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

Physical Review A

Berry’s phase in optical resonance

Demosthenes Ellinas, Stephen Mark Barnett, M.‐A. Dupertuis

Published Apr 1, 1989• 72 citations
Publisher

Abstract

We examine the role of Berry's geometrical phase [Proc. R. Soc. London, Ser. A 392, 45 (1984)] in the coherent excitation of atoms. The dynamics of a two-level atom prepared in a superposition of its eigenstates will be modified in a nontrivial fashion by the Berry phase. We extend Berry's formalism to treat the Liouville equation for the density matrix. This extension allows us to discuss statistical mixtures and to incorporate Berry's phase within the well-known Bloch-vector description of optical resonance. Furthermore, our density-matrix formalism provides the means of investigating Berry's phase in open, dissipative systems.

DOI
10.1103/physreva.39.3228

Related papers

Berry's Phase in the Coherent Excitation of Atoms

Stephen Mark Barnett, Demosthenes Ellinas, M.‐A. Dupertuis

The adiabatic variation of a Hamiltonian can cause the wavefunction, governed by the Hamiltonian, to acquire an unexpected phase. The existence of this phase (Berry's phase) is an additional element in the well-known quantum adiabatic theorem. Berry's phase is observable in the interference between two identically prepared systems only one of which is adiabatically varied. We show that a single quantum system prepared in a superposition of the eigenstates of its Hamiltonian leads to observable Berry phase effects at all times. We examine this principle within the context of two-level optical resonance.

Journal of Modern Optics•Mar 1, 1988•13 citations

Complement 2C: The density matrix and the optical Bloch equations

G. Grynberg, Alain Aspect, Claude Fabre +1 more

The arguments of Chapter 2, as well as of those of subsequent chapters, have as their foundation the formalism based on the state vector of a system of which the evolution is described by the Schrödinger equation. In fact, such an approach is badly suited to the case in which the coupling between an atom and its environment (for example through collisions with other atoms or spontaneous emission into formerly empty modes of the electromagnetic field) cannot be neglected. If the correlations induced by these interactions between the atom and its environment do not concern us and we are only interested in the evolution of the atom, the formalism of the density matrix must be employed. This provides a description at all times of the state of the atom, although a state vector for the atom alone cannot be defined. In this formalism the effect of the environment on the atom is accounted for by the introduction of suitable relaxation terms (Section 2C.1) in the equation of evolution of the density matrix. An important application of the density matrix is to the case of a two-level atomic system for which the relaxation terms lead to its deexcitation to a level of lower energy. We shall show that in this case the density matrix can be represented by a vector, known as the Bloch vector , which will allow us to give simple geometrical pictures of the evolution of the system.

Cambridge University Press eBooks•Sep 2, 2010•0 citations

Exact solution and Berry phase for the dissipative two-mode optical system

Bang‐Pin Hou, Shun-Jin Wang, Wei-Can Yu +1 more

We have explored the dynamical algebraic structure of the dissipative two-mode system. On the basis of the algebraic structure, we have obtained the exact eigensolutions of the Liouvillian superoperator of its master equation by using an algebraic dynamical method. Then we investigate the Berry phase of the system within the density-matrix formalism.

Journal of Physics A Mathematical and General•Aug 5, 2004•1 citation

Berry’s geometrical phases in ESR in the presence of a stochastic process

Dan Gamliel, Jack H. Freed

Berry's [Proc. R. Soc. London, Ser. A 392, 45 (1984)] geometrical phase is discussed in the context of dissipative evolution of an interacting spin system, governed by the stochastic Liouville equation. An analytical treatment is given for a possible ESR experiment on an interacting electron-nucleus system, modulated by two-site jumps. Geometrical phases are shown to be relevant to systems of this type, when their Hamiltonian changes slowly with time. A method for obtaining higher-order corrections to the adiabatic approximation is demonstrated. It is found that if the jumps are slow relative to the rate of change of the Hamiltonian, their effect reduces to familiar line broadening, and the geometrical phases may be observed experimentally. Equations are also set up for a similar ESR experiment on an electron-nucleus system undergoing isotropic rotational diffusion, and a brief discussion of the equations follows.

