction with the multi~cor:nponent laser field E = ffie L::~ ek. (t)e-i"'kt, disthe and JL lS the electronic is the magneto-dipole nudel, dipole moment operator one. Hf = -H.#t-e(rka'VaEp)rkP

SLv(E) = SvL(E), Svv(E) = Su(E) The degree of chirality form on account ofEqn

(8)

(4) then takes the

and quadrupole components of the interaction Hamiltonian, where H is, the total strength of the magnetic field in the laser field, m is the magnetic dipole moment of the electronic configuration, ,Tkis the vector radius of the kth electron and e is the electron charge; L-ris the relaxation describes the relaxation Using will prove synthesis solution Eqn (6) tor of a required employing fields processes}9 the dynamics superoperator, we tor laser-assisted preferential Liouvillian, which

(0 X = (nL) -n~»

[Su(E)

-Sw(E)]

(9)

For an illl tiaJly raceInlC mIXture, nL = nv, Eqn ( 9) dearly ..(0) (0)
shows that the initial racemicity of the mixture of the incident solution, will be preserved in time. For quadrupole/magnetodipole configuration racemic interaclaser fields tor the struc-

..

tion and coplanar polarizations racemicity circularly

that any scenario dipole n :L ~

we will receive the same result-preserving of an initially whereas incident laser fields polarization

type of enantiomers interaction polarizations

flom a racemic

and achiral structure result in no change in chirality in a racemic

polarized

of the incident

ture the initial

racemicity with

can break down. rotational

In other words, is a specific laser fields, in

Saú after inversion solution.

D. Therefore, all such kinds of

one of the conditions of a chiral medium configuration

tor laser-assisted

control of chiral states symmetry

scenarios are useless tor controlling

of the polarizations

of the incident

The inversion superoperator n in terms of the operators R acting on the wavefunctions can be written in the SchrÆdinger pictureasn=R0R-landintheHeisenbergpictureittakes the form n-l arbitrary flom = R-1 0 R. In addition, U"p~)U;l any rotation Cl" at the density to the rotation angle Ip leaves the initial symmetric L~ D is equivalent

which encodes the helicity of the problem. Such symmetry analysis applied to the scenarios Refsl-7 dipole shows that the scenarios in Refs 3-7, transitions, are more effective employing

than those in Refs 1 of the polarizations

and 2. All the described scenarios require tor their successful implementation of the incident use of helical structure fields or, as will be shown, a preliminary

matrix unchanged,

= p~). Then, one can easily see

Eqn (6) that transition

inversion of the superoperator S(E). Taking also info account that the Hamiltonian of a free motion is a symmetric function with respect to inversion (we neglect hefe weIl-known weak interactionszo because their contribution is much smaller than the considered after inversion the form n8r(E)R.-1 = Texp effects), i.e., n-1Ho = Ho, one can obtain dynamics superoperator in the transformed

alignment of the chiral molecules in a solution, which is aseparate difficult problem. In our early work15.16 we suggested as a solution to this problem using a non-coplanar configuration of the polarizations of the incident laser fields. Summarizing dated analyzing field-chiral ity criteria this section of the paper, we have elucithe symmetry properties of incident laser two key qualitative feasibil-

matter interaction tor laser control

of molecular

chiral states. First,

{ -~ r (
11 Jo

[UÆl(n-1Hr)Uo '

0]

configuration of the polarizations of the incident laser fields must have a helical structure, otherwise a preliminary spatial alignment of chiral molecules in a racemic solution is required. Second, suggested scenarios will be effective only tor the chiral molecules of which the dynamics are weakly along the reaction coordinate with the dynamits (internal rotation) coupled

)
+ nL-rn-l Here the transformation equivalent to the inversion the latter being equivalent d-r

}
(7) Hamilt~an ~s = -d,

of the interaction of the dipole to inversion

moment'Rd

along other degrees of freedom.

of the electric field LASER PREFERENTIAL SYNTHESIS ENANTIOMERS FROM A RACEMIC H 0 ANO HOOO MOLECULES 22 To proceed further, molecule OF V APOR OF

strength E. Inversion of the incident laser field in 3D spate can be decoupled info a mirror reflection with respect to an arbitrary plane and a corresponding rotation. In the case of a coplanar fields, coplanar polarization configuration configuration of the incident rotation laser

we need at this point to specify a chiral apply to an analysis chiral structures-the tor laser prefhydrogen

3D inversion polarization

reduces to a simple

because

that we will

is invariant

with respect with L-r is

erential synthesis scenarios suggested in later sections. One of the simplest molecular peroxide molecule (HzOz) or its isotopomer (HOOD)-suits our purpose weIl, fits the feasibility criteria outlined earlier

to reflection,

if its polarization

plane is used as a reflection

plane. Then, keeping in mind that SaP(E) are invariant respect to any rotation and the relaxation Uouvillian

Copyright@2002 JohnWiley & Sans, Ltd.

