Active stabilisation of a micro-sized fibre cavity using tilt locking to enable quantum operations on single ions

Abstract

In this thesis, the tilt locking scheme is applied to create an error signal that monitors length changes in a fibre-based microcavity. To find a robust and precise locking technique is an essential step towards quantum operations on single rare-earth ions doped in microcrystals.
Quantum computing and information is a frontier of modern physics. Many scholars believe that Quantum technology will have a significant impact on future computation and communication. There are currently multiple approaches to building quantum computers. At the moment, there is no clear picture of which approach for quantum operation is going to be the most applicable.
The quantum information group at Lund University focuses on rare-earth-ions doped into crystals to be used as qubits. The long-lived energy levels of these ions can be used for quantum computations. It is necessary to make use of the Purcell effect to enable the interaction with single ions. This effect describes the emission probability for a photon by an atom in an optical resonator.
The reduction of the volume leads to an enhanced emission probability and therefore enables single ion readouts. By placing the substrate in an optical microcavity with a length of just a few micrometres, the phase volume is reduced. These planoconcave cavities consist of a coated concave fibre-tip on one side and a highly reflective mirror on the other.
Vibrations in the cavity length of the cavity are currently the main limitations. There are well-known ways to actively stabilise the length of cavities, such as the Pound-Drever-Hall stabilisation, side-of-fringe locking, or the so-called tilt locking. In this work, the different locking techniques are compared and tested for their applicability to stabilise fibre-based microcavity.
In a short cavity, the resonant peaks are very far apart such that we can only use the resonant frequency, which is also used for the ion manipulations because the next resonance is no longer in the high reflectivity range of the coating. To avoid interfering with the main experiment, we base our locking scheme on the higher-order transverse modes of the cavity. These higher orders naturally occur in the cavity due to the asymmetric shape. This work derives the coupling coefficients of an incoming Gaussian beam into the higher-order transverse modes of the cavity to study the resulting error signal.
The wavelength of the light which excites the higher orders does not disturb the fundamental quantum operations. Furthermore, a test setup to show the functionality of the tilt locking scheme for the microcavity was built and tested.
In this thesis, I theoretically and experimentally demonstrate the tilt locking error signal of a microcavity.

Popular Abstract

Quantum mechanics is one of the most well-established theories in modern physics. But in our day-to-day life, we barely observe any quantum effects. This is because quantum states need to be kept isolated from the environment to stay in a quantum state. To uncouple the quantum states from the environment is one of the main challenges that need to be overcome when building a quantum computer. In Lund, we want to build a quantum computer prototype that uses ions in crystals as quantum states. With laser light, we can interact with the single ions and measure their internal state. But single ions can always only emit and absorb a single photon. To make it more likely for the ions to interact with the light, we put them into a cavity. A cavity, in this case, is two mirrors in between which the light bounces back and forth.
When a peak of the light wave in the cavity perfectly lines up with the peak of the wave from the previous round-trip, so-called constructive interference occurs. This means the light could bounce up to thousands of times before escaping the cavity. This leads to a large enhancement of the emission from the ions. For the peaks from all round-trips to line up perfectly, however, the distance between the mirrors must be exactly an integer number of wavelengths and very stable.
The biggest problem we face at the moment is that these mirrors are vibrating, which disturbs the perfect line-up, and reduces the emission enhancement. There are tricks on using the light that bounces back and forth in the cavity to detect these vibrations. When we make the laser light enter the cavity with a slight angle, the light takes a different path inside the cavity compared to the light without an angle. This different path means that the vibrations of the mirrors affect them differently.
We place a detector behind the cavity to detect the two light beams. In this signal, we can see the vibration of mirrors and correct them. Several techniques to do this are well known and have been very successfully used, for example, to detect gravitational waves. The difficulty for the cavity we use in Lund is that we have to work with an extremely short cavity to interact with the single ions. The distance between the two mirrors in our setup is less than the thickness of a human hair. This short length makes it difficult to find a suitable scheme to measure the vibration in our cavity.
In this work, we find a method of using a tilted incoming beam to measure the vibrations sufficiently well. This technique, known as tilt locking, promises to enable the interaction with single ions in the next-generation experiment.

• author: Hansen, Jannek
• supervisor: Andreas Walther
• organization: Atomic Physics; Department of Physics
• course: FYSM60 20211
• year: 2021
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• keywords: Quantum computation, optical cavity, microcavity, locking, tilt locking, cavity stabilization, Gaussian-Hermitian modes, quantum computer, higher-order transverse modes
• language: English
• id: 9047795
• date added to LUP: 2021-06-07 16:08:53
• date last changed: 2021-06-07 16:08:53