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A Stark future for quantum control.

03 Feb 2011-Journal of Physical Chemistry A (American Chemical Society)-Vol. 115, Iss: 4, pp 357-373

TL;DR: An overview of developments using the nonresonant dynamic Stark effect within the fields of time-resolved molecular dynamics and quantum control, with particular emphasis on the notion that "dynamics" and "control" are not distinct disciplines.

AbstractWe present an overview of developments using the nonresonant dynamic Stark effect within the fields of time-resolved molecular dynamics and quantum control, drawing on examples from our own recent ...

Topics: Stark effect (56%)

Summary (2 min read)

Introduction

  • The static and dynamic behavior of electrons and atomic nuclei determines the properties of all molecular systems.
  • A natural approach to exerting control over atomic and molecular systems is therefore through the application of externally applied electromagnetic fields.
  • Implicitly, this is the study of the electrical forces present in the system.
  • As such, the notions of observing and controlling molecular dynamics are strongly connected.
  • Control may lead to improved observation and hence better dynamical understanding.

Observation

  • The authors understanding of molecular structure and dynamics is based primarily on the Born-Oppenheimer (BO) approximation, which relies on the fact that nuclei are much heavier than electrons and therefore usually move more slowly.
  • The ability to not only measure this anisotropy but to correlate it with the recoil velocity offers a powerful probe of the overall dynamics.23-29 Vector correlations of rotational angular momentum polarization in molecular photofragments provide much information on the shape of the potential energy surfaces involved in the evolution from reactants to products.
  • Albert is currently a Principal Research Officer within the Steacie Institute for Molecular Sciences and Program Leader of the Molecular Photonics Group.
  • In the case of both time-resolved and frequency-resolved measurements, there are a vast number of different experimental techniques that may be employed and observables that may be monitored.
  • While such studies are of huge importance in furthering their understanding of many fundamental processes, the next level of development within the field of molecular dynamics centers around the desire to move beyond this passive approach and into a regime where the dynamics are actively controlled.

Control

  • As discussed previously, electric forces underpin the dynamics of all chemical processes.
  • A renaissance in the field of laser control began in the 1980s with the work of Brumer and Shapiro,1,59 who considered using quantum interference effects to manipulate chemical reactions.
  • The second-order NRDSE operates via a polarizability interaction (often also referred to as a Raman interaction).
  • In special cases, the linear nonresonant dynamic Stark effect may also be applied to the quantum control of molecular systems but requires dipole-allowed transitions between the controlled states.

DC Stark Effect

  • In the presence of homogeneous electric fields, atomic spectral lines are observed to split into multiple components due to the applied field “mixing” quantum states of different orbital angular momentum quantum number, l.
  • This is analogous to the Zeeman effect,84 discovered several years earlier in 1897, that is induced by a magnetic field and lifts the degeneracy of states with different magnetic quantum numbers, ml.
  • Formally, the general Hamiltonian for an atomic or molecular system in the presence of a static homogeneous electric field may be written as follows where H0 is the field-free Hamiltonian with corresponding eigenstates ψn and energy levels En.
  • The extent of this mixing is dependent on the strength of the field (a stronger field means more mixing), and this gives rise to the concept of a Stark map that describes the energy levels in a quantum system as a function of field strength.
  • Some good illustrative examples may be found in the work of Goodgame and Softley.

Nonresonant Dynamic Stark Effect

  • The derivation of the nonresonant dynamic Stark effect Hamiltonian can be developed from a number of approaches.
  • With a little more effort on the part of the experimenter, however, the distribution of a molecular axis relative to the transition moment may still be inferred from the value that is obtained.
  • As a consequence of the relative energy shift induced by the different polarizabilities, R, for state 1 and state 2, the position of the point where the potential energy curves for these two states cross will be altered.
  • (4) The relatively long dissociation lifetime of the IBr excited state (>500 fs) means that the control field may be applied precisely at various points along the dissociation coordinate using nonresonant IR pulses on the order of 100 fs duration, something easily achieved with modern ultrafast sources.

Conclusions and Outlook

  • The authors have discussed the notion that in order to fully understand dynamical processes in chemical systems, that is, the evolution of the electrical forces in the system as reactants transform into products, it is generally desirable to make the most differential measurement possible.
  • Dynamically induced phase shifts also offer some interesting possibilities when applied to systems that do not dissociate directly.
  • Another important step in the development of the DSC approach to chemical control will be its application to larger, more complex systems.
  • As an analogy, the methods appear more and more like their notions of look, touch, and think.
  • The links between quantum control and quantum information are still developing, but there are a number of exciting avenues.

