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

IEEE Journal of Quantum Electronics

4C1 - Nonlinear effects in an NMR experiment

J. Pommier, H. Benoit

Published Sep 1, 1966• 3 citations
Publisher

Abstract

We have studied multiple-photon transition in a low-field nuclear magnetic resonance (NMR) experiment. It is well known that a saturation of the NMR occurs when using a sufficiently high alternating magnetic field which induces multiple-photons transitions. We show theoretically that these multiphoton transitions are accompanied by an harmonic generation. For an-photon transition, this generation occurs mostly on thenth and (n \pm 1)th harmonic. For an irradiating field2H_{1} \cos \omegat of pulsation ω such thatn\omega= \gamma H_{0}=\omega_{0}where H0is the steady field and θ is the angle between H0and H1the amplitudesS\min{n}\max{n}andS\min{n}\max{n+1}of these components are given byS\min{n}\max{n} = f_{n}(\theta) (H_{1})^{n},S\min{n}\max{n+1} = \cos \theta f_{n}(\theta) (H_{1})^{n+1}. We have verified these equations in a low-field NMR experiment (H_{0} = 0.7Gs/s), polarizing first a flowing liquid in a high magnetic field. The liquid then flows in a modified Bloch spectrometer. The receiving coil is still perpendicular to the steady field but it is possible to adjust the angle θ between the axis of the emission coils (H1field) and the steady-field H0. Using a synchronous detection at the output of the receiving coil on the pulsation(n - 1) \omega, n\omega, or(n + 1) \omega, we have directly detected multiphoton transistions. The above equations have been verified forn = 2ton = 5. There are slight discrepancies at high excitation which may be explained taking into account a large saturation.

DOI
10.1109/jqe.1966.1074071

Related papers

Four-field excitation of multiphoton NMR resonances in spin I=(1/2)

Eric M. Krauss, Shimon Vega

The use of four pulsed rf fields for the excitation of multiphoton resonances in a two-level system is investigated. A general theoretical description of the experiment is provided based on the Floquet formalism and application of basic conservation laws to the overall transition process. The predictions of the theory are compared with computer simulations of the time evolution of the magnetization according to the exact time-dependent Hamiltonian. It is shown that N-photon resonances occur when the fields are applied at frequencies \ifmmode\pm\else\textpm\fi{}k\ensuremath{\omega} and \ifmmode\pm\else\textpm\fi{}l\ensuremath{\omega} from the Larmor frequency, where k and l are positive integers having no common factors and where 0\ensuremath{\le}k<l, k+l=N. For any resonance k photons are taken from the outer field pair and l are taken from the inner field pair. A total of 2[(l+k)!]/(k!l!) mutually interfering transition pathways exist for the overall process and the resultant magnitude of the effective N-photon field is very sensitive to the relative initial phases of the rf fields. The spiral motion observed for multiphoton resonances induced by double-frequency irradiation is absent here when the field intensities are symmetrical. In addition, the fraction of total applied rf intensity available for multiphoton pumping is considerably greater than for two fields. Phase cycling to enhance detection of multiphoton effects and multiphoton spin locking are considered.

Physical Review A•Jul 1, 1986•27 citations

Saturation effects in magnetic resonances for a general magnetic field configuration

Noriaki Tsukada, T. Koyama, Toru Ogawa

Various magnetic resonances appearing in optical pumping experiments have been analysed theoretically and experimentally. However, there is little work on the saturation effects caused by strong RF fields. Recently, The saturation effects of the multiple quantum resonances and of the Haroche resonances have been investigated by Stenholm (1972) and by Tsukada and Ogawa (1973). The saturation effects are treated for the more general case of a static magnetic field in an arbitrary direction with respect to the oscillating RF field. The experimental results are compared with the exact solutions computed by the numerical integration of the Bloch equation. It is shown experimentally and theoretically that the resonances similar to the Haroche resonance appear at omega /sub ///=n omega , where omega /sub ///= gamma H/sub ///, n is an integer, H/sub /// is the parallel component of the static magnetic field with respect to the oscillating RF field, and gamma is the gyromagnetic ratio.

Journal of Physics B Atomic and Molecular Physics•May 11, 1974•10 citations

Synchronization with harmonics in an injected nuclear-magnetic-resonance laser

Yu. V. Pavlov, А.Н. Пивкин, R. M. Umarkhodzhaev +1 more

In injected lasers, only synchronization of the order $1/1$ (when a frequency of laser oscillations becomes equal to the master laser frequency) is usually observed. Such locking appears due to single-photon transitions in a laser. We show that with the use of multiple-photon transitions a higher-order synchronization can arise. We present the results of numerical simulations and the preliminary experimental observations, which demonstrate that in the mercury NMR laser, with the use of triple-photon transitions, a frequency of locked laser oscillations becomes three times higher than the frequency of an external rf magnetic field. Such synchronization appears only in the case of a linearly polarized (oscillating) external magnetic field. For the circularly polarized (rotating) external field, only synchronization of the order $1/1$ is possible.

