By* Quantum Control* we denote the (continuous measurement and) control of systems that exhibit noise at or below the quantum limit. The Quantum Control group is located at the Institute for Gravitational Physics at Leibniz Universität Hannover, and in this context our work is focused mostly on (quantum) optical systems and subsystems of interferometric gravitational wave detectors (GWDs).

The design sensitivity of future GWDs will be limited by the *quantum nature of light*. At high detection frequencies (above approx. 50 Hz) detection noise in the form of *photon shot **noise* (SN) will dominate the overall noise budget, whereas for low frequencies (from approx. 12 to 50 Hz) *radiation pressure noise* (RPN) of the laser light, manifesting as backaction noise, will be the dominating noise source.

*Backaction cancellation* is a highly topical research area, as backaction noise at a (micro-)mechanical oscillator imprints phase noise on the interferometer light field. This phase modulation — caused by RPN — can potentially mask the gravitational wave signal to be detected.

*Precision metrology*, such as interferometric gravitational wave detection, relies heavily on control to suppress occuring noise sources, both technical and quantum. As an example, the interferometric gravitational wave detector GEO600 utilises more than 250, partially nested loops to be operational. On the controls side of our research we are working towards combining methods of *modern control* (such as Linear Quadratic Gaussian and Kalman filtering) with *coherent control* to obtain new, optimal interferometer topologies. In a more traditional approach we also devise new stabilisation techniques for optical resonators in high-precision metrology experiments.

**Our research areas, briefly:**

**Coherent quantum noise cancellation**

– Reducing the deleterious effect of radiation pressure noise (RPN) by means of destructive interference with an anti-noise process

– Realisation of a “negative mass oscillator” by an ancilla cavity (consisting of a non-degenerate squeezer and a beam splitter) coupled to the optomechanical meter cavity*Enhanced-sensitivity phase measurements using non-classical light at high frequencies*

– Squeezing at every free spectral range (FSR) of the sub-threshold optical parametric oscillator (OPO)

– High-frequency large bandwidth photodetectio

– High-precision cavity spectroscopy using high-frequency squeezed light**Opto-Mechanics**

-Set up of a membrane in the middle (MIM) cavity and a membrane at the edge (MATE) cavity which will be suitable for CQNC [1]

-Using an independent probe and pump beam to measure and generate an optical spring effect

-infere optomechanical coupling strength by measurements of optical spring

-measurement of coupling strength with optomechanical induced transparency (OMIT) [2]

-optical spring will be used to fine tune optomechanical parameters with respect to CQNC*Meta-Materials*– High reflective lightweight metasurfaces made from silicon nanospheres– Scattering processes for different topologies*(currently on hold) Modern control techniques for a quantum optical MIMO system*

– Systematic approach for optimality & robustness

– Inherently multi-input multi-output (MIMO)

– Linear Quadratic Gaussian control (LQG)

– Kalman filtering

– Time-varying Kalman filtering, an auto-locking scheme that overcomes the non-trivial, non-linear locking challenge