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A stark future for quantum control
Townsend, Dave; Sussman, Benjamin J.; Stolow, Albert
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A Stark Future for Quantum Control
Dave Townsend,*
,†
Benjamin J. Sussman,
and Albert Stolow
School of Engineering and Physical Sciences, Heriot-Watt UniVersity, Edinburgh, EH14 4AS, United Kingdom,
and Steacie Institute for Molecular Sciences, National Research Council of Canada, 100 Sussex DriVe,
Ottawa, Ontario, K1A 0R6, Canada
ReceiVed: September 23, 2010; ReVised Manuscript ReceiVed: NoVember 15, 2010
We present an overview of developments using the nonresonant dynamic Stark effect within the fields of
time-resolved molecular dynamics and quantum control, drawing on examples from our own recent work.
Particular emphasis is placed on the notion that “dynamics” and “control” are not distinct disciplines and that
a clear synergy exits between these areas which has, up to now, been somewhat underexploited. The dynamic
Stark effect is a universal interaction which we expect to have broad applicability.
Introduction
The static and dynamic behavior of electrons and atomic
nuclei determines the properties of all molecular systems. The
electromagnetic forces driving such behavior ultimately impose
limits on the feasibility and rates of all molecular processes and
therefore underpin all of chemistry (and, by extension, biology).
A natural approach to exerting control over atomic and
molecular systems is therefore through the application of
externally applied electromagnetic fields. The electromagnetic
fields created by modern lasers generate forces comparable to
those that bind atoms and molecules and can do so on the natural
time scales of their motions. Consequently, lasers offer an ideal
tool for effecting control over molecular processes, and achiev-
ing this goal has become one of the “grand challenges” within
the field of chemistry over the past three decades.
1-11
From a chemical point of view, an understanding of dynami-
cal behavior may be formulated in terms of the various
mechanistic pathways that connect an initial set of states (or
reactants) to a final set of states (or products). The study of
chemical dynamics is therefore often concerned with developing
an understanding of the detailed evolution of the electronic and
nuclear degrees of freedom as the reaction coordinate connecting
reactants to products is traversed. Implicitly, this is the study
of the electrical forces present in the system.
A commonly cited notion of chemical control centers around
the desire to precisely manipulate the relative yields of the
various product states that may be formed in a given reaction
process, that is, to influence rather than just passively observe
the dynamics. However, even in the absence of any control
strategy, the dynamics of many molecular processes are not well
understood. This has served as a strong motivating factor in
the development of increasingly sophisticated or “differential”
experimental techniques to study dynamical processes. As we
shall discuss in more detail below, the use of externally applied
electromagnetic control fields can also be used to further enhance
the differential nature of these observation-based measurements,
for example, by preparing a specific state before a measurement
rather than starting with a thermal distribution. As such, the
notions of observing and controlling molecular dynamics are
strongly connected. Control may lead to improved observation
and hence better dynamical understanding. Improved under-
standing of the system dynamics may then, in turn, ultimately
lead to more refined strategies for control.
Observation
Our understanding of molecular structure and dynamics is
based primarily on the Born-Oppenheimer (BO) approximation,
which relies on the fact that nuclei are much heavier than
electrons and therefore usually move more slowly. The nuclear
motion (vibrations and rotations) may therefore be adiabatically
separated from the motion of the electrons in the system, and
this leads naturally to the concept of electronic energy land-
scapes (potential energy surfaces) determined by fast-moving
electrons, over which the much slower nuclear motion evolves.
This adiabatic approximation is central to enabling the discussion
of dynamical processes to be framed in terms of a language
which includes the concept of well-defined vibrational energy
states, and it has proved very successful in modeling the
behavior of simple molecules. Even in these simple systems,
however, the coupling between the nuclear and electronic
degrees of freedom is often not negligible, especially when
electronically excited states are being considered. In the excited
states of larger and more complex systems, there is growing
evidence that these breakdowns of the BO approximation are,
in fact, the rule rather than the exception.
12,13
They are also
known to be central to biological function in fundamentally
important processes such as vision and photosynthesis.
14-18
There is, therefore, a fundamental challenge to develop our
understanding of non-BO dynamics for molecular systems and
ultimately extend this to complex environments, such as
solutions, bulk materials, liquid and solid surfaces, interfaces,
and biological systems.
Deviations from the BO limit take on a variety of names when
discussed within the field of molecular dynamics. Nonadiabatic
processes, radiationless transitions, internal conversion, elec-
tronic relaxation, curve crossing, and conical intersection may
all, however, be interpreted as a coupling (i.e., energy transfer)
between the electronic and nuclear degrees of freedom (as
described by the initial BO picture) within the evolving chemical
system. Over the past four decades or more, the development
of techniques to probe the role of these processes with an ever-
increasing level of detail has been central to furthering the
understanding of chemical dynamics.
* To whom correspondence should be addressed.
Heriot-Watt University.
National Research Council of Canada.
J. Phys. Chem. A 2011, 115, 357–373 357
10.1021/jp109095d 2011 American Chemical Society
Published on Web 12/23/2010