J. Raman Spectrosc. 33: 962-973 2002;


966 S. Bychkov S. et al.
and its vapor can be used in an experimental realization of the suggested scenarios. As any chiral molecule, hydrogen peroxide has a doubleweil ground-state potential with the minima corresponding to the L- and D-chiral states. The potential barrier separating time two minima determines For such a small molecule these between L- and D-states. the tunnelling or transition as hydrogen peroxide, this time lies in the picosecond region and, therefore, the chiral transition dynamics are of oscillatory type. This is far flom the case with stable enantiomers, largely polyatomic molecules, that attract most attention owing to their practical interest and for which the transition time could be many orders of magnitude higher than for small molecules because the potential barrier separating the minima for the chiral states is much higher (in the limit of organic or biomolecules, the transition time could be on the order of years to millions of years). Nevertheless, studying the hydrogen peroxide molecule can give us an insight into the fundamental mechanisms controlling molecular chiral states, both theoretically and in an experiment. Moreover, the creation and control of dynamic chiral states are directly connected with the quantum entanglement of these states,2l which plays a crucial role in speeding up the algorithms of quantum information processing.22.23 Therefore, molecular chiral states could be considered, in principle, as an embodiment for the physical realization of a qubit (quantum bit of information). Dynamics of free H2O2 and HOOD molecules The hydrogen peroxide (H2ý2) molecule or its isotopomer, the deuterated hydrogen peroxide molecule (HOOD), arethe simplest molecules showing helicity of their structure-four nuclei, one of which located out-cf-plane, result in a helical or chiral3D non-coplanar structure as shown in Fig. 2. It can be described in terms of interna! coordinates (9,9l.~. Tl. T2,T3) introduced in Fig. 2. The helicity of the molecule depends on the torsional angle 9. The complete set of angles, which are to be taken into account in describing the molecule's dynamics, include additionally Euler angles240 = (IJ.qJ.æ) that describe the rotation of the molecule asa whole.25 The free dynamics of a such kinds of molecules have been investigated both experimentally, with the help of absorption spectroscopy,26-28and theoretically, performing ab initio calculations and applying empirical methods.29-3l The theoretical results are in good agreement with experiment and show that coupling between the molecule's dynamics along the reaction (chiral) coordinate 9 and along other coordinates can be neglected. Then, the number of essential coordinates of the molecules to be taken into account is reduced to just four: the torsional angle 9 and three Euler angles O. The chiral dynamics of the H2ý2 and HOOD molecules are therefore determined by motion of the light hydrogen (deuterium) nuclei around the 0-0 bond formed flom a) Trans: Position Vcis position Cis b)

I];I~I

i :

Vtran

90

7t

27t

Figure 2. (a)Geometry of the hydrogen peroxide (H202) molecule with a helical structure and corresponding molecular degrees of freedom: '1. '2 and '3 are the distances between nuclei, 01 and 02 are the bending angles and 0 is the torsional angle (reactioncoordinate). (b)Ground-state double-weil potential for a molecule with helical structure similar to the hydrogenperoxide molecule versus torsional angle. .. much ~eavler. oxygen ~uclel. For ~ fre.e molecule, ~e dynaIn1cs .of light nuclel deco~ples mto m.terna! rotation along torslonal angle 9 ~d theu total rotation as a whole along the rotational angle 9,which is taken between the angle separating two proton bonds. For the scenarios employing Raman pumping schemes (see Fig. 1), the dynamics of the heavy oxygen nuclei forming an 0-0 bond may be considered in the zeroth approximation as classical and, therefore, coupling between rotation of the molecule as a whole and its internal rotation is negligible. Hence the only dFmic coordinates to be considered are the angles 9 and 9 that should be described as quantum-mechanical operators, whereas the two other angles determining the direction of the 0-0 bond can be treated in the zeroth approximation as classical values, which should be statistically distributed when an ensemble of molecules is considered. This approximation perfectly fits our purpose to demonstrate the feasibility of the laser preferential synthesis scenarios. As a result, a simplest two-dimensional model Hamiltonian of the free molecule's dynamics takes the form AA A H = He + H9 A JLzz H9 = Zr... A a Jzz= -111"ij:8" A a J88 -11100 = (10)

A JL88A He = T~ + V(9).

where JL88 JLzz the components of the inverse tensor of and are inertia, corresponding to the interna! rotation and rotation of the molecule asa whole along æangle. They can be estimated as JL88 4JLzz 2/(mHail) for H2O2 and JL88 3/(2mHail), ~ ~ ~ JLzz~ 1/(3mHail) for HOOD, where aH is the length of

Copyright @2002 JOMWiley & Sons, Ud.

J. Raman Spedrosc. 2002; 962-973 33:


I

i

I]:;I~I
a) H202 v 2460cm"' b) ,v HOOD 2460cm"1

Laser coherent control molecular of chiralstates 967
still much smaller than those tor the rest of the intramolecular degrees of freedom. This prevents the rotational-torsional excitation from rapid decay via the intramolecular energy redistribution mechanisms and preserves the coherence during the excitation of the moleCule. Excitation schemes used tor preferentiallaser synthesis from a racemic solution will be discussed in the following sections. Quantum entanglement of the rotational-torsional states and photoinduced chirality For an ensemble of spatially aligned H2~ or HOOD with defined orientation angles, one can easily creat e a coherent superposItion 0f L -an d D -states SllnpIy

n n

=1

111' " 27t e " e .molecules d (b) HOOD II Flgure 3. Ground-state double-weil potentialstor (a) H202
an moecues.

..

