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:quant-ph/0608036 · Annalen der Physik

Two interacting spins in external fields. Four-level systems

Vladislav G. Bagrov, Mario Cesar Baldiotti, Dmitri M Gitman, A.D. Levin

Published Dec 21, 2006• 14 citations
arXivHTMLPDF

Abstract

In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two-spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two-spin equations on the basis of already known exact solutions of the one-spin equation. Besides, we present some exact solutions for the two-spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time-independent spin interaction and a time-independent external background. A possible analogue of the Rabi problem for the two-spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.

DOI
10.1002/andp.200610231

Related papers

Two interacting spins in external fields. Four‐level systems

Vladislav G. Bagrov, Mario Cesar Baldiotti, Dmitri M Gitman +1 more

Abstract In the present article, we consider the so‐called two‐spin equation that describes four‐level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two‐spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two‐spin equations on the basis of already known exact solutions of the one‐spin equation. Besides, we present some exact solutions for the two‐spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time‐independent spin interaction and a time‐independent external background. A possible analogue of the Rabi problem for the two‐spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.

Annalen der Physik•Mar 14, 2007•5 citations

Spin equation and its solutions

V. G. Bagrov, D. M. Gitman, M. C. Baldiotti +1 more

The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0+1)-dimensional case. Two-level systems can be described by an SE with a particular form of the external field. In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE. We describe the general solution of the SE and solve the inverse problem for this equation. We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions. Finally, we find a new set of exact solutions of the SE.

•Jan 1, 2005•28 citations

Spin equation and its solutions

V.G. Bagrov, D.M. Gitman, M.C. Baldiotti +1 more

The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0+1)-dimensional case. Two-level systems can be described by an SE with a particular form of the external field. In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE. We describe the general solution of the SE and solve the inverse problem for this equation. We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions. Finally, we find a new set of exact solutions of the SE.

arXiv:quant-ph/0502034•Annalen der Physik•Dec 1, 2005•33 citations

8. Spin equation and its solutions

The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions.We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0 + 1)-dimensional case.Two-level systems can be described by an SE with a particular form of the external field.In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE.We describe the general solution of the SE and solve the inverse problem for this equation.We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions.Finally, we find a new set of exact solutions of the SE.

De Gruyter eBooks•Aug 4, 2014•0 citations

Spin equation and its solutions

Vladislav G. Bagrov, Dmitri M Gitman, Mario Cesar Baldiotti +1 more

Abstract The aim of the present article is to study in detail the so‐called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0+1)‐dimensional case. Two‐level systems can be described by an SE with a particular form of the external field. In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE. We describe the general solution of the SE and solve the inverse problem for this equation. We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions. Finally, we find a new set of exact solutions of the SE.

Annalen der Physik•Dec 1, 2005•10 citations

Two and three coupled spins in magnetic field

Dmitry Gitman, Mario Cesar Baldiotti, Marcelo Meireles dos Santos

We consider three spin systems in the parallel magnetic fields and present some of possible exact solutions.In addition, we discuss an analogue of the Rabi problem for three-spin system.In order to do this, we reduce the problem of three coupled spins, an 8-level system, to a problem of a 3-level system in an effective field.We explicitly construct the evolution operator of the system in two special cases: when the fields and interaction are the same in all the spins but with a arbitrary time-dependence of the fields, and when the spins are subjected to a circular magnetic field (the Rabi problem).Some applications of these results are discussed.

•Apr 14, 2014•0 citations
In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two-spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two-spin equations on the basis of already known exact solutions of the one-spin equation. Besides, we present some exact solutions for the two-spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time-independent spin interaction and a time-independent external background. A possible analogue of the Rabi problem for the two-spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.
Abstract In the present article, we consider the so‐called two‐spin equation that describes four‐level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two‐spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two‐spin equations on the basis of already known exact solutions of the one‐spin equation. Besides, we present some exact solutions for the two‐spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time‐independent spin interaction and a time‐independent external background. A possible analogue of the Rabi problem for the two‐spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.
The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0+1)-dimensional case. Two-level systems can be described by an SE with a particular form of the external field. In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE. We describe the general solution of the SE and solve the inverse problem for this equation. We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions. Finally, we find a new set of exact solutions of the SE.
The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0+1)-dimensional case. Two-level systems can be described by an SE with a particular form of the external field. In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE. We describe the general solution of the SE and solve the inverse problem for this equation. We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions. Finally, we find a new set of exact solutions of the SE.
The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions.We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0 + 1)-dimensional case.Two-level systems can be described by an SE with a particular form of the external field.In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE.We describe the general solution of the SE and solve the inverse problem for this equation.We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions.Finally, we find a new set of exact solutions of the SE.
Abstract The aim of the present article is to study in detail the so‐called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0+1)‐dimensional case. Two‐level systems can be described by an SE with a particular form of the external field. In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE. We describe the general solution of the SE and solve the inverse problem for this equation. We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions. Finally, we find a new set of exact solutions of the SE.
We consider three spin systems in the parallel magnetic fields and present some of possible exact solutions.In addition, we discuss an analogue of the Rabi problem for three-spin system.In order to do this, we reduce the problem of three coupled spins, an 8-level system, to a problem of a 3-level system in an effective field.We explicitly construct the evolution operator of the system in two special cases: when the fields and interaction are the same in all the spins but with a arbitrary time-dependence of the fields, and when the spins are subjected to a circular magnetic field (the Rabi problem).Some applications of these results are discussed.