“Zero-order” measurements such as the simple observation
of product yields from a given chemical process are clearly
insufficient to infer much dynamical information. With a little
more effort on the part of the experimenter, however, improved
“first-order” observations, for example, the energy partitioning
among the internal degrees of freedom within the reactants and
products, may begin to provide some degree of insight into the
transit along the reaction coordinate, as illustrated, for example,
in the classic “early” and “late” barrier pictures for chemical
reactions.
19,20
In order to take this line of investigation further,
even higher-order, or increasingly differential, measurements
are required. As a first step up this ladder of experimental
complexity, one may begin to consider the angular direction in
which various products are ejected, or scattered, with respect
to a given frame of reference. In the laboratory frame, this is
typically taken to be the polarization vector of a laser pulse
that initiates a (unimolecular) photochemical process or the axis
along which a (bimolecular) collision between reactant species
takes place. As a next step, one may then begin to correlate
energy- and angle-resolved information, investigating the varia-
tion in product internal energy as a function of scattering angle.
The multiplexing advantages offered by the advent of position-
sensitive, 2D imaging methods over the past two decades made
such a task a readily viable experimental undertaking.
21,22
Correlated measurements of this type begin to reveal many
subtle details of the transit along the reaction coordinate
connecting reactants to products. However, one may still go
further in an attempt to develop an even more complete picture.
In addition to the recoil velocity of the products, there are other
vector properties present in the system, specifically, the various
angular momenta in the products, that may exhibit significant
polarization anisotropy. The ability to not only measure this
anisotropy but to correlate it with the recoil velocity offers a
powerful probe of the overall dynamics.
23-29
Vector correlations
of rotational angular momentum polarization in molecular
photofragments provide much information on the shape of the
potential energy surfaces involved in the evolution from
reactants to products. Observations of electronic angular mo-
mentum polarization in atomic photofragments are perhaps even
more powerful, yielding insight into the coupling (and associated
phase shifts) between different potential energy surfaces in-
volved in mediating the dynamics in molecular systems. This
point is particularly apparent if one views the unpaired electrons
in the recoiling photofragments as having previously formed
part of the “fabric” of the potential energy surfaces in the system
under study prior to dissociation. Finally, one may also consider
photoelectron angular distributions (PADs) from photoioniza-
tion. Such distributions are a superposition of many “partial
waves” with different angular momenta, l, and the overall
appearance of such distributions is highly sensitive to the
amplitude and relative scattering phase of these various constitu-
ent components, in turn providing detailed information on the
symmetry of the state from which ionization occurred.
30-33
As a next step toward further improving the differential nature
of dynamics experiments, one may begin to consider the
possibility of making measurements in the molecular frame of
reference rather than that of the laboratory frame. For the case
of a simple photodissociation, these two frames are effectively
commensurate, assuming that the time scale of fragmentation
is fast compared to the period of molecular rotation, the so-
called axial recoil limit. However, more sophisticated experi-
mental approaches are often required to extract molecular frame
information in many other types of processes. This includes
systems that deviate from the axial recoil limit, systems that
produce more than two fragments upon dissociation (including,
for example, the cases of dissociative photoionization or
photodetachment), and systems where dissociation is not a
dominant mechanism. The use of multibody coincidence tech-
niques
34
has been successfully demonstrated as a route to
obtaining molecular frame measurements in some of these types
