# Ion Ring Trap

## The Platform

This ion trap features a unique geometry among surface ion traps – three circular electrodes in the center create a highly circularly symmetric potential, allowing ions to be trapped in a ring. This symmetry offers numerous possibilities, such as ion crystals with perfectly even spacing and no edge effects. These features can be exploited to simulate quantum systems with periodic boundary conditions, in which one can study effects such as quantum friction and quantum phase transitions of a one-dimensional periodic crystal. The rotational symmetry of this system also makes it a great platform to study and control one of the most conceptually simple quantum systems: the quantum rotor. For more information see PRL 118, 053001 (2017).

## Current Projects

### Coherent control of a quantum rotor by light carrying orbital angular momentum

Using the ring trap we have realized a quantum rotor system, which exhibits quantized angular momentum. It consists of just a single pair of ions that can freely rotate about each other. Using laser light incident at a slight angle from the normal to the rotor plane, we can impart angular momentum onto the rotor and create superpositions of these quantized angular momentum states. See PRL 123, 133202 (2019) for more information. This technique however, which uses a plane wave of light, is limited in how much angular momentum can be transferred. We aim to implement a more sophisticated method in which light with a phase gradient in the angular direction can carry an arbitrary but controllable angular momentum to impart onto the rotor, offering more control and allowing the creation of more interesting rotor states.

### Demonstration of indistinguishability by direct particle exchange

The symmetrization postulate of quantum mechanics requires that the state of a system of two
identical quantum particles obey exchange symmetry, in which the multiparticle wavefunction is
unchanged under an exchange of the two particles if they are bosons, and acquires only a minus
sign under this exchange if they are fermions. This symmetry erases the distinct identities that
this pair of particles would otherwise have, and has a wide range of implications that have been
observed in many different ways over many decades. We aim to demonstrate this by using our quantum
rotor to exchange a single pair of ^{40}Ca^{+} ions by using a superposition of different angular momentum
states, thus directly interfering them with each other.