A 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. However, to date iterative Fourier transform algorithms have been predominantly used. 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.Comment: 11 pages, 4 figure

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

The authors acknowledge funding from the Leverhulme Trust Research Project Grant RPG-2013-074 and from the EPSRC grant GR/T08272/01.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.PostprintPeer reviewe

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 towards 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.Publisher PDFPeer reviewe

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

This research was supported by UK EPSRC grant GR/T08272/01, IOP Scotland and the Leverhulme Trust Research Project Grant RPG-2013-074.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.Peer reviewe

Feedback-enhanced algorithm for aberration correction of holographic atom traps

We show that a phase-only spatial light modulator can be used to generate non-trivial light distributions suitable for trapping ultracold atoms, when the hologram calculation is included within a simple and robust feedback loop that corrects for imperfect device response and optical aberrations. This correction reduces the discrepancy between target and experimental light distribution to the level of a few percent (RMS error). We prove the generality of this algorithm by applying it to a variety of target light distributions of relevance for cold atomic physics.Comment: 5 pages, 4 figure

Potential landscaping for ultracold atoms using holographic optical traps

The development of new laser beam shaping methods is important in a variety of fields within optics, atomic physics and biophotonics. Spatial light modulators offer a highly versatile method of time-dependent beam shaping, based on imprinting a phase profile onto an incident laser beam that determines the intensity in the trapping plane laser field. The calculation of the required phase is a well-known inverse problem, which can be tackled with different approaches. Our method based on conjugate gradient minimisation [1] not only allows the calculation of smooth and accurate intensity profiles suitable for trapping cold atoms, but can also be used to generate multi-wavelength traps [2] and for simultaneous control over both the intensity and the phase of the light [3], with exceptionally high reconstruction fidelity. References: [1] T Harte, et al., "Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms" Opt. Express 22, 26548 (2014) [2] D Bowman, et al., "Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments" Opt. Express 23, 8365 (2015) [3] D Bowman, et al., "High-fidelity phase and amplitude control of phase-only computer generated holograms using conjugate gradient minimisation" Opt. Express 25, 11692 (2017)PostprintNon peer reviewe

High-fidelity phase and amplitude control of phase-only computer generated holograms using conjugate gradient minimisation

Funding: Leverhulme Trust (RPG-2013-074); EPSRC (EP/G03673X/1; EP/L015110/1).We demonstrate simultaneous control of both the phase and amplitude of light using a conjugate gradient minimisation-based hologram calculation technique and a single phase-only spatial light modulator (SLM). A cost function, which incorporates the inner product of the light field with a chosen target field within a defined measure region, is efficiently minimised to create high fidelity patterns in the Fourier plane of the SLM. A fidelity of F = 0.999997 is achieved for a pattern resembling an LG01 mode with a calculated light-usage efficiency of 41.5%. Possible applications of our method in optical trapping and ultracold atoms are presented and we show uncorrected experimental realisation of our patterns with F = 0.97 and 7.8% light efficiency.Publisher PDFPeer reviewe

Guiding Neutral Atoms with a Wire

We demonstrate guiding of cold neutral atoms along a current carrying wire. Atoms either move in Kepler-like orbits around the wire or are guided in a potential tube on the side of the wire which is created by applying an additional homogeneous bias field. These atom guides are very versatile and promising for applications in atom optics.Comment: 4 pages, 6 figures, submitted to PR

Atom Chips

Atoms can be trapped and guided using nano-fabricated wires on surfaces, achieving the scales required by quantum information proposals. These Atom Chips form the basis for robust and widespread applications of cold atoms ranging from atom optics to fundamental questions in mesoscopic physics, and possibly quantum information systems

Cold atoms in space: community workshop summary and proposed road-map

We summarise the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with the European Space Agency (ESA) and national space and research funding agencies