Abstract
We discuss the effects of many-body coherence on the speed of evolution of ultracold atomic gases and the relation to quantum speed limits. Our approach is focused on two related systems, spinless fermions and the bosonic Tonks-Girardeau gas, which possess equivalent density dynamics but very different coherence properties. To illustrate the effect of the coherence on the dynamics we consider squeezing an anharmonic potential which confines the particles and find that the speed of the evolution exhibits subtle, but fundamental differences between the two systems. Furthermore, we explore the difference in the driven dynamics by implementing a shortcut to adiabaticity designed to reduce spurious excitations. We show that collisions between the strongly interacting bosons can lead to changes in the coherence which results in different evolution speeds and therefore different fidelities of the final states.
Highlights
While the Heisenberg energy-time uncertainty relation is often viewed as a purely fundamental restriction on quantum mechanical measurements, it has implications for dynamical processes
We have explored the differences in the dynamics of many-particle systems composed of spinless fermions and hardcore bosons
Beginning with the average speed after a sudden quench, we have demonstrated that coherences play an important role in the evolution of the reduced state of both systems, with interparticle collisions between bosonic particles causing the system to decohere quickly
Summary
While the Heisenberg energy-time uncertainty relation is often viewed as a purely fundamental restriction on quantum mechanical measurements, it has implications for dynamical processes This was first formally recognized by Mandelstam and Tamm (MT) [1], who used the standard deviation of the energy to introduce the lower bound, τQSL hπ /(2 H ), on the minimum time required to transform a given quantum state into a final one. Applying and testing this idea by designing shortcuts for many-particle systems is a formidable problem as it requires one to solve many-particle systems exactly While this is not possible in general, noteworthy recent experimental progress has allowed realization of the textbook example of a strongly correlated bosonic quantum gases in one dimension, the socalled Tonks-Girardeau (TG) gas. The speed of the dynamics during the STA is qualitatively similar to the one predicted by the QSL and highlights the importance of coherence in the control of many-body quantum states
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