# PhD Projects

## Entanglement and measurement precision beyond the standard quantum limit

### Generation and verification of non-gaussian cw-light and application in non-classical interferometry (Hammerer/ Schnabel)

In this PhD project we will investigate the possibility to generate pure, non-Gaussian quantum states of continuous wave light in a nonlinear resonator. To start with, we will explore this question on the basis of an optical Kerr-nonlinearity such as it can be realized in optomechanical systems. In subsequent steps we will consider more complex nonlinearities. In order to describe these systems we will employ a recently discovered connection between the formalism of matrix product states and cavity quantum electrodynamics.

### Back action evading measurements based on entanglement (Hammerer/ Heurs)

Continuous measurements are usually accompanied by back action effects which limit the achievable sensitivity. Recently a new, entanglement-based method for back action evasion was introduced and demonstrated in the context of magnetometry. In this PhD project we will explore the connection between entanglement and back action evasion in more theoretical detail. The requirements in presence of losses and decoherence shall be investigated for a broad class of experimental platforms. Finally, we will apply these general ideas to various systems under experimental investigation in this GRK.

## Noise in transport

### Electrical noise in complex quantum dot systems (Haug/ Oestreich)

For quantum dot systems which consist of two or more semiconducting quantum dots the fluctuations in the electrical current are measured either by counting the individual electrons tunneling through the dots or by analyzing the time dependence of the tunneling current directly. Such measurements allow to obtain knowledge about the interactions and correlations in the quantum system.

### Noise in two-dimensional systems with quantizing magnetic fields (Haug/ Werner)

High-mobility two-dimensional electron gases show the quantum Hall effect and the fractional quantum Hall effect in high magnetic fields. Electrical noise measurements allow to investigate in more detail the special nature of these quantum states. In addition to single layers also coupled two-dimensional electron gases will be investigated.

## Control of optical-mechanical systems for gravitational wave detection

### Control of opto-mechanical systems by optical feedback-loops (Heurs/ Hammerer)

This project aims to design and realise an experiment with a micro-oscillator, opto-mechanically coupled to an optical cavity, which will be able to show coherent noise cancellation, finally leading to radiation-pressure limited measurements.

### Stabilization of a squeezed-light source by modern control (Heurs/ Danzmann/ Schnabel)

Goal of this project is the characterisation of a squeezed-light source with its many interacting parameters (cavity length, pump power, crystal temperature, ...) and its translation into a state space model. Modern control will be used to optimally stabilise the system and reduce its noise below the standard quantum limit

## Spin noise and entanglement in solid state systems

### Spin noise on single semiconductor quantum dots beyond the standard quantum limit (Oestreich/ Schnabel)

This project involves the interconnection between spin noise spectroscopy and the generation of squeezed light with the aim to study the complex interaction of solitary, strongly localized electron or hole spins with their local nuclear spin environment under the condition of minimal perturbation.

### Entanglement of rare-earth atom ensembles in the solid state and verification by spin noise spectroscopy (Oestreich/ Hammerer)

The objective of this project is the photon mediated entanglement of two distinct rare-earth atom ensembles embedded in a solid state environment. The entanglement production and verification is based upon spin noise spectroscopy.

## Effective quantum information theories and renormalization groups

### Quantum simulation and effective theories of opto-mechanical systems (Osborne/ Hammerer)

In this project optomechanical systems will be studied as an experimentally viable resource for the simulation of strongly correlated quantum fields.

### Tensor network and Monte-Carlo methods for correlated quantum systems (Osborne/ Werner)

The goal of this project is to extend now-mature Monte-Carlo methods to the TNS setting to study the dissipative dynamics of strongly correlated lattice systems.

## Noise correlation in ultracold polar molecular quantum gases

### Evaluation, development and implementation of effective detection methods for polar molecules (Ospelkaus/Hammerer)

The goal of this project is to develop efficient imaging techniques for molecules. Whereas atomic systems can easily be imaged with a high signal to noise ratio by means of absorption or fluorescence of atoms, the application of these techniques to molecules is inhibited by the complex molecular level structure inhibiting quasi-closed cycling transitions. Within this project, imaging techniques for molecules relying e.g. on dispersive interactions between light and molecules will be developed and evaluated.

### Preparation and analysis of complex quantum many-body phases of polar molecules (Ospelkaus/ Hammerer/Osborne)

The goal of this project is to establish the necessary experimental tools for the noise correlation analysis of complex dipolar quantum phases.

## Nonclassical Quantum Noise Correlations in optical and optomechanical systems

### Multipartite Einstein-Podolsky-Rosen-Steering (Schnabel/Werner)

“Steering“ describes a quantum effect, that was discussed by Einstein, Podolsky, and Rosen in 1935. Only now this effect has been investigated for more than two parties. The goal of this PhD project is the experimental demonstration of EPR-steering involving three or more parties on the basis of multi-mode squeezed light.

### Squeezed-light generation in optomechanical systems (Schnabel/ Hammerer)

Light in a coherent state that is reflected off a movable mirror is generally converted into a squeezed state via its radiation pressure force. To be able to observe this effect the light power needs to be high and the thermally excited motion of the mirror needs to be low. The goal of this PhD project is the observation of optomechanical squeezed-light generation using a cooled SiN membrane. Such an experiment realizes quantum mechanical coupling of light and mechanical motion.

## Statistics of continuous measurements and small sub-ensembles

### Qualitative formulation of a compromise between perturbation and information access in continuous measurements (Werner/ Hammerer)

### Continuous quantum processes an memories (Werner/ Schnabel)

### Equilibrium states of small, partial quantum systems under the influence of short range interactions (Werner/ Osborne)