Resonance fluorescence experiments

Resonance fluorescence experiments using modulated excitation 

Introduction and experimental technique. The classical theory of resonance fluorescence, in which the atoms are treated as dipole oscillators processing at the Larmor frequency, leads one to predict that interesting effects will also occur if the atoms are excited by light whose intensity is periodically modulated. As the external magnetic field is varied in these experiments a point is reached at which the Larmor frequency, equals the angu- 

The first resonance fluorescence experiments using intensity-modulated excitation were performed by Aleksandrov (1963) and independently by Corney and Series (1964 a,b). 

The apparatus used by Corney (1968) in a more detailed investigation of the phenomenon is shown in Fig.15.13. The 

The intensity of the fluorescent light was monitored by a photomultiplier and the time-dependent signal was isolated by an amplifier tuned to 462 kHz. The radiofrequency modulation of the fluorescent light was readily confirmed by this method, but the small percentage modulation of the incident light made phase-sensitive detection essential for detailed studies. This technique had the advantage that the amplitudes of the in-phase and quadrature components 

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The photons emitted by the de-excitation of nuclear levels that are populated in the course of radioactive decays can be resonantly scattered. Nuclear resonance fluorescence experiments can give information on the velocity distribution of recoil atoms and the chemical modifications following transmutations and on the slowing-down process of hot atoms. This technique can be applied in gaseous, liquid, and solid systems, giving an advantage over Mossbauer spectroscopy. Nuclear resonance fluorescence has been reviewed, with particular reference to the following systems ... 

In most laboratory sources the excitation temperature decreases towards the boundary of the discharge region. Consequently the absorption in this part of the source is increased and the profile of the emitted radiation is not only appreciably broadened but often shov/s a pronounced dip at the centre of the line. This effect is known as self reversal and it has been studied in detail by Cowan and Diecke (1948). It is particularly important that self reversal is avoided in the lamps used in the resonance fluorescence experiments described in Chapters 15-17, for the strengths of the signals are proportional to the intensity at the line centre frequency... 

The Hanle effect and the theory of resonance fluorescence experiments... 

Next we proceed to develop the theory o resonance fluorescence experiments using the ensemble density matrix to describe the system of atoms. The important concepts of optical and radio-frequency coherence and of the interference of atomic states are discussed in detail. As an illustration of this theory general expressions describing the Hanle effect experiments are obtained. These are evaluated in detail for the frequently employed example of atoms whose angular momentum quantum numbers in the ground and excited levels are J =0 and Jg=l respectively. Finally resonance fluorescence experiments using pulsed or modulated excitation are described. 

The relatively simple apparatus, high sensitivity, and the selective nature of the optical excitation used in many resonance fluorescence experiments combine to make this method the most accurate method for measuring atomic lifetimes. In many cases the experimental measurements may be made at densities which are so low that the effect of resonance trapping and collision broadening are completely absent. In these cases the experimental results are usually quoted with errors in the range 3-5 per cent. The method is suitable for precision lifetime measurements and may for this reason allow a set of relative oscillator strengths obtained by the absorption or emission methods to be placed on a reliable absolute basis. 

In resonance fluorescence experiments, however, we are never able to study just a single atom, rather we are forced to investigate the properties of a sample containing N atoms. The measurable properties of this sample are then given in terms of the average values,, of a set of physical observables taken over the ensemble of independent atoms where... 

The theory of resonance fluorescence experiments therefore reduces to a study of the solutions of the Liouville equation for appropriate forms of the Hamiltonian operator 30. 

In resonance fluorescence experiments we are usually interested in just two electronic levels, one of which is normally the electronic ground state. The wavefunctions required for the expansion of this restricted density matrix consist of the ground-state basis functions p> and those of the excited state represented by m). These wave-functions are eigenfunctions of the angular momentum opera-tors J and with angular momentum quantum numbers given hy (J ,y) and (J ,m) respectively. 

Fig.15.10. Geometry for theoretical description of resonance fluorescence experiments.

IS, 8, Resonance fluorescence experiments using pulsed excitation... 

Theory of resonance fluorescence excited by modulated light. Theoretical expressions for the intensity of light observed in resonance fluorescence experiments using modulated excitation can be obtained by a simple extension of equation (15.41). We now assume that the energy density of the incident radiation, U((o,t), is amplitude modulated at... 

However, the importance of this experiment lies not so much in the result quoted above as in the demonstration of the feasibility of the optical double-resonance method. This pioneering work stimulated renewed interest in resonance fluorescence experiments and opened up a new branch of atomic physics. We shall now derive a detailed expression for the shape of the resonance signal and consider what further information can be obtained by careful studies of the linewidth. 

The density range over which most resonance fluorescence experiments can be performed is such that only... 

Comment on collisional depolarization studies. The resonance fluorescence experiments described above have served to stimulate and test the development of recent sophisticated theories of collision broadening. However, the hope that new information on interatomic forces would be obtained by these experiments has not been realized. This is largely because the observed broadening is the mean effect of collisions averaged over all possible relative orientations and over the thermal velocity distribution of the ensemble. It may be that in the future more detailed information on the interatomic potentials could be obtained by combining tunable dye laser excitation and atomic beam scattering techniques. 

Modulation of light from incoherent sources. The light beats observed in resonance fluorescence experiments should be clearly distinguished from those observed by Forrester et aZ.(1955). In that experiment an exceedingly weak modulation was detected in the light emitted from a conventional mercury lamp. In this source the atoms are excited by random collisions and the ensemble density matrix possesses zero hertzian coherence. The beat frequencies observed were due to the mixing at the detector of the radiation frequencies emitted by different atoms and... 

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