Most of this review has focused on collisions of cold, trapped atoms in a light field. Understanding such collisions is clearly a significant issue for atoms trapped by optical methods, and historically this subject has received much attention by the laser cooling community. However, there is also great interest in ground-state collisions of cold neutral atoms in the absence of light. Most of the early interest in this area was in the context of the cryogenic hydrogen maser or the attempt to achieve Bose–Einstein condensation (BEC) of trapped doubly spin-polarized hydrogen. More recently the interest has turned to new areas such as pressure shifts in atomic clocks or the achievement of BEC in alkali systems. The actual realization of BEC in 87Rb [15], 23Na [103], 7Li [56, 57], 4He* [310, 330] and H [138] has given a tremendous impetus to the study of collisions in the ultracold regime. Collisions are important to all aspects of condensates and condensate dynamics. The process of evaporative cooling which leads to condensate formation relies on elastic collisions to thermalize the atoms. The highly successful mean field theory of condensates depends on the sign and magnitude of the s-wave scattering length to parameterize the atom interaction energy that determines the mean field wavefunction. The success of evaporative cooling, and having a reasonably long lifetime of the condensate, depend on having sufficiently small inelastic collision rates that remove trapped atoms through destructive processes.

Introduction

If, while approaching on an unbound ground-state potential, two atoms absorb a photon and couple to an excited bound molecular state, they are said to undergo photoassociation. Figure 5.1 illustrates the process. At long range electrostatic dispersion forces give rise to the ground-state molecular potential varying as C6/R6. If the two atoms are homonuclear, then a resonant dipole–dipole interaction sets up ±C3/R3 excited-state repulsive and attractive potentials. Figure 5.2 shows the actual long-range excited potential curves for the sodium dimer, originating from the 2S½ + 2P3/2 and 2S½ + 2P½ separated atom states. For cold and ultracold photoassociation processes the long-range attractive potentials play the key role; the repulsive potentials figure importantly in optical shielding and suppression, the subject of Chapter 6. In the presence of a photon with frequency ωp the colliding pair with kinetic energy kBT couples from the ground-state to the attractive molecular state in a free–bound transition near the Condon point RC, the point at which the difference potential just matches ћωp.

Scanning the probe laser ωp excites population of vibration–rotation states in the excited bound potential and generates a free–bound spectrum. This general class of measurements is called photoassociative spectroscopy (PAS) and can be observed in several different ways. The observation may consist of bound-state decay by spontaneous emission, most probably as the nuclei move slowly around the outer turning point, to some distribution of continuum states on the ground potential controlled by bound–free nuclear Franck–Condon overlap factors.

In the 1980s the first successful experiments [312] and theory [98], demonstrating that light could be used to cool and confine atoms to submillikelvin temperatures, opened several exciting new chapters in atomic, molecular, and optical (AMO) physics. Atom interferometry [6, 8], matter–wave holography [294], optical lattices [192], and Bose–Einstein condensation in dilute gases [18, 95] all exemplified significant new physics where collisions between atoms cooled with light play a pivotal role. The nature of these collisions has become the subject of intensive study not only because of their importance to these new areas of AMO physics but also because their investigation has led to new insights into how cold collision spectroscopy can lead to precision measurements of atomic and molecular parameters and how radiation fields can manipulate the outcome of a collision itself. As a general orientation Fig. 1.1 shows how a typical atomic de Broglie wavelength varies with temperature and where various physical phenomena situate along the scale. With de Broglie wavelengths on the order of a few thousandths of a nanometer, conventional gas-phase chemistry can usually be interpreted as the interaction of classical nuclear point particles moving along potential surfaces defined by their associated electronic charge distribution. At one time liquid helium was thought to define a regime of cryogenic physics, but it is clear from Fig. 1.1 that optical and evaporative cooling have created “cryogenic” environments below liquid helium by many orders of magnitude.

Cold and ultracold collisions occupy a strategic position at the intersection of several powerful themes of current research in chemical physics, in atomic, molecular and optical physics, and even in condensed matter. The nature of these collisions has important consequences for optical manipulation of inelastic and reactive processes, precision measurement of molecular and atomic properties, matter–wave coherence and quantum-statistical condensates of dilute, weakly interacting atoms. This crucial position explains the wide interest and explosive growth of the field since its inception in 1987. Obviously due to continuing rapid developments the very latest new results cannot appear in book form, but the field is sufficiently mature that a fairly comprehensive account of the principal research themes can now be undertaken. The hope is that this account will prove useful to newcomers seeking a point of entry and as a reference for those already initiated.

After a general introduction and a brief review of the elements of scattering theory in Chapters 1 and 2, the next four chapters treat collisions taking place in the presence of one or more light fields. The reason for this is simply historical. After the development of the physics of optical cooling and trapping from the early to mid 1980s, the first generation of collisions experiments applied this light-force physics to cool and confine atoms in traps and beams.