.

the O-:-H bo~d. P~a~eters of the symmetric double-well potential are glven m Flg. 3. In accordance with Eq. (10), interna! rotation of the molecule and its rotation as a whole are independent, so that eigenfunctions of the corresponding Hamiltonians are r~presente~ with the ~ensor products of th:ir individual elgenfunctions, producmg the separable statesm the product space 1i = 1itonl 1irot of the rotational 1irot and torsional 18> 1itorsspaces. The rotational eigenfunctions are represented with the twofold degenerate exponential or cosine-sine wavefunctions 1 ,"inæ 1 -1 .-HOOD In,") = ~e , In,..) = ~cosne, ~smne (11) Eigenfunctions of the torsional Hamiltonian H9 are the antisymmetric and symmetric couples, 1/IA(9) and 1/15(9), if the torsional angle equal to zero is chosen at the torsional energy trans-barrier maximum 9 = 1I. It is worth noting that both the 1/15 and 1/IA energy levels possessan additional small splitting due to tunnelling through a sufficiently high but finite cis-barrier (Fig. 3). This cis-splitting is of the order of 10-4 cm-1, which is small enough to be neglected. The eigenfunctions of the total free energy potential are combined as the tensor products of the form Ichirality, rotation) = Ichirality) 18> Irotation), where the chirality basic states are denoted by indices A and 5, which do not correspond to the L- and D-states, but to their antisymmetric and symmetric combinations, and the rotation basis states are denoted by integral indices n with the corresponding subscript c or s. Therefore, tor the eigenstates we use the notation IA, n,..) or 15,n,.s) with the parameters determining the chiral and rotation states,respectively. Typical frequencies of the rotational motion tor the H2O2 moleCule are comparable to those tor torsional dynamics, but they are much higher than the frequency of 0-0 bond rotation, which we skip in the discussion hefe. The 0-0 bond orientation angles then are treated hefe as nondynamit dassical variables revealing only at the averaging over the molecule's orientation angles. The characteristic frequenciesofthecoupledrotational-torsionaldynamicsare

applymg coherent Raman pumpmg to the corresponding 15) -+- IA) transition. By contrast, tor an ensemble of randomly oriented molecules, the non-coplanarity criterion outlined earlier prevents this simple solution and one haBto align the molecules first. Earlier we suggested a scheme with Raman pumping;3, 14 which employs rotational alignment of the molecules in a strong laser field due to the laser-induced rotation over the rotation angle 9 with the frequency of one of the Raman components. However, using such a scheme requires, owing to the non-resonant character of interaction, intensities dose to the ionization lirnit, which is difficult to realize in an experiment. A preferential laser synthesis scenario from H2~ or vapor proposed here employs a completely different ideaofcoherentcontrolofthephasesofrotational-torsional statesphasesvia entanglement of the rotational and torsional subsystemsin the process of pumping molecules by incident laser fields. In an attempt to elucidate this idea we should firstdiscussthepropertiesofmolecule'srotational-torsional dynamits under the resonant interaction, which involves only two torsional states 15),IA) and two rotational states 10),In) (at this stage,we neglect tor simplicity the rotational degeneration). As a result of interaction dynamits, a molecule goes into the coherent state, which, in the general case, is an entangled (not separable in the form of the tensor product) rotational-torsional state: 11/Ienu =c111/1tJ +c211/1v +c311/13) +C4J1/I.) 11/1) = IL)I+) ~ ID)I-) 11/1) = IL)I-) ~ ID)I+) (12) 1,2 .J2' 3.4 .J2 where 1+) = 0 ~,I-) 0 =~ and In) is an

..,

eigenrotational state. The new rotational basis I~) is chosen hefe by analogy with the basis of symmetric and antisymmetric functions made of the chiral basis states IL) and ID). If one considers two partides A and B as a material implementation of the rotational and torsional degrees of freedom, e.g. two polarization-entangled photons, the terrninology of quantum information theory can be used by analogy. For example, states 11/11.2.3,4) then the are

Copyright@2002JohnWiley & Sons, Ltd.

J. Raman Spectrosc. 33: 962-973 2002;


968 S. Bychkov S. et al.
well-known Bell states.32In particular, the state produced under biharmonic excitation of the transition 15,0) -+ IA, 2) at some time instants coincides either with the 11/11) or the 11/Ivstate. This means that under coherent excitation the joint rotational-torsional symmetry is revealed in the form of quantum entanglement. Although this symmetry is preserved, it does not contradict unequal transition probabilities to the L- and D-states for a fixed rotational state, provided that it is restored in the form of the reverse asymmetry for the other corresponding rotational state. Construction of a preferential laser synthesis scenario of required enantiomers from a racemic solution proposed here should include several steps: first, an excitation of the rotational-torsional dynamics, which should generate a properly entangled state; next, applying additional laser pulses to provide non-equal population of the rotational states 1+) and I-), which initially have equal probabilities being incoherently and equally formed out of the basis states 10) and In); then, applying a probe field to register the induced chirality. This probe field will scatter in accordance with its phase relations to the previous waves and, having some definite phase, scatter asin a chiral medium becausethe totalrotational-chiralsymmetryisrevealedonlyattemporal oscillations, being broken at a single time instant. The efficiency of an experimental scheme realizing the above- described abstract scheme is typically determined from the requirements of the specific registration scheme and system. We can, for example, consider registration of the polarization plane rotation, which reveals the chiral f th d b d .4(0) properties 0 e me lum, as rt ecomes gyrOtrOplC unng the time of an experiment for the laser synthesis. Therefore,

