*Reinhold Blumel*

# Teaching and Research

### List of Publications

Curriculum Vitae

Courses

# Research

### ION TRAPPING

Paul Trap

Dynamic Kingdon Trap

### QUANTUM CHAOS

Ray Splitting Quantum Graphs Microwave Ionization Chaotic Scattering Chaos in Atomic Physics

### EXACT SOLUTIONS OF “UNSOLVABLE” PROBLEMS

Step-in-a-Box

Finite Quantum Square Well

### SUPER COMPUTING WITH RECYCLED PC’s

## ION TRAPPING

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.

### Paul Trap

- 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.

### Dynamic Kingdon Trap

## QUANTUM CHAOS

### Ray Splitting

### Quantum Graphs

### Microwave Ionization

### Chaotic Scattering

## EXACT SOLUTIONS OF “UNSOLVABLE” PROBLEMS

### Step-in-a-Box

- 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.*, Eur. J. Phys.**26**(2005) 423--439] by Yu Dabaghian and R. Jensen**27**, L1–L4 (2006).

### Finite Quantum Square Well

- R. Blümel,
*Solution of the finite quantum square-well problem*, J. Phys. A: Math. Gen.**38**, L673–L678 (2005).

## SUPER COMPUTING WITH RECYCLED PC’s

- R. Blümel,