Introduction

Photoassociation uses optical fields to produce bound molecules from free atoms. Optical fields can also prevent atoms from closely approaching, thereby shielding them from shortrange inelastic or reactive interactions and suppressing the rates of these processes. Recently several groups have demonstrated shielding and suppression by shining an optical field on a cold atom sample. Figure 6.1(a) shows how a simple semiclassical picture can be used to interpret the shielding effect as the rerouting of a ground-state entrance channel scattering flux to an excited repulsive curve at an internuclear distance localized around a Condon point. An optical field, blue detuned with respect to the asymptotic atomic transition, resonantly couples the ground and excited states. In the cold and ultracold regime particles approach on the ground state with very little kinetic energy. Excitation to the repulsive state effectively halts their approach in the immediate vicinity of the Condon point, and the scattering flux then exits either on the repulsive excited state or on the ground state. Figure 6.1(b) shows how this picture can be represented as a Landau–Zener (LZ) avoided crossing of field-dressed potentials. As the blue-detuned suppressor laser intensity increases, the avoided crossing gap around the Condon point widens, and the semiclassical particle moves through the optical coupling region adiabatically. The flux effectively enters and exits on the ground state, and the collision becomes elastic.

Introduction

The use of spectroscopic techniques to study crossed molecular beam scattering has been both fruitful and difficult to accomplish. The advantage of using laser spectroscopy to detect the products in crossed molecular beam scattering experiments is that one can obtain quantum-state-selective information about the scattering process. The disadvantage is that it is difficult to design an experiment with sufficient wavelength and spatial resolution and detection sensitivity. For this reason until quite recently laser induced fluorescence (LIF) was the only laser-based technique used for the quantum-state-selective detection of scattering products [1–5]. Recently the technique of ion imaging has been used to increase the sensitivity of ionization detection such that resonance-enhanced multi-photon ionization (REMPI) can now be used to detect molecular beam scattering products. Suits et al. were the first, in the early 1990s, to apply ion-imaging techniques to bimolecular scattering [6]. Since then, ion imaging has been found to be a powerful tool for the study of bimolecular inelastic scattering. Ion imaging has been used to measure differential cross-sections (DCSs) [6,7], as well as to measure collision-induced rotational alignment [8] and orientation [9]. In this chapter we will focus on a new application of ion imaging, the retrieving of correlated energy transfer distributions from crossed molecular beam ion imaging experiments.

The previous studies of bimolecular collision systems consisted of a diatomic target molecule colliding with a rare gas atom. The monatomic collider gas has no internal energy, and a single rotational state of the diatomic molecule was detected, using REMPI.

Introduction

This chapter aims to introduce you to the practical aspects of molecular dynamics research using imaging methods. Imaging is a rapidly advancing experimental technique full of possibilities. This puts you in position to make unique and important contributions to the field of reaction dynamics, and you will be the first person to see the secrets of nature appear on your camera screen. Every scientist lives in part for this exciting result and velocity map imaging more than any other method presents the full picture in living color!

Velocity map imaging is the present day variant of the ion imaging method invented by David Chandler and Paul Houston in 1987 [1]. We discovered the advantages of a simple electrostatic lens for the ion imaging method in 1997 [2]. The improvement was so dramatic that David Chandler convinced us to give it the new name, velocity map imaging. Undoubtedly, you or some other clever scientist will discover a new trick to make imaging work even better in the future. Imaging has much to offer in present-day molecular dynamics research, as illustrated in this chapter. This introduction will lead to the following chapters in this book on experimental aspects, data analysis, angular momentum theory, photoionization, and alternative methods.

Introduction

For many years two-dimensional (2-D) and three-dimensional (3-D) fragment imaging techniques have been successfully used in the study of molecular structure [1] and for the study of the dynamics of various molecular dissociation processes, such as photodissociation [2], dissociative recombination [3], atom–molecule collision induced dissociation [4], dissociative charge exchange [5], and others (see review by Zajfman and Heber [6]). The basic experimental scheme includes induced dissociation of a single molecule, from either a molecular ion beam or gas target, and the fully correlated measurement of the asymptotic velocity vectors of the outgoing fragments. If the initial velocity of the molecule is large, then all the fragments will be projected into a cone defined by the ratio of their transverse velocities and the initial beam velocity. In such a case, the transverse velocities are deduced from the 2-D position on the surface of a position sensitive detector, while the longitudinal velocities can be derived from the time of arrival at the detector. The specific physical information provided by the images depends on the particular dissociation process. In general, one obtains information about the initial molecular quantum state prior to the dissociation and the final state of the fragments and about the dynamics of the reaction, such as angular dependence, kinetic energy release or potential curves.

