Advances in Laser Spectroscopy

We present a semiclassical approach to the line shape problem in high resolution laser spectroscopy which includes,in a unified density matrix formalism, the influences of the beam geometry, of the molecular recoil and of the second-order Doppler effect. A fully covariant second-quantized extension of the formalism is outlined. We give also a general derivation of intensities for all non-linear processes using Racah algebra in Liouville space. We describe diagrammatic representations of the perturbative solutions of the equations suitable for all laser spectroscopy techniques. Simple topological rules characterize Doppler-free processes. The diagrams and their associated diagrammatic rules are illustrated by their applications to the computation of Ramsey fringes in the case of single photon, Doppler-free two-photon and saturation spectroscopies. Finally we show how light-shifts can be calculated by this method and find, as expected, that the shifts for Ramsey fringes are reduced by the ratio of the laser beam radius to the zone separation when compared to the shifts for the single zone signal.

During the last five years, numerous experimental and theoretical studies have been carried out on highly excited atoms in the presence of an uniform field, magnetic or electric. The aim of these four lectures was to describe our present knowledge of this subject which is of a great theoretical interest and which recently reaped a large profit from laser spectroscopy.

These notes will give an elementary formalism to acquaint the students with the simplest aspects of the theory. It will provide background theoretical material for the applications to high resolution spectroscopy. The presentation will be tutorial. The lectures will then be followed by a review of the recent work of the author’s laboratory in the area of Doppler free spectroscopy.

One of the most powerful spectroscopic techniques available for the measurement of weak absorption is the use of frequency modulation of the source complemented by phase sensitive detection. This approach is highly effective in separating the interesting narrow resonance features from the broad background profile. While optimum amplitude of the frequency modulation leads to recovery of nearly the full signal component, it also leads to broadened resonance profiles which are not immediately related to the physical resonances of interest. Furthermore, it is attractive to employ high modulation frequencies to take advantage of the nearly universal situation that one finds experimentally, namely the concentration of excess noise toward low frequencies. Ultimately then, the resonance profiles of interest are further “distorted” by the modulation process when the modulation frequency is comparable to the resonance width. This constraint is particularly painful in contemporary ultrahigh resolution optical experiments when the measured lines may only be of ~ kiloHertz width.

Methods of Doppler-free laser spectroscopy are reviewed, including several recent advances such as FM sideband or polarization intermodulation techniques. New approaches to laser frequency stabilization are also discussed. Precision studies of the simple hydrogen atom serve to illustrate the power of high resolution laser spectroscopy, and to point out future challenges and opportunities.

An individual elementary/atomic particle kept at rest in free space for extended periods, is an ideal object for high resolution spectroscopy. All external causes for line broadening or shifts such as 1. and 2. order Doppler and transit time effects as well as Zeeman or Stark effects are eliminated for such a system. This ideal has been approximated most closely so far in experiments on an individual Ba⁺ ion localized in a Paul (rf) quadrupole trap to ∿2000Å by optical side band cooling and made visible, all accomplished by means of laser

beams. High resolution spectroscopy on an individual electron/positron localized to <200 µm by rf side band cooling in a Penning trap employing a 50 kG field has already yielded the most precise data on the magnetic moments of these particles and also provided a severe test of the CPT theorem for charged elementary particles. Furthermore, localization of an elementary particle in space is one of the most fundamental problems in physics and worthy of study on its own merit.

No doubt, tunable lasers play an important role in scientific investigations and in technical applications. Therefore we find a strong interest to improve tunable lasers and to extend their frequency range: Dye lasers today have excellent properties as tunable systems but their operation area is limited to the visible region and the close vicinity. Within the last four to five years there was a strong development of color center lasers and they became the near infrared counterpart to the dye lasers. The active material in dye and color center lasers — dyes and color center crystals — are no natural products. However dyes were already available in large numbers, whereas each new color center crystal suitable as laser material had to be developed, making the progress in color center lasers so tedious. Nevertheless the state of the art of color center lasers was continuously improved. In the first part of this lecture recent improvements that have been achieved by my coworker G. Litfin will be reported.

Molecules whose electronic transitions lie in the UV portion of the electromagnetic spectrum far outnumber those in the visible. Consequently, it is of considerable chemical interest to extend tunable coherent light sources to shorter wavelengths. Potential applications are numerous including photo-chemical, kinetic, analytical and spectroscopic studies. Because dye lasers are limited to wavelengths above 330 nm, the production of deeper UV light requires the use of non linear optics such as sum frequency mixing and harmonic generation¹.

The laser has become an important tool for studying elementary chemical processes and for analytical applications, while the use of lasers to initiate chemical reactions by selective excitation of reactants is still very much in its infancy and the awaited breakthrough has not yet occurred. It may be that recent developments in laser technology, e.g. excimer lasers will change the whole picture, and that applications in chemistry such as laser-induced chemical reactions or synthesis will come close to reality.

