Concepts and Paradoxes in a Quantum Universe

I will present our recent experimental work using electromagnetically induced transparency in laser-cooled atoms to measure the nonlinear phase shift created by a single post-selected photon, and its enhancement through "weak-value amplification." Put simply, due to the striking effects of "post-selective" quantum measurements, a (very uncertain) measurement of photon number can yield an average value much larger than one, even when it is carried out on a single photon. I will say a few words about possible practical applications of this "weak value amplification" scheme, and their limitations. Time permitting, I will also describe other future and past work using "weak measurement," such as our studies quantifying the disturbance due to a measurement and what happens when it destroys interference; and our project to measure "where a particle has been" as it tunnels through a classically forbidden region – our prediction being that it will make it from one side of the barrier to the other without spending any significant time in the middle.

The question of the time reversibility of quantum mechanics with measurements is one that has been debated for some time. In this talk, I will present new work exploring our ability to distinguish the forward from the time-reverse measurement records of continuous quantum measurements. The question involves both the conditions for the time-reversibility of the quantum trajectory equations of motion, as well as statistical distinguishability of the arrow of time. I will present the case with and without postselection on the final state, and connect the issue to a similar topic in nonequilibrium statistical physics. This work generalizes and pushes the two-time reformulation of quantum mechanics developed by Yakir Aharonov and collaborators beyond arbitrarily weak measurements. I will also discuss how this proposal can be implemented with continuously monitored superconducting quantum circuits. In collaboration with Alexander Korotkov, Justin Dressel, Areeya Chantasri, and Kater Murch Funded by the John Templeton Foundation.

Quantum tunneling is one such phenomenon that is essential for a number of devices that are now taken for granted. However, our understanding of quantum tunneling dynamics is far from complete, and there are still a number of theoretical and experimental challenges. The dynamics of the quantum tunneling process can be investigated if we can create a large tunneling region. We have achieved this using a linear Paul trap and a quantum tunneling rotor, which has resulted in the successful observation of the Aharonov–Bohm effect in tunneling particles. Also, this result shows that the spatially separated phonon can be interfered.

The Kochen-Specker (KS) theorem can gives rise to logical paradoxes under pre- and post-selection in which the contextual behavior is confined to specific observables of a system. Weak measurements allow direct experimental observation of the nonclassical behavior of these specific observables. This presents an experimental advantage over other tests of KS inequalities which rule out a particular class of counterfactual noncontextual hidden variable models, but can never specify where the contradiction occurs, nor make any direct observation of its consequences. The confined contextuality can always be interpreted as a logical pre- and post-selection paradox, such as the 3-box paradox, the Quantum Cheshire Cat, or the Quantum Pigeonhole Effect. This confined contextuality was recently observed using neutron inferometry for KS sets of up to 17 qubits. Details of the theory and experimental results will be presented.

Superconducting circuit technology has rapidly developed over the past several years to become a leading contender for realizing a scalable quantum computer. Modern circuit designs are based on the transmon qubit, which coherently superposes macroscopic charge oscillations. Measurements of a transmon are fundamentally weak and continuous in time, with projective measurements emerging only after a finite duration. Adding gates, such measurements may then implement ancilla-based measurements of controllable strength. Recent experiments have used both types of weak measurement to great effect: for monitoring qubit evolution, and for showing violations of a hybrid Bell-Leggett-Garg inequality.

Curiosity about how the world works can lead to beneficial progress in technology, and vice-versa. This kind of interplay can be found in quantum nanoscience, where foundationally motivated experiments and technologically motivated experiments often use similar materials and techniques, because both involve extending the realm of non-classical behaviour. At a higher level, curiosity about ultimate questions such as meaning and purpose can create an environment that is conducive to scientific breakthroughs, and many of the best minds in science have also been curious about deeper realities. Eugene Wigner described the miracle of the effectiveness of mathematics as a wonderful gift which we neither understand nor deserve. The same could be said of curiosity.