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:0802.2779 · Journal of Physics B Atomic Molecular and Optical Physics

Multiphoton Bloch–Siegert shifts and level splittings in a three-level system

Peter L. Hagelstein, Irfan U. Chaudhary

Published May 6, 2008• 2 citations
arXivHTMLPDF

Abstract

In previous work we studied the spin-boson model in the multiphoton regime, using a rotation that provides a separation between terms that contribute most of the level energies away from resonance, and terms responsible for the level splittings at the anticrossing. Here, we consider a generalization of the spin-boson model consisting of a three-level system coupled to an oscillator. We construct a similar rotation and apply it to the more complicated model. We find that the rotation provides a useful approximation to the energy levels in the multiphoton region of the new problem. We find that good results can be obtained for the level splittings at the anticrossings for resonances involving the lower two levels in regions away from accidental or low-order resonances of the upper two levels.

DOI
10.1088/0953-4075/41/10/105603

Related papers

Multiphoton Bloch-Siegert shifts and level-splittings in spin-one systems

Peter L. Hagelstein, Irfan U. Chaudhary

Abstract. We consider a spin-boson model in which a spin 1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch-Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch-Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed. PACS numbers: 32.80.Bx,32.60.+i,32.80.Rm,32.80.WrMultiphoton Bloch-Siegert shifts and level-splittings in spin-one systems 2 1.

•Nov 21, 2012•2 citations

Multiphoton Bloch–Siegert shifts and level-splittings in spin-one systems

Peter L. Hagelstein, Irfan U. Chaudhary

We consider a spin-boson model in which a spin-1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch–Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch–Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed.

arXiv:0709.3557•Journal of Physics B Atomic Molecular and Optical Physics•Jan 24, 2008•9 citations

Level splitting in association with the multiphoton Bloch–Siegert shift

Peter L. Hagelstein, Irfan U. Chaudhary

We present a unitary equivalent spin-boson Hamiltonian in which terms can be identified which contribute to the Bloch-Siegert shift, and to the level splittings at the anticrossings associated with the Bloch-Siegert resonances. First-order degenerate perturbation theory is used to develop approximate results in the case of moderate coupling for the level splitting.

arXiv:0709.1961•Journal of Physics B Atomic Molecular and Optical Physics•Jan 24, 2008•19 citations

Excitation transfer in two two-level systems coupled to an oscillator

Peter L. Hagelstein, Irfan U. Chaudhary

We consider a generalization of the spin-boson model in which two different two-level systems are coupled to an oscillator, under conditions where the oscillator energy is much less than the two-level system energies, and where the oscillator is highly excited. We find that the two-level system transition energy is shifted, producing a Bloch-Siegert shift in each two-level system similar to what would be obtained if the other were absent. At resonances associated with energy exchange between a two-level system and the oscillator, the level splitting is about the same as would be obtained in the spin-boson model at a Bloch-Siegert resonance. However, there occur resonances associated with the transfer of excitation between one two-level system and the other, an effect not present in the spin-boson model. We use a unitary transformation leading to a rotated system in which terms responsible for the shift and splittings can be identified. The level splittings at the anticrossings associated with both energy exchange and excitation transfer resonances are accounted for with simple two-state models and degenerate perturbation theory using operators that appear in the rotated Hamiltonian.

arXiv:0803.1906•Journal of Physics B Atomic Molecular and Optical Physics•Jun 23, 2008•5 citations

Bloch-Siegert shift for multiphoton resonances

Peter L. Hagelstein, Irfan U. Chaudhary

Recently there has been theoretical and experimental interest in Bloch-Siegert shifts in an intense photon field. A perturbative treatment becomes difficult in this multiphoton regime. We present a unitary transform and rotated model, which allows us to get accurate results away from the level anticrossings. A simple variational energy estimate leads to a new expression for the dressed two-level system energy which is accurate, and useful over a wide range of the dimensionless coupling constant.

arXiv:0709.1958•Sep 12, 2007•1 citation

Multiphoton Raman transitions and Rabi oscillations in driven spin systems

A. P. Saǐko, Siarhei A. Markevich, Ryhor Fedaruk

In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.

arXiv:1807.05086•Physical Review A•Oct 5, 2018•24 citations
In previous work we studied the spin-boson model in the multiphoton regime, using a rotation that provides a separation between terms that contribute most of the level energies away from resonance, and terms responsible for the level splittings at the anticrossing. Here, we consider a generalization of the spin-boson model consisting of a three-level system coupled to an oscillator. We construct a similar rotation and apply it to the more complicated model. We find that the rotation provides a useful approximation to the energy levels in the multiphoton region of the new problem. We find that good results can be obtained for the level splittings at the anticrossings for resonances involving the lower two levels in regions away from accidental or low-order resonances of the upper two levels.
Abstract. We consider a spin-boson model in which a spin 1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch-Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch-Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed. PACS numbers: 32.80.Bx,32.60.+i,32.80.Rm,32.80.WrMultiphoton Bloch-Siegert shifts and level-splittings in spin-one systems 2 1.
We consider a spin-boson model in which a spin-1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch–Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch–Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed.
We consider a generalization of the spin-boson model in which two different two-level systems are coupled to an oscillator, under conditions where the oscillator energy is much less than the two-level system energies, and where the oscillator is highly excited. We find that the two-level system transition energy is shifted, producing a Bloch-Siegert shift in each two-level system similar to what would be obtained if the other were absent. At resonances associated with energy exchange between a two-level system and the oscillator, the level splitting is about the same as would be obtained in the spin-boson model at a Bloch-Siegert resonance. However, there occur resonances associated with the transfer of excitation between one two-level system and the other, an effect not present in the spin-boson model. We use a unitary transformation leading to a rotated system in which terms responsible for the shift and splittings can be identified. The level splittings at the anticrossings associated with both energy exchange and excitation transfer resonances are accounted for with simple two-state models and degenerate perturbation theory using operators that appear in the rotated Hamiltonian.
In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.