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Journal of Physics B Atomic Molecular and Optical Physics

Two-mode multiphoton transitions

Lung Ko, Michael W. Noel, Jonathan M. Lambert, Thomas F. Gallagher

Published Jul 20, 1999• 11 citations
Publisher

Abstract

We have investigated multiphoton transitions driven by two harmonically related microwave fields in a two-level system. We observed pronounced dependence of the Rabi frequency on the amplitudes and relative phase of the fields in the low field limit and found that the Rabi frequency of the combined fields was given by the phasor sum of the Rabi frequencies of the individual fields. For strong fields, each individual Rabi frequency is modified by the presence of the other field and this intuitive phasor addition is no longer valid.

DOI
10.1088/0953-4075/32/14/316

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We have investigated multiphoton transitions driven by two harmonically related microwave fields in a two-level system. We observed pronounced dependence of the Rabi frequency on the amplitudes and relative phase of the fields in the low field limit and found that the Rabi frequency of the combined fields was given by the phasor sum of the Rabi frequencies of the individual fields. For strong fields, each individual Rabi frequency is modified by the presence of the other field and this intuitive phasor addition is no longer valid.
In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.
We investigate the multiphoton quantum dynamics of a leaking single-mode quantized cavity field coupled with a resonantly driven two-level system possessing permanent dipoles. The frequencies of the interacting subsystems being considered are very different, e.g., the microwave range for the cavity and the optical domain for the frequency of the two-level emitter, respectively. In this way, the emitter couples to the resonator mode only via its diagonal dipole moments. Furthermore, the generalized Rabi frequency resulting from the external coherent driving of the two-level subsystem is also assumed to be different from the resonator's frequency or its multiples. As a consequence, this highly dispersive interaction regime is responsible for the cavity multiphoton quantum dynamics and photon conversion from the optical to microwave range, respectively.
We have measured the emission spectra of two-level-like atoms driven by a spatially inhomogeneous bichromatic field comprised of one resonant and one off-resonant component. Under these excitation conditions, observed spectra consist of several narrow peaks appearing on top of a broad continuumlike structure. This experimental approach provides for selective observation of those spectral features having a Rabi-frequency-independent emission frequency. Such emission processes involve multiphoton transitions, with one leg being spontaneous, between dressed-state levels differing only in their photonic quantum numbers; i.e., between equivalent dressed-state-doublet sublevels. Related vacuum-mediated transitions have recently been invoked as an underlying mechanism of inversionless gain.
We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving field is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mollow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving field. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we show that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.
Multiphoton up/down conversion in a transmon circuit, driven by a pair of microwaves tuned near and far off the qubit resonance, has been observed. The experimental realization of these high order non-linear processes is accomplished in the three-photon regime, when the transmon is coupled to weak bichromatic microwave fields with the same Rabi frequencies. A many-mode Floquet formalism, with longitudinal coupling, is used to simulate the quantum interferences in the absorption spectrum that manifest the multiphoton pumping processes in the transmon qubit. An intuitive graph theoretic approach is used to introduce effective Hamiltonians that elucidate main features of the Floquet results. The analytical solutions also illustrate how controllability is achievable for desired single- or multiphoton pumping processes in a wide frequency range.