Physical Review A•Sep 8, 2010•2 citations

Multiphoton nonlinear frequency mixing effects on the coherent electromagnetically induced absorption spectra of Rb85 atoms under a longitudinal magnetic field: Theory and experiment

Zeeshan Ali Safdar Jadoon, Heung‐Ryoul Noh, Jin‐Tae Kim

Multiphoton nonlinear frequency mixing effects on coherent electromagnetically induced absorption spectra of $^{85}\mathrm{Rb}$ atoms using two orthogonal linear polarizations of strong-coupling and weak probe beams are investigated theoretically and experimentally with respect to an applied longitudinal magnetic field and coupling powers. Herein, we confirm that at least five-photon interactions in solving density matrix equations for the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of $^{85}\mathrm{Rb}$ atoms are required to explain experimentally observed coherent electromagnetically induced absorption spectra when a quantum axis is selected as the propagation direction of co-propagating coupling and probe laser beams. Distinct calculated spectral differences owing to variations in the magnetic field and coupling power between three- and five-photon interactions are confirmed. The obtained asymmetrical spectral shapes match very well with those calculated from five-photon interactions considering the off-resonant ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=2,3$ transitions. Genuine coherent spectral shapes are observed with a single laser combined with two acousto-optic modulators, wherein the spectral resolution is limited because of the decoherence rate between Zeeman sublevels in the ground state from transit-time relaxation.

Physical Review A•Dec 22, 2020•8 citations

Response to Double Irradiation of a Nuclear Spin System: General Treatment and New Multiple Quantum Transitions

Pietro Bucci, Massimo Martinelli, S. Santucci

A general theory has been developed to calculate the response, in NMR conditions, of a spin system irradiated by two nearly resonant waves having different frequencies and intense enough to produce an appreciable saturation. The absorption signal has been calculated employing the statistical operator technique, treating the electromagnetic field by the second quantization formalism. Two kinds of transitions are expected: The first one arises from processes in which n photons of one wave are emitted and n photons of the other wave are absorbed, the second one arises from processes involving the emission of n photons of one wave and the absorption of n ± 1 photons of the other. In the first case all the transitions coalesce in a single dispersionlike signal, which occurs when the frequencies of the two waves are nearly the same; in the second case a many-line spectrum occurs in which emission and absorption lines are present. The experimental results here reported strictly agree with theoretical previsions.

The Journal of Chemical Physics•Dec 15, 1970•49 citations

Magnetic resonance in quantum computing and in accurate measurements of the nuclear moments of atoms and molecules

Zhichen Liu, Richard A. Klemm

Modern experimental techniques can generate magnetic fields of the form H(t) = H0 z-hat + H1 [x-hat cos(ωt) + y-hat sin(ωt)], at frequencies within an order of magnitude of the nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) frequencies, ωn0 and ωe0, respectively, when acting on atoms or molecules. We derive simple closed-form expressions for the exact nuclear- and electronic-spin wave functions that enable controlled transitions between entangled states, allowing an atom or molecule to function as a quantum computer. These solutions also enable precise NMR or EPR measurements of nuclear moments in atoms and molecules. We present examples relevant to measurements of the nuclear moments of 14N, 7Li, and 133Cs. Because existing hyperfine measurements of the lowest three nuclear moments of 133Cs are mutually inconsistent, the proposed NMR/EPR experiments provide a route to measuring all seven of its nuclear moments with high precision.

