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

Physical Review Letters

Quantum Beats and Quantum Mechanics

I. R. Senitzky

Published Dec 29, 1975• 18 citations
Publisher

Abstract

Quantum beats are analyzed by means of a boson-type second-quantization method which exhibits the collective behavior of $n$-level systems and displays both quantum mechanical and classical (or semiclassical) results. Theoretical criteria for predicting the existence of beats are found which differ from those in the recent literature and indicate a reevaluation of suggested experiments.

DOI
10.1103/physrevlett.35.1755

Related papers

Description of n -level systems in cooperative behavior. III. Quantum beats

I. R. Senitzky

Quantum beats in the radiation field of "three-level" atoms are analyzed by means of a previously developed boson-second-quantization (BSQ) formalism. Two types of atoms are considered: type I, in which beats are due to transitions from each of two closely spaced upper levels to a single lower level, and type II, in which beats are due to transitions between a single upper level and each of two closely spaced lower levels. This classification is motivated by the claim found in the literature that semiclassical theory and quantum theory give qualitatively different results concerning the existence of beats in the case of type-II atoms. The terminology associated with beats is made precise by distinguishing between amplitude modulation at the beat frequency of the transition frequency field $E$, and the existence of a spectral component at the beat frequency in ${E}^{2}$. With respect to the former, no qualitative difference is found in the predictions from semiclassical theory and quantum theory; with respect to the latter, results that appear paradoxical from an intuitive viewpoint are discussed. It is shown that for the case in which the atoms are all in the same coherent superposition of energy states, with all levels occupied, semiclassical and quantum-mechanical results become equivalent as the number of atoms increases. Reference is made to the disturbance caused by the measurement processes in the case of a single atom. The essential difference in spontaneous emission beats between type-I and type-II atoms [with the ground state(s) unoccupied] is explained by the fact that the phase of the beat amplitude may be determined by preparation of the initial state in type-I atoms but may not be determined in type-II atoms.

Physical Review A•Jan 1, 1977•10 citations

Description of n -level systems in cooperative behavior. II. Energy states, coherent states, and classical limit theories

I. R. Senitzky

This paper discusses the suitability of a boson-second-quantization (BSQ) formalism for the description of cooperative atomic behavior---such as that encountered in quantum optics or laser-type phenomena. The physical significance of BSQ energy states and atomic coherent states, as well as the corresponding first quantization descriptions, are discussed. Specialization to the case in which the individual atomic systems are characterized by two levels allows comparison of the BSQ theory with other theories of cooperative behavior, not all of which can be generalized to the case of more than two levels. Passage to the classical limit, an analytical process that must be possible for macroscopic phenomena, is shown to be accomplished very simply in the BSQ formalism by conversion of the small number of collective (quantum mechanical) variables to classical random variables which are prescribed according to the quantum state of the total system. It is found that conventional semiclassical theory is a special case of the fully classical limit of the BSQ formalism, the specialization being the requirement that the system be in an atomic coherent state. The justification for the identification of coherent states with a classical description and energy states with a quantum-mechanical description, found in some of the literature on two-level systems, is questioned.

Physical Review A•Jan 1, 1977•10 citations

Theoretical Treatments of Quantum Beats

Michitoshi Hayashi, Ruey‐Feng Chang, Kuo Kan Liang +6 more

Basic theoretical treatments of quantum beats are presented using the effective Hamiltonian method and the density matrix method. To describe the states involved in quantum beats, the molecular-eigen state basis set and the zeroth order basis set are introduced. Based on these basis sets for the two-state model, the condition under which molecular coherence can be created is discussed.

Journal of Applied Science and Engineering•Sep 1, 2000•0 citations

A. Fluctuation phenomena in quantum optics. B. The construction of a CO 2 TEA laser

Chi‐Wai Chow

This dissertation may be divided into three parts. In the first part we propose and analyze the use of quantum beat phenomena to test neoclassical radiation theory (NCT) and quantum electrodynamics CQED). For a beam foil type of experiment with atoms having one upper level and two closely spaced lower levels, all coherently excited, NCT predicts the presence of quantum beats in the emitted radiation; beats are not expected in QED. QED predicts beats when many atoms are pres­ ent, in agreement with recent photon-echo experiments. An experiment to test NCT and QED is suggested. In the second part of this dissertation we calculate, via the quantum noise operator approach, the power spectral density of a laser subjected to a symmetry-breaking injected signal. The resulting spec­ trum is sharpened. It is further noted that these considerations are potentially of interest in producing high intensity fields in small focal volumes. The final portion of this dissertation contains a description of a high power CO2 TEA laser that was built for use in laser isotope separation experiments. This laser, whose output pulses are each of the order of a few joules, will be used in studies concerning the laser enrichment of SF^ and the temporal behavior of hot electrons in InSb.

•Aug 1, 1975•0 citations

Multilevel quantum beats: An analytical approach

C. Leichtle, Ilya Sh. Averbukh, W. P. Schleich

We study the temporal behavior of generic transient signals originating from multilevel quantum systems. Such signals typically arise in the physics of wave packets in atoms, molecules, cavity QED, and ion traps and consist of a sum of a large number of harmonics whose frequencies depend nonlinearly on the sequential number of the harmonic. In particular, we focus on the semiclassical limit. Here, quantum beats between individual terms in the underlying sum lead to characteristic features of the signal in different time regimes, such as collapse, fractional revivals, and full revivals. We present a universal recipe for describing analytically all of the details of these features. Our approach is based on a specific representation of the sum of harmonics, which is most convenient in each of these time regions of interest. This brings out in a most natural way the phenomenon of fractional revivals and full revivals and explains their fine structures observed in recent experiments. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Dec 1, 1996•93 citations

Quantum-beat phenomena described by quantum electrodynamics and neoclassical theory

Weng W. Chow, Marlan O. Scully, John O. Stoner

We propose and analyze the use of quantum-beat phenomena to test neoclassical radiation theory (NCT) and quantum electrodynamics (QED). For a beam-foil type of experiment with atoms having one upper level and two closely spaced lower levels, all coherently excited, NCT predicts the presence of quantum beats in the emitted radiation; beats are not expected in QED. QED predicts beats when many atoms are present, in agreement with recent photon-echo experiments. An experiment to test NCT and QED is suggested.

