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Physical Review A

Effects of interference between different-order transition processes

Noriaki Tsukada, Takashi Nakayama, Sumiaki Ibuki, T. Akiba, Kazunaru Tomishima

Published Apr 1, 1981• 5 citations
Publisher

Abstract

The transition probabilities and the shifts of the crossing and anticrossing points of a two-level system (spin-1/2 atom) under the simultaneous influence of a static magnetic field and three orthogonal oscillating rf fields are calculated by using the resolvent formalism in which the rf fields are quantized. A new interference effect, which can be called "crossing of the third kind" in the rf transition, is predicted, and can be interpreted as the interference between different-order transition processes such as single- and two-photon processes, single- and three-photon processes, and so on. Furthermore, for coexistence of the single- and two-photon processes and of the single- and three-photon processes, we can obtain expressions of the transition probabilities (or effective dipole-coupling coefficients) similar to the results obtained in our previous paper, where the interference between single- and two-photon processes were treated by using the time-dependent Schr\"odinger equation.

DOI
10.1103/physreva.23.1855

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The transition probabilities and the shifts of the crossing and anticrossing points of a two-level system (spin-1/2 atom) under the simultaneous influence of a static magnetic field and three orthogonal oscillating rf fields are calculated by using the resolvent formalism in which the rf fields are quantized. A new interference effect, which can be called "crossing of the third kind" in the rf transition, is predicted, and can be interpreted as the interference between different-order transition processes such as single- and two-photon processes, single- and three-photon processes, and so on. Furthermore, for coexistence of the single- and two-photon processes and of the single- and three-photon processes, we can obtain expressions of the transition probabilities (or effective dipole-coupling coefficients) similar to the results obtained in our previous paper, where the interference between single- and two-photon processes were treated by using the time-dependent Schr"odinger equation.
Energies of the coupled system of a spin-1/2 atom in a static magnetic field and an oscillating rf field are analyzed with the resolvent formalism and numerically calculated by quantizing the rf field, for the general case that the strong rf field is oriented in an arbitrary direction to the static magnetic field. It is shown that, if the component of the static field along the direction of the rf field has particular values, level crossings take place and multiphoton transitions by even or odd numbers of rf photons become forbidden, even when the polarization of the rf field satisfies the parity condition for the multiphoton transitions. Particular attention is given to the direction and amount of the shifts of the level crossings by the rf field, together with the shifts of the anticrossings or of the multiphoton transitions. Theoretical results are verified by the optical-pumping experiments with cesium vapor.
Quantum interference and coherence effects in the interaction of atoms with the quantized electromagnetic field are investigated theoretically. A general master equation for the description of atom-field interactions is introduced. The interplay of the concepts of complementarity and interference in the time-energy domain are studied on the basis of the fluorescence light emitted by a single laser-driven atom, where the coherence of spontaneous processes gives rise to quantum interference in the spectrum of resonance fluorescence. The vacuum-induced dipole-dipole interaction in pairs of multi-level atoms is analyzed. It is shown that the interaction between orthogonal transition dipole moments of different atoms does not only influence the system dynamics crucially, but implies that the few-level approximation in general cannot be applied to near-degenerate Zeeman sublevels of the atomic level scheme. Potential applications of dipole-dipole interacting multi-level atoms for the implementation of decoherence-free subspaces and the generation of entanglement between atomic states are examined. The generation of an entangled state of the radiation field with a macroscopic number of photons is discussed on the basis of a single-atom laser.
Second-order interference effects in the spontaneous emission by two identical two-level atoms, separated a distance apart and both initially excited, are considered. On the basis of the analysis in our previous paper published in 2004, within fourth-order perturbation, detailed analysis of the second-order quantum interference in the emitted field is made. The interference arises both from single-photon states and two-photon states owing to interferences between different decaying sequences. By detailed analysis we have found some cancellations between single-photon and two-photon interference terms, and an interpretation of this is given. The contributions from the single- and the two-photon states as well as the total interference are analysed numerically for various interatomic distances and times. The contribution from a two-photon state is mostly larger than that from a single-photon state except when the atomic electric dipole is large, in which case the two contributions can be comparable. It is shown that the emission patterns from the two interacting atoms provide more information on atom–atom correlations than the decay time evolution of the atomic states population does. The number of interference fringes and the distance between them depend on the interatomic distance in a similar fashion to Young's interference fringes.
Exact expressions for the transition probabilities of a three-level atom interacting with a rotating magnetic field are obtained, and used to obtain the double-quantum resonance shift of sixth order and the linewidths to fourth order of perturbation theory. The treatment is extended to deal with overlap effects, oscillating fields and atomic systems with more energy levels. Numerical calculations are performed to check the validity of the analytic expressions and to obtain results applicable at higher field strengths. Although the majority of the detailed work is concerned with the double-quantum resonance, the formalism is general, and the methods may be applied to single-quantum or higher multiple-quantum transitions.
A resonance, induced by a DC field in a two-photon transition of an atom between states with opposite parity, results in a number of new effects related to the polarization of photons. These effects are caused by the interference of the non-resonant second-order dipole-forbidden amplitude and of a resonant part of the DC field-induced third-order amplitude. The linear and circular dichroism for the cross section of the process is revealed and analysed in detail for a two-photon excitation of the state from the ground state with a resonance on an state, induced by a DC electric field. The numerical data for alkali atoms demonstrate that the effects have quantitative characteristics of sufficiently large magnitudes and may be observed in experiments.