296 research outputs found
Non-Abelian braiding of light
Many topological phenomena first proposed and observed in the context of
electrons in solids have recently found counterparts in photonic and acoustic
systems. In this work, we demonstrate that non-Abelian Berry phases can arise
when coherent states of light are injected into "topological guided modes" in
specially-fabricated photonic waveguide arrays. These modes are photonic
analogues of topological zero modes in electronic systems. Light traveling
inside spatially well-separated topological guided modes can be braided,
leading to the accumulation of non-Abelian phases, which depend on the order in
which the guided beams are wound around one another. Notably, these effects
survive the limit of large photon occupation, and can thus also be understood
as wave phenomena arising directly from Maxwell's equations, without resorting
to the quantization of light. We propose an optical interference experiment as
a direct probe of this non-Abelian braiding of light.Comment: 5+13 pages, 2+3 figures; v4 has stylistic revisions to the main text
and expanded SM featuring new numerical results providing direct confirmation
of non-Abelian braiding, as well as a discussion of the relationship to
Majorana zero modes. Accepted in PR
Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the Fermi-Hubbard model
We demonstrate the existence of exact atypical many-body eigenstates in a
class of disordered, interacting one-dimensional quantum systems that includes
the Fermi-Hubbard model as a special case. These atypical eigenstates, which
generically have finite energy density and are exponentially many in number,
are populated by noninteracting excitations. They can exhibit Anderson
localization with area-law eigenstate entanglement or, surprisingly, ballistic
transport at any disorder strength. These properties differ strikingly from
those of typical eigenstates nearby in energy, which we show give rise to
diffusive transport as expected in a chaotic quantum system. We discuss how to
observe these atypical eigenstates in cold-atom experiments realizing the
Fermi-Hubbard model, and comment on the robustness of their properties.Comment: 6+epsilon pages, 4 figures; v2 is published versio
Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy
Protected zero modes in quantum physics traditionally arise in the context of
ground states of many-body Hamiltonians. Here we study the case where zero
modes exist in the center of a reflection-symmetric many-body spectrum, giving
rise to the notion of a protected "infinite-temperature" degeneracy. For a
certain class of nonintegrable spin chains, we show that the number of zero
modes is determined by a chiral index that grows exponentially with system
size. We propose a dynamical protocol, feasible in ongoing experiments in
Rydberg atom quantum simulators, to detect these many-body zero modes and their
protecting spectral reflection symmetry. Finally, we consider whether the zero
energy states obey the eigenstate thermalization hypothesis, as is expected of
states in the middle of the many-body spectrum. We find intriguing differences
in their eigenstate properties relative to those of nearby nonzero-energy
eigenstates at finite system sizes.Comment: 8+1 pages, 5+1 figure
Braiding and Gapped Boundaries in Fracton Topological Phases
We study gapped boundaries of Abelian type-I fracton systems in three spatial
dimensions. Using the X-cube model as our motivating example, we give a
conjecture, with partial proof, of the conditions for a boundary to be gapped.
In order to state our conjecture, we use a precise definition of fracton
braiding and show that bulk braiding of fractons has several features that make
it \textit{insufficient} to classify gapped boundaries. Most notable among
these is that bulk braiding is sensitive to geometry and is "nonreciprocal,"
that is, braiding an excitation around need not yield the same phase as
braiding around . Instead, we define fractonic "boundary braiding,"
which resolves these difficulties in the presence of a boundary. We then
conjecture that a boundary of an Abelian fracton system is gapped if and only
if a "boundary Lagrangian subgroup" of excitations is condensed at the
boundary, this is a generalization of the condition for a gapped boundary in
two spatial dimensions, but it relies on boundary braiding instead of bulk
braiding. We also discuss the distinctness of gapped boundaries and transitions
between different topological orders on gapped boundaries.Comment: 18 pages, 21 figures. v2: Typo fixes, added references. v3: Published
version. Some corrections to figure
Floquet Supersymmetry
We show that time-reflection symmetry in periodically driven (Floquet)
quantum systems enables an inherently nonequilibrium phenomenon structurally
similar to quantum-mechanical sypersymmetry. In particular, we find Floquet
analogues of the Witten index that place lower bounds on the degeneracies of
states with quasienergies and . Moreover, we show that in some cases
time reflection symmetry can also interchange fermions and bosons, leading to
fermion/boson pairs with opposite quasienergy. We provide a simple class of
disordered, interacting, and ergodic Floquet models with an exponentially large
number of states at quasienergies and , which are robust as long as
the time-reflection symmetry is preserved. Floquet supersymmetry manifests
itself in the evolution of certain local observables as a period-doubling
effect with dramatic finite-size scaling, providing a clear signature for
experiments.Comment: 5+4 pages, 3+1 figures. v2 includes additional connections with SUSY
and a new Appendix containing a discussion of robustness to
time-reflection-breaking perturbations. This version accepted to PR
Occupation of topological Floquet bands in open systems
