Polynomial pseudosupersymmetry underlying a two-level atom in an external electromagnetic field

Samsonov, B. F.; Shamshutdinova, V. V.; Гитман, Д. М.

doi:10.1007/s10582-005-0124-9

Cited by 5 publications

(9 citation statements)

References 7 publications

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“…Starting from the simplest case 0 const ε = ε = , a family of new nontrivial potentials (biases), for which Schrödinger's equation (1) could be solved exactly, was found. In the present work, we take advantage of the results obtained in [24][25][26][27] to describe the time evolution of the flux qubit and the time dependence of the qubit localization probability and to calculate its time-averaged values. Let us consider first the behavior of the flux qubit with the bias ( )…”

Section: Exactly Solvable Bias Pulsesmentioning

confidence: 99%

“…Then the states } { 0 , 1 of the flux qubit have the definite (clockwise or counterclockwise) direction of superconducting current circulating in the loop. The above-mentioned non-periodic time-dependent bias pulses are the potentials for which Schrödinger's equation (1) can be solved exactly [24][25][26][27]. Thus, the probability calculated using these exact solutions is, for example, the probability P ↑ of the clockwise current direction.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of superconducting qubits with exactly solvable bias pulses

Shamshutdinova

Kiyko²,

Shevchenko³

et al. 2008

Russ Phys J

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The dynamics of a quantum two-state system (qubit) with external control bias pulses of special shapes is considered. The bias pulses represent the potentials for which the Schrödinger equation can be solved exactly. The probability to register a definite direction of the current in a loop and its time-averaged values are calculated for the flux qubit; calculations are performed both analytically and numerically in the presence of relaxation and decoherence within the framework of the density matrix formalism. It is demonstrated that there exist external bias pulses for which the definite current direction probability is a monotonically increasing function of time that approaches a limiting value exceeding 1/2. The probability to find the system in the excited state is calculated, and the possibility of inverse population in a properly driven two-state system is demonstrated given that the relaxation and decoherence rates are small enough.

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Section: Exactly Solvable Bias Pulsesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of superconducting qubits with exactly solvable bias pulses

Shamshutdinova

Kiyko²,

Shevchenko³

et al. 2008

Russ Phys J

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“…A subsequent use of separate factorization relations of type (13) and intertwining relations of type (9) yields…”

Section: Polynomial Pseudo-supersymmetry Of a Two-level Systemmentioning

confidence: 99%

“…Omitting the details, let us consider the behavior of the probability to populate the excited level obtained as a result of a two-fold transformation with different factorization constants. The transformed potential f 2 is obtained in [9] f…”

Section: Transformations Of the Rabi Oscillationsmentioning

confidence: 99%

“…The authors of [6] give an overview of the known results and obtain new classes of exact solutions to this equation. Among the methods of analysis of exactly solvable spin equations, the method of intertwining operators [7]- [9] plays a special role, since it reveals a new type of symmetry related with two-level systems [8,9], called the polynomial pseudo-supersymmetry.…”

Section: Introductionmentioning

confidence: 99%

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Two-level systems: Exact solutions and underlying pseudo-supersymmetry

2007

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Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a polynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.

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Matching method and exact solvability of discrete -symmetric square wells

Znojil¹

2006

J. Phys. A: Math. Gen.

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Discrete PT −symmetric square wells are studied. Their wave functions are found proportional to classical Tshebyshev polynomials of complex argument. The compact secular equations for energies are derived giving the real spectra in certain intervals of non-Hermiticity strengths Z. It is amusing to notice that although the known square well re-emerges in the usual continuum limit, a twice as rich, upside-down symmetric spectrum is exhibited by all its present discretized predecessors. PACS 03.65.Ge, 03.65.

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Polynomial pseudosupersymmetry underlying a two-level atom in an external electromagnetic field

Cited by 5 publications

References 7 publications

Dynamics of superconducting qubits with exactly solvable bias pulses

Dynamics of superconducting qubits with exactly solvable bias pulses

Two-level systems: Exact solutions and underlying pseudo-supersymmetry

Matching method and exact solvability of discrete -symmetric square wells

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