Search results for “radicals”

An introduction to the Steinberg representation of a finite group of Lie type — its alternating-sum construction from parabolic inductions, worked out explicitly for SL_2.

Two pathological phenomena for algebraic groups over general bases — a group degenerating between the multiplicative and additive group across a DVR, and a non-affine identity component — built as centralizers in SL_n.

Cold atomic ensembles are among the most versatile tools in modern physics research. They play a key role in advancing next-generation frequency standards, qubit architectures, and quantum sensing technologies. Many experiments demand prolonged spatial confinement of atoms to facilitate extended interactions with electromagnetic fields, achievable through electric, magnetic, gravitational, or optical trapping mechanisms.

A cornerstone of atomic trapping is the magneto-optical trap (MOT), which relies on six counterpropagating laser beams and a pair of anti-Helmholtz coils to produce a radially symmetric quadrupole magnetic field with a central zero point.

Alternatively, optical dipole traps exploit the electric dipole interaction with a tightly focused, fardetuned high-power laser beam, offering weaker confinement than MOTs—typically below 1 mK. Unlike MOTs, these traps permit extremely weak optical excitation, circumventing limitations imposed by radiation pressure. Additionally, their trapping mechanism is largely insensitive to ground-state magnetic sublevels (neglecting tensor polarizability effects), enabling versatile configurations such as optical lattices.

Figure 1: Image of atoms trapped in the MOT. The atomic cloud is at the center of the image. The cloud dimensions are approximately 1 mm.

ble of confining Rb 87 atomic clouds at temperatures near 175 µ K. For dipole trapping, we adopted a farred-detuned (1012 nm) laser system, chosen for its dual functionality: we plan to use it both as a trapping beam and as one component in two-photon Rydberg excitation schemes. A further advantage of this configuration is its potential to confine Rydberg atoms while meeting the magic wavelength condition for ground-to-Rydberg transitions.

Magic-wavelength optical dipole traps offer particularly powerful advantages for cold atom manipulation. At this specific wavelength, the light shift for two atomic states becomes identical, effectively decoupling the internal atomic dynamics from the external motional states. This enables long coherence times for quantum operations while maintaining strong spatial confinement. Furthermore, such traps allow state-insensitive confinement, which is crucial for precision measurements and quantum information processing. The magic wavelength condition also facilitates efficient Rydberg excitation by providing identical trapping potentials for both ground and Rydberg states, minimizing decoherence during excitation processes.

We characterized the dipole trap intended for atom transfer, achieving a maximum depth of 3 mK under our experimental conditions—surpassing the Doppler cooling limit and ensuring efficient atomic confinement.