Floquet topological insulators are noninteracting quantum systems that, when
driven by a time-periodic field, are described by effective Hamiltonians whose
bands carry nontrivial topological invariants. A longstanding question concerns
the possibility of selectively populating one of these effective bands, thereby
maximizing the system's resemblance to a static topological insulator. We study
such Floquet systems coupled to a zero-temperature thermal reservoir that
provides dissipation. We find that the resulting electronic steady states are
generically characterized by a finite density of excitations above the
effective ground state, even when the driving has a small amplitude and/or
large frequency. We discuss the role of reservoir engineering in mitigating
this problem.Comment: 10 pages, 3 figures; v2 contains updated references; v3 is revised
and expande
Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation
We study the eigenstate properties of a nonintegrable spin chain that was
recently realized experimentally in a Rydberg-atom quantum simulator. In the
experiment, long-lived coherent many-body oscillations were observed only when
the system was initialized in a particular product state. This pronounced
coherence has been attributed to the presence of special "scarred" eigenstates
with nearly equally-spaced energies and putative nonergodic properties despite
their finite energy density. In this paper we uncover a surprising connection
between these scarred eigenstates and low-lying quasiparticle excitations of
the spin chain. In particular, we show that these eigenstates can be accurately
captured by a set of variational states containing a macroscopic number of
magnons with momentum . This leads to an interpretation of the scarred
eigenstates as finite-energy-density condensates of weakly interacting
-magnons. One natural consequence of this interpretation is that the
scarred eigenstates possess long-range order in both space and time, providing
a rare example of the spontaneous breaking of continuous time-translation
symmetry. We verify numerically the presence of this space-time crystalline
order and explain how it is consistent with established no-go theorems
precluding its existence in ground states and at thermal equilibrium.Comment: 13 pages, 8 figures; v2 updated reference
Topological gaps without masses in driven graphene-like systems
We illustrate the possibility of realizing band gaps in graphene-like systems
that fall outside the existing classification of gapped Dirac Hamiltonians in
terms of masses. As our primary example we consider a band gap arising due to
time-dependent distortions of the honeycomb lattice. By means of an exact,
invertible, and transport-preserving mapping to a time-independent Hamiltonian,
we show that the system exhibits Chern-insulating phases with quantized Hall
conductivities . The chirality of the corresponding gapless edge
modes is controllable by both the frequency of the driving and the manner in
which sublattice symmetry is broken by the dynamical lattice modulations.
Finally, we discuss a promising possible realization of this physics in
photonic lattices.Comment: 8 pages, 3 figures; added discussion of distinctness from Haldane
model; corrected reference
Stroboscopic Symmetry-Protected Topological Phases
Symmetry-protected topological (SPT) phases of matter have been the focus of
many recent theoretical investigations, but controlled mechanisms for
engineering them have so far been elusive. In this work, we demonstrate that by
driving interacting spin systems periodically in time and tuning the available
parameters, one can realize lattice models for bosonic SPT phases in the limit
where the driving frequency is large. We provide concrete examples of this
construction in one and two dimensions, and discuss signatures of these phases
in stroboscopic measurements of local observables.Comment: 6+6 pages, 4+2 figures; v2 includes revised discussion of measurement
protocol; v3 is expanded, with plots from additional numerical simulations
including all Magnus corrections; v4 is version accepted to PR
Configuration-Controlled Many-Body Localization and the Mobility Emulsion
We uncover a new non-ergodic phase, distinct from the many-body localized
(MBL) phase, in a disordered two-leg ladder of interacting hardcore bosons. The
dynamics of this emergent phase, which has no single-particle analog and exists
only for strong disorder and finite interaction, is determined by the many-body
configuration of the initial state. Remarkably, this phase features the
of localized and extended many-body states at fixed
energy density and thus does not exhibit a many-body mobility edge, nor does it
reduce to a model with a single-particle mobility edge in the noninteracting
limit. We show that eigenstates in this phase can be described in terms of
interacting emergent Ising spin degrees of freedom ("singlons") suspended in a
mixture with inert charge degrees of freedom ("doublons" and "holons"), and
thus dub it a (ME). We argue that grouping
eigenstates by their doublon/holon density reveals a transition between
localized and extended states that is invisible as a function of energy
density. We further demonstrate that the dynamics of the system following a
quench may exhibit either thermalizing or localized behavior depending on the
doublon/holon density of the initial product state. Intriguingly, the
ergodicity of the ME is thus tuned by the initial state of the many-body
system. These results establish a new paradigm for using many-body
configurations as a tool to study and control the MBL transition. The ME phase
may be observable in suitably prepared cold atom optical lattices.Comment: 20 pages, 12 figure
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