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The Journal of Chemical Physics

Multiquantum electron paramagnetic resonance transitions excited in a two-level system by tetrachromatic microwave irradiation

Małgorzata Jeleń, Wojciech Froncisz

Published Dec 1, 1998• 8 citations
Publisher

Abstract

A method to excite multiquantum transitions in a two-level system by application of continuous irradiation with a four-frequency microwave field is presented. The generated signal is composed of many intermodulation sidebands at different frequencies, which arise from the multiquantum transitions. These processes involve an odd number of photons, that are absorbed from, or emitted to two, three, or four fields. The correspondence between the frequency spectrum of the signal and possible pathways of multiquantum processes is found with recourse to the many mode Floquet theory. The reported experiments demonstrate the multiquantum origin of the detected intermodulation sidebands and their properties.

DOI
10.1063/1.477588

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A method to excite multiquantum transitions in a two-level system by application of continuous irradiation with a four-frequency microwave field is presented. The generated signal is composed of many intermodulation sidebands at different frequencies, which arise from the multiquantum transitions. These processes involve an odd number of photons, that are absorbed from, or emitted to two, three, or four fields. The correspondence between the frequency spectrum of the signal and possible pathways of multiquantum processes is found with recourse to the many mode Floquet theory. The reported experiments demonstrate the multiquantum origin of the detected intermodulation sidebands and their properties.
In 1959, E. T. Jaynes suggested that resonant, multiquantum processes could provide an efficient method of frequency conversion at high frequency and high powers. This conversion is mediated by a gas or solid composed of molecules having a strong electric-dipole absorption at a frequency /spl Omega/. Such a system can resonantly absorb energy from an electromagnetic field at all odd subharmonic of /spl Omega/. The /spl omega/ /spl ap/ /spl Omega/ /(2n + 1) subharmonic absorption is said to correspond to a 2n + 1 quantum process. The excited (driven) molecular system has electric dipole moments at all odd harmonics of the drive /spl omega/. The resonant dipole moment at a frequency (2n + 1)/spl omega/ /spl ap/ /spl Omega/ generates an electromagnetic field resulting in the frequency conversion process proposed by Jaynes. Here we report theoretical calculations and experimental observation of this multiquantum frequency conversion in a traveling-wave structure.
The use of four pulsed rf fields for the excitation of multiphoton resonances in a two-level system is investigated. A general theoretical description of the experiment is provided based on the Floquet formalism and application of basic conservation laws to the overall transition process. The predictions of the theory are compared with computer simulations of the time evolution of the magnetization according to the exact time-dependent Hamiltonian. It is shown that N-photon resonances occur when the fields are applied at frequencies \ifmmode\pm\else\textpm\fi{}k\ensuremath{\omega} and \ifmmode\pm\else\textpm\fi{}l\ensuremath{\omega} from the Larmor frequency, where k and l are positive integers having no common factors and where 0\ensuremath{\le}k<l, k+l=N. For any resonance k photons are taken from the outer field pair and l are taken from the inner field pair. A total of 2[(l+k)!]/(k!l!) mutually interfering transition pathways exist for the overall process and the resultant magnitude of the effective N-photon field is very sensitive to the relative initial phases of the rf fields. The spiral motion observed for multiphoton resonances induced by double-frequency irradiation is absent here when the field intensities are symmetrical. In addition, the fraction of total applied rf intensity available for multiphoton pumping is considerably greater than for two fields. Phase cycling to enhance detection of multiphoton effects and multiphoton spin locking are considered.
Experimentally achievable conditions where only weak off-resonant fields are used to excite coherence in a two-level system are explored. A brief review of previous theoretical results useful in treating multifrequency irradiation sequences is provided. Using an approximation method based on the Floquet formalism we derive an expression for the effective field strength as a function of the phases and amplitudes of the applied irradiation fields. Some of these results are rederived and/or explained in a simplified manner. Under conditions of four-frequency irradiation, three-photon excitation of a two-level system in NMR is experimentally demonstrated on the spin-1/2 system of the 31P nucleus in phosphoric acid. The behavior of the three-photon resonance is explored as a function of all important experimental parameters. The results of these tests conform closely to the theoretical predictions. Possible uses of multifrequency irradiation schemes in NMR are suggested.
A general theory has been developed to calculate the response, in NMR conditions, of a spin system irradiated by two nearly resonant waves having different frequencies and intense enough to produce an appreciable saturation. The absorption signal has been calculated employing the statistical operator technique, treating the electromagnetic field by the second quantization formalism. Two kinds of transitions are expected: The first one arises from processes in which n photons of one wave are emitted and n photons of the other wave are absorbed, the second one arises from processes involving the emission of n photons of one wave and the absorption of n ± 1 photons of the other. In the first case all the transitions coalesce in a single dispersionlike signal, which occurs when the frequencies of the two waves are nearly the same; in the second case a many-line spectrum occurs in which emission and absorption lines are present. The experimental results here reported strictly agree with theoretical previsions.
The expression for the absorption coefficient in two-photon resonance transitions is deduced under general conditions. No particular restrictions are imposed on the level system or on the frequencies and intensities of the fields. The following cases are considered: (i) a two-level system (with and without singularities) irradiated by a single wave and (ii) a three-level system irradiated by two waves. Some theoretical and experimental disagreements reported by authors of previous papers are examined and clarified by the present theory.
Abstract In this paper, we present a theoretical investigation of multiphoton processes between a single atom and a multimode optical or microwave field. At first, we examine two-photon excitation, which involves the simultaneous excitation of two photons in different cavity modes by a single atom. We demonstrate that when the transition frequency of an atom is equal to the sum of the frequencies of two cavity modes, there exists a resonant coupling between the atom and the two-mode cavity field, which leads to the simultaneous excitation of the two cavity photons with the atom initially in its excited state. Moreover, we found that this coupling is coherent and reversible, allowing the atom initially in the ground state to simultaneously absorb all the photons from the cavities and transit to its excited state. Finally, we also show that this coherent interaction, in principle, can be extended to describe multiphoton processes between a single atom and a multimode cavity field, such as a three-mode cavity. The parameters used in the numerical simulation are based on the experimentally demonstrated values in circuit quantum electrodynamics systems.