of system.
35-40
A second strategy, which will form one of the
main themes for discussion in this article, is to try to “overlap”
the molecular and laboratory frames of reference through the
use of externally applied aligning or orienting fields.
The development of modern laser sources has enabled
experimentalists to develop approaches that seek to interrogate
dynamical processes in chemical systems with increasingly high
levels of precision. Broadly speaking, these approaches may
be broken down into two main categories, time-resolved and
frequency-resolved measurements. In the case of the latter, one
is able only to probe the products formed in the asymptotic
region of the reaction coordinate, owing to the long temporal
duration of the laser pulses relative to the typical time scales of
reaction dynamics. However, the narrow line width laser sources
used in such measurements often enable the products to be
probed in a quantum-state-specific manner. This high level of
spectroscopic resolution is a powerful tool for enabling the
dynamics of a chemical event to be inferred. In the case of time-
resolved measurements, one is effectively able to follow the
evolution of the system dynamics in real time as the reaction
coordinate is traversed, but there is always a trade off in terms
of spectroscopic resolution as the broader bandwidth associated
with so-called “ultrafast” laser pulses means that quantum-state-
specific measurements are not usually possible. This trade off
of energy versus time resolution means that a combination of
Dave Townsend is currently a lecturer at Heriot-Watt University in
Edinburgh, with research interests in the area of time-resolved molecular
spectroscopy and dynamics. Dave began his university career studying
chemistry as an undergraduate at the University of Nottingham, where he
then remained to undertake a Ph.D. with Prof. Katharine Reid, studying
angle-resolved photoionization dynamics of polyatomic molecules. Fol-
lowing on from this, he spent time as a postdoctoral researcher at the
University of Oxford with Prof. Tim Softley, investigating the translational
control of atomic and molecular Rydberg states, and then studied in the
group of Prof. Arthur Suits at SUNY Stony Brook, using imaging methods
to study vector correlations in molecular photodissociation. Between 2004
and 2007, he was a Visiting Fellow at the National Research Council of
Canada in Ottawa.
Benjamin Sussman is a Research Officer in the Steacie Institute for
Molecular Sciences at the National Research Council of Canada and a
Research Fellow at Worcester College, University of Oxford. His research
investigates the intersection of quantum control, quantum information, and
photonics. He studied physics as an undergraduate at the University of
Waterloo before obtaining his M.Sc. at the University of British Columbia.
He graduated with a Ph.D. in Physics from Queen’s University in 2007.
Albert Stolow studied chemistry and physics at Queen’s University. He
then obtained his Ph.D. from the University of Toronto, studying under
John C. Polanyi. Albert was then an NSERC postdoctoral fellow with Yuan
T. Lee at the University of California, Berkeley, where he became interested
in the dynamics of polyatomic molecules. In 1992, he joined the Femto-
second Science Program of the Steacie Institute for Molecular Sciences
(National Research Council of Canada) to begin research in the area of
femtosecond dynamics based on time-resolved photoelectron spectroscopy.
Albert is currently a Principal Research Officer within the Steacie Institute
for Molecular Sciences and Program Leader of the Molecular Photonics
Group. He is Adjunct Professor of Chemistry and Adjunct Professor of
Physics at Queen’s University and Adjunct Professor of Physics at the
University of Ottawa. His group’s research interests include ultrafast
molecular dynamics and quantum control, nonlinear optical spectroscopy,
molecular strong-field physics, and nonlinear microscopy of live cells. He
is a Fellow of both the American Physical Society and the Optical Society
of America, has won several prizes, including the Keith Laidler Award of
the Chemical Society of Canada, and sits on the editorial boards of various
international journals.
358 J. Phys. Chem. A, Vol. 115, No. 4, 2011 Townsend et al.

