Citation
Helou, Bassam Mohamad (2019) Testing Alternative Theories of Quantum Mechanics with Optomechanics, and Effective Modes for Gaussian Linear Optomechanics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KJ1K9268. https://resolver.caltech.edu/CaltechTHESIS:12182018142547647
Abstract
Optomechanics has made great strides in theory and experiments over the past decade, which culminated in the first direct detection of gravitational waves in 2015 by LIGO. This thesis explores how optomechanics can be used to test fundamental physics other than the theory of general relativity. Our emphasis will be on falsifiable theories (ultimately, only experiments can decide whether a theory is correct) that address two outstanding issues in quantum mechanics: the measurement problem, and reconciling quantum mechanics with the theory of general relativity. In particular, we show that the space experiment LISA pathfinder places aggressive bounds on two objective collapse models, which are nonlinear stochastic modifications of the Schroedinger equation that can resolve the measurement problem. Moreover, we show that stateoftheart torsion pendulum experiments can test the SchroedingerNewton theory, which is the nonrelativistic limit of a nonlinear theory combining quantum mechanics with a fundamentally classical spacetime.
Along the way, we propose how to resolve two major difficulties with determining the predictions of nonlinear quantum mechanics in an actual experiment. First, we cannot use the density matrix formalism in nonlinear quantum mechanics and so we have to suggest and justify a particular ensemble for the thermal bath. Separating out quantum and classical fluctuations helped us propose a reasonable ensemble. Second, most researchers believe that deterministic nonlinear quantum mechanics must violate the nosignaling condition. We show this isn't necessarily the case because different interpretations of quantum mechanics make different predictions in nonlinear quantum mechanics. We propose an interpretation, the causalconditional prescription, that doesn't violate causality by noticing that once we fix an initial state, the evolution of a system under many nonlinear theories is equivalent to evolution under a linear Hamiltonian with feedback. The mapping allows us to leverage the tools of quantum control, and it tells us that if the nonlinear parameters of a nonlinear Hamiltonian respond causally (i.e. with an appropriate delay) to measurement results, then the theory can be made causal.
We also contribute to the theory of quantum optomechanics. We introduce two new bases that one can view environment modes with. In linear optomechanics a system interacts with an infinite number of bath modes. We show that the interaction can be reduced to one with finite degrees of freedom. Moreover, at any particular time, the system is correlated with only a finite number of bath modes. We show that if we make the assumption that we can measure any commuting environment modes, then this basis allows us to understand the oneshot quantum CramerRao bound in a simple way, and allows us to sweep large parameter regimes and so find promising optomechanics topologies for quantum state preparation tasks that we can then analyze without the assumption of being able to measure any observable of the environment. We also use this basis to show that when we are interested in the conditional dynamics of a test mass, we can only adiabatically eliminate a lossy cavity when we measure the optomechanical system at a slow enough rate. Finally, we develop an analytic filter for obtaining the state of a generic optomechanical system that interacts linearly with its environment and is driven by Gaussian states, and where the outgoing light is measured with a nonlinear photoncounting measurement. We hope that our work will help researchers explore optomechanics topologies that make use of photon counters.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Quantum Mechanics, Optomechanics, SchroedingerNewton theory, collapse models, nonlinear quantum mechanics  
Degree Grantor:  California Institute of Technology  
Division:  Engineering and Applied Science  
Major Option:  Applied Physics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Group:  TAPIR, Astronomy Department  
Thesis Committee: 
 
Defense Date:  11 December 2018  
Record Number:  CaltechTHESIS:12182018142547647  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:12182018142547647  
DOI:  10.7907/KJ1K9268  
Related URLs: 
 
ORCID: 
 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  11321  
Collection:  CaltechTHESIS  
Deposited By:  Bassam Helou  
Deposited On:  27 Mar 2019 20:51  
Last Modified:  04 Mar 2020 22:06 
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