A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Motivated by far-reaching applications ranging from quantum simulations of complex processes in physics and chemistry to quantum information processing1, a broad effort is currently underway to build large-scale programmable quantum systems. Such systems provide insights into strongly correlated quantum matter2–6, while at the same time enabling new methods for computation7–10 and metrology11. Here we demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms, featuring strong interactions controlled by coherent atomic excitation into Rydberg states12. Using this approach, we realize a quantum spin model with tunable interactions for system sizes ranging from 64 to 256 qubits. We benchmark the system by characterizing high-fidelity antiferromagnetically ordered states and demonstrating quantum critical dynamics consistent with an Ising quantum phase transition in (2 + 1) dimensions13. We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation14, experimentally map the phase diagram and investigate the role of quantum fluctuations. Offering a new lens into the study of complex quantum matter, these observations pave the way for investigations of exotic quantum phases, non-equilibrium entanglement dynamics and hardware-efficient realization of quantum algorithms. A programmable quantum simulator with 256 qubits is created using neutral atoms in two-dimensional optical tweezer arrays, demonstrating a quantum phase transition and revealing new quantum phases of matter.

Quantum phases of matter on a 256-atom programmable quantum simulator

Structured Light from Lasers

We demonstrate the trapping and manipulation of single neutral atoms in reconfigurable arrays of optical tweezers. Our approach offers unparalleled speed by using a Texas Instruments Digital Micro-mirror Device (DMD) as a holographic amplitude modulator with a frame rate of 20,000 per second. We show the trapping of static arrays of up to 20 atoms, as well as transport of individually selected atoms over a distance of 25{\mu}m with laser cooling and 4{\mu}m without. We discuss the limitations of the technique and the scope for technical improvements.

Single-atom trapping and transport in DMD-controlled optical tweezers

Acoustic holograms are a low cost method for generating arbitrary diffraction limited pressure distributions in 3 dimensions. However, at present, the creation of complex fields using this approach is limited by the inability of these holograms to independently modulate both the phase and amplitude of an incident wave. In this work, it is shown that this limitation can be circumvented by using two phase holograms, designed using an iterative Fourier transform algorithm, to form the phase conjugate of a back-propagated target pattern over a predefined surface. An experimental test-case, designed to generate the letters “UCL” with the uniform amplitude and phase, is prepared to demonstrate the feasibility of this technique. Field measurements from this sample show that the modulation of both the phase and amplitude of the acoustic field can be achieved with this approach.

Phase and amplitude modulation with acoustic holograms

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 LG10 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.

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

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 $LG^{0}_{1}$ 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.

M. Anderson

Papers

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

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