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Laser Physics Letters

Quantum preservation of the measurements precision using ultra-short strong pulses in exact analytical solution

K. Berrada, Hichem Eleuch

Published Aug 22, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1612-202x/aa7ba7

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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.
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 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.
We investigate the problem of parameter estimation for the superposition of coherent fields under perfect and lossy regimes. We show the optimal range for higher precision of phase estimation by exactly solving a model consisting of a Schrödinger-cat state (SCS) subject to zero-temperature under a decoherence effect due to a dissipative interaction with an environment. We find the phenomenon that the quantum Fisher information (QFI), namely, the precision of estimation, is slowly reduced with the environment effect and affected by the photon number effects. We find that revivals and retardation of the QFI loss may occur by adjusting the mean photon number, and increasing the photons strongly enhances the coherence and hence augments the resolution of the parameter estimation. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the coherent field and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the mean photon number. These features make the SCS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.
Quantum sensors allow us to measure weak oscillating fields with incredible precision. One common approach is to use the time evolution of a single two-level system (or a qubit) in conjunction with applied control pulses to measure the oscillating field. For high-frequency fields, the time interval required between the applied pulses decreases, meaning that errors due to the finite width of the pulses can become important. This paper presents an alternative scheme that does not rely on applying pulses with short time intervals. Our scheme uses two interacting qubits. In the presence of an oscillating field, the interaction strength changes. The oscillating field can be estimated by measuring the change in this interaction strength. We quantify the precision of this estimate by calculating the Fisher information. We show the effect of noise on our scheme and discuss how control pulses can be applied to mitigate the impact of noise. Importantly, the time interval between these pulses need not be very short.
We study the dynamics of a two-level system driven by an off-resonance few-cycle pulse which has a phase jump $\ensuremath{\phi}$ at t=t0t={t}_{0}t=t0​, in contrast to many-cycle pulses, under the nonrotating-wave approximation (NRWA). We give a closed form analytical solution for the evolution of the probability amplitude ∣Ca(t)∣|{C}_{a}(t)|∣Ca​(t)∣ for the upper level. Using the appropriate pulse parameters like the phase jump $\ensuremath{\phi}$, jump time t0{t}_{0}t0​, pulse width $\ensuremath{\tau}$, frequency $\ensuremath{\nu}$, and Rabi frequency ${\ensuremath{\Omega}}_{0}$ the population transfer after the pulse is gone can be optimized and, for the pulse considered here, an enhancement factor of 106−−108{10}^{6}--{10}^{8}106−−108 was obtained.
In this paper, based on the idea of reverse engineering, we propose a scheme to find analytical expressions of a laser pulse that allows for controlling the evolution of two-level systems as desired, regardless of the time-dependent phase of the system. The pulse relates to particular functions that predefine the evolution of a system. For illustration, we present concrete examples of driving the system from an arbitrary initial state to a final state along the user-prescribed particular way in both closed and open quantum systems. Simulation results indicate that the desired evolutionary path is accurately obtained when the rotating wave approximation (RWA) is satisfied. Most importantly, the scheme allows us to maintain system coherence and populations even in the presence of certain dephasing and thermal noises. Thus it may naturally find applications in quantum computing and quantum memories.