Micromotion minimization using Ramsey interferometry

We minimize the stray electric field in a linear Paul trap quickly and accurately, by applying interferometry pulse sequences to a trapped ion optical qubit. The interferometry sequences are sensitive to the change of ion equilibrium position when the trap stiffness is changed, and we use this to determine the stray electric field. The simplest pulse sequence is a two-pulse Ramsey sequence, and longer sequences with multiple pulses offer a higher precision. The methods allow the stray field strength to be minimized beyond state-of-the-art levels. Using a sequence of nine pulses we reduce the 2D stray field strength to (10.5±0.8)mVm-1 in 11s measurement time. The pulse sequences are easy to implement and automate, and they are robust against laser detuning and pulse area errors. We use interferometry sequences with different lengths and precisions to measure the stray field with an uncertainty below the standard quantum limit. This marks a real-world case in which quantum metrology offers a significant enhancement. Also, we minimize micromotion in 2D using a single probe laser, by using an interferometry method together with the resolved sideband method; this is useful for experiments with restricted optical access. Furthermore, a technique presented in this work is related to quantum protocols for synchronizing clocks; we demonstrate these protocols here.

Linear quadrupole Paul trap with a charged filament

A charged filament stretched along the axis of a linear electrodynamic trap performs an oscillatory-rotational motion, as a result of which the charged particles are captured by the filament in the regions of the antinodes. Such a dynamic thread is actually an additional trap inside the Paul trap.

Double-well trap for charged microparticles

We propose a double-well linear Paul trap for particle’s spatial selection according to the charge-to-mass ratio. To perform spatial selection we implemented an experimental setup that permits to detect particles’ positions in the double-well trap from three different view-points: top, front left, and front right. The setup gives an opportunity to monitor the particles’ axial density distribution in real-time. We have shown a strong correlation between axial position of separated localization areas and the DC voltages applied to the rod and end-cap electrodes. We have experimentally determined the critical localization parameters where double-well mode acquires for all the trapped charged microparticles. According to the experimental data and a numerical simulation a upper value of charge-to-mass ratio of the trapped microparticles was estimated.

Riemann zeros from Floquet engineering a trapped-ion qubit

The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in random matrix theory and quantum chaos for decades. Here we present an experimental observation of the lowest non-trivial Riemann zeros by using a trapped-ion qubit in a Paul trap, periodically driven with microwave fields. The waveform of the driving is engineered such that the dynamics of the ion is frozen when the driving parameters coincide with a zero of the real component of the zeta function. Scanning over the driving amplitude thus enables the locations of the Riemann zeros to be measured experimentally to a high degree of accuracy, providing a physical embodiment of these fascinating mathematical objects in the quantum realm.

Theoretical fractional formulation of a three-dimensional radio frequency ion trap (Paul-trap) for optimum mass separation

We investigate the dynamics of an ion confined in a Paul–trap supplied by a fractional periodic impulsional potential. The Cantor–type cylindrical coordinate method is a powerful tool to convert differential equations on Cantor sets from cantorian–coordinate systems to Cantor–type cylindrical coordinate systems. By applying this method to the classical Laplace equation, a fractional Laplace equation in the Cantor–type cylindrical coordinate is obtained. The fractional Laplace equation is solved in the Cantor–type cylindrical coordinate, then the ions is modelled and studied for confined ions inside a Paul–trap characterized by a fractional potential. In addition, the effect of the fractional parameter on the stability regions, ion trajectories, phase space, maximum trapping voltage, spacing between two signals and fractional resolution is investigated and discussed.