Testing Alternative Theories of Quantum Mechanics with Optomechanics, and Effective Modes for Gaussian Linear Optomechanics

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 non-linear stochastic modifications of the Schroedinger equation that can resolve the measurement problem. Moreover, we show that state-of-the-art torsion pendulum experiments can test the Schroedinger-Newton theory, which is the non-relativistic limit of a non-linear 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 non-linear quantum mechanics in an actual experiment. First, we cannot use the density matrix formalism in non-linear 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 non-linear quantum mechanics must violate the no-signaling condition. We show this isn't necessarily the case because different interpretations of quantum mechanics make different predictions in non-linear quantum mechanics. We propose an interpretation, the causal-conditional prescription, that doesn't violate causality by noticing that once we fix an initial state, the evolution of a system under many non-linear 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 non-linear parameters of a non-linear 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 one-shot quantum Cramer-Rao 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 non-linear photon-counting measurement. We hope that our work will help researchers explore optomechanics topologies that make use of photon counters.</p

Macroscopic Quantum Mechanics in a Classical Spacetime

We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects’ internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency—with a difference that depends on the internal structure of the object—and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another

LISA pathfinder appreciably constrains collapse models

Spontaneous collapse models are phenomological theories formulated to address major difficulties in macroscopic quantum mechanics. We place significant bounds on the parameters of the leading collapse models, the continuous spontaneous localization (CSL) model, and the Diosi-Penrose (DP) model, by using LISA Pathfinder’s measurement, at a record accuracy, of the relative acceleration noise between two free-falling macroscopic test masses. In particular, we bound the CSL collapse rate to be at most (2.96±0.12)×10−8  s−1. This competitive bound explores a new frequency regime, 0.7 to 20 mHz, and overlaps with the lower bound 10−8±2  s−1 proposed by Adler in order for the CSL collapse noise to be substantial enough to explain the phenomenology of quantum measurement. Moreover, we bound the regularization cutoff scale used in the DP model to prevent divergences to be at least 40.1±0.5  fm, which is larger than the size of any nucleus. Thus, we rule out the DP model if the cutoff is the size of a fundamental particle.We acknowledge support from the National Science Foundation Grants No. PHY-1404569 and No. PHY1506453, from the Australian Research Council Grants No. FT130100329 and No. DP160100760, and from the Institute for Quantum Information and Matter, a Physics Frontier Cente

Measurable signatures of quantum mechanics in a classical spacetime

We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schrödinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator’s center-of-mass wave function differ from the predictions of standard quantum mechanics [H. Yang, H. Miao, D.-S. Lee, B. Helou, and Y. Chen, Phys. Rev. Lett. 110, 170401 (2013)]. This difference is largest for low-frequency oscillators, and for materials, such as tungsten or osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum’s dynamics. Due to the nonlinearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wave-function collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light’s phase fluctuations’ spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology