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

arXiv:1008.3337 · Journal of Experimental and Theoretical Physics Letters

Decay of rabi oscillations induced by magnetic dipole interactions in dilute paramagnetic solids

E. I. Baibekov

Published May 1, 2011• 25 citations
arXivHTMLPDF

Abstract

Decay of Rabi oscillations of equivalent spins diluted in diamagnetic solid matrix and coupled by magnetic dipole interactions is theoretically studied. It is shown that these interactions result in random shifts of spin transient nutation frequencies and thus lead to the decay of the transient signal. Averaging over random spatial distribution of spins within the solid and over their spectral positions within magnetic resonance line, we obtain analytical expressions for the decay of Rabi oscillations. The rate of the decay in the case when the half-width of magnetic resonance line exceeds Rabi frequency is found to depend on the intensity of resonant microwave field and on the spin concentration. The results are compared with the literature data for E ′ 1 centers in glassy silica and [AlO 4 ] 0 centers in quartz.

DOI
10.1134/s002136401105002x

Related papers

Transient nutations decay in diluted paramagnetic solids: a radiation damping mechanism

N Ya Asadullina, T Ya Asadullin

Here, a theory of the intensity and concentration dependent damping of nutation signals observed by Boscaino et al. (Phys. Rev B 48, 7077 (1993); Phys. Rev. A 59, 4087 (1999)) and by others in various two-level spin systems is proposed. It is shown that in diluted paramagnetic solids contribution of dipole-dipole interaction to the nutation decay is negligibly small. We elaborated a cavity loss (radiation damping) mechanism that explains the intensity- and concentration dependence of the damping. It is shown that instead of ordinary Bloch's transverse T2 and longitudinal T1 damping parameters the decay of transverse and longitudinal spin components in nutation process are described by one and the same intensity-, concentration-, frequency- and time dependent damping parameter.

arXiv:1503.07641•Mar 26, 2015•1 citation

Effect of the Bloch-Siegert shift on the frequency responses of Rabi oscillations in the case of nutation resonance

A. P. Saǐko, Г. Г. Федорук

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω rf is close to the Rabi frequency ω 1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies n ω rf and n ω rf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω 1 − ω rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω rf + ɛ increases, while the amplitude at the difference frequency ω rf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E ′ 1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.

Journal of Experimental and Theoretical Physics Letters•Apr 1, 2008•25 citations

Effect of the Bloch-Siegert Shift on the Frequency Responses of Rabi Oscillations in the Case of Nutation Resonance

A. P. Saǐko, Fedoruk, G. G.

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω_{rf} is close to the Rabi frequency ω_{1} in a micro-wave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency εare accompanied by higher-frequency oscillations at frequencies nω_{rf} and nω_{rf}\pm ε, where n = 1, 2, .... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency εon the sign of the detuning ω{1} -ω{rf} from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω_{rf} +εincreases, while the amplitude at the difference frequency ω_{rf} -εdecreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.

arXiv:0806.0534•Jun 3, 2008•0 citations

Two-pulse nutational echo in spin systems

V. S. Kuz’min, Г. Г. Федорук

The decay of two-pulse nutational echo has been experimentally investigated in S equals 1/2 spin systems (E' centers in silica) at microwave frequency. We have found that damping is well described by single exponential decay function. When the time delay between the pulses increases the measured echo amplitude decreases with the decay rate of 1/T1, as expected from a T1-T2 model (Bloch model), and does not depend on the Rabi frequency (chi) . But with increasing of the first pulse duration t1 the measured decay rate depends on (chi) linearly. Theoretical calculations within the high-field Torrey approximation give linear dependence of the decay rate on (chi) with increasing of the duration t1. The agreement between the theoretical and experimental results is only qualitative. We assume that the strong difference between the theoretical prediction and the observed (chi) -dependence of the decay is caused by the frequency noise of the microwave radiation.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 26, 1997•2 citations

Transient nutations decay: The effect of field-modified dipolar interaction

S. Agnello, R. Boscaino, M. Cannas +2 more

The anomalous behavior of transient nutations is experimentally investigated in a set of two-level $(S=\frac{1}{2})$ spin systems differing only in spin concentration. Our results show that the non-Bloch power dependence of the decay rate of transient nutations is a concentration-dependent effect, which is more and more pronounced in more and more concentrated samples. The experimental results are interpreted in the framework of the recent theory by Shakhmuratov et al. [Phys. Rev. Lett. 79, 2963 (1997)] and support the hypothesis that the anomalous decay of transient nutations in solids originates from radiation-induced changes of the dipolar field, rather than from residual fluctuations of the nominally coherent field.