arXiv:2602.11233•Feb 11, 2026•0 citations
We have studied multiple-photon transition in a low-field nuclear magnetic resonance (NMR) experiment. It is well known that a saturation of the NMR occurs when using a sufficiently high alternating magnetic field which induces multiple-photons transitions. We show theoretically that these multiphoton transitions are accompanied by an harmonic generation. For an-photon transition, this generation occurs mostly on thenth and (n \pm 1)th harmonic. For an irradiating field2H_{1} \cos \omegat of pulsation ω such thatn\omega= \gamma H_{0}=\omega_{0}where H0is the steady field and θ is the angle between H0and H1the amplitudesS\min{n}\max{n}andS\min{n}\max{n+1}of these components are given byS\min{n}\max{n} = f_{n}(\theta) (H_{1})^{n},S\min{n}\max{n+1} = \cos \theta f_{n}(\theta) (H_{1})^{n+1}. We have verified these equations in a low-field NMR experiment (H_{0} = 0.7Gs/s), polarizing first a flowing liquid in a high magnetic field. The liquid then flows in a modified Bloch spectrometer. The receiving coil is still perpendicular to the steady field but it is possible to adjust the angle θ between the axis of the emission coils (H1field) and the steady-field H0. Using a synchronous detection at the output of the receiving coil on the pulsation(n - 1) \omega, n\omega, or(n + 1) \omega, we have directly detected multiphoton transistions. The above equations have been verified forn = 2ton = 5. There are slight discrepancies at high excitation which may be explained taking into account a large saturation.
The use of four pulsed rf fields for the excitation of multiphoton resonances in a two-level system is investigated. A general theoretical description of the experiment is provided based on the Floquet formalism and application of basic conservation laws to the overall transition process. The predictions of the theory are compared with computer simulations of the time evolution of the magnetization according to the exact time-dependent Hamiltonian. It is shown that N-photon resonances occur when the fields are applied at frequencies \ifmmode\pm\else\textpm\fi{}k\ensuremath{\omega} and \ifmmode\pm\else\textpm\fi{}l\ensuremath{\omega} from the Larmor frequency, where k and l are positive integers having no common factors and where 0\ensuremath{\le}k<l, k+l=N. For any resonance k photons are taken from the outer field pair and l are taken from the inner field pair. A total of 2[(l+k)!]/(k!l!) mutually interfering transition pathways exist for the overall process and the resultant magnitude of the effective N-photon field is very sensitive to the relative initial phases of the rf fields. The spiral motion observed for multiphoton resonances induced by double-frequency irradiation is absent here when the field intensities are symmetrical. In addition, the fraction of total applied rf intensity available for multiphoton pumping is considerably greater than for two fields. Phase cycling to enhance detection of multiphoton effects and multiphoton spin locking are considered.
Various magnetic resonances appearing in optical pumping experiments have been analysed theoretically and experimentally. However, there is little work on the saturation effects caused by strong RF fields. Recently, The saturation effects of the multiple quantum resonances and of the Haroche resonances have been investigated by Stenholm (1972) and by Tsukada and Ogawa (1973). The saturation effects are treated for the more general case of a static magnetic field in an arbitrary direction with respect to the oscillating RF field. The experimental results are compared with the exact solutions computed by the numerical integration of the Bloch equation. It is shown experimentally and theoretically that the resonances similar to the Haroche resonance appear at omega /sub ///=n omega , where omega /sub ///= gamma H/sub ///, n is an integer, H/sub /// is the parallel component of the static magnetic field with respect to the oscillating RF field, and gamma is the gyromagnetic ratio.
In injected lasers, only synchronization of the order 1/11/11/1 (when a frequency of laser oscillations becomes equal to the master laser frequency) is usually observed. Such locking appears due to single-photon transitions in a laser. We show that with the use of multiple-photon transitions a higher-order synchronization can arise. We present the results of numerical simulations and the preliminary experimental observations, which demonstrate that in the mercury NMR laser, with the use of triple-photon transitions, a frequency of locked laser oscillations becomes three times higher than the frequency of an external rf magnetic field. Such synchronization appears only in the case of a linearly polarized (oscillating) external magnetic field. For the circularly polarized (rotating) external field, only synchronization of the order 1/11/11/1 is possible.
Multiphoton nonlinear frequency mixing effects on coherent electromagnetically induced absorption spectra of 85Rb^{85}\mathrm{Rb}85Rb atoms using two orthogonal linear polarizations of strong-coupling and weak probe beams are investigated theoretically and experimentally with respect to an applied longitudinal magnetic field and coupling powers. Herein, we confirm that at least five-photon interactions in solving density matrix equations for the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of 85Rb^{85}\mathrm{Rb}85Rb atoms are required to explain experimentally observed coherent electromagnetically induced absorption spectra when a quantum axis is selected as the propagation direction of co-propagating coupling and probe laser beams. Distinct calculated spectral differences owing to variations in the magnetic field and coupling power between three- and five-photon interactions are confirmed. The obtained asymmetrical spectral shapes match very well with those calculated from five-photon interactions considering the off-resonant ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=2,3$ transitions. Genuine coherent spectral shapes are observed with a single laser combined with two acousto-optic modulators, wherein the spectral resolution is limited because of the decoherence rate between Zeeman sublevels in the ground state from transit-time relaxation.
A general theory has been developed to calculate the response, in NMR conditions, of a spin system irradiated by two nearly resonant waves having different frequencies and intense enough to produce an appreciable saturation. The absorption signal has been calculated employing the statistical operator technique, treating the electromagnetic field by the second quantization formalism. Two kinds of transitions are expected: The first one arises from processes in which n photons of one wave are emitted and n photons of the other wave are absorbed, the second one arises from processes involving the emission of n photons of one wave and the absorption of n ± 1 photons of the other. In the first case all the transitions coalesce in a single dispersionlike signal, which occurs when the frequencies of the two waves are nearly the same; in the second case a many-line spectrum occurs in which emission and absorption lines are present. The experimental results here reported strictly agree with theoretical previsions.
Modern experimental techniques can generate magnetic fields of the form H(t) = H0 z-hat + H1 [x-hat cos(ωt) + y-hat sin(ωt)], at frequencies within an order of magnitude of the nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) frequencies, ωn0 and ωe0, respectively, when acting on atoms or molecules. We derive simple closed-form expressions for the exact nuclear- and electronic-spin wave functions that enable controlled transitions between entangled states, allowing an atom or molecule to function as a quantum computer. These solutions also enable precise NMR or EPR measurements of nuclear moments in atoms and molecules. We present examples relevant to measurements of the nuclear moments of 14N, 7Li, and 133Cs. Because existing hyperfine measurements of the lowest three nuclear moments of 133Cs are mutually inconsistent, the proposed NMR/EPR experiments provide a route to measuring all seven of its nuclear moments with high precision.