A scalable hardware and software control apparatus for experiments with hybrid quantum systems

Modern experiments with fundamental quantum systems - like ultracold atoms, trapped ions, single photons - are managed by a control system formed by a number of input/output electronic channels governed by a computer. In hybrid quantum systems, where two or more quantum systems are combined and made to interact, establishing an efficient control system is particularly challenging due to the higher complexity, especially when each single quantum system is characterized by a different timescale. Here we present a new control apparatus specifically designed to efficiently manage hybrid quantum systems. The apparatus is formed by a network of fast communicating Field Programmable Gate Arrays (FPGAs), the action of which is administrated by a software. Both hardware and software share the same tree-like structure, which ensures a full scalability of the control apparatus. In the hardware, a master board acts on a number of slave boards, each of which is equipped with an FPGA that locally drives analog and digital input/output channels and radiofrequency (RF) outputs up to 400 MHz. The software is designed to be a general platform for managing both commercial and home-made instruments in a user-friendly and intuitive Graphical User Interface (GUI). The architecture ensures that complex control protocols can be carried out, such as performing of concurrent commands loops by acting on different channels, the generation of multi-variable error functions and the implementation of self-optimization procedures. Although designed for managing experiments with hybrid quantum systems, in particular with atom-ion mixtures, this control apparatus can in principle be used in any experiment in atomic, molecular, and optical physics.Comment: 10 pages, 12 figure

An Aharonov-Bohm interferometer for determining Bloch band topology

The geometric structure of an energy band in a solid is fundamental for a wide range of many-body phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an Aharonov-Bohm interferometer that measures the magnetic flux penetrating a given area in real space, we realize an atomic interferometer to measure Berry flux in momentum space. We demonstrate the interferometer for a graphene-type hexagonal lattice, where it has allowed us to directly detect the singular $\pi$ Berry flux localized at each Dirac point. We show that the interferometer enables one to determine the distribution of Berry curvature with high momentum resolution. Our work forms the basis for a general framework to fully characterize topological band structures and can also facilitate holonomic quantum computing through controlled exploitation of the geometry of Hilbert space.Comment: 5+5 page

Design of a Littrow-type diode laser with independent control of cavity length and grating rotation

We present a novel, to the best of our knowledge, extended-cavity diode laser based on a modified Littrow configuration. The coarse wavelength adjustment via the rotation of a diffraction grating is decoupled from the fine tuning of the external cavity modes by positioning a piezo transducer behind the diode laser, making the laser robust against misalignment and hysteresis even with long external cavities. Two laser prototypes with external cavities of different lengths were tested with a 780 nm laser diode, and locked to an atomic reference. We observed a mode-hop-free frequency tunability broader than the free spectral range of the external cavity upon changes in its length. The design is well suited to atomic and molecular experiments demanding a high level of stability over time

A compact radiofrequency drive based on interdependent resonant circuits for precise control of ion traps

Paul traps are widely used to confine electrically charged particles like atomic and molecular ions by using an intense radiofrequency (RF) field, typically obtained by a voltage drop on capacitative electrodes placed in vacuum. We present a RF drive realized on a compact printed circuit board (PCB) and providing a high-voltage RF signal to a quadrupole Paul trap. The circuit is formed by four interdependent resonant circuits $-$ each of which connected to an electrode of a Paul trap $-$ fed by low-noise amplifiers, leading to an output voltage of peak-to-peak amplitude up to 200 V at 3.23 MHz. The presence of a single resonant circuit for each electrode ensures a strong control on the voltage drop on each electrode, e.g. by applying a DC field through a bias tee. Additionally, the moderate quality factor Q = 67 of the resonant circuits ensures a fast operation of the drive, which can be turned on and off in less than 10 $\mu$s. Finally, the RF lines are equipped with pick-ups that sample the RF in phase and amplitude, thus providing a signal that can be used to actively control the voltage drop at the trap's electrodes. Thanks to its features, this drive is particularly suited for experiments in which high trap stability and excellent micromotion compensation are required.Comment: 7 pages, 8 figure

Bloch state tomography using Wilson lines.

Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems. Using an ultracold gas of rubidium atoms loaded in a honeycomb optical lattice, we realize strong-force dynamics in Bloch bands that are described by Wilson lines and observe an evolution in the band populations that directly reveals the band geometry. Our technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multiband Chern and Z₂ numbers.This work was supported by the Alfred P. Sloan Foundation, the European Commision (UQUAM, AQuS), Nanosystems Initiative Munich, the Harvard Quantum Optics Center, the Harvard-MIT CUA, NSF Grant No. DMR-1308435, the DARPA OLE program, the AFOSR Quantum Simulation MURI, the ARO-MURI on Atomtronics, and the ARO-MURI Quism program.This is the author accepted manuscript. The final version is available from the American Association for the Advancement of Science via http://dx.doi.org/10.1126/science.aad581