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arXiv:1908.05205

Spin State Dynamics in a Bichromatic Microwave Field: Role of Bright and Dark States in coupling with Reservoir

Wojciech Gawlik, Piotr Olczykowski, Mariusz Mrózek, Adam M. Wojciechowski

Published Aug 14, 2019• 0 citations
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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.

DOI
10.48550/arxiv.1908.05205

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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.
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.
Summary form only given. We have performed a series of experiments on coherent population trapping (CPT) in the presence of strong magnetic flux densities up to 1 mT. CPT can be observed in /spl Lambda/-systems where two ground states are coupled to a common excited state by two near-resonant light fields. Effective formation of ground state coherences takes place when the frequency difference of the light fields precisely matches the ground state splitting. This process leads to reduced absorption in the medium and thus reduced fluorescence intensity ("dark resonance") at the optical resonance frequency.
In cavity quantum electrodynamics (cQED) and particularly superradiance, emitters are typically assumed to be independent, interacting only through light shared via a common mode. While such photon-mediated interactions lead to a rich spectrum of collective optical effects, direct dipole-dipole interactions within the emitter ensemble are generally viewed as a source of decoherence. Here, we uncover a new role for direct spin-spin interactions as a drive for the superradiant dynamics of a hybrid system of nitrogen-vacancy center spins in diamond coupled to a superconducting microwave cavity. After an initial fast superradiant burst, we observe an unexpected train of subsequent emission pulses followed by quasi-continuous masing for up to one millisecond. We show that this surprising behavior arises from spectral hole refilling, where spin inversion is redistributed into the superradiant window of spins resonant with the cavity. We report measurements that clearly exclude other cQED-related effects, and performed microscopic simulations of up to one million spins, which demonstrate that the observed self-induced masing is indeed driven by dipole-dipole interactions between the spins. These findings open new pathways for exploring complex spin-spin interactions in dense disordered systems and offer possibilities for ultra-narrow linewidth solid-state superradiant masers powered purely by microwave-driven spin control.