different experimental approaches (both time- and frequency-
resolved) are often required to develop a complete mechanistic
picture; that is, there is no “one size fits all” approach, and data
from a number of different, complementary techniques (with
different associated observables) are often necessary. In the case
of both time-resolved and frequency-resolved measurements,
there are a vast number of different experimental techniques
that may be employed and observables that may be monitored.
Reflecting this, the field of molecular dynamics has grown
enormously to encompass the detailed study of many types of
molecular processes with ever-increasing degrees of sophistica-
tion. However, although hugely diverse in terms of scope and
application, the vast majority of these dynamical studies are all
bound together by one common feature, namely, that the
observations are typically of a passive nature. In other words,
the investigator sets a chain of dynamical events in motion and
then either follows directly (time-resolved) or infers indirectly
from the set of chemical outcomes (frequency-resolved) the
mechanistic pathways connecting the set of initial and final
states. While such studies are of huge importance in furthering
our understanding of many fundamental processes, the next level
of development within the field of molecular dynamics centers
around the desire to move beyond this passive approach and
into a regime where the dynamics are actively controlled.
Control
As discussed previously, electric forces underpin the dynamics
of all chemical processes. In order to exert control over a
chemical outcome, the use of additional, externally applied,
electric fields is therefore a natural approach. This is not a new
idea in many respects; the example of simple catalysis (for
example, the case of adsorption on a metal surface) is one of
externally applied fields (from the surface) being used to directly
affect a chemical outcome by reducing the activation barrier
along the reaction coordinate connecting the reactants to a
specific set of products s the most commonly cited form of
control when applied to molecular systems. However, externally
applied static electromagnetic fields have also been used
effectively as a form of “control” to enhance the otherwise
passive observation of chemical processes, rather than modify
the likelihood of a specific outcome per se. For example, the
use of hexapole devices as well as so-called “brute-force”
methods to select oriented neutral molecules has been employed
in “stereodynamic” studies of bimolecular reactions.
41-44
This
is effectively a form of control applied to the rotational degree
of freedom, as will be expanded upon later. Other types of
approach have also been used to exert control over the
translational degree of freedom of neutral atoms and molecules
via electrostatic interactions.
The first and perhaps most famous example of translational
control over neutral species was the Stern-Gerlach experiment,
45
in which inhomogeneous magnetic fields were use to deflect a beam
of silver atoms. Of the other, more recent approaches developed
to control motion in neutral systems, perhaps the most well-known
is the Stark decelerator developed by Meijer and co-workers,
46,47
which has found application in the rapidly growing area of cold
molecule physics.
48
A very similar idea has also been explored by
Softley and co-workers,
49-52
who have used the Stark effect as
a tool to control translational motion in atomic and molecular
Rydberg states in a manner analogous to that of the Meijer
group. An important yet subtle difference in this approach is
that, owing to the much larger Stark shifts exhibited by
moderately high lying electronically excited Rydberg states
(typically with principal quantum numbers in the n ) 10-20
region), dramatically smaller field gradients (on the order of a
few hundred V/cm rather than the kVs/cm required for ground-
state systems) are all that is required to exert significant
translational control. This increased magnitude of the Stark shift
relative to that typically seen in ground electronic state
configurations is a consequence of the linear rather than
quadratic Stark shifts that result due to l degeneracy, as well as
the inherently more polarizable nature of the loosely bound
Rydberg electron. (There are no linear Stark shifts in nonde-
generate states.) This issue of polarizability (both relative and
absolute) will be an important consideration when we come, in
subsequent sections, to examine the nonresonant dynamic Stark
effect as a tool for control.
An alternative strategy to achieve control is through the use
of externally applied coherent electromagnetic radiation, that
is, laser light. This idea has been exploited for translational
control using the Stark effect in a similar manner to that
described above for static fields;
53-55
however, it is the use of
laser fields for the direct control of chemical reactions that will
form the central basis for the remainder of the brief discussion
outlined here. Perhaps the first operational approach to control-
ling quantum states with external fields was given by Lamb in
1969.
56
Lamb argued that a practical discussion of quantum
states should include a program for making them, and he offered
such a method for producing arbitrarily shaped wave functions.
The advent of intense, coherent laser sources extended the work
of constructing arbitrary control, although initial hopes of
achieving bond-selective chemistry through targeted resonant
excitation of specific vibrational modes proved unsuccessful in
the vast majority of cases, owing to the rapid statistical
repartitioning of internal energy, the phenomenon commonly
known as intramolecular vibrational energy redistribution
(IVR).
57,58
More complex and subtle strategies for achieving
chemical control using laser fields were therefore needed.
A renaissance in the field of laser control began in the 1980s
with the work of Brumer and Shapiro,
1,59
who considered using
quantum interference effects to manipulate chemical reactions.
This was first experimentally demonstrated by Gordon and co-
workers.
60
If two different laser-induced transitions to a specific
target state occur with amplitudes A
1
) |A
1
|e
iφ
1
and A
2
) |A
2
|e
iφ
2
,
then the overall probability for populating that state is given
by
The phases φ
1
and φ
2
may be independently controlled by
altering the laser phases, and hence, the overall transition can
be influenced. This coherent control approach is similar in some
respects to Young’s famous two-slit experiment where optical
interference is observed due to multiple pathways to a screen;
adding or subtracting a phase to one pathway has the effect of
shifting the interference fringes. Within the coherent control
approach, the “control” is mediated entirely by the laser phase
that initiates a given photochemical event. The subsequent
scattering phase then remains unaltered as the initially prepared
reactant states evolve toward the products.
A second related approach to laser-induced control of
photochemical processes was proposed by Tannor and Rice,
who considered control over reactions that could form different
reaction products in the ground electronic states of molecules.
4,61
Activation barriers were circumvented via other electronically
excited states, where the absence of these barriers allowed free
movement of a wavepacket to a target region of the potential
P ) |A
1
|
2
+ |A
2
|
2
+ 2|A
1
||A
2
| cos(φ
1
- φ
2
) (1)
Feature Article J. Phys. Chem. A, Vol. 115, No. 4, 2011 359

