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arXiv:1106.3365 · Physical Review B

Tunable multiphoton Rabi oscillations in an electronic spin system

Sylvain Bertaina, Nickolas Groll, L. Chen, I. Chiorescu

Published Oct 20, 2011• 9 citations
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Abstract

We report on multiphoton Rabi oscillations and controlled tuning of a multilevel system at room temperature ($S=5/2$ for Mn${}^{2+}$:MgO) in and out of a quasiharmonic level configuration. The anisotropy is much smaller than the Zeeman splittings, e.g., the six-level scheme shows only a small deviation from an equidistant diagram. This allows us to tune the spin dynamics by compensating for the cubic anisotropy with either a precise static-field orientation or a microwave field intensity. Using the rotating-frame approximation, the experiments are explained very well by both an analytical model and a generalized numerical model. The calculated multiphoton Rabi frequencies are in excellent agreement with the experimental data.

DOI
10.1103/physrevb.84.134433

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We report on multiphoton Rabi oscillations and controlled tuning of a multilevel system at room temperature (S=5/2S=5/2S=5/2 for Mn2+{}^{2+}2+:MgO) in and out of a quasiharmonic level configuration. The anisotropy is much smaller than the Zeeman splittings, e.g., the six-level scheme shows only a small deviation from an equidistant diagram. This allows us to tune the spin dynamics by compensating for the cubic anisotropy with either a precise static-field orientation or a microwave field intensity. Using the rotating-frame approximation, the experiments are explained very well by both an analytical model and a generalized numerical model. The calculated multiphoton Rabi frequencies are in excellent agreement with the experimental data.
Large-spin Mn2+ ions (S=5/2) diluted in a nonmagnetic MgO matrix of high crystalline symmetry are used to realize a six-level system that can be operated by means of multiphoton coherent Rabi oscillations. This spin system has a very small anisotropy which can be tuned in situ to reversibly transform the system between harmonic and nonharmonic level configurations. Decoherence effects are strongly suppressed as a result of the quasi-isotropic electron interaction with the crystal field and with the 55Mn nuclear spins. These results suggest new ways of manipulating, reading, and resetting spin quantum states which can be applied to encode a qubit across several quantum levels.
We report on multiple photon monochromatic quantum oscillations (Rabi oscillations) observed by pulsed EPR (Electron Paramagnetic Resonance) of Mn2+^{2+}2+ (S=5/2) impurities in MgO. We find that when the microwave magnetic field is similar or large than the anisotropy splitting, the Rabi oscillations have a spectrum made of many frequencies not predicted by the S=1/2 Rabi model. We show that these new frequencies come from multiple photon coherent manipulation of the multi-level spin impurity. We develop a model based on the crystal field theory and the rotating frame approximation, describing the observed phenomenon with a very good agreement.
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 performed quantum manipulations of the multilevel spin system S=5/2S=5/2S=5/2 of a Mn2+{\mathrm{Mn}}^{2+}Mn2+ ion, by means of a two-tone pulse drive. The detuning between the excitation and readout radio frequency pulses allows one to select the number of photons involved in a Rabi oscillation as well as increase the frequency of this nutation. Thus detuning can lead to a resonant multiphoton process. Our analytical model for a two-photon process as well as a numerical generalization fit well the experimental findings, with implications for the use of multilevel spin systems as tunable solid state qubits.
Quantum systems driven by strong oscillating fields are the source of many interesting physical phenomena. In this work, we experimentally study the dynamics of a two-level system of a single spin driven in the strong-driving regime where the rotating-wave approximation is not valid. This two-level system is a subsystem of a single nitrogen-vacancy (NV) center in diamond coupled to a first-shell 13C^{13}\mathrm{C}13C nuclear spin at a level anticrossing point. This near degeneracy occurs in the ${m}_{s}=\ifmmode\pm\else\textpm\fi{}1$ manifold of the electron spin when the energy level splitting between the ${m}_{s}=\ensuremath{-}1$ and +1+1+1 states due to the static magnetic field is $\ensuremath{\approx}127$ MHz and thus equal to the splitting due to the 13C^{13}\mathrm{C}13C hyperfine interaction. The transition frequency of this electron spin two-level system in a static magnetic field of 28.9 G is 1.7 MHz and it can be driven only by the component of the radio-frequency (RF) field along the NV symmetry axis. Electron spin Rabi frequencies in this system can reach tens of MHz even for moderate RF powers. The simple sinusoidal Rabi oscillations that occur when the amplitude of the driving field is small compared to the transition frequency evolve into complex patterns when the driving field amplitude is comparable to or greater than the energy level splitting. We observe that the system oscillates faster than the amplitude of the driving field and the response of the system shows multiple frequencies.
Abstract Recent electron spin resonance experiments on CaWO 4_44​ 4 :Gd 3+^{3+}3+ 3 + and other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance, together with another microwave field (image drive) with a frequency smaller than the Larmor frequency. These observations are confirmed by the new experimental results reported in this paper. We use numerical and analytical techniques to study the interplay between the microwave drives and three different mechanisms of relaxation. The first model describes a magnetic moment subject to microwave fields, interacting with a bath of two-level systems which acts as a source of decoherence and dissipation. The second model describes identical, interacting magnetic moments, subject to the same microwave fields. The decay of the Rabi oscillations is now due to the interactions. Third, we study Rabi oscillation decay due to the inhomogeneity of the microwave radiation. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that are not readily accessible experimentally. Graphic abstract