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Acta Physica Sinica

Implementing quantum control for the temporal evolution of the wave function of the quantum state by using a phase-controlled light field

Li Yongfang, Ren Li-Qing, Ma Rui-Qiong, Rong Fan, Juan Liu, 陕西师范大学物理学与信息技术学院,西安 710062

Published Jan 1, 2010• 3 citations
Publisher

Abstract

We investigate the interaction between a two-level atomic system and a phase controllable light field. The quantum diffraction of the population probability for the excited state is described analytically. The physical sense of the wave function evolution is analyzed in detail. The polarization of the atoms is shown with the help of Cornu spiral of the wave function and the temporal evolution of the real and imaginary part for the wave function. It is shown that the polarization of the atoms and the temporal evolution of the wave function as well as the propagation of light can be controlled by manipulating the phase of the light field.

DOI
10.7498/aps.59.1671

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Journal of Physics B Atomic Molecular and Optical Physics•Aug 19, 2019•16 citations
We investigate the interaction between a two-level atomic system and a phase controllable light field. The quantum diffraction of the population probability for the excited state is described analytically. The physical sense of the wave function evolution is analyzed in detail. The polarization of the atoms is shown with the help of Cornu spiral of the wave function and the temporal evolution of the real and imaginary part for the wave function. It is shown that the polarization of the atoms and the temporal evolution of the wave function as well as the propagation of light can be controlled by manipulating the phase of the light field.
We study the interaction between the shaped chirped laser pulse and a two-level atomic system. The analytical solution of the population probability on the excited state is obtained by the first order perturbation theory. We show that the temporal evolution of the wave function on the excited state is similar to the grating diffraction. By varying the modulation adepth and the compensation phase we demonstrate that the quantum coherent control for the population probability on the excited state can be achieved. We present a new method for measuring the wave function by the quantum holography principle.
Abstract In this study, the nonresonant two-photon absorption process in a two-level atom, induced by a weak chirped pulse, is theoretically investigated in the frequency domain. An analytical expression of the wave function expressed by Fresnel functions is obtained, and the two-photon transition probability (TPTP) versus the integral bandwidth, spectral width, and chirp parameter is analyzed. The results indicate that the oscillation evolution of the TPTP result from quantum diffraction of the wave function, which can be explained by analogy with Fresnel diffraction from a wide slit in the spatial domain. Moreover, the ratio between the real and imaginary parts of the excited state wave function and, hence, the atomic polarization, can be controlled by the initial phase of the excitation pulse. In some special initial phase of the excitation pulse, the wave functions with purely real or imaginary parts can be obtained by measuring the population probability. This work provides a novel perspective for understanding the physical details of the interactions between atoms and chirped light pulses in the multiphoton process.
Abstract The interaction of 3-level atom with two resonant quantum fields is investigated and an analytical solution is obtained. The effect of coherent population trapping and formation of a ‘dark’ state is analyzed. The atomic and field dynamics is found to be very sensitive to the photon statistics and relative phases of the initial quantum field states. The effect of quantum ‘death’ and ‘birth’ of atomic transitions and mean photon number evolution is demonstrated. Strong entanglement between atomic and field subsystems arising during the interaction is found and studied in details.
Quantum information processing tasks have been implemented in various physical platforms. In this thesis, we consider two specific implementations: Part I presents a detailed study of the interaction of a single atom with a light pulse. Part II examines the case of a quantum controlled-phase gate in circuit quantum electrodynamics in the ultrastrong coupling regime. They are both actively pursued by many research groups. In Part I, we first present the framework for a single two-level atom interacting with the quantized electromagnetic field. The effect of temporal and spectral properties of the pulses on atomic excitation is studied for both Fock state and coherent state pulse. The detailed analysis of atomic excited state population is provided for single photon pulse with various temporal shapes. The work is then extended to a more general case with two spatial-modes and multi-photon pulses. The difference between Fock state and coherent state pulse on atomic excitation is further investigated. We find that at few photon levels, the maximum atomic excitation probability is a monotonic function of photon number for the coherent state pulse, but not for the Fock state pulse. Furthermore, we show that the atomic dynamics can be controlled by the initial relative phase between the two counter-propagating coherent state pulses incident on the atom, which is not the case with two Fock state pulses. The theoretical prediction is then compared with an experiment, where a single trapped 87Rb atom interacts with coherent state pulses engineered in temporal shape of rising exponential and rectangular form. Next, we propose a quantum memory setup based on a single two-level atom in a half cavity with a moving mirror. The efficiency of the quantum storage process is studied analytically and
The present study described about the interaction of a two level atom and squeezed field with time varying frequency. By applying a sinusoidal variation\nin the frequency of the field, the randomness in population inversion is reduced and the collapses and periodic revivals are regained. Quantum optics is an emerging field in physics which mainly deals with the interaction of atoms with quantised electromagnetic fields. Jaynes-Cummings Model (JCM) is a key model among them, which describes the interaction between a two level atom and a single mode radiation field. Here the study begins with a brief history of light, atom and their interactions. Also discussed the interaction between atoms and electromagnetic fields. The study suggest a method to manipulate the population inversion due to interaction and control the randomness in it, by applying a time dependence on the frequency of the interacting squeezed field.The change in behaviour of the population inversion due to the presence of a phase factor in the applied frequency variation is explained here.This study also describes the interaction between two level atom and electromagnetic field in nonlinear Kerr medium. It deals with atomic and field state evolution in a coupled cavity system. \nOur results suggest a new method to control and manipulate the population of states in two level atom radiation interaction,which is very essential for quantum information processing.We have also studied the variation of atomic population inversion with time, when a two level atom interacts with light field, where\nthe light field has a sinusoidal frequency variation with a constant phase. In both coherent field and squeezed field cases, the population inversion variation is completely different from the phase zero frequency modulation case. It is observed that in the presence of a non zero phase φ, the population inversion oscillates sinusoidally.Also the collapses and revivals gradually disappears when φ increases\nfrom 0 to π/2. When φ = π/2 the evolution of population inversion is identical to the case when a two level atom interacts with a Fock state. Thus, by applying a phase shifted frequency modulation one can induce sinusoidal oscillations of atomic inversion in linear medium, those normally observed in Kerr medium. \nWe noticed that the entanglement between the atom and field can be controlled by\nvarying the period of the field frequency fluctuations. The system has been solved numerically and the behaviour of it for different initial conditions and different susceptibility values are analysed. It is observed that, for weak cavity coupling the effect of susceptibility is minimal. In cases of strong cavity coupling, susceptibility factor modifies the nature in which the probability oscillates with time. Effect\nof susceptibility on probability of states is closely related to the initial state of the system.
Abstract We present an analytical electric field expression to simultaneously control the population and phase dynamics of two-level quantum systems. The presented electric field is obtained by a reverse engineering technique after the desired population and phase evolution pathways of the system have been specified. Upon application of this laser field, the system is driven from an arbitrary quantum state superposition to the desired population distribution; meanwhile the phase of one of the states proceeds according to a predefined path. The robustness of the engineered electric field is demonstrated by numerical simulations on the example of the 3s → 3p transition of atomic sodium. Furthermore, the limitations of the presented technique, which arise due to the application of the rotating wave approximation, are thoroughly analyzed and discussed.