I];!;!
directions, Tl and T2are the electrons' radius-vectors, Eisthe field strength amplitude and Wis the probe field frequency. The coupling coefficient K is responsible for the phase correlation of the electronic vibrations and, consequently, determines the unequal representation of the right- and lefthanded configurations of the molecule, that is the responding electronic chirality. There exist several microscopic models to calculate K, depending on the specific type of a molecule. In thecaseoflargemoleculesithasanon-zerovalueowingto the secondary re-emission (ie. electron-electron interaction via the electromagnetic field) of the optically active electrons, which can be calculated using the Kirkwood model.36 In the opposite case of small, simple molecules, the main mechanism is overlapping of the electron clouds. For H2O2 and HOOD molecules this latter mechanism is a prevailing one, but the overlapping is rather weak because the distance between the oscillators is relatively large, ao "" 1.5 A, and electron clouds are localized at the distance of a Bohr radius, aB"" 0.5A, which is much smaller than ao. Hence, 4 the gyration operator d, which determines the polarization response AQ i 4 ~ P = Z[d x E] (14) can be written as an expansion over the small parameter K/w5: 4 4(0) 4(1) d = d + d (K) + ...(15) where d depends only on the nuclei configuration chirality, h d (K) d 4(1) th chirality f th I ctr
w ereas etermmes

.

..

.

.

e

0

e ee

omc

.

the choice

expenment lS
the maximum

..

of a specific

dir tl d
ec y
possible

working

etermme
of

.

transItion

d b th f b ..component. y e alm 0 0 taining Th
scattered polarization. .

to be used

.

m an

e gyrOtrOplC

.

po

I

anza

.

ti

on

ro

t ti'
a

on

elSen

ffect

'

th

d e t er-

signal

the

The

latter

is determined determines

by the

gyration

operator,

which,

in

mm ed b y th e quan tum -mec hanical average " gtven m E qn (15) Wl. th a dditi on al averagmg . . ro ta tions. .

0 f th e opera t or over th e 0 - 0

its turn, To

...,aXISactivity the optical the optical actiVlty,

in the medium. we can use classl.magnetic

.

1 W.

th th e assump

ti on th a t th e excl. tin ge I ec tr 0'

calculate

wave propaga t es along the z aXls,1t yte ld s A0 21te2kao COS2 " -. d() = -:;--(2 2) COS sm 9 2B " me wo-w

..

.

cal models adopted for quadrupole and magnetic dipole moments.33.34 the H2O2 and HOOD molecules the most For appropriate model is the classical model of Kuhn,35treating the chiral molecule asa system of two coupled harmonic electronic oscillators moving at some distance from one another in orthogonal directions. In the case of H2ý2 and HOOD theyare evidently associated with the O-H and O-H or
0 -on Db d s. Th e dist b anceao tw e th een eos cillat

4 A d = (0,0, d),

d(l)(K) = ~ ~-..!:!. ~ ~ sin 9 A me (w~ -w2) (w~ -w2) (16)
where A is the wavelength of the probe field. From Eqn (16),

to scill

theen I

gth0 f the
' ti

0

0

ators mo on can e wn en as
..2 m~+w~+KI)=-Ie( . k ~

-on. b

0b
. tt

d Th

en,

theequaonso ti .
) -iwt

. orslsequ

al

f th

e

it follows that the gyr ation operator depends only on the
d yn amic rotational-torsional coordinates 9 and 9. For the

case of stable chirality when it is impossible to control any
~ ~

e

0

.rl)(e.n~e

~

rotational

independent averaging over the rotational angle - so that 9,

angles,

the

term

dIa) would

become

zero

after

meii+ W~I) K~ = -ie(k. TV(&' n,,)e-iw/ +

(13)

where meis the electron mass, Wo the oscillator frequency, is K is the coupling coefficient, k is the wavevector of the probe field, n~ and n" are the unit vectors along the ~ and I)

the optical rotation is determined only with the second couple coefficient dependent term. At this point it is WOrth stressing that the quantum entanglement described earlier leads to the fact that Kindependent term dIa) is not equal to zero after partial

copyright 2002 Wiley& Sons, @ John Ud.

J.Raman Spectrosc. 33:962-973 2002;


I];I~I
averaging only that after this over the term, the 0-0 bond rotation and_goes over 9. This to zero means a molecule in the

Laser coherent ofmolecular states 969 control chiral
rotational state I+} or I-} and the chiral

last rotational although

averaging

state IL} or ID}:

untypical

for a general
a new

discussion
of X= ![p(L, 2 +) -p(D, +)] + ![p(L, 2 -) -p(D, -)] (20)

of the gyrotropic properties, yields achievingopticalrotationwithoutbreakingthetotalisotropic

possibility

symmetry, torsional

when the correlations states are present. reaches entangled obtain

between

the rotational

and

g=

![p(L, 2

+) -p(D,

+)]

-![p(L, 2

-)

-p(D,

-)]

