Photon wave packet

Engel V and Metiu H 1994 2-Photon wave-packet interferometry J. Chem. Rhys. 100 5448... 

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

The nonlinear relationship due to the final term causes the wave packet to spread as it propagates. Dropping it assumes that W is so small that the detector can be placed close enough to the scattering target to neglect the spread. Note that only for a photon wave packet is E strictly proportional to k E = tick. The physical situation that we will ultimately consider is that W tends to zero. In section 3.2.2 we showed that the absence of time resolution in an experiment results in the experiment being equivalent to an incoherent superposition of independent experiments, each with an incident plane wave, i.e. an incident wave packet of zero width. 

Figure 8.2 Time dependence of the probability Pe(t) of observing the spontaneously decaying two-level system in its excited state at the center of a closed spherical cavity The number of resonantly interacting field modes is of the order of rR/ 7rc and depends on the size of the cavity R. For FR/c = 10 (upper figure) a spatially localized photon wave packet is generated by spontaneous emission and can be reabsorbed again by the two-level system at the center of the cavity at later times. For FR/c = 1 (lower figure) only a small number of cavity modes interact resonantly and the two-level system performs approximate Rabi oscillations governed by the vacuum Rabi frequency.

G. Alber, Photon wave packets and spontaneous decay in a cavity, Phys. Rev. A 46 (1992) R5338. 

The probability amplitude (b k, L/c)b] k,0)) gives direct information on the photon absorption process. Let the specific volume per molecule be the quantization volume V. The probability that a photon (wave packet) can pass through this volume of linear dimension L without being scattered is... 

Theoretically, the phenomena of optical activity can be described with the tools already developed. A photon (wave packet) with wave vector k is scattered from polarization ni k) to n2 k) (and the same energy) with probability amplitude... 

In the discussion of the experimental approaches to study molecular resonances, the quantum theory of photon wave packet scattering forms the natural framework. It is thus necessary to recall some of the main features of wave packet scattering (Messiah, 1965 Newton, 1966 Goldberger and Watson, 1965a) with special reference to photophysical phenomena (Shore, 1967). We begin with a brief review of the basic concepts in the formal description of time evolution. Then we consider more in detail the process of scattering of a coherent photon wave packet by a molecule. The expressions for the basic experimental observables are derived, with special emphasis on time-resolved studies. Detection is assumed to take place under short time conditions, in a lateral, nonforward direction so that no coherence of the photon states scattered by different molecules must be considered. 

In a typical experiment, a beam of photon wave packets is emitted from a collimated source. Thereafter the experimenter has no control over the evolution of the system, until the photons scattered by the molecular target reach his detector. In practice, source and detector are located sufficiently far from the target, so that photon-molecule interaction can be neglected during the processes of photon emission and detection. 

We first consider the photodetector and invoke an operational equivalent of the detection process (Goldberger and Watson, 1965b Glauber, 1965 Mandel, 1966). We specialize to the case of fast, broad-band detectors giving a count whenever the photon wave packet is in the active volume of the photocounter. The probability density for a photon in state l / (f)> to be localized at the position r is equal to the square of the wavefunction detection probability can be expressed as the integral over the detecting volume. 

For the unscattered part (64) of the photon wave packet, detected for example in the forward direction, we get similarly a detection amplitude of the form... 

By means of the general description of the incident light beam given in this section, combined with the previous results on photon wave packet scattering, we are now in a position to consider in detail the typical experimental approaches employed in the photophysical studies of molecular resonances. 

The characteristic conditions for time-dependent scattering processes are conveniently discussed by introducing the concept of time delay suffered by the photon wave packet interacting with the molecule (Goldberger and Watson, 1965a Newton, 1966). In practice this time delay may be defined as the difference between the detection times and of the scattered and nonscattered parts of a photon packet by fast detectors at the same distance from the target. A necessary condition for the time-resolved experimental observation is then that the time delay... 

We consider the general case where, according to Eqs. (122), a number M of molecular resonant states with complex energy E = e — iyJ2 is selected by the incident photon wave packets to take part in delayed scattering. The resonances are taken to be well separated, so that, if denotes the energy level spacing, one has... 

Generally, for light sources other than mode-locked or single-mode lasers, the statistical features must be taken into account as well the mean energies of the photon wave packets are regarded as random variables distributed according to a classical probability function of a characteristic width A j e the energy profile of these non-transform-limited or chaotic pulses has then a width of the order... 

---