Monitoring quantum systems: speed limits and symmetry breaking (SLIDES)

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In this talk we consider the continuous monitoring of quantum systems and elucidate the role of the measurement back action in quantum dynamics. Specifically, we consider the limits to the speed of evolution under continuous quantum measurements.  The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. It is shown that there are trajectories for which standard QSL are violated.  We determine the dispersion of the speed of evolution and characterize the full statistics of single trajectories.
In a second part of the talk, we focus on spontaneous symmetry breaking (SSB), that is responsible for structure formation in scenarios ranging from condensed matter to cosmology. SSB is broadly understood in terms of perturbations to the Hamiltonian governing the dynamics or to the state of the system. Under continuous quantum measurements, the acquisition of information during the measurement process induces a measurement back-action that we identify as the crucial ingredient for SSB. An observer can thus tailor the topology of the vacuum manifold and the pattern of symmetry breaking by monitoring different observables.

LUNCH TIME

Quantum states with a positive partial transpose are useful for metrology (SLIDES)

We show that multipartite quantum states that have a positive partial transpose with respect to all bipartitions of the particles can outperform separable states in linear interferometers. We introduce a powerful iterative method to find such states. We present some examples for multipartite states and examine the scaling of the precision with the particle number. Some bipartite examples are also shown that possess an entanglement very robust to noise. We also discuss the relation of metrological usefulness to Bell inequality violation. We find that quantum states that do not violate any Bell inequality can outperform separable states metrologically. We present such states with a positive partial transpose, as well as with a non-positive positive partial transpose.

[1] Phys. Rev. Lett. 120, 020506 (2018)

Acoustic Traps and Lattices for Electrons in Semiconductors (SLIDES)

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We propose and analyze a solid-state platform based on surface acoustic waves for trapping, cooling, and controlling (charged) particles, as well as the simulation of quantum many-body systems. We develop a general theoretical framework demonstrating the emergence of effective time-independent acoustic trapping potentials for particles in two- or one-dimensional structures. As our main example, we discuss in detail the generation and applications of a stationary, but movable, acoustic pseudolattice with lattice parameters that are reconfigurable in situ. We identify the relevant figures of merit, discuss potential experimental platforms for a faithful implementation of such an acoustic lattice, and provide estimates for typical system parameters. With a projected lattice spacing on the scale of ∼100  nm, this approach allows for relatively large energy scales in the realization of fermionic Hubbard models, with the ultimate prospect of entering the low-temperature, strong interaction regime. Experimental imperfections as well as readout schemes are discussed.

Coffee Break

One Component Quantum Mechanics and a Universal Leakage Elimination Operator (SLIDES)

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We use a Feshbach P-Q partitioning technique to derive a closed one-component integro-differential equation. The resultant equation properly traces the footprint of the target state in quantum control theory. The physical significance of the derived dynamical equation is illustrated by both general analysis and concrete examples. Leakage from an encoded subspace to the rest of the system space is a particularly serious problem for which leakage elimination operators (LEOs) were introduced. By using the resultant dynamical equation, we show that the effectiveness of LEOs depends on the integral of the pulse sequence in the time domain, which has been missing because of the idealization of pulse sequences. Our results are applied to adiabatic paths and a three- level system for the nitrogen-vacancy centers under an external magnetic field and are illustrated by the fidelity dynamics of LEO sequences, ranging from regular rectangular pulses, random pulses, and even disordered (noisy) pulses.