Abstract:
This thesis discusses the non-equilibrium dynamics of one-dimensional quantum
many-body systems. In particular, we investigate two distinct situations in which
interesting dynamical properties arise, i.e., when the quantum evolution is subject
to kinetic constraints or competes with an artificial dissipation through stochastic
resets. Both topics have attracted considerable interest in the last decade,
as they offer a playground to theoretically investigate the long-standing question
of how isolated quantum systems evolve under non-equilibrium conditions. From
the experimental point of view, the recent technological progress in the control
and manipulation of ultracold atomic gases has led to new breakthroughs in the
domains of quantum simulation and quantum computation. Key for the latter
applications is the utilization of atomic Rydberg states in which atoms, trapped in
optical tweezers, interact via state-dependent electrostatic dipolar forces. These
strong interactions make Rydberg systems ideal for the realization of kinetic constraints,
which cause a restriction of the connectivity between many-body states
in the Hilbert space.
A prominent example of a kinetic constraint is the Rydberg blockade, in which
an excited Rydberg atom prevents the surrounding atoms to be excited to the
Rydberg state. This effect has been largely exploited to implement controlled gates
and complex many-body dynamics. Much less explored is the opposite situation,
called the facilitation (or anti-blockade) constraint, where the interactions shift
the otherwise detuned laser in resonance. In this case only atoms at the correct
distance to an already excited atom are resonantly driven by the laser, thereby
creating an “avalanche” of excitations.
The first part of the thesis is devoted to the study of the facilitation dynamics
in Rydberg chains. The facilitation constraint favours the dynamical creation of
contiguous Rydberg excitations. We find that the resulting Rydberg excitation
“cluster” develops long-range interactions that cause the onset of Bloch oscillations,
preventing the system from reaching an ergodic stationary state. Contrary
to the blockade constraint, facilitation is more challenging to implement in current
Rydberg quantum simulators. The reason for this difficulty is that facilitation is
particularly affected by mechanical effects and position disorder. These two problems
originate respectively from the mechanical forces that displace the atoms
from their initial positions and the spreading of the atomic wave functions in the
optical traps. The interplay between the electronic degrees of freedom and the
vibrational ones leads to a coupling between the (internal) Rydberg dynamics and
the (external) atomic motion. We find that such spin-phonon coupling inhibits
the facilitation mechanism, suppressing the expansion of the excitation cluster.
This vibronic interaction can be also exploited to explore molecular physics in
Rydberg atom arrays. We show this by considering a system composed of three
atoms trapped in optical tweezers that form an equilateral triangle. We find that
the atomic vibrations in the traps break the electronic degeneracy and generate
a structural Jahn-Teller distortion, paving the way towards the exploration of
molecular physics at the exaggerated length scales typical of Rydberg systems.
The second part of the thesis investigates the effects of stochastic resetting on the
stationary properties of quantum many-body spin systems. Stochastic resetting
is a process that interrupts the dynamics of a system at random times and resets
it to a certain state. Then the dynamics restarts again. This process leads
very generally to a non-equilibrium stationary state. When the choice of the reset
state is determined by the outcome of a measurement taken immediately before
resetting, we find that resetting induces an emergent non-Markovian open dynamics,
described by a generalized Lindblad equation. We also show that stochastic
resetting can generate quantum correlation and collective behaviour even in a non-interacting system, showing its potential for quantum sensing applications.
The structure of the thesis is as follows. In the first chapter we introduce the
topics covered in the thesis and provide useful references for the reader. In the
second chapter we review the physics of Rydberg systems, including their single-body
properties and their interactions. We also explain how Rydberg quantum
simulators are used for the implementation of kinetic constraints. In the third
chapter we review the physics of stochastic resetting and the main mathematical
techniques used in the thesis. In the fourth chapter we summarize the original
results contained in the thesis. The fifth chapter is dedicated to the conclusions
and an outlook on possible future research directions.
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