If the molecule are all rnaximally

one of the Bell states states, for the

l1/ri}, which with

For the quantum after given averaging in Eqn

state the

determined

with yields

Eqn (12), the average

Eqn

(19),

then in accordance zeroth-order

projectors, of

values

Eqn (3) and

(16) we

gyration

(20) in the form -C3c4)' analysis scenario molecules one with of which the

d(O) # 0, although for the degree X = O. This means that in H2~with coupled rotational-torsional

of chirality we obtain zero, and HOOD-like molecules dynamics, optical rotation chirality. average, temporal situation thinks of it

2 X = 2!Jte(clci Preliminary laser H2~ synthesis or HOOD fields, JA,2c} the g = ICII shows flom + IC2r -IC312 -IC412 (21)

that an effective an initially use two

preferential vapor of

rnay be present In can other words,

even in the absence if the medium dynamics, rotation only at first

of the average on shows This on~

racemic pairs

is racemic which media.

should excites

of Raman transition the other

undergo

temporal of optical

pumping 15, O} excites field-one scattered gyration

the coupled (LI2o+ (J)AS and Then,

oscillations

in the

frequency

seems .paradoxic~ the chiral prop~rties the

S~ght, when

rotational

10)

12) transition. of the biharmonic medium as we will with

a probe

~f the

medium shows

as something that which there

stable. could be

of the components in wave the excited

pumps-is

However, realized

diScusslon

above

a photoinduced

a so-called

conditional states, whereas

chirality

is the property of the degree

producing, signal.

show in the next section,

of the rotational of chirality

the definition rotations. molecules,

an NOA-CARS

haB nothing

to do with

For the case of H2O2 or HOOD chirality 15, O} the the vapor chirality weak can be excited IA,2c)

the conditional pumping show an of the that for

Scenario racemic As was

of

preferentiallaser

synthesis

flom

a

by the biharmonic Our can by be the ratio estimates used in

solution pointed of out in the previous section, flom pumping Raman the to an effective

transition. that

densities determined

experiment term yields

scenario solution We

preferential employ to much D-states resonant use

laser the

synthesis Raman

a racemic scheme. pulses with time the of the on

K-dependent to register. stronger effect registered question the

should hefe

a too is

signal-to-noise whether chirality The

The due

question to the the

propose

resonant longer in than order

therefore

a much

a pulse between advantages induced

duration Land of the

transition flom

conditional same by the an

can be basically answer evaluation variance to this of of the

under

benefit The then

conditions. approximate

can be given value chirality of

interaction. oscillation of the pumping fields determine

phase

average and

rotational-torsional in the phases of pumping

depends

dimensionless

gyration

the difference i.e. the phases

Raman

pulses,

operators g cx: sin9cos2B, X cx:sin9 (17)

the controllable

chiral state oscillation at each time instant. If we cannot control the phases of the laser pulses, the chiral state will be affected randomly. controlling all For an phases the experimental of the Raman oscillations for all demonstration pulses is not of in a notion

These

two

operators,

being

dependent commute

only with listed

on each

the other

rotaand

of the

effect,

tional-torsional therefore have

coordinates, the same

so crucial different physically

because molecules small we skip

induced

phases

eigenfunctions

below:

are the same

the molecules Keeping this

volume further

of the medium. detailed of the

IL}I+},

IL}I-}, 10} + 12c}

ID}I+},

ID}I-}, 10} -12c}

in

mind,

discussion phases

of the impact on the induced in Fig. 4. that

of the

random

character scheme will

laser

I+} =
J2

I-} =
J2

(18)

chirality.
The excitation discussed be made above is shown under of H2~ All further estirnates with the assumption molecules

Th

en, tral spec

th

t f. t t b tt th f e opera crs 0 m eres can e wn en m e orm d ti.we ecomposl on as

.

.

.

0

f

are working temperature

the vapor pressure.

at room

and normal

.D X = (IL}(LI-I

L )( I)@(I+}(+I+I-}(-I) G+}(+I-I-}(-I) (19)

The excitation scheme employs three laser pulses frequencies (J)l, CO2 and (J)Japplied to the rotational-torsional subsystem, which satisfy the resonance conditions

with (J)}2 ~

g = (IL}(LI-ID}(LJ)@

CV20 (J)ASand + Their terms averaging of the joint gives the corresponding p(L, average values in with The pulse

(J)13~ (LI2o. duration for the pulsed biharmonic by two excitation key factors.

probabilities

:i:) and p(D,

:i:) of finding

frequencies

(J)l, CO2 determined is

copyright ce2002JohnWiley & Sons, Lid.

J. Roman Spectrosc. 33: 962-973 2002;


970 S. Bychkov S. etal.
Qe and pumping ~ ~ ~ 0>1 A,2. 8,2. AO , 8,0 Figure 4. Excitation scheme tor a non-racemic
H202 or HOOD molecules (vapor) with the use ot

l]il~1
Qr are the Rabi frequencies of the rotational-torsional fot the biharmonic 15,0) --*

transition

~

IA,2.,) by the fields with simultaneously, biharmonic

the frequencies WlI ">2 and, pumping of the rotational

0>1 A,2c 8,2c

10) --* 12) transition by the fields with the frequencies WlI li>3. Neglecting fot simplicity the relaxation processes, the degree of chirality and gyration on the basis of Eqns (6), (19), and (22) take the form x= r 00"4 00"1 0[ PoÆ ) A' A g = 2(TrUÆ1ulchir) 0 ulrot)UoS[(E)1>o)Æ
ansion

2(T U-lA(chir) A

A(rot)