Physical Review A•Apr 1, 1975•100 citations
Quantum beats are analyzed by means of a boson-type second-quantization method which exhibits the collective behavior of nnn-level systems and displays both quantum mechanical and classical (or semiclassical) results. Theoretical criteria for predicting the existence of beats are found which differ from those in the recent literature and indicate a reevaluation of suggested experiments.
Quantum beats in the radiation field of "three-level" atoms are analyzed by means of a previously developed boson-second-quantization (BSQ) formalism. Two types of atoms are considered: type I, in which beats are due to transitions from each of two closely spaced upper levels to a single lower level, and type II, in which beats are due to transitions between a single upper level and each of two closely spaced lower levels. This classification is motivated by the claim found in the literature that semiclassical theory and quantum theory give qualitatively different results concerning the existence of beats in the case of type-II atoms. The terminology associated with beats is made precise by distinguishing between amplitude modulation at the beat frequency of the transition frequency field EEE, and the existence of a spectral component at the beat frequency in E2{E}^{2}E2. With respect to the former, no qualitative difference is found in the predictions from semiclassical theory and quantum theory; with respect to the latter, results that appear paradoxical from an intuitive viewpoint are discussed. It is shown that for the case in which the atoms are all in the same coherent superposition of energy states, with all levels occupied, semiclassical and quantum-mechanical results become equivalent as the number of atoms increases. Reference is made to the disturbance caused by the measurement processes in the case of a single atom. The essential difference in spontaneous emission beats between type-I and type-II atoms [with the ground state(s) unoccupied] is explained by the fact that the phase of the beat amplitude may be determined by preparation of the initial state in type-I atoms but may not be determined in type-II atoms.
This paper discusses the suitability of a boson-second-quantization (BSQ) formalism for the description of cooperative atomic behavior---such as that encountered in quantum optics or laser-type phenomena. The physical significance of BSQ energy states and atomic coherent states, as well as the corresponding first quantization descriptions, are discussed. Specialization to the case in which the individual atomic systems are characterized by two levels allows comparison of the BSQ theory with other theories of cooperative behavior, not all of which can be generalized to the case of more than two levels. Passage to the classical limit, an analytical process that must be possible for macroscopic phenomena, is shown to be accomplished very simply in the BSQ formalism by conversion of the small number of collective (quantum mechanical) variables to classical random variables which are prescribed according to the quantum state of the total system. It is found that conventional semiclassical theory is a special case of the fully classical limit of the BSQ formalism, the specialization being the requirement that the system be in an atomic coherent state. The justification for the identification of coherent states with a classical description and energy states with a quantum-mechanical description, found in some of the literature on two-level systems, is questioned.
This dissertation may be divided into three parts. In the first part we propose and analyze the use of quantum beat phenomena to test neoclassical radiation theory (NCT) and quantum electrodynamics CQED). For a beam foil type of experiment with atoms having one upper level and two closely spaced lower levels, all coherently excited, NCT predicts the presence of quantum beats in the emitted radiation; beats are not expected in QED. QED predicts beats when many atoms are pres­ ent, in agreement with recent photon-echo experiments. An experiment to test NCT and QED is suggested. In the second part of this dissertation we calculate, via the quantum noise operator approach, the power spectral density of a laser subjected to a symmetry-breaking injected signal. The resulting spec­ trum is sharpened. It is further noted that these considerations are potentially of interest in producing high intensity fields in small focal volumes. The final portion of this dissertation contains a description of a high power CO2 TEA laser that was built for use in laser isotope separation experiments. This laser, whose output pulses are each of the order of a few joules, will be used in studies concerning the laser enrichment of SF^ and the temporal behavior of hot electrons in InSb.
We study the temporal behavior of generic transient signals originating from multilevel quantum systems. Such signals typically arise in the physics of wave packets in atoms, molecules, cavity QED, and ion traps and consist of a sum of a large number of harmonics whose frequencies depend nonlinearly on the sequential number of the harmonic. In particular, we focus on the semiclassical limit. Here, quantum beats between individual terms in the underlying sum lead to characteristic features of the signal in different time regimes, such as collapse, fractional revivals, and full revivals. We present a universal recipe for describing analytically all of the details of these features. Our approach is based on a specific representation of the sum of harmonics, which is most convenient in each of these time regions of interest. This brings out in a most natural way the phenomenon of fractional revivals and full revivals and explains their fine structures observed in recent experiments. \textcopyright{} 1996 The American Physical Society.
We propose and analyze the use of quantum-beat phenomena to test neoclassical radiation theory (NCT) and quantum electrodynamics (QED). For a beam-foil type of experiment with atoms having one upper level and two closely spaced lower levels, all coherently excited, NCT predicts the presence of quantum beats in the emitted radiation; beats are not expected in QED. QED predicts beats when many atoms are present, in agreement with recent photon-echo experiments. An experiment to test NCT and QED is suggested.