Exponential decay and geometric aspect of transition probabilities in the adiabatic limit

Joye, Alain; Kunz, H. R.; Pfister, Charles-Edouard

doi:10.1016/0003-4916(91)90297-l

Cited by 91 publications

(97 citation statements)

References 7 publications

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“…Similar theoretical predictions were independently made by Joye, Mileti, P® ster and Kunz [10,11]. Up to now only one experiment has been reported, performed on a nuclear spin± the corresponding path is open.…”

Section: Introductionsupporting

confidence: 78%

“…An adiabatic energy surface corresponding to a two-level system is usually de® ned through the square root of a complex function, as is the case in equation (10), and is therefore a double-valued function. To emphasize the mathematical properties of such functions, consider the generic case of…”

Section: The D Ykhne ± D Avis± Pechukas M Ethodmentioning

confidence: 99%

“…The point t 0 is referred to as a branch point. The real part of the adiabatic energy surfaces E ± , given in equation (10), are the two sheets of the Riemann surface draw in ® gure 1. As mentioned before, for transitions to occur under the adiabatic assumption, | Y(t ) must`reach ' a branch point around which the transition between the adiabatic energy levels takes place.…”

Section: The D Ykhne ± D Avis± Pechukas M Ethodmentioning

confidence: 99%

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Observation of the geometric amplitude factor in an optical system

Bouwmeester¹,

Karman²,

Dekker³

et al. 1996

Journal of Modern Optics

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A bstract.By manipulating the discrete optical levels inside an optical resonator, we obtain a classical realization of a twisted Landau ± Zener model.We experimentally demonstrate the geometric amplitude factor in the transition amplitude that arises for this model. We consider in particular the region of parameter space addressed in the original study of the geometric amplitude factor by M. V. Berry [7].

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Section: Introductionsupporting

confidence: 78%

Section: The D Ykhne ± D Avis± Pechukas M Ethodmentioning

confidence: 99%

Section: The D Ykhne ± D Avis± Pechukas M Ethodmentioning

confidence: 99%

See 1 more Smart Citation

Observation of the geometric amplitude factor in an optical system

Bouwmeester¹,

Karman²,

Dekker³

et al. 1996

Journal of Modern Optics

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show abstract

“…This only happens when the interaction between the quantum system and its environment is time-dependent and is a consequence of the time variation of a set of parameters. As in the case of imaginary geometric phases appeared in the transition probabilities of non-real Hamiltonians in the non-adiabatic regime [2,3,4] here also the integral over the parameter space k does not have to be a close loop. The condition (35) allows us to say directly from the expression of L H D if the dissipative effect in the master equation gives an imaginary geometric correction to the Berry phase [1].…”

Section: Discussionmentioning

confidence: 89%

Adiabatic approximation in the density matrix approach: non-degenerate systems

Pinto¹,

Romero²,

Thomaz³

2002

Physica A: Statistical Mechanics and its Applications

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We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric phases for periodic Hamiltonians obtained previously by M.V. Berry are recovered in the present approach. We determine the necessary condition satisfied by the coefficients of the linear expansion of the non-unitary part of the Liouvillian in order to the imaginary phases acquired by the elements of the density matrix, due to dissipative effects, be geometric. The results derived are model-independent. We apply them to spin 1 2 model coupled to reservoir at thermodynamic equilibrium.

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“…Here the critical point, z c , is determined as a solution of the equation, ε k (z c ) = 0, in the complex plane obtained by analytical continuation, t → z [30][31][32][33][34][35][36][37][38]. Similarly, if initially the system was in the excited state: |ψ k (0) = |u + (k, 0) , so that α k (0) = 0 and β k (0) = 1, the result of integration yields…”

Section: B Adiabatic Basismentioning

confidence: 99%

Non-Hermitian quantum annealing in the ferromagnetic Ising model

Nesterov¹,

Zepeda²,

Berman³

2013

Phys. Rev. A

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We developed a non-Hermitian quantum optimization algorithm to find the ground state of the ferromagnetic Ising model with up to 1024 spins (qubits). Our approach leads to significant reduction of the annealing time. Analytical and numerical results demonstrate that the total annealing time is proportional to ln N , where N is the number of spins. This encouraging result is important in using classical computers in combination with quantum algorithms for the fast solutions of NPcomplete problems. Additional research is proposed for extending our dissipative algorithm to more complicated problems.

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Exponential decay and geometric aspect of transition probabilities in the adiabatic limit

Cited by 91 publications

References 7 publications

Observation of the geometric amplitude factor in an optical system

Observation of the geometric amplitude factor in an optical system

Adiabatic approximation in the density matrix approach: non-degenerate systems

Non-Hermitian quantum annealing in the ferromagnetic Ising model

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