U S (E)A A

(24)

mixture ot
w three

h
ere

th tr
e

.ti
'

superopera

.P plcosecond

laser pulses.

ul d ses, expresse W1 th th e h eI p 0 f th e tim e eV 0 I u ti on operator, corresponding to the action of the multi-component field, is simply a unitary operator:

.

t or

f or

th

e

rec

tanguI

ar

s ha

pe

First, in order to employ methods

of coherent control, the S[(E) = U[(E) 0 Ur1(E), At room temperature state corresponds

. UnE) = exp ( -~H[t) Ii matrix (25)

pulse duration should be less than the dephasing time r-1 of the working transition, which fot agas at normal temperature and atmospheric the pulse tunnelling pressure is of the order of t"p« r-1 ~ 10 ns. by Second, the pulse duration has a lower limit determined

and normal

pressure, the equilibrium of the form 1>0 ~ rota-

to the density

spectral width, which should be less than the 12 1 frequency, 8 ~ 10 s-, to obtain a resonantly the pulse duration should ober 8-1 « t"p« r-1 and its optimal value lies in range, t"p ~ 10-11 s. The lower the pressure,

(1/2)[u(chir) 0 u(rot) + u~chir) uJrot>j. 0 1 1 In the frame of the model of photoinduced tional-torsional dynamics presented theexpressionsasgiveninEqn (24)withthehelpofcomputer algebra, which results in the following equations: = Ax(t"p)SinwAst, Ax(t"p)=

enhanced signal. Therefore, the inequalities the picosecond

hefe, one can calculate

the longer is the pulse duration

th

that may be chosen owing to d theco llisIon al d ep h asmgrae t r .X ere uctionm The information on the chiral properties of the medium

..

.

.

2QeQr 2Q 2 2sinQet"psin -t"p Qe + Qr 2 (26)

(solution, dynamics,

vapor) which

is encoded in the rotational-torsional is described in terms of the excited

g=A(1)(t"p)sin(W2Q+WAS)t+A(2)(t"p)sin(W2Q-WAS)t g g whereQ=..úir+fi;andAj1,2)arerepresentedbyequations

states 15,0), IA,O), 15,2.,), IA,2.,), 15,2.), IA,z.),wherethe degeneration complete of the excited rotational analysis states is included. The dynamic of the simplest analysis system includes the degeneration so that we

similar to those fot Ax' Sofar, wehavebeendiscussingthedynamicsofhydrogen peroxide molecules. The photoinduced molecules essentially differ to H2~, dynamics of HOOD are Ramanare approximafrom those of H2O2 molecules where these transitions

six states, but fot a qualitative

does not affect the chiral properties

essentially,

can reduce the system to the tour levels 15,0), IA, 0),15,2.,), and IA, 2.,). These basis states, as was revealed in analysis of their linear combinations in the form of Eqn (19), are responsible fot the gyrotropic properties of the media. In terms of the rotational-torsional states [Eqn (11)], the interaction Hamiltonian in the rotating wave approximation (RW A) takes the form H[ = IiQru~chir) 0 ulrot) + IiQe( -u~chir) 0 u~rot)+ ulchir) 0 ulrot1 (22) where u(chir) = ~(IL)(LI+ID)(DI), 1.J2 i u~chir)= "J2(IL)(DI-ID)(LI), u(rot) = ~(I+)(+I+I-)(-I) 1.J2 i u~rot)= "J2°+)(-I-I-)(+I) 1 ulrot) = "J2°+)(+I-I-)(-I) (23)

becauseall the transitions in the HOOD molecule active, in contrast forbidden and allowed only in the quadrupole

tion. Also, the laser pulses intensities t"p ~ 10-11 s should fit the condition sponds to the saturation ionization threshold than the threshold Equations of the 0-0

fot the pulse duration of Qt"p ~ 1, where Q correthe they are much lower angles the

regime, and fot H2O2 approach fot the HOOD molecules. to the fixed orientation be averaged should over

values, whereas intensity and

(26) correspond bond

corresponding orientation angles cpand 1J,included in the Rabi frequencies as parameters. Analyzing these equations, one can and the the total solution show that fo~ non-saturating int.ensities, Qt"p ~< 1, coplanar multi-component laser field configuration, effect of the photoinduced non-racemicity in the does not vanish. Moreover, the order of ~agnitude at the

ulchir) = -32°L)(LI-ID)(DI), 2

of the degree of chirality and the gyration remams samelevelasforthepreciselyspatiallyalignedO-Obonds of the molecules.

copyright Ig 2002JohnWiley & Sons, Ltd.

J. Raman Spectrosc. 33: 962-973 2002;


I];I;!
REGISTRATION OF PHOTOINDUCED CHIRALITY BY MEANS OF NOA-CARS h .polarization In accord ance Wl' th Eqn (26), apotom d uced gyration wave is generated in the medium, which oscillates in time and space at a combined frequency CIJzoWAS~ Wu. Scattering + of one of the biharmonic pulsed fields at this photoinduced

Laser coherent contral molecular states 971 of chiral
can readily obtain, with the help of Eqns (28), (26)and (27), an expression tor the NOA-CARS signal amplitude t:a with vector ea= [k x e"'1 at the end of the medium: ]/k z z t:a = ~~ ~kao(cosz1JAg(1'p»)IP.,t:"'1L 2k. (wo-W ) (29)

.

gyration wave gives rise to the NOA-CARS signal. In this ti ill discu ss the regIstra ti on scheme m d etail ' sec on, we w li ty th bl ( ) d ill f an w assume or Slffip Cl at an ensem e vapor f chiral I cu! d b nl fi ld 0 mo e es lS excrte y0 two pumpmg (F 4) hi h gh t 0 per f ormy the pre f erentiall es.. 19. ,w c lS enou aser

.

