Population control of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mi>s</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi>p</mml:mi></mml:math>transitions in hydrogen

Analytic solutions are developed for two-state systems (e.g. qubits) strongly perturbed by a series of rapidly changing pulses, called 'kicks'. The evolution matrix may be expressed as a time ordered product of evolution matrices for single kicks. Single, double, and triple kicks are explicitly considered, and the onset of observability of time ordering is examined. The effects of different order of kicks on the dynamics of the system are studied and compared with effects of time ordering in general. To determine the range of validity of this approach, the effect of using pulses of finite widths for 2s − 2p transitions in atomic hydrogen is examined numerically.

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“…V (t) dt 1. (ii) Degenerate basis states [26]. In this case the energy levels of the two unperturbed states are nearly the same.…”

Section: Analytical Solutionsmentioning

confidence: 98%

“…paper [26]. We present results for the occupation probability of the target state, P 2 , which includes both 2p 1/2 and 2p 3/2 states, as a function of time.…”

Section: S − 2p Transition In Hydrogenmentioning

confidence: 99%

Sudden switching in two-state systems

Shakov

McGuire

Kaplan

et al. 2006

J. Phys. B: At. Mol. Opt. Phys.

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“…5(a) from which we see that the concurrence decreases faster as the mean thermal excitation number n is increased. For the coherent state, equation (38) is plotted in Fig. 5(b) from which the exponential decrease of concurrence is evident.…”

Section: Dynamics Of Entanglement Between the Qubitsmentioning

confidence: 99%

“…In particular, we examine the idealized case of zerogap qubits, focusing on the entanglement dynamics of the four Bell states with the oscillator initially in either a thermal state, a coherent state or a number state. A study of the dynamics of a degenerate qubit interacting with a classical field, and a discussion of a physical system which can be treated as a degenerate qubit, has been given by Shakov and McGuire [38].…”

Section: Introductionmentioning

confidence: 99%

Two Qubits Tavis-Cummings Model Beyond the Rotating Wave Approximation: Degenerate Regime

Agarwal,

Rafsanjani,

Eberly

2011

Preprint

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We study the dynamics of two qubits interacting with a single mode of a harmonic oscillator beyond the rotating wave approximation in the ideally degenerate regime. Exact analytic expressions are obtained for state properties of interest, including qubit entanglement for a certain class of initial states of the oscillator and the qubits. Qualitative differences and similarities in the evolution of the qubits in the degenerate regime when the oscillator is treated quantum mechanically and classically are discussed.

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“…Entanglement is a characteristic of quantum mechanics, describing correlations between quantum systems and having no exact classical analog [4], Transition between two discrete states has ever been described by two-state models under certain conditions [5]. Several studies [6,7] have suggested the feasibility of classical entanglement model by examining the classical analog of entanglement through Bohmian mechanics [8,9].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics Governing Quantum Transition Behavior

Yang¹,

Han²,

Hsiao³

2007

International Journal of Nonlinear Sciences and Numerical Simulation

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In quantum mechanics, the only known quantitative index describing a state transition process is the occupation probability. In this paper, we propose three new quantitative indices, namely, complex transition trajectory, quantum potential, and total quantum energy, to give an elaborate description of statetransition behavior, which otherwise cannot be manifested in terms of occupation probability. The new quantitative indices and the nonlinear dynamics governing quantum transition behavior are derived from the quantum Hamilton mechanics that provides a unified description of the entire transition process from an initial state to a final state via an entangled state. The proposed nonlinear analysis of transition behavior will be applied to the transition in a hydrogen atom from the 1s state to the 2s state.

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Population control of2s−2ptransitions in hydrogen

Cited by 14 publications

References 21 publications

Sudden switching in two-state systems

Sudden switching in two-state systems

Two Qubits Tavis-Cummings Model Beyond the Rotating Wave Approximation: Degenerate Regime

Nonlinear Dynamics Governing Quantum Transition Behavior

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