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Physical Review A

Atomic coherence decay due to interactions with strong coherent radiation

Giuseppe Compagno, Franco Persico

Published May 1, 1977• 15 citations
Publisher

Abstract

The time development of $N$ two-level atoms linearly coupled to a monochromatic, long-wavelength radiation field is studied. Both systems are assumed to be initially in coherent states, the radiation mode being strongly populated with an average number $n$ of photons larger than $N$. The decay of atomic coherence can be followed up to a time ${t}^{*}$, after which the perturbation expansion in powers of ${n}^{\ensuremath{-}\frac{1}{2}}$ used to solve the problem breaks down. We show that it increases proportional to ${t}^{2}$ at large times, as measured from the variances of the components of the total angular momentum of the atoms. The results are briefly discussed in connection with the problem of conversion of incoherent into coherent radiation.

DOI
10.1103/physreva.15.2032

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Physical Review A•Aug 1, 1970•201 citations
The time development of NNN two-level atoms linearly coupled to a monochromatic, long-wavelength radiation field is studied. Both systems are assumed to be initially in coherent states, the radiation mode being strongly populated with an average number nnn of photons larger than NNN. The decay of atomic coherence can be followed up to a time t∗{t}^{*}t∗, after which the perturbation expansion in powers of n\ensuremath−12{n}^{\ensuremath{-}\frac{1}{2}}n\ensuremath−21​ used to solve the problem breaks down. We show that it increases proportional to t2{t}^{2}t2 at large times, as measured from the variances of the components of the total angular momentum of the atoms. The results are briefly discussed in connection with the problem of conversion of incoherent into coherent radiation.
We consider a system of NNN two-level atoms initially in the ground state and interacting with a small [$〈n(t=0)〉\ensuremath{\ll}N$] coherent radiation field. The field is assumed to be monochromatic, and its wavelength is taken to be much larger than the dimensions of the region of the NNN atoms. The statistical properties of both the atomic system and the radiation field are studied as functions of time. Using the Holstein-Primakoff transformation, it is shown that the initial coherence of the system tends to disappear after the energy of the system has been exchanged between atoms and field a number of times approximately given by N〈n(t=0)〉\frac{N}{〈n(t=0)〉}〈n(t=0)〉N​.
The emission spectrum is found for transitions between a pair of atomic levels which are coupled by a coherent applied field, in the case in which decay to other levels of lower energy takes place during the emission process. The problem is solved by first finding the spectral distribution of radiation emitted by an atom which is initially prepared in some combination of the two coupled states, and which then decays to states of lower energy. (The solution found to this initial-value problem is valid even when many photons are emitted before the decay takes place.) It is then shown how the solution so obtained may be used to describe the case in which the atom is continually excited to the pair of levels in question by a weak, incoherent pumping mechanism. Limiting cases are discussed and compared with those which apply when no decay out of the two-dimensional subspace of coupled states takes place. The method of solution, which is based on an evaluation of the appropriate atomic correlation function by means of the quantum fluctuation-regression theorem, is compared to the method of simply adding imaginary terms, proportional to the decay constants, to the state energies. The latter method is of far more restricted validity, in that it depends on a particular strong inequality which must be assumed to hold between the decay constants.
The dynamics of a degenerate two-mode electromagnetic field coupled to a single two-level atom is investigated both analytically and numerically. New quantum effects are discussed concerning the time dependence of the photon number and of its fluctuations, assuming that at t = 0 one of the modes is coherent and the other is empty. The field dynamics are dominated by oscillatory net exchanges of a large number of photons between the two modes, displaying amplitude decay. Over a longer time scale, revivals and collapses in the field populations take place. The time scales of these phenomena are much larger than those of the atomic Rabi oscillations decay. Moreover, the system attains a highly non-classical regime in which the field intensity in each mode is subjected to strong fluctuations even for a large initial number of photons in the coherent mode. Various correlations between atomic and field dynamics are pointed out, and the physical origin of the new quantum effects is briefly discussed. Finally, using our fully quantized calculations, we comment on the validity of the atomic homodyne detection proposed by Wilkens and Meystre.
The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.
The interaction of a resonant radiation field with two-level atoms (in the long-wavelength limit) is described by a Hamiltonian trilinear in the boson operators. It is shown that the dynamics of the system can be determined nearly exactly if either at least one of the three modes is strongly populated for all times or any two modes are separately strong in two complementary time domains. Explicit results are given in two important specific cases: (i) pumping of a ground-state atomic system by a coherent radiation field and (ii) coherent spontaneous emission. The results are compared with previously known approximate results. Our results are also applicable to certain parametric processes such as parametric amplification, frequency conversion, Raman and Brillouin scattering, etc., where an identical trilinear Hamiltonian is used to describe these processes.
Coherent spontaneous emission from a system of NNN two-level atoms interacting with a quantized radiation field is treated for the case in which Dicke's "cooperation number" rrr is macroscopically large. It is shown how to modify the quasiclassical approach to this problem to incorporate quantum effects that are lost in the self-consistent-field approximation. The statistics of the emitted radiation are found to vary markedly with the initial state of the system of atoms. The photon statistics tend to that typical of blackbody radiation when the initial state of the atomic system is that which would result from incoherent pumping ($m\ensuremath{\sim}r$). When, on the other hand, the atoms are initially in a superradiant state ($m\ensuremath{\ll}r$), the emitted radiation may be represented approximately by a coherent state.