# PhD Projects

### Open positions

*Pre- and Retrodiction of Quantum States of Solid State Defect Centers*

We aim to study the optical detection of spin dynamics in defect centers of solid state systems such as Phosphorous defects in Silicon. Continuous time monitoring of the spin dynamics allows to predict at any time the quantum state of the spin conditioned on the photocurrent based on the formalism of stochastic Schrödinger equations. Recently, the converse problem has been studied theoretically, namely the retrodiction of a past quantum state given the same measurement. The goal of this project will be to apply these concepts to long-lived defect centers in order to test and improve our understanding of the quantum dynamics of these solid state systems. More information: [click]

*Counting statistics in single-electron tunneling through quantum dots*

Single electrons in quantum dots are used in quantum sensing and quantum information applications. Real time detection of single-electron tunneling through quantum dots is possible and from such data the full counting statistics for the quantum mechanical tunneling events is obtained. Recently it was shown that the statistics of tunneling through single quantum dots can be not only detected but also influenced and manipulated by e.g. involving feedback. The present project focuses on analyzing and manipulating the counting statistics in single-electron tunneling through more complex quantum systems which consist of up to four quantum dots. More information: [click]

*Spin dynamics in isotopically purified silicon *

This project comprises the experimental optical investigation of the spin dynamics in isotopically purified silicon via optical laser spectroscopy at low temperatures. The hyperfine-induced spin decoherence of localized, phosphor bound electrons can be massively prolonged by isotopically enriching the nuclear spin-free isotope ^{28}Si, which is a prerequisite in a potential solid-state spin based quantum information processing. The samples are provided via collaborations and this work focusses on the experimental investigation of the complex spin dynamics in an advanced laboratory environment.

Requirements: We expect an appropriate academic education with a master degree or equivalent in physics with exceptional marks – preferably in solid state physics or quantum optics – a broad interest in physics, and good speaking and writing skills in English.

Supervisor: Prof. Dr. Michael Oestreich, Institute of Physics, Leibniz Universität Hannover

*Quantum radiation pressure noise cancellation schemes in next-generation interferometricgravitational wave detectors *

Current interferometric gravitational wave detectors (such as Advanced LIGO) are already largely at the quantum limit of sensitivity. This project focuses on a quantum noise cancellation scheme for future detector generations, using destructive interference with an anti-noise process to coherently cancel quantum radiation pressure noise. The experimental „ingredients“ needed for the realisation of this scheme are polarisation non-degenerate non-classical light sources, opto-mechanical resonators using different micro-mechanical oscillators at cryogenic temperatures, and subtle control schemes. This work is conducted in the highly active collaborative research environment at the AEI Hannover within the LIGO Scientific Collaboration.

Requirements: We expect an appropriate academic education with a master degree or equivalent in physics with exceptional marks – preferably in quantum opto-mechanics – a broad interest in physics, and good speaking and writing skills in English.

Supervisor: Prof. Dr. Michèle Heurs, Institute of for Gravitational Physics, Leibniz Universität Hannover

# Closed positions

*Spin qubits in GaAs/AlGaAs quantum dots (closed position)*

This project will underpin developments in solid-state quantum computing and quantum communications. We aim to understand the physics of spin quantum bits (qubits) in ultra-high quality GaAs/AlGaAs quantum dots. Highly entangled photon qubits have been demonstrated recently in this new system, and it is now a challenge to investigate the correlations between photon and spin qubits. This work will pave the way towards a solid-state quantum repeater based on semiconductor platforms.

Requirements: We expect an appropriate academic education with a master degree or equivalent in physics with exceptional marks – preferably in solid state physics or quantum optics – a broad interest in physics, and good speaking and writing skills in English.

Supervisor: Prof. Dr. Fei Ding, Institute of Physics, Leibniz Universität Hannover

**Evaluation, development and implementation of effective cooling and detection methods for polar molecules**** (closed position)**

The goal of this project is to develop efficient imaging techniques for molecules. Whereas atomic systems can easily be cooled and imaged using laser light, the application of these techniques to molecules is inhibited by the complex molecular level structure inhibiting quasi-closed cycling transitions. Within this project, cooling and imaging techniques for molecules will be developed and evaluated.

Requirements: We expect an appropriate academic education with a master degree or equivalent in physics with exceptional marks – preferably in solid state physics or quantum optics – a broad interest in physics, and good speaking and writing skills in English.

Supervisor: Prof. Dr. Silke Ospelkaus, Institute for Quantum Optics, Leibniz Universität Hannover

## Entanglement and measurement precision beyond the standard quantum limit (closed)

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

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) (closed)

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 (closed)

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

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) (closed)

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 (closed)

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

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) (closed)

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 (closed)

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

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) (closed)

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 (closed)

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

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) (closed)

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 (closed)

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

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) (closed)

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 (closed)

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

“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) (closed)

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 (closed)

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

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

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