energy surface from which a transition back to the ground
electronic state was initiated. In a sense, this so-called
pump-dump control strategy may be viewed as a multiplexed
or wavepacket version of the Brumer-Shapiro approach, where
broad bandwidth laser pulses were used in the former and
narrow line widths in the latter.
A number of approaches have investigated the application
of adiabatically varied resonant laser fields. Perhaps the most
well-known of these is stimulated Raman adiabatic passage
(STIRAP), which is typically utilized in a three-level lambda
system, where a resonant field connects the ground state with
the intermediate state and a second resonant field connects the
intermediate state with the target state. The eigenstates of the
rotating wave Hamiltonian can be solved analytically and have
a solution that transfers population completely from the ground
state to the target state. An alternative interpretation is that the
resonant field that connects that intermediate and target state
dresses the system so that the other laser field can directly
transfer population into the dressed state that correlates with
the target state. Bergmann and co-workers
62
present a detailed
introduction to this type of control strategy, and the reader is
directed there for further information.
One of the most recent developments within the field of laser-
based control has been the use of intense femtosecond laser
pulses in conjunction with adaptive feedback-learning algorithms
to optimize the yield of specific photoproduct channels.
8,63,64
This approach exploits the large coherent bandwidth and very
high field intensities intrinsic to such pulses and has been
successfully demonstrated in the fragmentation-ionization of
polyatomic molecules.
9,10
One challenge with the strong field
approach is that numerous, simultaneously occurring processes
are potentially responsible for contributing to the observed final
outcome.
5
These potentially include high-order multiphoton
ionization, enhanced ionization,
65,66
nonadiabatic multielectron
ionization,
67
and Coulomb explosion,
68
multiphoton resonances
leading to propagation on multiple potential energy surfaces,
dynamic Stark effects, adiabatic passage by light-induced
potentials,
69-71
and bond hardening/softening.
2,72-76
In molecular
systems in particular, the theory describing these individual
effects is not always well-quantified, and therefore, the challenge
of modeling (or understanding in detail) a situation where all
of these processes may contribute to the system dynamics is
often insurmountable.
Control Interaction
A compelling approach for addressing all of the challenges
outlined in the previous sections is the second-order nonresonant
dynamic Stark effect (NRDSE). This is a universal interaction
that is easily applied with modern laser technology. It exploits
the response of a quantum system to the intensity envelope of
a laser pulse rather than the oscillating electric field, that is, the
effect is highly independent of the spectral content (optical
frequencies) of the pulse. The second-order NRDSE operates
via a polarizability interaction (often also referred to as a Raman
interaction). In special cases, the linear nonresonant dynamic
Stark effect may also be applied to the quantum control of
molecular systems but requires dipole-allowed transitions
between the controlled states.
77
Because all systems containing
electrons are inherently polarizable to some degree, the NRDSE
approach to control may therefore, in principle, always be
applicable and is the focus of the remainder of our discussion.
The NRDSE approach requires limited a priori spectral knowl-
edge of the system (Hamiltonian) under consideration because
the only important issue in this regard is that the laser field is
nonresonant with respect to any real transitions.
In previous publications, we have successfully demonstrated
the use of the NRDSE as a tool for the control of molecular
axis alignment
78,79
and in the control of chemical branching
ratios.
80,81
It should be stressed here that these two effects are
identical in terms of the physical control mechanism; they simply
act upon different degrees of freedom within the molecular
system in question (rotations and vibrations, respectively). More
recently, we have also used the Stark effect for transferring
population in atomic gas ensembles.
82
In the following sections,
we shall explore this assertion in more detail.
DC Stark Effect
The static, or DC Stark, effect is a well-known physical
phenomena that was first reported by Johannes Stark in 1914.
83
In the presence of homogeneous electric fields, atomic spectral
lines are observed to split into multiple components due to the
applied field “mixing” quantum states of different orbital angular
momentum quantum number, l. This is analogous to the Zeeman
effect,
84
discovered several years earlier in 1897, that is induced
by a magnetic field and lifts the degeneracy of states with
different magnetic quantum numbers, m
l
. The magnitude of the
observed Stark effect splitting may exhibit a linear dependence
with applied electric field strength for degenerate l states or,
much weaker, quadratic dependence for nondegenerate l states.
Formally, the general Hamiltonian for an atomic or molecular
system in the presence of a static homogeneous electric field
may be written as follows
where H
0
is the field-free Hamiltonian with corresponding
eigenstates ψ
n
and energy levels E
n
. Within the electric dipole
approximation, the interaction term, V, between the molecule
and the laser field takes the form
where µ is the dipole moment operator and E is the function
associated with the constant linear electric field. At the simplest
level of interpretation, we can view the effect of the field as
mixing the field-free eigenstates, producing a new distribution
of energy levels within the system under investigation, and these
new levels may be expressed as linear combinations of the field-
free eigenstates
The extent of this mixing is dependent on the strength of the
field (a stronger field means more mixing), and this gives rise
to the concept of a Stark map that describes the energy levels
in a quantum system as a function of field strength. Some good
illustrative examples may be found in the work of Goodgame
and Softley.
85
Nonresonant Dynamic Stark Effect
Following eq 1, the semiclassical Hamiltonian for a quantum
system in the presence of a time-dependent laser field of
frequency ω may be written as
H ) H
0
+ V (2)
V )-µ · E (3)
ψ
Field
)
i
a
i
ψ
i
Field-free
(4)
H(t) ) H
0
+ V(t) (5)
360 J. Phys. Chem. A, Vol. 115, No. 4, 2011 Townsend et al.