Introduction

One of the most exciting advances in chemical physics in recent years has been the emergence and development of femtochemistry. This has been brought about largely because of advances in ultrafast laser technology, particularly the discovery of self-mode locking in Ti:sapphire and the development of chirped pulse or regenerative amplifiers. Another important innovation has been the development of a variety of linear and nonlinear spectroscopic techniques to probe electronic and nuclear dynamics. Nonlinear methods have been particularly useful in the study of solvation dynamics in the condensed phase. In the gas phase, where the density of molecules is much lower, ionization techniques such as pump-probe mass spectrometry have more often been employed. However, mass spectrometry can only provide the time-dependent population of a chemical species, in other words, kinetic information. In order to extract more detailed information on the reaction dynamics, measurements of the velocity vectors of the photoelectrons and fragment ions produced upon ionization are required. As we have seen in the preceding chapters, an imaging detector placed at the end of a time-of-flight mass spectrometer can easily accomplish such measurements. In this chapter we explore how ultrafast lasers can be coupled with charged particle imaging to develop experimental probes of ultrafast dynamic processes in molecules, such as electronic dephasing (radiationless transitions) and intramolecular vibration energy redistribution (IVR).

Introduction

Many problems in molecular dynamics demand the simultaneous measurement of a particle's speed and angular direction; the most demanding require the measurement of this velocity in coincidence with internal energy. Studies of molecular reactions, energy transfer processes, and photodissociation events can be understood completely only if the internal energies and velocities of all products are specified.

Consider the case of a monochromatic photodissociation that produces two fragments A and B. Even if the internal energy distributions of A and B were each measured separately, it would still be necessary to obtain information on their recoil speed in order to determine the internal energy of B given a selected level of A. Measurement of the coincident level of B would further require that only one parent molecule be dissociated in any particular experiment – a true coincidence experiment. Angular information is also desirable. In photodissociations, for example, the recoil angle with respect to the polarization vector of the dissociating light provides information about the transition moment in the parent molecule and the time-scale of dissociation. Because reactions in molecular beams have many of these same requirements, new techniques for simultaneous measurement of velocity and internal energy are quite important to molecular dynamics.

Many of the current techniques for making simultaneous velocity and internal energy measurements are based on imaging of product molecules or particles with microchannel plate (MCP) detectors.

Introduction

Charged particle imaging provides us with very beautiful pictures that offer graphic insight into chemical dynamics. Although it is often the case that general dynamical information can be deduced by simple inspection of the primary data, the images obtained in the typical imaging experiment are, in fact, projections of a three-dimensional (3-D) object onto a two-dimensional (2-D) screen. In order to extract all the information potentially available to us we need to consider what data recovery techniques are available to reconstruct the 3-D velocity distribution of the charged particles created in the experiment from the image we actually record.

There are two fundamentally different approaches; inversion methods and forward convolution methods. Inversion methods make use of the fact that if the original (3-D) distribution has an axis of cylindrical symmetry its (2-D) projection parallel to this axis contains enough information to unambiguously reconstruct the full (3-D) distribution. As we have seen in the previous two chapters, such an axis of symmetry in laboratory space can be found in many photodissociation or bimolecular scattering experiments. However, if there is no cylindrical symmetry in the experiment, a forward convolution method is generally necessary. Here, the experiment is simulated in a computer model that produces (2-D) data that are then compared with the experimental data. By iteratively optimizing parameters in the computer model the best reconstruction of the experimental data is sought.

Introduction

Houston and Chandler introduced ion imaging in 1987 [1], demonstrating for the first time the potential of this method to be used in chemical dynamics studies. In most chemical dynamics experiments the desired quantity to measure is the state-resolved differential cross section (dσ/dΩ) [2]. This quantity is defined as the amount of product of a chemical reaction, be it a half collision (photodissociation) or a full collision, that is scattered into a unit solid angle per unit of time. Borrowing from the methods of nuclear physics, the pioneers of scattering experiments used the time-of-flight method (TOF) [3] coupled to a rotatable detector to map out dσ/dΩ. Initial experiments employed a universal ionizer to ionize and subsequently detect the products [3]. The universality of the method made it the most successful method for studying a large number of reactive collisions. However, its limited energy resolution was insufficient for detailed studies of unimolecular processes.

It was quickly realized that using high-resolution laser spectroscopic detection of the products would yield a great deal more information than the universal detection [3]. In order to obtain information concerning dσ/dΩ the most popular methods used were Doppler spectroscopy, TOF, or Doppler coupled with TOF [3]. Ion imaging was introduced as a method that combined Doppler and TOF. Its major drawback was its limiting energy resolution, typically 15-20%, coupled with the ‘magical and mysterious’ inverse Abel transformation.