Engineering Many-Body Quantum States with Sudden Quenches and Floquet Driving

Abstract

When a densely packed group of non-interacting hard core Bosons are held in the center
of a one dimensional lattice and released, their resulting expansion has a very curious
property: as the particles spread out the momentum distribution becomes sharply peaked
around q= ±π/2. This effect is known by the name of Dynamic Quasi Condensation
(DQC), as it emerges spontaneously with a peak height scaling as a sub linear power law
in time.
In this thesis, we demonstrate that the same signatures can occur in interacting
systems. Specifically, using time-dependent density-matrix renormalisation group we in-
vestigate the dynamics of an expanding gas of doublons, i.e. pairs of Fermions, which
are interacting via a strong repulsive force. The doublons are long lived due to energy
conservation. We show that as the state expands across the lattice the doublons dynam-
ically quasicondense at the band edges, consistent with the spontaneous emergence of an
η-condensate.
Our intuition on this numerically complex model is guided by perturbation theory,
which predicts that a good effective description is provided by an equivalent model of
hard core Bosons with nearest neighbour interactions. Using this simpler model, the
position of the quasi-condensate momentum peak can be accurately determined using
energy conservation.
Building on this, we study the effect of periodically driving the system during the
expansion. Floquet analysis reveals that doublon-hopping and doublon-repulsion are
strongly renormalised by the drive, breaking the η−SU(2) symmetry of the Hubbard
model. Numerical simulation of the driven expansion dynamics demonstrate that the
momentum in which doublons quasicondense can be controlled by the driving amplitude,
including recreating the non-interacting point for strong drive strengths. These results
point to new methods for inducing correlations far from equilibrium conditions, which
may overcome the extremely low temperature requirements of particular phases in cold
atoms experiments, and may have relevance to driven solid state systems.

Date of Award	13 Nov 2024
Original language	English
Awarding Institution	University of Bath
Supervisor	Stephen Clark (Supervisor), Marcin Mucha-Kruczynski (Supervisor) & Steven Andrews (Supervisor)