.

..

.

.

.

.'.

pumpmg-gIves

limit kT « w d Th h t ~.s. d d e p 0 om uce gyra b d b th ti th Rae yfr e gyra on escn f e man equency 0 f th b fi ld 0 e pro e e -one th ..,

synthesIs

from

a

raceffilC

solution

at

the

low

.

wave m e d(0) ~ hi h vector th ,w c fi ld e pumpmg e. f th fi ld f 0 e es0

ti

.. on

th

.

a me

to

e qua

dru

I I .. po e po anzation

1._~r..2,- .. where Wp = V 47rN&/m. lS the plasma frequency, k lS the wavevector of the probe pulse and L is the length of the . active medi um. z As follows from Eqn (29), the mtenslty Ia = clt:al /87r of . the NOA-CARS sIgnal depends not only on the intensities temperature f th biharm b als0 on thelr po I anzation 0 e oruc pumpmg, ut edi .properties. The latter determines the gyration value g after m um lS. ill Its averagmg over the lSOtrOplCally onented 0-0 bond. For osc ates at Sc .example, fÝr the counter-propagating clrcular polanzations attermg th Ram of the pump pulses we have g = 0 and Ia = O. e an .,

.

.

..

.

..

P (3)Q ,

which oscillates at the anti-Stokes (Stokes)frequency. This ti d th NOA CARS I po anza on response, m turn, m uces e th chiral f I hi h inf sIgna di w c th m ormation on e properties 0 bill de. 37 FeaSl ty studi es 0f the NOA d e me um lS enco CARS measurements fÝr the problem of distinguIShing

. . . ... .
..
d 37 f

.

..
f 0

.

fi ld ... I. e s m an expenment lS extreme y lffiportant. One sh 0uld k .. d th . ddi . th ful . al there eXISts . eep m mm at m a tion to e use Slgn
a prevailing strong coherent background from the medium due to the anti-Stokes scattenng on the Vlbration-rotational illa f th lecul T osc tions 0 e mo e. 0 cope Wl th this coh erent b ck d discriJnin ... f th ful ' I

The

cholce

of polanzation

schemes

of the

laser

pump

.

.

non-raceffilty
reporte

m
or

th

e me

di

um
edi

0
um

f chiral

l mo ecules
. mo

have
I ec ul es.

been.
Th e

a

groun,
Wlth

a

ation

0

e use ...

sIgna

. lS

to

be
of

made

, non-local response at the anti-Stokes frequency given by the quadrupole polarization p(3)Q and registered experimentally was assigned to the presence in the medium of the soluted mirror-asymmetric bioorganic molecules. In our case, the gyration vector of the photoinduced gyration wave in the medium oscillates at a frequency CLIl -Wz and one can readily obtain with the help of Eqns (15) and (16)a general expression fÝr the quadrupole polarization at the anti-Stokes frequency due to the photoinduced gyration wave: p(3)Q(Wa) ~N[d(WJ -Wz) x E(CLIl)], Wa= 2wJ -Wz (27) =

a pure

m

orgaruc

th bih
e

the

armoruc pump

.

use

of one

fi ld

of the

followmg

configurations

e:

37

(a) Polarization vectors of the pump fields are co-propagating; the polarization of the registered anti-Stokes signal is orthogonal to the polarization plane of the pump fields. (b) Polarization vectors of the pump fields are orthogonal to each other; the polarization plane of the registered anti-Stokes signal is orthogonal to the polarization plane of the probe field. (c) Pump fields are circularly polarized and counterpropagating, which leads to the complete suppression of the non-linear dipole polarization at the anti-Stokes frequency due to the photon's moment conservation.38 Brief analysis of these three choices shows that (a)is preferable from the experimental point of view; fÝr (b) the useful NOA-CARS signal has a strong background from the pump field and fÝr (c) we cannot control the molecular chirality. The corresponding experimental scheme is shown in Fig. 5. The polarization plane of the NOA-CARS signal when Raman pump pulses have collinear polarization vectors is in accordance with Eqn (27) orthogonal to the polarization plane of the probe pulse. QUALITATIVE RESULTS AND NUMERICAL

where N is the concentration of the vapor and E(w) = e"'1t:"'1ei"'1t. With the help of Eqn (27), one can calculate the scattered signal. In the slowly varying amplitude approximation, Eqn (27) transforms into the wave equation fÝr the amplitude t:a of the NOA-CARS signal, which fÝr a collinearly propagating Raman pumping pulses takes the form

2ika~ei(...t-kaz) az

= ~~p(3)Q(Wa) c2 atZ

(28)

where kais the wavevector of the NOA-CARS field, g = t -~ is the running coordinate and c is the speed of light in the vapor. For th!:; co~ear yumping scheme the phase-matching condition k. ~ 2kJ -kz is obeyed with good accuracy and we

ESTIMATES
Calculation of the intensity Ia of the NOA-CARS signal was made with approximation of constant pump fields, i.e. Ia « I~. We do not consider here the mo~e general case~f Ip ~ Ia as It can hardly be used fÝr preferentiallaser syntheslS

Copyright@ 2002John & Sons, Wiley Ltd.