Physical Review A•Apr 1, 1989•58 citations

Berry's phase in magnetic resonance

Dieter Suter, Gerard C. Chingas, Robert A. Harris +1 more

According to Berry, quantum states of a hamiltonian which varies adiabatically through a circuit C in parameter space may acquire geometrical phase factors exp (iγ(C)) in addition to the normal dynamical phase factors exp ((-i/ħ) ∝ E(t) dt). We present N.M.R. experiments in the rotating frame which bear out these predictions for simple conical circuits, and point out that they are related to familiar behaviour based on the classical Bloch equations and on Haeberlen-Waugh coherent averaging theory. Extensions to coupled spins and electric quadrupolar effects are discussed.

Molecular Physics•Aug 20, 1987•140 citations

Berry’s phase for atomic levels

Pervez Amirali Hoodbhoy

The ground-state hyperfine structure of atomic states is shown to exhibit interesting new aspects of the topological phase discovered by M. V. Berry [Proc. R. Soc. London, Ser. A 392, 45 (1984)]. In particular, although a nontrivial topological phase exists, monopoles are absent. A possible experiment to probe these aspects is discussed.

Physical Review A•Oct 1, 1988•4 citations
We examine the role of Berry's geometrical phase [Proc. R. Soc. London, Ser. A 392, 45 (1984)] in the coherent excitation of atoms. The dynamics of a two-level atom prepared in a superposition of its eigenstates will be modified in a nontrivial fashion by the Berry phase. We extend Berry's formalism to treat the Liouville equation for the density matrix. This extension allows us to discuss statistical mixtures and to incorporate Berry's phase within the well-known Bloch-vector description of optical resonance. Furthermore, our density-matrix formalism provides the means of investigating Berry's phase in open, dissipative systems.
The adiabatic variation of a Hamiltonian can cause the wavefunction, governed by the Hamiltonian, to acquire an unexpected phase. The existence of this phase (Berry's phase) is an additional element in the well-known quantum adiabatic theorem. Berry's phase is observable in the interference between two identically prepared systems only one of which is adiabatically varied. We show that a single quantum system prepared in a superposition of the eigenstates of its Hamiltonian leads to observable Berry phase effects at all times. We examine this principle within the context of two-level optical resonance.
The arguments of Chapter 2, as well as of those of subsequent chapters, have as their foundation the formalism based on the state vector of a system of which the evolution is described by the Schrödinger equation. In fact, such an approach is badly suited to the case in which the coupling between an atom and its environment (for example through collisions with other atoms or spontaneous emission into formerly empty modes of the electromagnetic field) cannot be neglected. If the correlations induced by these interactions between the atom and its environment do not concern us and we are only interested in the evolution of the atom, the formalism of the density matrix must be employed. This provides a description at all times of the state of the atom, although a state vector for the atom alone cannot be defined. In this formalism the effect of the environment on the atom is accounted for by the introduction of suitable relaxation terms (Section 2C.1) in the equation of evolution of the density matrix. An important application of the density matrix is to the case of a two-level atomic system for which the relaxation terms lead to its deexcitation to a level of lower energy. We shall show that in this case the density matrix can be represented by a vector, known as the Bloch vector , which will allow us to give simple geometrical pictures of the evolution of the system.
Berry's [Proc. R. Soc. London, Ser. A 392, 45 (1984)] geometrical phase is discussed in the context of dissipative evolution of an interacting spin system, governed by the stochastic Liouville equation. An analytical treatment is given for a possible ESR experiment on an interacting electron-nucleus system, modulated by two-site jumps. Geometrical phases are shown to be relevant to systems of this type, when their Hamiltonian changes slowly with time. A method for obtaining higher-order corrections to the adiabatic approximation is demonstrated. It is found that if the jumps are slow relative to the rate of change of the Hamiltonian, their effect reduces to familiar line broadening, and the geometrical phases may be observed experimentally. Equations are also set up for a similar ESR experiment on an electron-nucleus system undergoing isotropic rotational diffusion, and a brief discussion of the equations follows.
According to Berry, quantum states of a hamiltonian which varies adiabatically through a circuit C in parameter space may acquire geometrical phase factors exp (iγ(C)) in addition to the normal dynamical phase factors exp ((-i/ħ) ∝ E(t) dt). We present N.M.R. experiments in the rotating frame which bear out these predictions for simple conical circuits, and point out that they are related to familiar behaviour based on the classical Bloch equations and on Haeberlen-Waugh coherent averaging theory. Extensions to coupled spins and electric quadrupolar effects are discussed.