Quantum mechanics in rotating-radio-frequency traps and Penning traps with a quadrupole rotating field
- Department of Physics, Keio University, Kanagawa 223-8522 (Japan)
Quantum-mechanical analysis of ion motion in a rotating-radio-frequency (rrf) trap or in a Penning trap with a quadrupole rotating field is carried out. Rrf traps were introduced by Hasegawa and Bollinger [Phys. Rev. A 72, 043404 (2005)]. The classical motion of a single ion in this trap is described by only trigonometric functions, whereas in the conventional linear radio-frequency (rf) traps it is by the Mathieu functions. Because of the simple classical motion in the rrf trap, it is expected that the quantum-mechanical analysis of the rrf traps is also simple compared to that of the linear rf traps. The analysis of Penning traps with a quadrupole rotating field is also possible in a way similar to the rrf traps. As a result, the Hamiltonian in these traps is the same as the two-dimensional harmonic oscillator, and energy levels and wave functions are derived as exact results. In these traps, it is found that one of the vibrational modes in the rotating frame can have negative energy levels, which means that the zero-quantum-number state (''ground'' state) is the highest energy state.
- OSTI ID:
- 21408437
- Journal Information:
- Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
CHARGED PARTICLES
ELECTROMAGNETIC RADIATION
ENERGY LEVELS
FUNCTIONS
GROUND STATES
HAMILTONIANS
HARMONIC OSCILLATORS
IONS
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM MECHANICS
QUANTUM OPERATORS
RADIATIONS
RADIOWAVE RADIATION
TRAPS
WAVE FUNCTIONS