Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Applied Mechanics and Materials

Study of Multiple Quantum Beats in Atomic Wavepackets

Chang Jun Zhu, Bing Xue, Xue Jun Zhai, Jun Fang He

Published Jun 13, 2013• 0 citations
Publisher

Abstract

A theoretical model consisting of 5 energy levels in coupled four-wave mixing processes was proposed to analyze the coherent characteristics of atomic wavepackets using perturbative theory. The equations of motions of the density matrix were derived and the third-order density matrix elements were presented. Under the condition that the duration of laser pulses is sufficiently short, the system response was treated as impulse response. Moreover, in the lowest order perturbation theory, the third-order nonlinear polarization was obtained using rotating-wave approximation. The results show that multiple quantum beats are embedded in the coupled four-wave mixing signals, and coherent dynamics of wavepackets can be retrieved from the quantum beat dynamics.

DOI
10.4028/www.scientific.net/amm.325-326.119

Related papers

Dynamics of triple quantum beats retrieved from coupled four-wave mixing signals

Changjun Zhu, Bei Xu, Qing Chu +2 more

A theoretical model of coupled four-wave mixing (FWM) processes comprising five atomic energy levels was proposed to investigate the coherent characteristics of atomic wave packets using perturbation theory. As several states in atoms are coherently excited by a two-photon transition, triple coupled FWM can be produced, and triple quantum beats associated with the atomic energy levels are embedded in the FWM signals. Triple coupled FWM processes were achieved experimentally in Rb vapor by two-photon excitation using broadband optical pulses. A pump–probe scheme was utilized to record the time-varying FWM signals, and Fourier transform was applied to retrieve the quantum beats. Furthermore, short-time Fourier transform was implemented to investigate the dynamics of quantum beats. The results show that the coherent characteristics of atomic wave packets, which are intimately related to the dynamics of quantum beats, can be probed by coupled nonlinear optical wave mixing.

Journal of the Optical Society of America B•Feb 25, 2016•0 citations

Study on Coherent Dynamics of Alkali Metal Atomic Wave Packets

Chang Jun Zhu, Jun Fang He

A theoretical model consisting of 5 energy levels, with the three upper states coherently excited, was proposed to analyze the coherent characteristics of atomic wave packets using perturbative theory. Pump-probe technique was implemented to detect coupled difference frequency four-wave mixing processes for studying the coherent characteristics of Rb atomic wave packets. Quantum beats were extracted the time domain signal by Fourier transform. Moreover, the variation of quantum beats was gained by time-dependent Fourier transform. The results show that the coherent characteristics of alkali metal atomic wave packets are closely related to quantum beats embedded in the time delayed four-wave mixing signal. Theoretical results are consistent with experimental observations, possessing potential applications in multi-channel information encoding and decoding.

Key engineering materials•Jan 1, 2013•0 citations

Study of wavepacket dynamics in rubidium vapor by means of time-frequency analysis

Andrey A. Senin

Wavepackets are excited in rubidium vapor by intense ultrashort (∼100 fs) pulses centered at a wavelength of 620 nm or 770 nm. The generated atomic wavepackets are optically detected via a pump-probe experiment based on axially phase-matched parametric four-wave mixing (FWM). This nonlinear process results in coherent ultraviolet (UV) or violet emission that carries information about the relative number densities of the excited states. The frequency spectrum of the UV/violet signal intensity, recorded while varying the pump-probe time delay, shows the presence of quantum beats between energy levels involved in the FWM process. The time-frequency analysis of that temporal UV/violet data is done by means of the short-time Fourier transform that leads to retrieval of the temporal evolution of amplitude and phase of the quantum beats. The observed dynamics suggest that not only atomic but also molecular ( Rb*2 ) wavepackets are generated, and that the temporal history of the amplitude of the quantum beats reflects the production of the excited atomic fragments of Rb*2 dissociation. More precisely, changes in the Rb excited state number densities alter the third-order nonlinear susceptibility chi(3) of the Rb vapor, which affects generation of the output signal wave by FWM. Dissociation into several product states is detected, and their branching ratios are estimated. Thus, atomic wavepackets, combined with FWM, appear to be a sensitive new multichannel spectroscopic means to study the fundamental process of molecular dissociation.

