Reinhold Blumel
Teaching and Research
Research
Paul Trap
Dynamic Kingdon Trap
Ray Splitting
Quantum Graphs
Microwave Ionization
Chaotic Scattering
Chaos in Atomic Physics
Step-in-a-Box
Finite Quantum Square Well
The quest for manipulating matter at the atomic scale is currently one of the
central directions in research and
technology. Not so long ago the founders of quantum mechanics thought that
experimenting with atoms and ions is fundamentally impossible. Well, they were
wrong. But it was only fairly recently, well after the final formulation
of nonrelativistic quantum theory in the mid 1920's that first individual
electrons and then individual ions and atoms were trapped in electrodynamical
devices called atom and ion traps.
My research focuses on (i) design of novel electrostatic and electrodynamic particle traps
and (ii) the investigation of the dynamics of trapped neutral and charged particles.
Publications
- R. Blümel, J. M. Chen, E. Peik, W. Quint, W. Schleich,
Y. R. Shen and H. Walther,
Phase Transitions of Stored Laser-Cooled Ions,
Nature 334, 309--313 (1988).
- R. Blümel, C. Kappler, W. Quint and H. Walther,
Chaos and Order of Laser Cooled Ions in a Paul-Trap,
Phys. Rev. A 40, 808--823 (1989).
- R. Blümel, Hetero Charged Ion Clusters in a Paul Trap,
Z. Phys. D 16, 293--297 (1990).
- R. Blümel, E. Peik, W. Quint, and H. Walther, Phase Transitions
of Stored Laser-Cooled Ions, Acta Physica Polonica A 78,
419--432 (1990).
- R. Blümel, On the Integrability of the Two-ion Paul-Trap
in the Pseudo Potential Approximation, Phys. Lett. A 174,
174--175 (1993).
- R. Blümel, Comment on Regular and Chaotic Motions
in Ion Traps: A Nonlinear Analysis of Trap Equations,
Phys. Rev. A 48, 854--855 (1993).
- M. Moore and R. Blümel,
Quantum Manifestations of Order and Chaos in the Paul-Trap,
Phys. Rev. A 48, 3082--3091 (1993).
- J. W. Emmert, M. Moore and R. Blümel, Prediction of a
deterministic melting transition of two-ion crystals
in a Paul trap,
Phys. Rev. A 48, 1757--1760 (1993).
- M. G. Moore and R. Blümel, Prediction of an Alignment
Transition Region of Two-ion Crystals in a Paul Trap,
Phys. Rev. A 50, R4453--R4456 (1994).
- R. Blümel, Cooling-induced melting of ion crystals in a
Paul trap, Phys. Rev. A 51, 620--624 (1995).
- R. Blümel, An introduction to chaos in dynamic ion
traps, Physica Scripta T 59, 126--130 (1995).
- R. Blümel, Nonlinear Dynamics of Trapped Ions, Physica
Scripta T 59, 369--379 (1995).
- M. G. Moore and R. Blümel, An Improved Pseudo Potential for the
Two-Ion
Paul Trap, Physica Scripta T 59, 429--433 (1995).
- M. G. Moore and R. Blümel,
Prediction of Deterministic Melting
Regions of Two and Three Laser-cooled Ions in a Paul Trap,
Physica Scripta T 59, 434--437 (1995).
- R. Alheit, X. Z. Chu, M. Hoefer, M. Holzki,
G. Werth, and R. Blümel,
Nonlinear Collective Oscillations of an Ion Cloud
in a Paul Trap,
Phys. Rev. A 56, 4023--4031 (1997).
- M. A. N. Razvi, X. Z. Chu, R. Alheit, G. Werth and
R. Blümel,
Fractional frequency collective parametric resonances
of an ion cloud in a Paul trap, Phys. Rev. A 58,
R34--R37 (1998).
- B. Reusch and R. Blümel, Crystallized
Vortex Crystals,
Eur. Phys. J. D 3, 123--127 (1998).
- V. I. Savichev and R. Blümel, Squeezing close to
the stability boundaries of the Paul trap,
Phys. Lett. A 309, 211--214 (2003).
- I. Garrick-Bethell, Th. Clausen, and R. Blümel,
Universal instabilities of radio-frequency traps,
Phys. Rev. E 69, 056222 (2004), pp. 1--15.
Y. Dabaghian, R. V. Jensen and R. Blümel,
Exact trace formulas for a class of one-dimensional
ray-splitting systems, Phys. Rev. E 63,
066201, pp. 1--6 (2001).
R. Blümel and Y. Dabaghian, Combinatorial identities
for binary necklaces from exact ray-splitting trace
formulas,
J. Math. Phys. 42, 5832--5839 (2001).
Yu. Dabaghian, R. V. Jensen and R. Blümel,
One-dimensional quantum chaos: Explicitly solvable cases,
Pis'ma Zh. \'Eksp. Teor. Fiz. 74, 258--262 (2001);
JETP Lett. 74, 235--239 (2001).
R. Blümel, Yu. Dabaghian and R. V. Jensen,
Explicitly solvable cases of one-dimensional
quantum chaos,
Phys. Rev. Lett. 88, 044101 (2002).
R. Blümel, Yu. Dabaghian and R. V. Jensen,
Exact, convergent periodic-orbit expansions of
individual energy levels of regular quantum
graphs, Phys. Rev. E 65, 046222, 1--10 (2002).
Yu. Dabaghian, R. V. Jensen and R. Blümel,
Spectra of regular quantum graphs,
J. Exp. Theor. Phys. 94, 1201--1215 (2002);
Zh. Exp. Teor. Fiz. 121, 1399-1414 (2002).
Yu. Dabaghian and R. Blümel, Solution of
scaling quantum networks,
Pis'ma v. ZhETF 77, 629--632 (2003);
JETP Lett. 77, 530--533 (2003).
Yu. Dabaghian and R. Blümel, Explicit analytical
solution for scaling quantum graphs,
Phys. Rev. E 68, 055201(R) (2003), pp. 1--4.
Yu. Dabaghian and R. Blümel, Explicit spectral
formulas for scaling quantum graphs,
Phys. Rev. E 70, 046206 (2004), pp. 1--16.
A. S. Bhullar, R. Blümel, and P. M. Koch,
Ray splitting with ghost orbits: explicit, analytical
and exact solution for spectra of scaling
step potentials with tunneling,
J. Phys. A: Math. Gen. 38, L563--L569
(2005).
A. S. Bhullar, R. Blümel, and P. M. Koch,
Ghost orbit spectroscopy,
The Physical Review E (2006), in press.
R. Blümel,
Comment on 'Quantum chaos in elementary
quantum mechanics' [Eur. J. Phys. 26
(2005) 423--439] by Yu Dabaghian and R. Jensen,
Eur. J. Phys. 27, L1--L4 (2006).
- R. Blümel, Solution of the finite quantum
square-well problem,
J. Phys. A: Math. Gen. 38, L673--L678 (2005).
