Resonant interaction between coherent radiation and quantum systems is most often described within the framework of the rotating-wave approximation. In this case, only one of two counter-rotating linearly polarized components of the electromagnetic field interacts efficiently with the quantum system, while the effect of the second component is negligible. When the electromagnetic field is strong, the counter-rotating (the socalled antiresonance) component becomes efficient and the rotating-wave approximation can no longer be used. Violation of the rotating-wave approximation results in the Bloch-Siegert effect [1]. This effect leading to a shift of the resonance frequency is negligible for optical transitions, but becomes significant for precision nuclear magnetic resonance (NMR) experiments [2]. The Bloch-Siegert effect can also give rise to variations important for the operation of quantum computers [3]. At the same time, because of the interference of the counter-rotating electromagnetic-field components, the Bloch-Siegert effect provides a wonderful opportunity to measure not only the amplitude, but also the absolute phase of a monochromatic electromagnetic field [4].Interest has grown recently in studies of the interaction of two-level quantum systems with both continuous-wave [5,6] and pulsed [7] bichromatic radiation formed by fields with strongly different frequencies.Such an interest is explained by the importance and generality of the results for a wide range of physical objects, including, in particular, nuclear and electron spins in the NMR and EPR, double-well quantum dots, flux and charge qubits in superconducting systems, etc. Such systems are described with the use of the dressedstate approach by which the phenomenon of Rabi oscillations is analyzed. Note that the frequency of these oscillations depends on the efficiency of the interaction between the bichromatic radiation and quantum system, while their damping, on the coherence time of the quantum states. When quantum states dressed by the electromagnetic field are studied, the rotating-wave approximation is inevitably violated if the amplitude of the electromagnetic field exciting the transitions between the dressed states is comparable with the dressing-field amplitude. Hereafter, we consider electron two-level spin systems dressed by the bichromatic field formed by transverse microwave (MW) and longitudinal radio-frequency (RF) fields. It is known [7] that dressing by the electromagnetic field converts a twolevel system into a dynamic multilevel system. Since the MW-and RF-field frequencies are drastically different, bichromatic radiation ensures the excitation of intense multiphoton transitions in the case of the EPR. The direct study of the dynamics of multiphoton transi-The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) fiel...

The coherent dynamics of relaxing spin qubits driven by a classical bichromatic field comprising a strong resonant component and a weaker component with a frequency close to the strong-field Rabi frequency is studied. The double dressing by the bichromatic field modifies dephasing and dissipation processes. We demonstrate that detuning of the weakerfield frequency from the strong-field Rabi frequency prolongs the decay of Rabi oscillations between some doubly dressed states. The sensitivity of Rabi oscillations to the modified detuning-dependent relaxation is illustrated for nitrogen-vacancy qubits in diamond. We discuss a steady-state population inversion of the doubly dressed-state levels.

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Abstract. The study of microwave and radiofrequency multi-photon transitions in continuous wave (CW) EPR spectroscopy is extended to a Rabi resonance condition, when the radio frequency of the magnetic-field modulation matches the Rabi frequency of a spin system in the microwave field. Using the non-secular perturbation theory based on the Bogoliubov averaging method, the analytical description of the response of the spin system is derived for all modulation frequency harmonics. When the modulation frequency exceeds the EPR linewidth, multi-photon transitions result in sidebands in absorption EPR spectra measured with phasesensitive detection at any harmonic. The saturation of different-order multi-photon transitions is shown to be significantly different and to be sensitive to the Rabi resonance. The noticeable frequency shifts of sidebands are found to be the signatures of this resonance. The inversion of two-photon lines in some spectral intervals of the out-of-phase first-harmonic signal is predicted under passage through the Rabi resonance. The inversion indicates the transition from absorption to stimulated emission or vice versa, depending on the sideband. The manifestation of the primary and secondary Rabi resonance is also demonstrated in time-resolved steady-state EPR signals formed by all harmonics of the modulation frequency. Our results provide a theoretical framework for future developments in multi-photon CW EPR spectroscopy, which can be useful for samples with long spin relaxation times and extremely narrow EPR lines.

We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such dynamics: 1) the collapse and revival of oscillations in the population difference, 2) the simple exponential decay of the oscillations resulting in their steady state with the finite amplitude, and 3) the steady-state stabilization of the equally populated levels. The nonmonotonic Bessel-function-like dependence on the driving strength is also predicted for the decay rate of these oscillations. The features of this dependence are determined by the relative rates of energetic relaxation and pure dephasing.

Multiplication of spin qubits arises at double resonance in a bichromatic field when the frequency of the radio-frequency (rf) field is close to that of the Rabi oscillation in the microwave field, provided its frequency equals the Larmor frequency of the initial qubit. We show that the operational multiphoton transitions of dressed qubits can be selected by the choice of both the rotating frame and the rf phase. In order to enhance the precision of dressed qubit operations in the strong-field regime, the counter-rotating component of the rf field is taken into account.PACS: 03.67. Pp, 33.40.+f, 33.35.+r Theoretical models of quantum computations assume the existence of an ideal two-level quantum system (qubit) and the possibility of an exact description of the qubit's interaction with external electromagnetic fields [1]. It is known that the resonant interaction between electromagnetic radiation and qubit induces Rabi oscillations, which are the basis for quantum operations.The Rabi frequency ω R is defined by the amplitude of the electromagnetic field and usually is much smaller than the energy difference ω 0 (in frequency units) between the qubit's states.The "dressing" of qubit by the electromagnetic field splits each level into two giving rise to two new qubits with energy difference ω R . The spectrum of the multilevel "qubit + field" system consists of three lines at the frequencies ω 0 and ω 0 ± ω R (the Mollow triplet [2]). The second low-frequency electromagnetic field with the frequency close to the Rabi frequency ω R could induce an additional Rabi oscillation on dressed states of new qubits. These qubits are attracting interest because their coherence time is longer than that of the initial qubit [3 -5]. The results of studies of qubits dressed by bichromatic radiation formed by fields with strongly different frequencies are important for a wide range of physical objects, including, among others, nuclear

In the framework of the non-secular 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 have been 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 nitrogen-vacancy center in diamond [Z. Shu, et al., arXiv:1804. 10492] are well described in the frame of our approach. Our results provide new possibilities for coherent control of quantum systems.

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