•Jan 1, 2003•0 citations

On the non-linear spectroscopy including saturated absorption and four-wave mixing in two and multi-level atoms: a computational study

M Patel, Gerhard De Jager, Z Nkosi +2 more

In this paper we report on the study of two and multi-level atoms interacting with multiple laser beams. The semi-classical approach is used to describe the system in which the atoms are treated quantum mechanically via the density matrix operator, while the laser beams are treated classically using Maxwells equations. We present results of a two level atom interacting with single and multiple laser beams and demonstrate Rabi oscillations between the levels. The effects of laser modulation on the dynamics of the atom (atomic populations and coherences) are examined by solving the optical Bloch equations. Plots of the density matrix elements as a function of time are presented for various parameters such as laser intensity, detuning, modulation etc. In addition, phase-space plots and Fourier analysis of the density matrix elements are provided. The atomic polarization, estimated from the coherence terms of the density matrix elements, is used in the numerical solution of Maxwells equations to determine the behaviour of the laser beams as they propagate through the atomic ensemble. The effects of saturation and hole-burning are demonstrated in the case of two counter propagating beams with one being a strong beam and the other being very weak. The above work is extended to include four-wave mixing in four level atoms in a diamond configuration. Two co-propagating beams of different wavelengths drive the atoms from a ground state |1〉 to an excited state |3〉 via an intermediate state |2〉. The atoms then move back to the ground state via another intermediate state |4〉, resulting in the generation of two additional correlated photon beams. The characteristics of these additional photons are studied.

Journal of Physics Conference Series•Oct 1, 2017•0 citations

Intermixing between four-wave mixing and six-wave mixing in a four-level atomic system

Yanpeng Zhang, Andy W. Brown, Chenli Gan +1 more

We investigate the interplay between six-wave mixing (SWM) and four-wave mixing (FWM) resulting from atomic coherence and polarization beat in a four-level atomic system. The dressed FWM evolution and competition pathways can be controlled by the coupling field to exhibit two FWM and SWM turning points, FWM+SWM, and FWM+FWM interference regions. Quantum interference between two FWM or one FWM and one SWM channels leads to nonlinear signal enhancement and suppression under different conditions. The fifth-order nonlinear response can be obtained by the phase control of the polarization beat between the FWM and SWM signals.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 15, 2007•10 citations

Four-wave mixing and terahertz emission from three-level systems in quantum wells: Effects of inhomogeneous broadening

Xuejun Zhu, Mark S. Hybertsen, P. B. Littlewood +1 more

Using a perturbation theory based on the density-matrix formulation, we study the nonlinear optical responses of a noninteracting three-level model system to consecutive coherent pulsed excitations, as realized in several recent experiments involving excitonic transitions in quantum wells. The terahertz emission, which is a second-order response, and the four-wave mixing signal, a third-order response, are calculated within the rotating-wave approximation, in the presence of detuning, dephasing, and inhomogeneous broadening. We study the quantum beats in the photon echo from transient four-wave mixing experiments of a three-level system. We find that the temporal profile of the photon echo signal in the four-wave mixing experiments depends very strongly on the amount of inhomogeneous broadening of the energy levels involved. Both the position and the intensity of the peaks exhibit a smooth evolution from strong quantum beats to a conventional photon echo as the inhomogeneous broadening increases. These features from our noninteracting model system are compared with a recent experiment, and found to account for a number of experimental observations.

