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

Concepts in Magnetic Resonance

Concepts of NMR in quantum optics

Erwin Louis Hahn

Published Jan 1, 1997• 16 citations
Publisher

Abstract

Coherent, continuous-wave and pulsed-laser response of optical two-level systems are reviewed in terms of optical Bloch-Maxwell equations. The concept of the macroscopic magnetic moment reaction “radiation damping” field in NMR is extended to account for the threshold condition for maser-laser action in a cavity and for propagating optical, coherent, transient free-induction signals emitted by macroscopic electric dipole moments. Analogues of NMR in coherent optical transients are listed. A brief history is presented of early developments in magnetic resonace, leading to application of the Bloch equations to the semiclassical description of electric dipole two-level systems. © 1997 John Wiley & Sons, Inc.

DOI
10.1002/(sici)1099-0534(1997)9:2<69::aid-cmr2>3.0.co;2-k

Related papers

Macroscopic optical coherence phenomena

Erwin Louis Hahn

Principles of coherent radiation are reviewed as they apply to the coherent interaction between two quantum Ievel atomic oscillators and classical radiation fields.The equivalence between electric dipole and magnetic dipole interactions is outlined for macroscopic systems.The power mechanism for formation of coherent signals is briefly calculated.The self-induced transparency mechanism and area-theorem connected with this mechanism serves as a means of predicting properties of photon echoes.It is stressed that when the classical field is a self-consistent solution to both the equations of the density matrix and Maxwell's equations a reaction field need not be added.

Pure and Applied Chemistry•Jan 1, 1972•0 citations

Dynamical model of coherent circularly polarized optical pulse interactions with two-level quantum systems

Gabriela M. Slavcheva, Ortwin G. Hess

We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.

Physical Review A•Nov 3, 2005•19 citations

A quantum description of radiation damping and the free induction signal in magnetic resonance

James S. Tropp

We apply the methods of cavity quantum electrodynamics (CQED), to obtain a microscopic and fully quantum-mechanical picture of radiation damping in magnetic resonance, and the nascent formation of the free induction signal. Numerical solution of the Tavis-Cummings model - i.e., multiple spins 1∕2 coupled to a lossless single-mode cavity - shows in fine detail the transfer of Zeeman energy, via spin coherence, to excite the cavity - represented here by a quantized LC resonator. The case of a single spin is also solved analytically. Although the motion of the Bloch vector is non-classical, we nonetheless show that the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission) gives realistic estimates of macroscopic signal strength and the radiation damping constant in nuclear magnetic resonance. We also show how to introduce dissipation: cavity losses by means of a master equation, and relaxation by the phenomenological method of Bloch. The failure to obtain the full Bloch equations (unless semi-classical conditions are imposed on the cavity) is discussed in light of similar issues arising in CQED (and in earlier work in magnetic resonance as well), as are certain problems relative to quantization of the electromagnetic near-field.

The Journal of Chemical Physics•Jul 2, 2013•5 citations

Coherence and Stimulated Emission in the Tavis-Cummings Model: A Quantum Description of the Free Induction Signal and Radiation Damping in Magnetic Resonance

James S. Tropp

We numerically solve the Liouville equation for the Tavis Cummings model of multiple spins coupled to a lossless single mode cavity, starting from an initial condition with small numbers of fully polarized spins tipped by a specified angle, and the cavity in its ground Fock state. Time evolution of the magnetizations and cavity states, following small to medium nutation by a classical field, yields a microscopic quantum mechanical picture of radiation damping in magnetic resonance, and the formation of the free induction signal, that is, the transfer of Zeeman energy, via spin coherence, to cavity coherence. Although the motion of the Bloch vector is nonclassical, our quantum description is related to the macroscopic picture of NMR reception, by showing the close relationship between the usual radiation damping constant, and the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission.) That is, each is the product, of a nutation rate per oscillator current, and a current. Although the current in the damping constant is explicitly limited by cavity losses, which do not enter the formula for the Rabi frequency, we nonetheless show (in an appendix) how these losses can be introduced into our problem by means of a master equation. Numerical solution of the classical Bloch-Kirchhoff equations reinforces the conclusion that the strength of the free induction

arXiv:1210.0868•Oct 2, 2012•0 citations

Optical coherent transients: Generalized two-level solutions

Axel Schenzle, Richard G. Brewer

Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (${T}_{2}$) and population (${T}_{1}$) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime ${T}_{1}$ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.

