Darboux transformation for two-level system

Багров, В. Г.; Baldiotti, M. C.; Гитман, Д. М.; Shamshutdinova, V. V.

doi:10.1002/andp.200410138

Cited by 18 publications

(34 citation statements)

References 11 publications

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“…The first exact solution of the spin equation was found by Rabi [12] for an external field of the form F = (f 1 cos ωt, f 2 sin ωt, F 3 ), where f 1,2 , ω, and F 3 are real constants. A number of exact solutions of the spin equation were found in [8,13,14]. For periodic, or quasiperiodic, external fields, the equations of a two-level system have been studied by many authors using different approximation methods, e.g., perturbative expansions [15], see also [16].…”

Section: Spin Equationmentioning

confidence: 99%

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Two interacting spins in external fields. Four-level systems

Багров¹,

Baldiotti

Гитман

et al. 2007

Ann. Phys.

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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.

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Section: Spin Equationmentioning

confidence: 99%

“…In [14], one can find several functions f (t) for which exact solutions of the spin equation can be found.…”

Section: Constant Spin Interactionmentioning

confidence: 99%

Two interacting spins in external fields. Four-level systems

Багров¹,

Baldiotti

Гитман

et al. 2007

Ann. Phys.

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“…We note a decrease of the oscillation amplitude when δ approaches its critical value equal √ 3/2. This is why for δ close enough to the value √ 3/2 the minimal value of the probability P The result we have just obtained suggests us to consider a more general case [9,10], where function ǫ(τ ) being periodical depends on three parameters. One of them we fix by re-scaling both time and another parameter (frequency ω appearing in Eq.…”

Section: Dynamical Qubit Controllingmentioning

confidence: 79%

Dynamical qubit controlling via pseudo-supersymmetry of two-level systems

Samsonov¹,

Shamshutdinova²

2008

J. Phys. A: Math. Theor.

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Abstract. For a flux qubit considered as a two-level system, for which a hidden polynomial pseudo-supersymmetry was previously discovered, we propose a special time-dependent external control field. We show that for a qubit placed in this field there exists a critical value of tunnel frequency. When the tunnel frequency is close enough to its critical value, the external field frequency may be tuned in a way to keep the probability to detect a definite direction of the current circulating in a Josephson-junction circuit above 1/2 during a desirable time interval. We also show that such a behavior is not much affected by a sufficiently small dissipation.

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“…This leads to a solution obtained in [4]. We have found that equation (8) becomes very involved for the next transformation step.…”

Section: Transformations Of the Rabi Oscillationsmentioning

confidence: 87%

“…The function f 0 (t) plays the role of a "potential" in the non-Hermitian Dirac-like Hamiltonian h 0 (2). (For further details, see [3][4][5]. )…”

Section: Introductionmentioning

confidence: 98%