arXiv:cond-mat/9411118•Physical review. B, Condensed matter•Oct 15, 1994•7 citations
A theoretical model consisting of 5 energy levels in coupled four-wave mixing processes was proposed to analyze the coherent characteristics of atomic wavepackets using perturbative theory. The equations of motions of the density matrix were derived and the third-order density matrix elements were presented. Under the condition that the duration of laser pulses is sufficiently short, the system response was treated as impulse response. Moreover, in the lowest order perturbation theory, the third-order nonlinear polarization was obtained using rotating-wave approximation. The results show that multiple quantum beats are embedded in the coupled four-wave mixing signals, and coherent dynamics of wavepackets can be retrieved from the quantum beat dynamics.
A theoretical model of coupled four-wave mixing (FWM) processes comprising five atomic energy levels was proposed to investigate the coherent characteristics of atomic wave packets using perturbation theory. As several states in atoms are coherently excited by a two-photon transition, triple coupled FWM can be produced, and triple quantum beats associated with the atomic energy levels are embedded in the FWM signals. Triple coupled FWM processes were achieved experimentally in Rb vapor by two-photon excitation using broadband optical pulses. A pump–probe scheme was utilized to record the time-varying FWM signals, and Fourier transform was applied to retrieve the quantum beats. Furthermore, short-time Fourier transform was implemented to investigate the dynamics of quantum beats. The results show that the coherent characteristics of atomic wave packets, which are intimately related to the dynamics of quantum beats, can be probed by coupled nonlinear optical wave mixing.
A theoretical model consisting of 5 energy levels, with the three upper states coherently excited, was proposed to analyze the coherent characteristics of atomic wave packets using perturbative theory. Pump-probe technique was implemented to detect coupled difference frequency four-wave mixing processes for studying the coherent characteristics of Rb atomic wave packets. Quantum beats were extracted the time domain signal by Fourier transform. Moreover, the variation of quantum beats was gained by time-dependent Fourier transform. The results show that the coherent characteristics of alkali metal atomic wave packets are closely related to quantum beats embedded in the time delayed four-wave mixing signal. Theoretical results are consistent with experimental observations, possessing potential applications in multi-channel information encoding and decoding.
Wavepackets are excited in rubidium vapor by intense ultrashort (∼100 fs) pulses centered at a wavelength of 620 nm or 770 nm. The generated atomic wavepackets are optically detected via a pump-probe experiment based on axially phase-matched parametric four-wave mixing (FWM). This nonlinear process results in coherent ultraviolet (UV) or violet emission that carries information about the relative number densities of the excited states. The frequency spectrum of the UV/violet signal intensity, recorded while varying the pump-probe time delay, shows the presence of quantum beats between energy levels involved in the FWM process. The time-frequency analysis of that temporal UV/violet data is done by means of the short-time Fourier transform that leads to retrieval of the temporal evolution of amplitude and phase of the quantum beats. The observed dynamics suggest that not only atomic but also molecular ( Rb*2 ) wavepackets are generated, and that the temporal history of the amplitude of the quantum beats reflects the production of the excited atomic fragments of Rb*2 dissociation. More precisely, changes in the Rb excited state number densities alter the third-order nonlinear susceptibility chi(3) of the Rb vapor, which affects generation of the output signal wave by FWM. Dissociation into several product states is detected, and their branching ratios are estimated. Thus, atomic wavepackets, combined with FWM, appear to be a sensitive new multichannel spectroscopic means to study the fundamental process of molecular dissociation.
In this paper we report on the study of two and multi-level atoms interacting with multiple laser beams. The semi-classical approach is used to describe the system in which the atoms are treated quantum mechanically via the density matrix operator, while the laser beams are treated classically using Maxwells equations. We present results of a two level atom interacting with single and multiple laser beams and demonstrate Rabi oscillations between the levels. The effects of laser modulation on the dynamics of the atom (atomic populations and coherences) are examined by solving the optical Bloch equations. Plots of the density matrix elements as a function of time are presented for various parameters such as laser intensity, detuning, modulation etc. In addition, phase-space plots and Fourier analysis of the density matrix elements are provided. The atomic polarization, estimated from the coherence terms of the density matrix elements, is used in the numerical solution of Maxwells equations to determine the behaviour of the laser beams as they propagate through the atomic ensemble. The effects of saturation and hole-burning are demonstrated in the case of two counter propagating beams with one being a strong beam and the other being very weak. The above work is extended to include four-wave mixing in four level atoms in a diamond configuration. Two co-propagating beams of different wavelengths drive the atoms from a ground state |1〉 to an excited state |3〉 via an intermediate state |2〉. The atoms then move back to the ground state via another intermediate state |4〉, resulting in the generation of two additional correlated photon beams. The characteristics of these additional photons are studied.
We investigate the interplay between six-wave mixing (SWM) and four-wave mixing (FWM) resulting from atomic coherence and polarization beat in a four-level atomic system. The dressed FWM evolution and competition pathways can be controlled by the coupling field to exhibit two FWM and SWM turning points, FWM+SWM, and FWM+FWM interference regions. Quantum interference between two FWM or one FWM and one SWM channels leads to nonlinear signal enhancement and suppression under different conditions. The fifth-order nonlinear response can be obtained by the phase control of the polarization beat between the FWM and SWM signals.
Using a perturbation theory based on the density-matrix formulation, we study the nonlinear optical responses of a noninteracting three-level model system to consecutive coherent pulsed excitations, as realized in several recent experiments involving excitonic transitions in quantum wells. The terahertz emission, which is a second-order response, and the four-wave mixing signal, a third-order response, are calculated within the rotating-wave approximation, in the presence of detuning, dephasing, and inhomogeneous broadening. We study the quantum beats in the photon echo from transient four-wave mixing experiments of a three-level system. We find that the temporal profile of the photon echo signal in the four-wave mixing experiments depends very strongly on the amount of inhomogeneous broadening of the energy levels involved. Both the position and the intensity of the peaks exhibit a smooth evolution from strong quantum beats to a conventional photon echo as the inhomogeneous broadening increases. These features from our noninteracting model system are compared with a recent experiment, and found to account for a number of experimental observations.