Self-Consistent Projection Operator Theory for Quantum Many-Body Systems

We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient analytical and numerical approach. Besides its practical use it provides a novel interpretation and systematic extension of mean-field approaches and an adaption of open quantum systems theory to settings where a dynamically evolving environment has to be taken into account. We show its high accuracy for two significant classes of complex quantum many-body dynamics, unitary evolutions of non-equilibrium states in closed and stationary states in driven-dissipative systems.Comment: 13 pages, 4 figure

Self-Consistent Projection Operator Theory in Nonlinear Quantum Optical Systems: A case study on Degenerate Optical Parametric Oscillators

Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.Comment: Comments are welcom

Classical and quantum-linearized descriptions of degenerate optomechanical parametric oscillators

Recent advances in the development of modern quantum technologies have opened the possibility of studying the interplay between spontaneous parametric down-conversion and optomechanics, two of the most fundamental nonlinear optical processes. Apart from practical reasons, such scenario is very interesting from a fundamental point of view, because it allows exploring the optomechanical interaction in the presence of a strongly quantum-correlated field, the spontaneously down-converted mode. In this work we analyze such problem from two approximate but valuable perspectives: the classical limit and the limit of small quantum fluctuations. We show that, in the presence of optomechanical coupling, the well-known classical phase diagram of the optical problem gets modified by the appearance of new dynamical instabilities. As for the quantum-mechanical description, we prove the ability of the squeezed down-converted field to cool down the mechanical motion not only to thermal but also to squeezed thermal mechanical states, and in a way that can be much less sensitive to parameters (e.g., detuning of the driving laser) than standard sideband cooling.Comment: New version including the quantum linearized description of the system and appendices. Accepted in Physical Review

Thermoelastic Damping in MEMS Gyroscopes at High Frequencies

Microelectromechanical systems (MEMS) gyroscopes are widely used, e.g. in modern automotive and consumer applications, and require signal stability and accuracy in rather harsh environmental conditions. In many use cases, device reliability must be guaranteed under large external loads at high frequencies. The sensitivity of the sensor to such external loads depends strongly on the damping, or rather quality factor, of the high frequency mechanical modes of the structure. In this paper, we investigate the influence of thermoelastic damping on several high frequency modes by comparing finite element simulations with measurements of the quality factor in an application-relevant temperature range. We measure the quality factors over different temperatures in vacuum, to extract the relevant thermoelastic material parameters of the polycrystalline MEMS device. Our simulation results show a good agreement with the measured quantities, therefore proving the applicability of our method for predictive purposes in the MEMS design process. Overall, we are able to uniquely identify the thermoelastic effects and show their significance for the damping of the high frequency modes of an industrial MEMS gyroscope. Our approach is generic and therefore easily applicable to any mechanical structure with many possible applications in nano- and micromechanical systems

Optical two-mode squeezed interferometer for enhanced chip-integrated quantum-metrology

In this work we analyze the possibility to use two-mode squeezed light to improve the performance of existing sensor technology with the focus on its miniaturization. Based on a general four-wave mixing Hamiltonian, we formulate simple linearized equations that describe the FWM process below threshold and can be used to analyze the squeezing quality between the generated optical signal and idler modes. For a possible realization, we focus on the chip-integrated generation using micro-ringresonators and the impact of the design and the pump light on the squeezing quality is shown with the derived equations. With this we analyze the usage in quantrum metrology and analyze the application of two-mode squeezed light in a Mach-Zehnder interferometer and for a deeper understanding and motivation also in the application of a Sagnac-interferometer. Due to the impact of losses in these use cases, we show that the main usage is for small and compact devices, which can lead to a quantum improvement up to a factor of ten in comparison of using only classical light. This enables the use of small quantum-enhanced sensors with a comparable performance to larger classical sensors