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Laser Physics

Polarization locking of the two-level system with inhomogeneously broadened transition

R. N. Shakhmuratov

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Qualitative aspects of the polarization locking in phase with the driving field are discussed. It is shown that particles, with a resonant detuning smaller than Rabi frequency, can be preferentially oriented along the driving field amplitude. This direction determines a new quantization axis of the two-level system (TLS) driven by the resonant field. So, the behavior of the driven TLS can be described by a new nondriven TLS which reaches the equilibrium by the interaction with a reservoir or its environment. Eigenstates of the new TLS are symmetric and asymmetric superpositions of the original TLS states.

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Qualitative aspects of the polarization locking in phase with the driving field are discussed. It is shown that particles, with a resonant detuning smaller than Rabi frequency, can be preferentially oriented along the driving field amplitude. This direction determines a new quantization axis of the two-level system (TLS) driven by the resonant field. So, the behavior of the driven TLS can be described by a new nondriven TLS which reaches the equilibrium by the interaction with a reservoir or its environment. Eigenstates of the new TLS are symmetric and asymmetric superpositions of the original TLS states.
A method of making the dephasing time T2u{T}_{2u}T2u​ measurement in an ensemble of inhomogeneously broadened two-level systems is proposed. This method has its origin in the spin-locking technique developed in NMR. It is shown that in spite of inhomogeneous broadening it is possible to lock the induced polarization in phase with the driving field. The amplitude of the locked polarization can be as large as half of the first maximum of the nutation signal, i.e., of the polarization bump just after the pulse switch on. Decay of the locked polarization is caused by the T2u{T}_{2u}T2u​ dephasing or by the dephasing of the in-phase component of polarization.
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.
Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLS's). By going beyond the rotating-wave approximation, especifically to second-order in perturbation, we obtain the Bloch-Siegert shift of the TLS resonant frequency, in which the resonant frequency increases with the driving field amplitude. This frequency shift implies that short resonant πππ-pulses in which the Rabi frequency is approximately 40\% or higher of the transition frequency do not achieve complete inversion in TLS's. Hence, guided by analytical results based on the averaging technique, we propose two methods for obtaining population inversions in the TLS driven by short πππ-pulses: one with chirping and the other with pulse shaping and near resonance blue-shifted detuning. Both methods minimize dephasing due to the Bloch-Siegert shift, reduce the dependance of the excitation of the TLS on the pulse phase, and are very effective in achieving complete population inversions.
Expressions for polarization and population difference of a quantum system in the modulated optical field at the modulation frequency exceeding the transition line width have been obtained in the form of the Fourier series. The characteristic frequency of the system, or the Rabi frequency, has been determined numerically. It depends not only on the intensity of the carrier wave and the detuning magnitude but also on depth and frequency of modulation. The computational technique is applicable both for amplitude and phase modulation.
We study phase-synchronization in a driven two-level system coupled to a non-Markovian bosonic reservoir. The dynamics is described by treating the system-bath coupling and the coherent drive without invoking the rotating-wave approximation, and simulated using the numerically exact hierarchical equations of motion. We observe that a robust phase-locking develops and that the corresponding synchronization measure rapidly acquires a finite value when the system is tuned to what we identify as a resonant-ratio condition, namely when the ratio between the drive amplitude and its frequency coincides with a zero of the Bessel function J0J_0J0​. We provide an explanation for this phenomenon by means of a static approximation derived from a Fourier analysis of the periodically driven Hamiltonian.
Previously derived equations for the expectation values of the dynamical variables of a general two-level dipole system (TLS) coupled to a relaxation mechanism---of which the Bloch equations for a spin-\textonehalf{} magneticdipole system are a special case---are reformulated in the density-matrix formalism in order to point out the explicit difference in the relaxation terms between the present description, which includes electric-dipole systems, and that of conventional treatments that are based on the assumption that any TLS is equivalent to a spin-\textonehalf{} magnetic dipole. The original equations are then solved for a weak monochromatic driving field, and the frequency of maximum power absorption is shown to depend on the type of TLS under consideration. The case of a stronger monochromatic driving field and the resulting saturation effects are studied for a special TLS, a spatially linear electric dipole which may have permanent dipole moment. This case exhibits a strong-field resonance shift that depends on the magnitude of the permanent dipole moment. A driving field consisting of a strong component at resonance and a weak component near resonance is considered in connection with the same TLS. The polarization is shown to contain, in lowest order, a component at the difference frequency with an amplitude determined by the magnitude of the permanent dipole moment.