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arXiv:1001.1041 · Physical Review A

Dynamical control of two-level system decay and long time freezing

Wenxian Zhang, Jun Zhuang

Published Jan 12, 2009• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.79.012310

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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\ensuremathπ2\ensuremath{\pi}2\ensuremathπ 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.
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.
The possibility of the phase control for the excitation of a quantum system in the discrete spectrum under the action of a short high-intensity laser pulse with a controlled phase is theoretically analyzed. The analysis is performed using the example of the simplest two-level system (TLS) employing a numerical solution to equations for the optical Bloch vector. It is demonstrated that the excitation probability and the mean dipole moment of the quantum system, which determine the normal luminescence and the superradiance in the TLS ensemble, respectively, substantially depend on the phase of the laser pulse for relatively short and powerful laser pulses.
The interband polarization induced by two phase-locked pulses in a semiconductor shows strong interference effects depending on the time, ${\ensuremath{\tau}}_{1},$ separating the pulses. The four-wave mixing signal diffracted from a third pulse delayed by $\ensuremath{\tau}$ is coherently controlled by tuning ${\ensuremath{\tau}}_{1}.$ The four-wave mixing response is evaluated exactly for a two-level system coupled to a single LO phonon. In the weak coupling regime it shows oscillations with the phonon frequency which turn into sharp peaks at multiples of the phonon period for a larger coupling strength. Destructive interferences between the two phase-locked pulses produce a splitting of the phonon peaks into a doublet. For fixed $\ensuremath{\tau}$ but varying ${\ensuremath{\tau}}_{1},$ the signal shows rapid oscillations at the interband transition frequency, whose amplitude exhibits bursts at multiples of the phonon period.
We show that when a quantum many-body system is subjected to coherent periodic driving, the response may exhibit exotic freezing behavior in high driving frequency $(\ensuremath{\omega})$ regime. In a periodically driven classical thermodynamic system, freezing at high $\ensuremath{\omega}$ occurs when $1/\ensuremath{\omega}$ is much smaller than the characteristic relaxation time of the system and hence the freezing always increases there as $\ensuremath{\omega}$ is increased. Here, in the contrary, we see surprising nonmonotonic freezing behavior of the response with $\ensuremath{\omega}$, showing curious peak-valley structure. Quite interestingly, the entire system tends to freeze almost absolutely (the freezing peaks) when driven with a certain combination of driving parameters values (amplitude and $\ensuremath{\omega}$) due to coherent suppression of dynamics of the quantum many-body modes, which has no classical analog. We demonstrate this new freezing phenomenon analytically (supported by large-scale numerics) for a general class of integrable quantum spin systems.
The pulse control of dephasing is studied for a two-level quantum system (qubit) interacting with a quantum environment. It has been shown that dephasing in a qubit due to qubit–environment interactions can be suppressed by a sequence of periodic π pulses with infinitely short duration. To study how the effectiveness of the pulse control is affected by finite pulse duration t d , we calculate the time evolution of the reduced density operator for a qubit under a sequence of π pulses. We show that the pulse control is effective even for not short t d if a suitable pulse sequence is adopted.