Ion traps: some semiclassical observations

Mielnik, Bogdan; Ramirez, A. D.

doi:10.1088/0031-8949/82/05/055002

Cited by 12 publications

(48 citation statements)

References 58 publications

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“…They also occur in harmonic fields, though the results require a computer study [65,66,67]. Here, they can be given by the exact formula (43).…”

Section: Proposition 4 If β(T) = 0 In Some Intervalmentioning

confidence: 99%

Quantum operations: technical or fundamental challenge?

Mielnik¹

2013

J. Phys. A: Math. Theor.

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A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as 'operation factories' transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract δ-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov-Bohm criticism of the time-energy uncertainty principle, and some others, to verify the existence of fundamental precision limits of the position measurements or the reality of 'non-commutative geometries'.

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“…They also occur in harmonic fields, though the results require a computer study [65,66,67]. Here, they can be given by the exact formula (43).…”

Section: Proposition 4 If β(T) = 0 In Some Intervalmentioning

confidence: 99%

Quantum operations: technical or fundamental challenge?

Mielnik¹

2013

J. Phys. A: Math. Theor.

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“…It is worth to notice that the EL have been mainly studied for systems ruled by timedependent Hamiltonians, either in one or several dimensions [37,45,48,50,51,53,54] or for purely spin systems [39,40,44]. However, there are several works where the evolution loops are produced by time-independent Hamiltonians [30,33].…”

Section: Evolution Loopsmentioning

confidence: 99%

“…In the last decades there has been a growing interest in studying evolution loops (EL), which are circular dynamical processes such that the evolution operator of the system becomes the identity at a certain time [30,33,37,39,40,44,45,48,50,51,53,54]. They represent a natural generalization to what happens for the harmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

Harmonic Oscillator SUSY Partners and Evolution Loops

C.¹

2012

SIGMA

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Abstract. Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied.

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“…which is at the bottom of all quantum control problems for time dependent oscillator Hamiltonians [42,43,44,53,70,71,96]. Once having b(t), one immediately constructs u osc (t), as the simple pair of two b(t)-cells.…”

Section: Cylindrical Geometry: the Resistant Loopsmentioning

confidence: 99%

Magnetic operations: a little fuzzy mechanics?

Mielnik¹,

Ramirez²

2011

Phys. Scr.

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Abstract. We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry which enters into the traditional control problems. We show that its application extends beyond the usually considered time independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields lead to the stability maps differing from the traditional Strutt diagram.

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Ion traps: some semiclassical observations

Cited by 12 publications

References 58 publications

Quantum operations: technical or fundamental challenge?

Quantum operations: technical or fundamental challenge?

Harmonic Oscillator SUSY Partners and Evolution Loops

Magnetic operations: a little fuzzy mechanics?

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