Holographic realization of the prime number quantum potential.

We report the experimental realization of the prime number quantum potential VN (x), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. As a further application, we also implement a potential whose spectrum is given by the lucky numbers, a sequence of integers generated by a different sieve than the familiar Eratosthenes's sieve used for the primes. Our results pave the way toward the realization of quantum potentials with arbitrary sequences of integers as energy levels and show, in perspective, the possibility to set up quantum systems for arithmetic manipulations or mathematical tests involving prime numbers.

Measurement of vacuum pressure with a magneto-optical trap: A pressure-rise method.

The lifetime of an atom trap is often limited by the presence of residual background gases in the vacuum chamber. This leads to the lifetime being inversely proportional to the pressure. Here, we use this dependence to estimate the pressure and to obtain pressure rate-of-rise curves, which are commonly used in vacuum science to evaluate the performance of a system. We observe different rates of pressure increase in response to different levels of outgassing in our system. Therefore, we suggest that this is a sensitive method which will find useful applications in cold atom systems, in particular, where the inclusion of a standard vacuum gauge is impractical.

Light-induced atomic desorption in a compact system for ultracold atoms.

In recent years, light-induced atomic desorption (LIAD) of alkali atoms from the inner surface of a vacuum chamber has been employed in cold atom experiments for the purpose of modulating the alkali background vapour. This is beneficial because larger trapped atom samples can be loaded from vapour at higher pressure, after which the pressure is reduced to increase the lifetime of the sample. We present an analysis, based on the case of rubidium atoms adsorbed on pyrex, of various aspects of LIAD that are useful for this application. Firstly, we study the intensity dependence of LIAD by fitting the experimental data with a rate-equation model, from which we extract a correct prediction for the increase in trapped atom number. Following this, we quantify a figure of merit for the utility of LIAD in cold atom experiments and we show how it can be optimised for realistic experimental parameters.

Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments.

We demonstrate a method to independently and arbitrarily tailor the spatial profile of light of multiple wavelengths and we show possible applications to ultracold atoms experiments. A single spatial light modulator is programmed to create a pattern containing multiple spatially separated structures in the Fourier plane when illuminated with a single wavelength. When the modulator is illuminated with overlapped laser beams of different wavelengths, the position of the structures is wavelength-dependent. Hence, by designing their separations appropriately, a desired overlap of different structures at different wavelengths is obtained. We employ regional phase calculation algorithms and demonstrate several possible experimental scenarios by generating light patterns with 670 nm, 780 nm and 1064 nm laser light which are accurate to the level of a few percent. This technique is easily integrated into cold atom experiments, requiring little optical access.

Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms.

Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms.

Recent progress in Bose-Einstein condensation experiments.

When the atoms in a gas are cooled to extremely low temperatures, their quantum-mechanical nature starts to dominate the properties of the whole gas. Under the appropriate conditions, the atoms will 'condense' into a single quantum state of the system-a phenomenon known as Bose-Einstein condensation (BEC). The resulting 'condensate' behaves as a single, observable quantum-mechanical object. During the last decade, this new state of matter has displayed many remarkable properties. In this paper, we review some of the most recent experimental developments in the BEC field, highlighting the role of atomic interactions and the high degree of control with which condensates may be manipulated.