Physical Review A•May 1, 1999•23 citations

Rabi oscillation of spin-polarized rubidium in the spin-exchange relaxation-free regime

Yaxiang Wang, Junjian Tang, Binquan Zhou +4 more

The transient dynamics of atomic spins under oscillating and static magnetic fields have been studied in the spin-exchange relaxation-free (SERF) regime with a dual-beam configuration. The spin-relaxation rate can be accurately measured by detecting the transient response signal of the free induction decay (FID) process within several milliseconds. Leveraging this convenient method for measuring a large relaxation rate in a small cell volume, the dependence of the spin-relaxation rate on the probe intensity and ambient magnetic field was studied in the limit of low spin polarization. Moreover, by theoretical analysis of the dynamic evolution of the Rabi oscillation generated by a consecutive oscillating field and a small static magnetic field, we experimentally demonstrate that the amplitude of the Rabi oscillation is affected by the amplitude of the oscillating field in the SERF regime. According to the retrieved frequency of the FID signal and amplitude of relevant Rabi oscillation, the coil constants were 75.55 ± 0.78~nT/mA, 151.5 ± 0.9~nT/mA, and 116.6 ± 0.3~nT/mA along the x-, y-, and z-axes, respectively.

Optics Express•Aug 31, 2022•6 citations
Decay of Rabi oscillations of equivalent spins diluted in diamagnetic solid matrix and coupled by magnetic dipole interactions is theoretically studied. It is shown that these interactions result in random shifts of spin transient nutation frequencies and thus lead to the decay of the transient signal. Averaging over random spatial distribution of spins within the solid and over their spectral positions within magnetic resonance line, we obtain analytical expressions for the decay of Rabi oscillations. The rate of the decay in the case when the half-width of magnetic resonance line exceeds Rabi frequency is found to depend on the intensity of resonant microwave field and on the spin concentration. The results are compared with the literature data for E ′ 1 centers in glassy silica and [AlO 4 ] 0 centers in quartz.
Here, a theory of the intensity and concentration dependent damping of nutation signals observed by Boscaino et al. (Phys. Rev B 48, 7077 (1993); Phys. Rev. A 59, 4087 (1999)) and by others in various two-level spin systems is proposed. It is shown that in diluted paramagnetic solids contribution of dipole-dipole interaction to the nutation decay is negligibly small. We elaborated a cavity loss (radiation damping) mechanism that explains the intensity- and concentration dependence of the damping. It is shown that instead of ordinary Bloch's transverse T2 and longitudinal T1 damping parameters the decay of transverse and longitudinal spin components in nutation process are described by one and the same intensity-, concentration-, frequency- and time dependent damping parameter.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω rf is close to the Rabi frequency ω 1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies n ω rf and n ω rf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω 1 − ω rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω rf + ɛ increases, while the amplitude at the difference frequency ω rf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E ′ 1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω_{rf} is close to the Rabi frequency ω_{1} in a micro-wave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency εare accompanied by higher-frequency oscillations at frequencies nω_{rf} and nω_{rf}\pm ε, where n = 1, 2, .... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency εon the sign of the detuning ω{1} -ω{rf} from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω_{rf} +εincreases, while the amplitude at the difference frequency ω_{rf} -εdecreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
The decay of two-pulse nutational echo has been experimentally investigated in S equals 1/2 spin systems (E' centers in silica) at microwave frequency. We have found that damping is well described by single exponential decay function. When the time delay between the pulses increases the measured echo amplitude decreases with the decay rate of 1/T1, as expected from a T1-T2 model (Bloch model), and does not depend on the Rabi frequency (chi) . But with increasing of the first pulse duration t1 the measured decay rate depends on (chi) linearly. Theoretical calculations within the high-field Torrey approximation give linear dependence of the decay rate on (chi) with increasing of the duration t1. The agreement between the theoretical and experimental results is only qualitative. We assume that the strong difference between the theoretical prediction and the observed (chi) -dependence of the decay is caused by the frequency noise of the microwave radiation.
The anomalous behavior of transient nutations is experimentally investigated in a set of two-level (S=12)(S=\frac{1}{2})(S=21​) spin systems differing only in spin concentration. Our results show that the non-Bloch power dependence of the decay rate of transient nutations is a concentration-dependent effect, which is more and more pronounced in more and more concentrated samples. The experimental results are interpreted in the framework of the recent theory by Shakhmuratov et al. [Phys. Rev. Lett. 79, 2963 (1997)] and support the hypothesis that the anomalous decay of transient nutations in solids originates from radiation-induced changes of the dipolar field, rather than from residual fluctuations of the nominally coherent field.
The transient dynamics of atomic spins under oscillating and static magnetic fields have been studied in the spin-exchange relaxation-free (SERF) regime with a dual-beam configuration. The spin-relaxation rate can be accurately measured by detecting the transient response signal of the free induction decay (FID) process within several milliseconds. Leveraging this convenient method for measuring a large relaxation rate in a small cell volume, the dependence of the spin-relaxation rate on the probe intensity and ambient magnetic field was studied in the limit of low spin polarization. Moreover, by theoretical analysis of the dynamic evolution of the Rabi oscillation generated by a consecutive oscillating field and a small static magnetic field, we experimentally demonstrate that the amplitude of the Rabi oscillation is affected by the amplitude of the oscillating field in the SERF regime. According to the retrieved frequency of the FID signal and amplitude of relevant Rabi oscillation, the coil constants were 75.55 ± 0.78~nT/mA, 151.5 ± 0.9~nT/mA, and 116.6 ± 0.3~nT/mA along the x-, y-, and z-axes, respectively.