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Spin State Dynamics in a Bichromatic Microwave Field: Power Narrowing and Broadening of a Magnetic Resonance

Wojciech Gawlik, Mariusz Mrózek, Adam M. Wojciechowski

Published Aug 14, 2019• 0 citations
OpenAlex

Abstract

Driving an open spin system by two strong, nearly degenerate fields enables addressing populations of individual spin states, characterisation of their interaction with thermal bath, and measurements of their relaxation/decoherence rates. With such addressing we observe nested magnetic resonances having nontrivial dependence on microwave field intensity: while the width of one of the resonances undergoes a strong power broadening, the other one exhibits a peculiar field-induced stabilization. We also observe light-induced narrowing of such composite resonances. The observations are explained by the dynamics of bright and dark superposition states and their interaction with reservoir.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 16, 2003•0 citations
Driving an open spin system by two strong, nearly degenerate fields enables addressing populations of individual spin states, characterisation of their interaction with thermal bath, and measurements of their relaxation/decoherence rates. With such addressing we observe nested magnetic resonances having nontrivial dependence on microwave field intensity: while the width of one of the resonances undergoes a strong power broadening, the other one exhibits a peculiar field-induced stabilization. We also observe light-induced narrowing of such composite resonances. The observations are explained by the dynamics of bright and dark superposition states and their interaction with reservoir.
Driving an open spin system by two strong, nearly degenerate fields enables addressing populations of individual spin states, characterisation of their interaction with thermal bath, and measurements of their relaxation/decoherence rates. With such addressing we observe nested magnetic resonances having nontrivial dependence on microwave field intensity: while the width of one of the resonances undergoes a strong power broadening, the other one exhibits a peculiar field-induced stabilization. We also observe light-induced narrowing of such composite resonances. The observations are explained by the dynamics of bright and dark superposition states and their interaction with reservoir.
We apply a laser and two nearly degenerate microwave fields upon an ensemble of nitrogen-vacancy centers in diamond and observe magnetic resonance structures with two-component, composite shapes of nested Lorentzians with different widths. One component of them undergoes regular power-broadening, whereas the linewidth of the other one becomes power-independent and undergoes field-induced stabilization. We show that the observed width stabilization is a general phenomenon that results from competition between coherent driving and non-conservation of populations that occur in open systems. The phenomenon is interpreted in terms of specific combinations of state populations that play the role of bright and dark states.
Relaxation of a two-level system (TLS) into a resonant infinite-temperature reservoir with a Lorentzian spectrum is studied. The reservoir is described by a complex Gaussian-Markovian field coupled to the nondiagonal elements of the TLS Hamiltonian. The theory can be relevant for electromagnetic interactions in microwave high-Q cavities and muon spin depolarization. Analytical results are obtained for the strong-coupling regime, ${\ensuremath{\Omega}}_{0}\ensuremath{\gg}\ensuremath{\nu},$ where ${\ensuremath{\Omega}}_{0}$ is the rms coupling amplitude (Rabi frequency) and $\ensuremath{\nu}$ is the width of the reservoir spectrum. In this regime, the population difference and half of the initial coherence decay with two characteristic rates: most of the decay occurs at $t\ensuremath{\sim}{\ensuremath{\Omega}}_{0}^{\ensuremath{-}1},$ the relaxation being reversible for $t\ensuremath{\ll}({\ensuremath{\Omega}}_{0}^{2}\ensuremath{\nu}{)}^{\ensuremath{-}1/3},$ whereas for $t\ensuremath{\gg}({\ensuremath{\Omega}}_{0}^{2}\ensuremath{\nu}{)}^{\ensuremath{-}1/3}$ the relaxation becomes irreversible and is practically over. The other half of the coherence decays with a rate on the order of $\ensuremath{\nu},$ which may be slower by orders of magnitude than the time scale of the population relaxation. The above features are explained by the fact that at $t\ensuremath{\ll}{\ensuremath{\nu}}^{\ensuremath{-}1},$ the reservoir temporal fluctuations are effectively one-dimensional (adiabatic). Moreover, we identify the pointer basis, in which the reduction of the state vector occurs. The pointer states depend on the initial phase of the reservoir.
We present results of our research on two-field (two-frequency) microwave spectroscopy in nitrogen-vacancy ($\mathrm{N}{\mathrm{V}}^{\ensuremath{-}}$) color centers in a diamond. Both fields are tuned to transitions between the spin sublevels of the $\mathrm{N}{\mathrm{V}}^{\ensuremath{-}}$ ensemble in the 3A2{}^{3}{A}_{2}3A2​ ground state (one field has a fixed frequency while the second one is scanned). Particular attention is focused on the case where two microwave fields drive the same transition between two $\mathrm{N}{\mathrm{V}}^{\ensuremath{-}}$ ground state sublevels (${m}_{\mathrm{s}}=0\ensuremath{\leftrightarrow}{m}_{\mathrm{s}}=+1$). In this case, the observed spectra exhibit a complex narrow structure composed of three Lorentzian resonances positioned at the pump-field frequency. The resonance widths and amplitudes depend on the lifetimes of the levels involved in the transition. We attribute the spectra to coherent population oscillations induced by the two nearly degenerate microwave fields, which we have also observed in real time. The observations agree well with a theoretical model and can be useful for investigation of the NV relaxation mechanisms.
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 weaker-field 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.
Relaxation of a two-level system (TLS) into a resonant infinite-temperature reservoir with a Lorentzian spectrum is studied. The reservoir is described by a complex Gaussian-Markovian field coupled to the nondiagonal elements of the TLS Hamiltonian. The theory can be relevant for electromagnetic interactions in microwave high-Q cavities and muon spin depolarization. Analytical results are obtained for the strong-coupling regime, 0>ν, where Ω0 is the rms coupling amplitude (Rabi frequency) and ν is the width of the reservoir spectrum. In this regime, the population difference and half of the initial coherence decay with two characteristic rates: the most part of the decay occurs at t < (Ω0ν)-1/3 the relaxation becomes reversible for t ~ Ω0-1/3, whereas for t > (Ω02ν)-1/3 the relaxation becomes irreversible and is practically over. The other half of the coherence decays with the rate on the order of ν, which may be slower by orders of magnitude than the time scale of the population relaxation. The above features are explained by the fact that at t < ν-1 the reservoir temporal fluctuations are effectively one-dimensional (adiabatic). Moreover, we identify the pointer basis, in which the reduction of the state vector occurs. The pointer states are correlated with the reservoir, being dependent on the reservoir phase.