The far-infrared (FIR) part of the electromagnetic spectrum (1 mm – 30 µm) has been investigated far less than other regions, mainly because of the lack of suitable photon sources. Only in the past decade has the situation changed dramatically as a consequence of the discovery of the optically pumped FIR laser. Both spectral sources and fluorescent detection in the FIR cannot be realized in the laboratory since in spontaneous emission the transition rate is proportional to v³. Only the black-body was available as a source before the discovery of the laser. Also, classical linear absorption spectroscopy leads to unsatisfactory results in the FIR. In fact, the relative Doppler linewidth Δv_D/v ≃10⁻⁶ is independent of frequency. But on the other hand, any spectroscope based either on diffraction or interference (λ measurement) is scaled proportional to λ. Its size for the FIR must be about 100 times larger than for the visible in order to reach the same resolving power. A very high resolution with laboratory-size equipment can be obtained only in a frequency measuring apparatus. It has been practically realized by using the MIM diode and heterodyne techniques [1]. Again, this method works properly only with such highly monochromatic and coherent sources as the laser. Thus, high-resolution spectroscopy could not be extended to the FIR region before the discovery of the laser.

As is well known, nonlinear laser techniques provide means for high-resolution atomic and molecular spectroscopy. The power of these techniques can be further increased when they are applied to coupled three-level systems. In the present paper new high-resolution techniques developed in optically pumped molecular lasers are described. They refer to both Doppler-Doppler and Doppler-homogeneous folded configurations. Velocity-selective excitation yields Doppler tuning of the coupled transitions; sub-Doppler saturation features generated in the absorption can be observed in the reemission. In some cases resolutions beyond the limitations imposed by the homogeneous linewidths in two-level spectroscopy are achieved.

The classical techniques for studying the vibration-rotation spectra of molecules are broadband, based either on monochromators or on the Fourier transform principle. Their advantage is that the entire spectral region of interest can be covered, and the general view obtained in this way greatly facilitates the interpretation of a spectrum. Their main disadvantage is that they offer a resolution which is rarely better than 1 GHz, while the Doppler width is typically about 100 MHz. Even for fairly simple molecules there are often spectral regions where the density of lines is very high, and where there are no recognizable patterns. In such cases, a conventional unresolved spectrum will provide only rudimentary insight into the molecular vibration-rotation states.

Multiphoton ionization (MPI) and fragmentation, induced by (preferably UV) lasers can provide both dynamical information about the process itself and shows prospects as an efficient ion source e.g. in mass spectrometry. Within a certain experimental parameter range a generalized picture of the mechanism has evolved which this paper intends to summarize and to substantiate by showing some of the experimental evidence. It may also be argued that there is hope for laser specific unimolecular chemistry under special conditions.

The formation of micron-size particles in a gas system induced by laser radiation was reported for the first time by Tam, Moe and Happer [1] in 1975. In their experiment the argon laser beam passing through a gas mixture of caesium vapour, hydrogen and helium induced the formation of small white particles identified as caesium-hydride crystals. The observed phenomenon was called “laser snow.” Since then the laser snow effect has been observed in several gases illuminated by different laser lines [2–11]. Due to chemical reactions induced by laser light in a given gas system and subsequent condensation and coagulation processes small particles of size varying from 0.5 µ to 4 µ are formed. The particles cause intense scattering of laser light and they can be easily recognized by eye in the form of falling snow. A typical velocity of fall is of the order of mm/s.

Intense laser pulses with a time duration of several 10⁻¹² s were first observed in 1966.¹ It was immediately recognized by investigators in the field that these picosecond light pulses would allow direct investigations of ultrafast molecular processes in condensed phases. In fact, the first application of these pulses to a study of radiationless transitions of dye molecules was reported soon after.² Numerous investigations were conducted by several laboratories on a wide variety of problems in recent years.³ Considerable effort has been spent on the reproducible generation of well-defined pulses. As a result, quantitative investigations can be carried out on the time scale of picoseconds and subpicoseconds with carefully analysed pulses.

These lectures embrace two topics: (1) the laser spectroscopy of solids and (2) the effect of elastic collisions on atoms that are in a coherent superposition state due to preparation by a laser field.

The replacement of electrical currents by optical beams in information processing has become feasible due to the discovery of optical bistability and related devices⁺. An optically bistable device is one which can exhibit two steady transmission states for the same input intensity. A fabry-Perot resonator containing a medium with a nonlinear refractive index constitutes the simplest example of such a system. As a laser light is irradiated on the cavity and increased from zero to a maximum and back to zero, the output-input characteristic can show a hysteresis cycle: the lower and upper branches (Fig. 1) are locally stable and hence the system is said to be bistable. Under suitable choice of parameters a device of this kind can function e.g. as a memory, as an optical transistor and can be used in optical logic [2,3]. From a theoretical viewpoint, optical bistability constitutes an example of a first-order phase transition in a farfrom-equilibrium system [4] . In this paper we shall concentrate on the device aspects.

