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Laser Physics

Quantum control of the geometric phase in exact analytical solution using ultra-short strong pulses

K. Berrada, Hichem Eleuch

Published Sep 17, 2015• 1 citation
Publisher

Abstract

In the present paper, we study the geometric phase by considering a model that closely describes a realistic experimental scenario. We present an active way to control and quench the variation of the geometric phase using ultra-short strong pulses for a two-level quantum system with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we study the variation of the geometric phase with a few cycles pulse and a smooth phase jump over a finite time intervals. The control of the variation rate of the geometric phase is obtained by acting on the shape of the phase transient and other parameters of the considered system. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.

DOI
10.1088/1054-660x/25/10/105201

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In the present paper, we study the geometric phase by considering a model that closely describes a realistic experimental scenario. We present an active way to control and quench the variation of the geometric phase using ultra-short strong pulses for a two-level quantum system with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we study the variation of the geometric phase with a few cycles pulse and a smooth phase jump over a finite time intervals. The control of the variation rate of the geometric phase is obtained by acting on the shape of the phase transient and other parameters of the considered system. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.
Abstract Various schemes have been proposed to improve the parameter-estimation precision. In the present work, we suggest an alternative method to preserve the estimation precision by considering a model that closely describes a realistic experimental scenario. We explore this active way to control and enhance the measurements precision for a two-level quantum system interacting with classical electromagnetic field using ultra-short strong pulses with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we investigate the variation of the precision with a few cycles pulse and a smooth phase jump over a finite time interval. We show that by acting on the shape of the phase transient and other parameters of the considered system, the amount of information may be increased and has smaller decay rate in the long time. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.
Abstract By using the exact analytical solution and exploring the effect of ultra-short strong pulses in the presence of an external classical field for a two-level atom, we discuss the influence of the phase jump on the behavior of the atomic inversion, coherence and squeezing entropy during the time evolution of various pulse shapes. We show the optimal conditions to attain the phenomenon of coherence trapping. Moreover, we identify the range of physical parameters required for squeezing and its enhancement. The few-cycle pulses present new interesting features for controlling the physical quantities and are a good candidate to perform quantum optics tasks.
Abstract We investigate the effects of counterrotating terms on geometric phase and its relation to the resonance of the Rabi model. We apply the unitary transformation with a single parameter to the Rabi model and obtain the transformed Hamiltonian involving multiple harmonic terms. By combining the counter-rotating-hybridized rotating-wave method with time-dependent perturbation theory, we solve systematically time evolution operator and then obtain the geometric phase of the two-level system. Our results are beyond adiabatic approximation and rotating-wave approximation (RWA). Higher-order harmonic resonance happens when driving frequency is equal to higher-order subharmonic of the Rabi frequency. In comparison with numerically exact results, our calculated results are accurate over a wide range of parameters space, especially in higher-order harmonic resonance regimes. In these regimes we demonstrate geometric phases change dramatically while those of the RWA are smooth. The RWA is thoroughly invalid even if the driving strength is extremely weak. We find it is the higher-order harmonic terms that play an important role on the cyclic state and demonstrate the characters of geometric phase in higher-order harmonic resonance regime. We also present analytical formalism of the change rate of geometric phase and quasienergies, which agree well with numerically exact ones even in the strong driving case. The developed method can be applied to explore the dynamics of strongly driven qubits and physical properties of higher-order harmonic processes.
We study the general-setting quantum geometric phase acquired by a particle in a vibrating cavity. Solving the two-level theory with the rotating-wave approximation and the SU (2) method, we obtain analytic formulae that give excellent descriptions of the geometric phase, energy and wavefunction of the resonating system. In particular, we observe a sudden π-jump in the geometric phase when the system is in resonance. Similar behaviour is found in the geometric phase of a spin- particle in a rotating magnetic field. Our result suggests that the π-jump is a general feature for two-level systems, for which we developed a geometrical model to help visualize its evolution.
Recently, Rostovtsev et al (2009 Phys. Rev. A 79 063833) established an analytical treatment of the detuned atom–field interaction without using the rotating-wave approximation (RWA). Using this result, here we study qualitatively the dynamics of geometric phase (GP) and population transfer in a two-level atom interacting with an external off-resonant classical field for arbitrary pulse shape without using RWA. We use this exact method (without RWA) to reexamine the variation of populations and GP and compare the result with the RWA considering two kinds of the external field. We show that it is possible to control the GP dynamics by choosing suitable parameters of the atom–field system. Interestingly, we find that the variation of the populations and GP in the time is unchanged and it differs as we get further from the resonance. Moreover, we show that the Rabi frequency plays a role in reduction or augmentation of the periodic time interval for the GP. The solution is very suitable for atom–field systems, especially when the system is far from the resonance so that the RWA method breaks down.