Astronomical observations strongly suggest that the universe is mostly dark. Its two dominant components, dark energy and dark matter, remain among the most mysterious concepts in cosmology today. The effects of these two substances are imprinted in the remaining few percent of the universe that consists of normal (baryonic) matter. Dark energy is responsible for the accelerating expansion of the universe and the existence of dark matter is deduced from the orbital properties of stars in galaxies. In this talk, we discuss the observable effects of both these phenomena and applications of the Optimal Transport (OT) theory to approach them. OT has a fundamental connection to physical problems as most phenomena in nature are governed by optimization principles. Applications of OT touch many fields of physics from quantum mechanics to general relativity, among others. We address two independent astrophysical problems using OT techniques: Recovering the Galactic Potential with Optimal Transport Theory, and Optimal Transport Reconstruction of Baryon Acoustic Oscillations. Our results would develop novel ways to place stronger constraints on cosmology and dark energy; while also revealing the distribution of dark matter in galaxies, thus constraining dark matter's properties.

 Quantum control and measurement of mechanical oscillators have been achieved by coupling mechanical oscillators to auxiliary degrees of freedom in the form of optical or microwave cavities, allowing numerous advances such as quantum state transfer or mechanical entanglement. An enduring challenge in constructing such hybrid systems is the dichotomy of engineered coupling to an auxiliary degree of freedom, while being mechanically well isolated from the environment, that is, low quantum decoherence – which consists of both thermal decoherence and dephasing. We overcome this challenge by introducing a superconducting circuit optomechanical platform with a directly measured thermal decoherence rate of 20.5 Hz (corresponding to 7.7 milli-second T1) as well as a pure dephasing rate of 0.09 Hz [1]. This enables us to reach to 0.07 quanta motional ground state occupation (93% fidelity) and realize mechanical squeezing of -2.7 dB below zero-point-fluctuation. To directly measure the quantum-state lifetime, we observe the free evolution of the phase-sensitive squeezed state for the first time, preserving its non-classical nature over milli-second timescales. 

Furthermore, we show how to scale up optomechanical systems to arrays and lattices, realizing non-trivial topological modes in such multimode systems [2]. Using a novel technique to directly measure collective modeshapes, we explore the physics of edge states in optomechanical strained-graphene lattices.

Such ultra-low quantum decoherence and reproducible platform not only increases the fidelity of quantum control and measurement of macroscopic mechanical systems but may equally benefit interfacing with qubits, exploring emergent nonlinear dynamics in complex optomechanical systems, and places the system in a parameter regime suitable for tests of quantum gravity.

References:

[1] A. Youssefi, S. Kono, M. Chegnizadeh, and T.J. Kippenberg. A squeezed mechanical oscillator with milli-second quantum decoherence. Nature Physics, 2023.

[2] A. Youssefi, S. Kono, A. Bancora, M. Chegnizadeh, J. Pan, T. Vovk, and T.J. Kippenberg, Topological lattices realized in superconducting circuit optomechanics. Nature, 2022.