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Citations
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TL;DR: Results from direct quantum dynamics simulations reveal basic principles of polariton photochemistry as well as promising reactivities that take advantage of intrinsic quantum behaviors of photons.
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Abstract: 1. Introduction 2. Atoms as structured particles 3. Radiation 4. The laser-atom interaction 5. Picturing quantum structure and changes 6. Incoherence: rate equations 7. Coherence: the Schrodinger equation 8. Two-state coherent excitation 9. Weak pulse: perturbation theory 10. The vector model 11. Sequential pulses 12. Degeneracy 13. Three states 14. Raman processes 15. Multilevel excitation 16. Averages and the statistical matrix (density matrix) 17. Preparing superpositions 18. Measuring superpositions 19. Overall phase, interferometry and cyclic dynamics 20. Atoms affecting fields 21. Atoms in cavities 22. Control and optimization Appendices References Index.

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TL;DR: This Perspective examines the current strategies developed to achieve control of chemical processes with strong laser fields, as well as recent experimental advances that demonstrate that properties like the molecular absorption spectrum, the state lifetimes, the quantum yields and the velocity distributions in photodissociation processes can be controlled by the introduction of carefully designed strong Laser fields.
Abstract: Strong ultrashort laser pulses have opened new avenues for the manipulation of photochemical processes like photoisomerization or photodissociation. The presence of light intense enough to reshape the potential energy surfaces may steer the dynamics of both electrons and nuclei in new directions. A controlled laser pulse, precisely defined in terms of spectrum, time and intensity, is the essential tool in this type of approach to control chemical dynamics at a microscopic level. In this Perspective we examine the current strategies developed to achieve control of chemical processes with strong laser fields, as well as recent experimental advances that demonstrate that properties like the molecular absorption spectrum, the state lifetimes, the quantum yields and the velocity distributions in photodissociation processes can be controlled by the introduction of carefully designed strong laser fields.

