Mutually unbiased bases in dimension six: The four most distant bases

We consider the average distance between four bases in dimension six. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in dimension six. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically-found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases.Comment: 10 pages, 2 figures, 1 tabl

Alkali suppression within laser ion-source cavities and time structure of the laser ionized ion-bunches

The chemical selectivity of the target and ion-source production system is an asset for Radioactive Ion-Beam (RIB) facilities equipped with mass separators. Ionization via laser induced multiple resonant steps Ionization has such selectivity. However, the selectivity of the ISOLDE Resonant Ionization Laser Ion-Source (RILIS), where ionization takes place within high temperature refractory metal cavities, suffers from unwanted surface ionization of low ionization potential alkalis. In order to reduce this type of isobaric contaminant, surface ionization within the target vessel was used. On-line measurements of the efficiency of this method is reported, suppression factors of alkalis up to an order of magnitude were measured as a function of their ionization potential. The time distribution of the ion bunches produced with the RILIS was measured for a variety of elements and high temperature cavity materials. While all ions are produced within a few nanoseconds, the ion bunch sometimes spreads over more than 100 ms. This demonstrates that ions are confined within high temperature metallic cavities. It is the internal electrical field of these cavities that causes the ions to drifts to the extraction region and defines the dwell time of the ions in the cavity. Beam optics calculations were carried out to simulate the pulse shape of a RILIS ion bunch and are compared to the actual measurements

Optimal quantum control in nanostructures: Theory and application to generic three-level system

Coherent carrier control in quantum nanostructures is studied within the framework of Optimal Control. We develop a general solution scheme for the optimization of an external control (e.g., lasers pulses), which allows to channel the system's wavefunction between two given states in its most efficient way; physically motivated constraints, such as limited laser resources or population suppression of certain states, can be accounted for through a general cost functional. Using a generic three-level scheme for the quantum system, we demonstrate the applicability of our approach and identify the pertinent calculation and convergence parameters.Comment: 7 pages; to appear in Phys. Rev.

Tomographic Quantum Cryptography: Equivalence of Quantum and Classical Key Distillation

The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.Comment: 4 pages, 1 figur

Focusing a deterministic single-ion beam

We focus down an ion beam consisting of single 40Ca+ ions to a spot size of a few mum using an einzel-lens. Starting from a segmented linear Paul trap, we have implemented a procedure which allows us to deterministically load a predetermined number of ions by using the potential shaping capabilities of our segmented ion trap. For single-ion loading, an efficiency of 96.7(7)% has been achieved. These ions are then deterministically extracted out of the trap and focused down to a 1sigma-spot radius of (4.6 \pm 1.3)mum at a distance of 257mm from the trap center. Compared to former measurements without ion optics, the einzel-lens is focusing down the single-ion beam by a factor of 12. Due to the small beam divergence and narrow velocity distribution of our ion source, chromatic and spherical aberration at the einzel-lens is vastly reduced, presenting a promising starting point for focusing single ions on their way to a substrate.Comment: 16 pages, 7 figure

The High Resolution Spectrometer at ISOLDE

ISOLDE's HRS (High Resolution isotope Separator) was recommissioned in mid 2000, after a period out of service. Since then, the separator has routinely run with a mass resolution of 3000-4500 and during 2001 it delivered 72% of ISOLDE's radioactive output. A concerted effort has been made to understand the ion optics and optimise performance. In this paper we present an overview of the HRS and investigate the factors which limit the attainable mass resolution: ion-source emittance; optical aberrations; beam instrumentation and magnet stability