J,Raman Spectrosc. 33:962-973 2002;

-


972

S. S. Bychkov et al.

I]:;I~I

"i<;/ E OO
E1 ...LE. chiral

A new mechanism
molecules quantum with coherent

tor controlling
internal rotation, of

chiral
which the

states in simple
employs the

entanglement

rotational-torsional

47J ..07 ...' .whose ...' Figure 5. Excitation and detection of the conditional non-racemic state in H202 and HOOD vapors using NOA-CARS with suppression of the coherent background in the direction along the registered NOA-CARS signal polarization. [

states of the molecules,

hag been proposed.

It requires

no

preliminary spatial alignment of the molecules in a solution. Such a mechanism can also be applied to chiral molecules electronic structure shows no helical properties. A novel scenario tor the preferential laser synthesis of enantiomers molecules via in detail. It is quantum flom a racemic solution of simple chiral employing the mechanism of inducing chirality

entanglement

was proposed scheme realizing would
molecules
m the me

and analyzed this scenario be a suitable wave
Slffip

An experimental shown that
(vapor)
uced gyration

was discussed. NOA-CARS
of chiral
wave

suc

h

pump

. m
the

t ti. I d t th b f lin ens1 es ea 0 e num er 0 nonear

.

spectroscopic technique
in

tor both inducing

the gyration
and

processes
orf

P

thVIa
th e po

I

.

non-resonant
ti on sc h eme

susceptibility
h s own . m

tensor
P. 19. 5 ,W1

(3)NR Xijkl].
. th th e

thi

the
s p

h

medium
otom

.

d
the

..
the

di
um

detecting

.

1
y

anza .

use I 0 cul
mo e es,

e maXImum 19 N 10
~

concen -3
cm, an

tr
d

a

ti
th

on
e

0
ce

f
11

th
1

e vapor
gth en L

0
~

f chiral
10 cm,

by
cho1ce

regIStermg
of

NOA-CARS
of

sIgnal.
pump

W1th
laser

the
fields,

appropnate
the NOA-

polanzations

btain . we 0

finall y W1

. th

th e

h

I ep 0

f

E qn

(29)

th e

f 0

11 owmg

.CARS

signal

can

be

several

orders

of

magnitude

higher

than

. al numenc
gyra

timat es es.

P or
es g

th e vapor
~

fH 0
or th e

0 2 2 mo
. maXImum

I cul e es
all owe

th e
d

coherent
tor an

noise .

(background).

Properties
and HOOD

of

two

candidates

ti

on

tens1 ti es J11"2 ~ 1011 W cm -2 f or the p uls e d ura ti.been T pump on CARS . al m tens1ty Tp ~ 10-11 s. Th e correspon din g NOA -Slgn

. m

V

al

ue

.

rea

ch

10 -3

f

expenment-H2O2

molecules-have

analyzed in detail and preference

was made in favor of advantages.

.

.

HOOD molecules because of their symmetry

is J. ~ 102 W cm-2.

Por the vapor

of HOOD

molecules, A~knowledgen;tents ... This work was partially supported by RUSSIan Foundation for Basic Research grants Nos 01-02-16311 and 02-03-32200, INTAS Grant INFO 00-479 and the Waseda University International Exchange Fund (under an Exchange Program with Moscow State University).

the figures are much better: g ~ 0.25 tor the same pump intensities and the NOA-CARS signal intensity reaches 8 -2 the value of ~10 W cm .Such a striking difference m numerical estimates tor the H202 and HOOD molecules in the symmetrical properties is due to the difference molecules-in C2-asymmetric of these

contrast to H2O2, the HOOD molecule is of type.

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Por the vapor of HOOD molecules, in the case of saturating intensities giving a high gyration value g ~ 0.25, the quadrupole order of magnitude coherent background, linear polarization P(3)Q{w.) is of the same as the polarization p(3)D{w.) of the tor which the corresponding nonili .(3)D 10 15 CGSE This susceptib. ty 15 X ~ -.means

that the NOA-CARS signal essentially prevails over the unavoidable noise effects, e.g. due to the photoinduced anisotropy at high intensities.

CONCLUSIONS We have elucidated
the preferentiallaser

two key qualitative
synthes1s of enantiomers

feasibility
flom

criteria tor
a raceffilc

(L un d U rnversl ty) .or W

..

Sweden

9-12

ld Scientifi.c: S. mgapore, 1997 80 ;.
September 1996) Sundstom

V

(ed.)

solution.

First, the configuration

of the polarizations

of the

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incident laser fields must have a helical structure, otherwise a preliminary spatial alignment of chiral molecules in a racemic will solution is required. only Second, suggested molecules scenarios the be effective tor chiral tor which

dynamics along the reaction coordinate (interna! rotation) are weakly coupled with the dynamics along other degrees of freedom.

Copyright ce> 2002 John Wiley & Sons, Ltd.

J. RamanSpectrosc.2002; 33: 962-973


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J. Raman Spectrosc. 33: 962-973 2002;