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TL;DR: In this regime, it is shown that the molecular dynamics can be simulated quite accurately by a semiclassical surface-hopping scheme formulated in the adiabatic representation, showing how the choice of the representation is crucial in reproducing the results obtained by exact quantum dynamical calculations.
Abstract: The dynamics of molecules under strong laser pulses is characterized by large Stark effects that modify and reshape the electronic potentials, known as laser-induced potentials (LIPs). If the time scale of the interaction is slow enough that the nuclear positions can adapt to these externally driven changes, the dynamics proceeds by adiabatic following, where the nuclei gain very little kinetic energy during the process. In this regime we show that the molecular dynamics can be simulated quite accurately by a semiclassical surface-hopping scheme formulated in the adiabatic representation. The nuclear motion is then influenced by the gradients of the laser-modified potentials, and nonadiabatic couplings are seen as transitions between the LIPs. As an example, we simulate the process of adiabatic passage by light induced potentials in Na2 using the surface-hopping technique both in the diabatic representation based on molecular potentials and in the adiabatic representation based on LIPs, showing how the ch...

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Journal ArticleDOI
TL;DR: The presented results demonstrate generality, versatility, and robustness of this optical method for manipulating molecular enantiomers in the gas phase.
Abstract: We explore a pure optical method for enantioselective orientation of chiral molecules by means of laser fields with twisted polarization. Several field implementations are considered, including a pair of delayed, cross-polarized laser pulses, an optical centrifuge, and polarization-shaped pulses. We show that these schemes lead to out-of-phase time-dependent dipole signals for different enantiomers, and we also predict a substantial permanent molecular orientation persisting long after the laser fields are over. The underlying classical orientation mechanism common to all of these fields is discussed, and its operation is demonstrated for a range of chiral molecules of various complexity: hydrogen thioperoxide (HSOH), propylene oxide (CH3CHCH2O), and ethyl oxirane (CH3CH2CHCH2O). The presented results demonstrate generality, versatility, and robustness of this optical method for manipulating molecular enantiomers in the gas phase.

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References
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Abstract: This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the necessary mathematics, specifically spherical tensors and tensor operators, the author then investigates the 3-j, 6-j, and 9-j symbols. Throughout, the author provides practical applications to atomic, molecular, and nuclear physics. These include partial-wave expansions, the emission and absorption of particles, the proton and electron quadrupole moment, matrix element calculation in practice, and the properties of the symmetrical top molecule.

5,050 citations


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Abstract: This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the necessary mathematics, specifically spherical tensors and tensor operators, the author then investigates the 3-j, 6-j, and 9-j symbols. Throughout, the author provides practical applications to atomic, molecular, and nuclear physics. These include partial-wave expansions, the emission and absorption of particles, the proton and electron quadrupole moment, matrix element calculation in practice, and the properties of the symmetrical top molecule.

4,377 citations


Journal ArticleDOI
Abstract: The crossing of energy levels has been a matter of considerable discussion. The essential features may be illustrated in the crossing of a polar and homopolar state of a molecule. Let ψ1 ( x /R), ψ2 ( x /R) be two electronic eigenfunctions of a molecule with stationary nuclei. Let these eigenfunctions have the property that for R≫R, ψ1 has polar characteristics, ψ2 homopolar; while at R≪R, ψ2 has polar characteristics, ψ1 homopolar. In the region R=R these two eigenfunctions may be said to exchange their characteristics.

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Abstract: The application of electrostatic lenses is demonstrated to give a substantial improvement of the two-dimensional (2D) ion/electron imaging technique. This combination of ion lens optics and 2D detection makes “velocity map imaging” possible, i.e., all particles with the same initial velocity vector are mapped onto the same point on the detector. Whereas the more common application of grid electrodes leads to transmission reduction, severe trajectory deflections and blurring due to the non-point source geometry, these problems are avoided with open lens electrodes. A three-plate assembly with aperture electrodes has been tested and its properties are compared with those of grid electrodes. The photodissociation processes occurring in molecular oxygen following the two-photon 3dπ(3Σ1g −)(v=2, N=2)←X(3Σg −) Rydberg excitation around 225 nm are presented here to show the improvement in spatial resolution in the ion and electron images. Simulated trajectory calculations show good agreement with experiment and ...

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Abstract: The authors discuss the technique of stimulated Raman adiabatic passage (STIRAP), a method of using partially overlapping pulses (from pump and Stokes lasers) to produce complete population transfer between two quantum states of an atom or molecule. The procedure relies on the initial creation of a coherence (a population-trapping state) with subsequent adiabatic evolution. The authors present the basic theory, with some extensions, and then describe examples of experimental utilization. They note some applications of the technique not only to preparation of selected states for reaction studies, but also to quantum optics and atom optics.

1,776 citations