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Journal of the Optical Society of America B

Phase correlation in cascade spontaneous emission by a multilevel system: atomic memory

I. R. Senitzky

Published Dec 1, 1984• 8 citations
Publisher

Abstract

It is shown that phase correlation exists between two consecutive spontaneous-emission processes of an atom—although the phase in each individual process is random—when the atom is initially in a coherent superposition of the top and bottom levels. This correlation persists even when the two emission processes are separated by a finite time interval.

DOI
10.1364/josab.1.000879

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Journal of Experimental and Theoretical Physics•Jan 1, 2004•1 citation
It is shown that phase correlation exists between two consecutive spontaneous-emission processes of an atom—although the phase in each individual process is random—when the atom is initially in a coherent superposition of the top and bottom levels. This correlation persists even when the two emission processes are separated by a finite time interval.
The spontaneous emission of a set of NNN identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
Sub- and superradiant dynamics of spontaneously decaying atoms are manifestations of collective many-body systems. We study the internal dynamics and the radiation properties of two atoms in free space. Interesting results are obtained when the atoms are separated by less than half a wavelength of the atomic transition, where the dipole-dipole interaction gives rise to new coherent effects, such as (a) coherence between two intermediate collective states, (b) oscillations in the two-photon correlation G(2){G}^{(2)}G(2), (c) emission of two photons by one atom, and (d) the loss of directional correlation. We compare the population dynamics during the two-photon emission process with the dynamics of single-photon emission in the cases of a $\ensuremath{\Lambda}$ and a V scheme. We compute the temporal correlation and angular correlation of two successively emitted photons using the G(2){G}^{(2)}G(2) for different values of atomic separation. We find antibunching when the atomic separation is a quarter wavelength $\ensuremath{\lambda}∕4$. Oscillations in the temporal correlation provide a useful feature for measuring subwavelength atomic separation. Strong directional correlation between two emitted photons is found for atomic separation larger than a wavelength. We also compare the directionality of a photon spontaneously emitted by the two atoms prepared in phased-symmetric and phased-antisymmetric entangled states ${\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}⟩}_{{\mathbf{k}}_{0}}={e}^{i{\mathbf{k}}_{0}∙{\mathbf{r}}_{1}}\ensuremath{\mid}{a}_{1},{b}_{2}⟩\ifmmode\pm\else\textpm\fi{}{e}^{i{\mathbf{k}}_{0}∙{\mathbf{r}}_{2}}\ensuremath{\mid}{b}_{1},{a}_{2}⟩$ by a laser pulse with wave vector k0{\mathbf{k}}_{0}k0​. Photon emission is directionally suppressed along k0{\mathbf{k}}_{0}k0​ for the phased-antisymmetric state. The directionality ceases for interatomic distances less than $\ensuremath{\lambda}∕2$.
By considering a radiating gas as a single quantum-mechanical system, energy levels corresponding to certain correlations between individual molecules are described. Spontaneous emission of radiation in a transition between two such levels leads to the emission of coherent radiation. The discussion is limited first to a gas of dimension small compared with a wavelength. Spontaneous radiation rates and natural line breadths are calculated. For a gas of large extent the effect of photon recoil momentum on coherence is calculated. The effect of a radiation pulse in exciting "super-radiant" states is discussed. The angular correlation between successive photons spontaneously emitted by a gas initially in thermal equilibrium is calculated.
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.
Atomic systems with three or more equidistant energy levels, in which a cascade process is possible, are considered. Hamiltonians obtained for such systems are analogous to Heisenberg Hamiltonians, but for systems with integral spins. For Dicke states in multilevel systems, quantum-mechanical mean values of the energy of a cooperative system are calculated taking into account weak interactions between atoms. The type of emission preceding superradiant avalanche emission of the system is analyzed. It can be expected that a coherent state may be formed, in which collective processes affect one another not only via population of the intermediate common layer, but also via phasing of pure quantum states. The single superfluorescence pulse that can be formed in this case is not a simple superposition of two or more pulses of sequential superradiant transitions in two-level systems.