Quantum research with an arbitrary waveform generator

Precision is always important in research, and there are few areas requiring greater precision than that of quantum research. When the Institute for Quantum Optics and Quantum Information at Austria’s University of Innsbruck needed an arbitrary waveform generator (AWG) to generate a wide variety of signals for its research, it opted for a model from Spectrum Instrumentation.

Because of the variety of experiments the device would be used for, it was important to have an AWG that was easy to program using a PC so that the output could be easily customised to each use. A Spectrum M4i.6631-x8 was selected because, being on a PCI Express card, it could be incorporated into a PC and directly driven by it.

The first application for the instrument was applying a multiple-frequency signal in the radiofrequency regime. Each frequency component is realised using a sinusoidal function. The resulting beat signal is used to simultaneously address individual ions in a trapped-ion quantum simulator.

“We are doing the quantum simulation with trapped, cooled calcium ions, for which single-ion addressability is essential,” said Christine Maier, a researcher at the institute. “To achieve this, we send a laser beam through an acousto-optic deflector (AOD). The frequency of the radiofrequency signal, which one applies to this AOD crystal, defines the deflection angle of the laser beam and therewith it decides which ion of our linear ion string is addressed.

“The AWG now allows us to produce multiple-frequency signals, even with each having arbitrary amplitudes, which means that we can now address multiple ions in our ion string simultaneously. One advantage of this is that the experiment is faster because we don’t need to cycle through addressing each ion individually, one after the other.

“But it also opens up an entirely new field of study for us: up to now we could only investigate unperturbed energy transport in our ion chain. However, by addressing individual ions with arbitrary strength ... we now can create arbitrary potential barriers and study energy transport in disordered quantum systems. The AWG even allows us to program time-varying potentials to study dynamic disorder phenomena.”

The second application was the cancellation, via destructive interference, of undesired frequency mixing terms that arise, for example, when applying multiple-frequency signals to an acousto-optic modulator. As noted by Maier, “When applying multiple-frequency signals, several sum and difference frequency components will arise and finally map onto the optical signal that you are sending onto the ions. This brings two problems.

“First, you lose power from the frequency components that you actually want and second, the mixing terms could hit some resonance frequencies of the ion chain and destroy the quantum model that you want to simulate. Using the AWG enables us to cancel these undesired terms via destructive interference in real-time measurement and feedback loops.”

The Spectrum M4i-6631-x8 AWG.

The Spectrum AWG can replay loaded waveforms from its 4 GB of internal memory at speeds of up to 1.25 GS/s. The digital signal is converted into an analog output signal with a defined offset and amplitude using 16-bit D to A conversion to provide fine signal details that emulate those found in the real world. Any waveform can be replayed from a previously acquired waveform to a calculated or simulated waveform from DC to 400 MHz. It also has a FIFO streaming capability that enables it to generate arbitrary waveforms for hours at a time, unlike other AWGs that have reduced signal play times due to limited onboard memory. This enables tests to be carried out for much longer periods.

“It is highly configurable,” said Maier. “Two AWG channels, a choice of trigger options, external clock inputs, multiple and gated replay modes, looping functions and even the possibility to combine two trigger inputs via logic gates. This, combined with the high resolution and a sampling rate of 1.25 GS/s, made it the logical choice to provide the flexibility for the projects that we have now and, importantly, whatever needs we may have in the future with just one instrument.”

Top image caption: The ion trap at The Institute for Quantum Optics and Quantum Information at the University of Innsbruck.