In the traditional picture of an atom the only interaction of concern is the electromagnetic, acting between the nucleons and the electrons and among the electrons themselves. As every undergraduate knows this interaction is invariant under space inversion; the atomic Hamiltonian therefore commutes with the parity operator and in the absence of degeneracy the atomic eigenstates have definite parity. The well-known parity selection rules then follow directly.

The methods of nonlinear laser excitation of atoms and molecules¹ are very effective in various problems of laser spectroscopy. These lectures concern the application of the methods of multistep and multiphoton ionization of atoms, molecules and molecular bonds for their detection. This is of great importance in many applications.

The role of observation¹ and the attendant information lie at the heart of the problem of measurement and state reduction in quantum mechanics.² For the past few years we have been interested in specific calculations³ associated with this type of problem and the search for potentially realizable experiments probing the influence of an observer. In the following discussion we propose and analyze an experiment such that the presence of information accessible to an observer would qualitatively change the outcome of an experiment.

In this lecture we discuss in more detail two aspects of the photon scattering experiment which was presented in Prof. Scully’s lectures¹. This experiment is a quantum optical version of the two slit experiment² which is often used to clarify important questions concerning the process of measurement in quantum mechanics. In our version the two slits are replaced by two atoms at fixed positions, which are allowed to absorb and re-emitt photons. In this simple scattering system all aspects of the scattering process can be treated by explicit calculation. This makes it possible to formulate precisely and hence put into focus some basic quantum mechanical assertions about the measurement process which continue to be of interest today. Furthermore, our system is close enough to reality to allow for actual experiments to be performed, which in itself is an attractive feature.

In optical experiments, the precision of the measurement is often limited by the broadening of the linewidth caused by the interaction of the system under investigation with its environment, such as Doppler effect, collisions and spontaneous decay. It might seem that, after the Doppler or collision-broadened width has been eliminated using one of the many schemes introduced in the past for that purpose,¹ the natural linewidth remains the ultimate limit to high-resolution spectroscopy.

Phase conjugation is an important process¹ that inverts a phase front in space so that it retraces the path through which it came. This can be accomplished either with “rubber mirrors” or with nonlinear optics. It has useful applications in propagation through turbulent media, through bad optics, and through optical fibers. As such, the method interests people in astronomy, military weapons, laser induced fusion, and optical communications. Alternatively, we can turn the technique around to use it to study properties of the conjugating medium. In this paper, we outline this last application, using nonlinear optical techniques. We consider the propagation of two, three, and four-wave electromagnetic fields through “single-photon” two-level media and through two-photon multilevel media. We consider cw fields at first, allowing later treatment of pulsed fields by careful application of Fourier analysis. The approach provides various ways of measuring dipole (T₂) and level (T₁) lifetimes, Stark shifts, and other parameters characterizing the responses of media.

The present paper deals with the process of coherent Doppler frequency upconversion of an electromagnetic field by a periodic array of relativistic charged particles. In particular, we shall focus our attention on electrons which are accelerated in conventional machines (linear accelerators, storage rings, etc.) to an energy such that a “free electron” analysis is adequate, i.e., on particles in the “ballistic” regime. In this regime collective (plasma) effects are negligible. The scattering process we are dealing with is a linear one, to first approximation, and it does not suffer from the limitations which affect the behavior of the free electron laser (FEL) at short wavelengths. It is expected that the frequency dependence of the gain of the free electron laser may prevent in the future the operation of this device at wavelengths belonging to the UV or X-ray region of the spectrum unless a new generation of accelerators with very advanced performances is developed. The process we are considering is essentially composed of two steps: the formation of a “coherent” array of electrons (bunching) and the coherent scattering by this array of a static periodic magnetic field. The two steps are considered separately emphasizing on the most critical process of bunching.

There is one more possibility of light amplification due to the kinetic energy of free electrons. It is based not on amplifying the amplitude of a light wave as it interacts with electrons but on increasing its frequency on account of the Doppler effect caused by reflection of the laser pulse from a relativistic pulsed beam of high-density electrons. This effect may be called as amplification of the energy of a light pulse during its reflection from a relativistic mirror. For example, with the electron energy

the reflected pulse wavelength of CO₂ laser λ_o = 10 µm can be shifted to a region with λ ≅ 1µm. The critical density of electron cloud for λ = 1 µm N_cr ≅ 10²¹ cm⁻³.