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:0803.1906 · Journal of Physics B Atomic Molecular and Optical Physics

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

Peter L. Hagelstein, Irfan U. Chaudhary

Published Jun 23, 2008• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/41/13/135501

Related papers

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

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 a three-level system

Peter L. Hagelstein, Irfan U. Chaudhary

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.

arXiv:0802.2779•Journal of Physics B Atomic Molecular and Optical Physics•May 6, 2008•2 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

Two-level systems coupled to an oscillator: Excitation transfer and energy exchange

Peter L. Hagelstein, Irfan U. Chaudhary

We consider models in which two sets of matched two-level systems are coupled to a common oscillator in the case where the oscillator energy is small relative to the two-level transition energies. Since the two sets of two-level systems are coupled indirectly through the oscillator, excitation transfer from one set of two-level systems to the other is possible. In addition, the excitation energy from the two-level systems may be exchanged with the oscillator coherently, even though the oscillator energy may be orders of magnitude smaller than the two-level system transition energy. In the lossless case, we demonstrate these effects numerically, and also use an approximate diagonalization to show that these effects are expected from the model Hamiltonian. We augment the model to include loss effects, and show that loss enhances the excitation transfer effect by breaking the severe cancelation between different paths that occurs in the lossless case. We describe a simple approximate model wavefunction appropriate when the loss increases rapidly with energy. Within this model approximation, we present numerical and analytical results for excitation transfer and energy transfer rates, showing that they are greatly increased. Our study of these models is motivated in part by claims of excess heat production in electrochemical experiments in heavy water. We examine the question of whether the rates associated with this kind of model are sufficiently large to be relevant to the experimental claims. We find that consistency is possible given recent experimental results showing strong screening effects in low energy deuteron-deuteron fusion experiments in metals.

arXiv:cond-mat/0612306•Dec 12, 2006•4 citations

Bloch-Siegert shifts and multi-quantum transitions in spin-one systems

J.A. Hermann, S. Swain

The Bloch-Siegert-type shifts and multiple-quantum resonance shifts of a spin-one system subjected to an oscillating radio-frequency applied at right angles to a DC field have been calculated to sixth order in V, the amplitude of the oscillating field, for the single-quantum resonance, and to fourth order in V for the higher resonances. The level crossing criterion appropriate to two-level systems cannot be used here, and a resonance condition based on a previously derived analogue of Shirley's equation for spin-one systems is used instead. The calculation uses degenerate continued-fraction perturbation theory. Numerical calculations were performed in order to obtain the shape of the resonances, and partially check the analytic results. The atomic levels were assumed to be completely stable; the corrections due to finite atomic lifetimes are expected to be small.

Journal of Physics B Atomic and Molecular Physics•Aug 1, 1977•17 citations
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.
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.
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.
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.
We consider models in which two sets of matched two-level systems are coupled to a common oscillator in the case where the oscillator energy is small relative to the two-level transition energies. Since the two sets of two-level systems are coupled indirectly through the oscillator, excitation transfer from one set of two-level systems to the other is possible. In addition, the excitation energy from the two-level systems may be exchanged with the oscillator coherently, even though the oscillator energy may be orders of magnitude smaller than the two-level system transition energy. In the lossless case, we demonstrate these effects numerically, and also use an approximate diagonalization to show that these effects are expected from the model Hamiltonian. We augment the model to include loss effects, and show that loss enhances the excitation transfer effect by breaking the severe cancelation between different paths that occurs in the lossless case. We describe a simple approximate model wavefunction appropriate when the loss increases rapidly with energy. Within this model approximation, we present numerical and analytical results for excitation transfer and energy transfer rates, showing that they are greatly increased. Our study of these models is motivated in part by claims of excess heat production in electrochemical experiments in heavy water. We examine the question of whether the rates associated with this kind of model are sufficiently large to be relevant to the experimental claims. We find that consistency is possible given recent experimental results showing strong screening effects in low energy deuteron-deuteron fusion experiments in metals.
The Bloch-Siegert-type shifts and multiple-quantum resonance shifts of a spin-one system subjected to an oscillating radio-frequency applied at right angles to a DC field have been calculated to sixth order in V, the amplitude of the oscillating field, for the single-quantum resonance, and to fourth order in V for the higher resonances. The level crossing criterion appropriate to two-level systems cannot be used here, and a resonance condition based on a previously derived analogue of Shirley's equation for spin-one systems is used instead. The calculation uses degenerate continued-fraction perturbation theory. Numerical calculations were performed in order to obtain the shape of the resonances, and partially check the analytic results. The atomic levels were assumed to be completely stable; the corrections due to finite atomic lifetimes are expected to be small.