Physical Review A•Nov 1, 1976•83 citations

Pulse Propagation Through a medium Consists of Two Three-Level Atoms

R. N. Rabea, M. A. El-Deberky, M. M. A. Ahmed

The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon.

Al-Azhar Bulletin of Science•Nov 29, 2021•0 citations
Coherent, continuous-wave and pulsed-laser response of optical two-level systems are reviewed in terms of optical Bloch-Maxwell equations. The concept of the macroscopic magnetic moment reaction “radiation damping” field in NMR is extended to account for the threshold condition for maser-laser action in a cavity and for propagating optical, coherent, transient free-induction signals emitted by macroscopic electric dipole moments. Analogues of NMR in coherent optical transients are listed. A brief history is presented of early developments in magnetic resonace, leading to application of the Bloch equations to the semiclassical description of electric dipole two-level systems. © 1997 John Wiley & Sons, Inc.
Principles of coherent radiation are reviewed as they apply to the coherent interaction between two quantum Ievel atomic oscillators and classical radiation fields.The equivalence between electric dipole and magnetic dipole interactions is outlined for macroscopic systems.The power mechanism for formation of coherent signals is briefly calculated.The self-induced transparency mechanism and area-theorem connected with this mechanism serves as a means of predicting properties of photon echoes.It is stressed that when the classical field is a self-consistent solution to both the equations of the density matrix and Maxwell's equations a reaction field need not be added.
We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.
We apply the methods of cavity quantum electrodynamics (CQED), to obtain a microscopic and fully quantum-mechanical picture of radiation damping in magnetic resonance, and the nascent formation of the free induction signal. Numerical solution of the Tavis-Cummings model - i.e., multiple spins 1∕2 coupled to a lossless single-mode cavity - shows in fine detail the transfer of Zeeman energy, via spin coherence, to excite the cavity - represented here by a quantized LC resonator. The case of a single spin is also solved analytically. Although the motion of the Bloch vector is non-classical, we nonetheless show that the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission) gives realistic estimates of macroscopic signal strength and the radiation damping constant in nuclear magnetic resonance. We also show how to introduce dissipation: cavity losses by means of a master equation, and relaxation by the phenomenological method of Bloch. The failure to obtain the full Bloch equations (unless semi-classical conditions are imposed on the cavity) is discussed in light of similar issues arising in CQED (and in earlier work in magnetic resonance as well), as are certain problems relative to quantization of the electromagnetic near-field.
We numerically solve the Liouville equation for the Tavis Cummings model of multiple spins coupled to a lossless single mode cavity, starting from an initial condition with small numbers of fully polarized spins tipped by a specified angle, and the cavity in its ground Fock state. Time evolution of the magnetizations and cavity states, following small to medium nutation by a classical field, yields a microscopic quantum mechanical picture of radiation damping in magnetic resonance, and the formation of the free induction signal, that is, the transfer of Zeeman energy, via spin coherence, to cavity coherence. Although the motion of the Bloch vector is nonclassical, our quantum description is related to the macroscopic picture of NMR reception, by showing the close relationship between the usual radiation damping constant, and the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission.) That is, each is the product, of a nutation rate per oscillator current, and a current. Although the current in the damping constant is explicitly limited by cavity losses, which do not enter the formula for the Rabi frequency, we nonetheless show (in an appendix) how these losses can be introduced into our problem by means of a master equation. Numerical solution of the classical Bloch-Kirchhoff equations reinforces the conclusion that the strength of the free induction
Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (T2{T}_{2}T2​) and population (T1{T}_{1}T1​) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime T1{T}_{1}T1​ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.
The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon.