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arXiv:1701.07865 · Physical review. B./Physical review. B

Absorption spectrum of a two-level system subjected to a periodic pulse sequence

Herbert F. Fotso, V. V. Dobrovitski

Published Jun 1, 2017• 10 citations
arXivHTMLPDF

Abstract

We investigate how the quantum control of a two-level system (TLS) coupled to photons can modify and tune the TLS's photon absorption spectrum. Tuning and controlling the emission and the absorption are of great interest, e.g., for the development of efficient interfaces between stationary and flying qubits in modern architectures for quantum computation and quantum communication. We consider periodic pulse control, where the TLS is subjected to a periodic sequence of the near-resonant Rabi driving pulses, each pulse implementing a ${180}^{\ensuremath{\circ}}$ rotation. For small interpulse delays, the absorption spectrum features a pronounced peak of stimulated emission at the pulse frequency, similar satellite peaks with smaller spectral weights, and the net absorption peaks on the sides. As long as the detuning between the carrier frequency of the driving and the TLS transition frequency remains moderate, this spectral shape shows little change. Therefore, the pulse control allows shifting the absorption peak to a desired position and locks the overall absorption spectrum to the carrier frequency of the driving pulses. A detailed description of the spectrum and its evolution as a function time, the interpulse spacing, and the detuning is presented.

DOI
10.1103/physrevb.95.214301

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We investigate how the quantum control of a two-level system (TLS) coupled to photons can modify and tune the TLS's photon absorption spectrum. Tuning and controlling the emission and the absorption are of great interest, e.g., for the development of efficient interfaces between stationary and flying qubits in modern architectures for quantum computation and quantum communication. We consider periodic pulse control, where the TLS is subjected to a periodic sequence of the near-resonant Rabi driving pulses, each pulse implementing a 180\ensuremath∘{180}^{\ensuremath{\circ}}180\ensuremath∘ rotation. For small interpulse delays, the absorption spectrum features a pronounced peak of stimulated emission at the pulse frequency, similar satellite peaks with smaller spectral weights, and the net absorption peaks on the sides. As long as the detuning between the carrier frequency of the driving and the TLS transition frequency remains moderate, this spectral shape shows little change. Therefore, the pulse control allows shifting the absorption peak to a desired position and locks the overall absorption spectrum to the carrier frequency of the driving pulses. A detailed description of the spectrum and its evolution as a function time, the interpulse spacing, and the detuning is presented.
We study the emission spectrum and absorption spectrum of a quantum emitter when it is driven by various pulse sequences. We consider the Uhrig sequence of πxπ_xπx​ pulses, the periodic sequence of πxπyπ_xπ_yπx​πy​ pulses and the periodic sequence of πzπ_zπz​ pulses (phase kicks). We find that, similar to the periodic sequence of πxπ_xπx​ pulses, the Uhrig sequence of πxπ_xπx​ pulses has emission and absorption that are, with small variations, analogous to those of the resonance fluorescence spectrum. In addition, while the periodic sequence of πzπ_zπz​ pulses produces a spectrum that is dependent on the detuning between the emitter and the pulse carrier frequency, the Uhrig sequence of nonequidistant πxπ_xπx​ pulses and the periodic sequence of πxπyπ_xπ_yπx​πy​ pulses have spectra with little dependence on the detuning as long as it stays moderate along with the number of pulses. This implies that they can also, similar to previously studied periodic sequence of πxπ_xπx​ pulses, be used to tune the emission or absorption of quantum emitters to specific frequencies, to mitigate inhomogeneous broadening and to enhance the production of indistinguishable photons from emitters the solid state.
Abstract We study the emission spectrum and absorption spectrum of a quantum emitter when it is driven by various pulse sequences. We consider the Uhrig sequence of nonequidistant π x pulses, the periodic sequence of π x π y pulses and the periodic sequence of π z pulses (phase kicks). We find that, similar to the periodic sequence of π x pulses, the Uhrig sequence of π x pulses has emission and absorption that are, with small variations, analogous to those of the resonance fluorescence spectrum. In addition, while the periodic sequence of π z pulses produces a spectrum that is dependent on the detuning between the emitter and the pulse carrier frequency, the Uhrig sequence of nonequidistant π x pulses and the periodic sequence of π x π y pulses have spectra with little dependence on the detuning as long as it stays moderate along with the number of pulses. This implies that they can also, similar to the previously studied periodic sequence of π x pulses, be used to tune the emission or absorption of quantum emitters to specific frequencies, to mitigate inhomogeneous broadening and to enhance the production of indistinguishable photons from emitters in the solid state.
The optical spectrum of a quantum system is jointly determined by the properties of the emitter and the driving field. All-optical spectral control can hence be a promising method to engineer the properties of single photon emitters for quantum technological applications. It was proposed that driving a two-level system with a periodic sequence of optical pi-pulses during the excited state lifetime shifts the emission and absorption maximum to an arbitrarily detuned pulse carrier frequency, enabling the mitigation of spectral diffusion in noisy emitters. In this article, we report on the first experimental observation of this effect. We implement the protocol on a solid-state emitter and reduce its inhomogeneously broadened optical linewidth close to the lifetime limit. By detuning the excitation laser, we are able to concentrate approximately half of the absorption to a freely selectable target frequency. Our approach is solely based on properties of coherently evolving quantum systems, rendering it applicable to a wide range of individual and ensembles of quantum emitters.
We investigate with exact numerical calculation coherent control of a two-level quantum system's decay by subjecting the two-level system to many periodic ideal $2\ensuremath{\pi}$ phase modulation pulses. For three spectrum intensities (Gaussian, Lorentzian, and exponential), we find both suppression and acceleration of the decay of the two-level system, depending on difference between the spectrum peak position and the eigen frequency of the two-level system. Most interestingly, the decay of the two-level system freezes after many control pulses if the pulse delay is short. The decay freezing value is half of the decay in the first pulse delay.
In order to control the state of a two-level quantum system (e.g. the spin state of an ion qubit), optical frequency combs perform a two-photon stimulated Raman process through stimulated absorption from one comb tooth and stimulated emission into another comb tooth. If the two-level energy gap is an integer multiple of the repetition rate of the laser, resonant Rabi oscillations are excited. When these latter have a frequency close to the qubit’s transition one, a strongly anharmonic phase-locked cycle may exist on the Bloch sphere, which generates a sub-harmonic series of very narrow, equally spaced, spectral lines. If the repetition rate of an optical frequency comb is appropriately tuned to these latter (up to the average carrier envelope frequency), a highly resonant dynamical regime of the two-level system should be reached where the Raman stimulated absorption and emission processes would occur for any pair of adjacent comb teeth.
Multiphoton transition probability can be manipulated by tailoring the ultrashort laser pulses. In this paper, we theoretically and experimentally investigate the influence of the absorption bandwidth and line shape on the coherent control of two-photon transitions in two-level system by manipulating the femtosecond laser pulse with the $\ensuremath{\pi}$ spectral phase step. A coherent feature with a coherent peak and two coherent dips can be achieved if the absorption bandwidth is less than twice of the laser spectral bandwidth. The absorption bandwidth decides the coherent peak or dip intensity, and the absorption line shape affects the symmetry of the two coherent dips.