Spin-Boson Quantum Phase Transition in Multilevel Superconducting Qubits.

Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on nonlinear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wave function over many charge states. Numerical renormalization group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, which are relevant for a large class of devices.

Insights on heterogeneity in blinking mechanisms and non-ergodicity using sub-ensemble statistical analysis of single quantum-dots.

Photo-luminescence (P-L) intermittency (or blinking) in semiconductor nanocrystals (NCs), a phenomenon ubiquitous to single-emitters, is generally considered to be temporally random intensity fluctuations between "bright" ("On") and "dark" ("Off") states. However, individual quantum-dots (QDs) rarely exhibit such telegraphic signals, and yet, a vast majority of single-NC blinking data are analyzed using a single fixed threshold which generates binary trajectories. Furthermore, while blinking dynamics can vary dramatically over NCs in the ensemble, the extent of diversity in the exponents (mOn/Off) of single-particle On-/Off-time distributions (P(tOn/Off)), often used to validate mechanistic models of blinking, remains unclear due to a lack of statistically relevant data sets. Here, we subclassify an ensemble of QDs based on the emissivity of each emitter and subsequently compare the (sub)ensembles' behaviors. To achieve this, we analyzed a large number (>1000) of blinking trajectories for a model system, Mn+2 doped ZnCdS QDs, which exhibits diverse blinking dynamics. An intensity histogram dependent thresholding method allowed us to construct distributions of relevant blinking parameters (such as mOn/Off). Interestingly, we find that single QD P(tOn/Off)s follow either truncated power law or power law, and their relative proportion varies over subpopulations. Our results reveal a remarkable variation in mOn/Off amongst as well as within subensembles, which implies multiple blinking mechanisms being operational amongst various QDs. We further show that the mOn/Off obtained via cumulative single-particle P(tOn/Off) is distinct from the weighted mean value of all single-particle mOn/Off, evidence for the lack of ergodicity. Thus, investigation and analyses of a large number of QDs, albeit for a limited time span of a few decades, are crucial to characterize the spatial heterogeneity in possible blinking mechanisms.

Density Propagator for Many-Body Localization: Finite-Size Effects, Transient Subdiffusion, and Exponential Decay.

We investigate charge relaxation in quantum wires of spinless disordered fermions (t-V model). Our observable is the time-dependent density propagator Π_{ϵ}(x,t), calculated in windows of different energy density ϵ of the many-body Hamiltonian and at different disorder strengths W, not exceeding the critical value W_{c}. The width Δx_{ϵ}(t) of Π_{ϵ}(x,t) exhibits a behavior dlnΔx_{ϵ}(t)/dlnt=ß_{ϵ}(t), where the exponent function ß_{ϵ}(t)≲1/2 is seen to depend strongly on L at all investigated parameter combinations. (i) We confirm the existence of a region in phase space that exhibits subdiffusive dynamics in the sense that ß_{ϵ}(t)<1/2 in a large window of times. However, subdiffusion might possibly be transient, only, finally giving way to a conventional diffusive behavior with ß_{ϵ}=1/2. (ii) We cannot confirm the existence of many-body mobility edges even in regions of the phase diagram that have been reported to be deep in the delocalized phase. (iii) (Transient) subdiffusion 0<ß_{ϵ}(t)≲1/2 coexists with an enhanced probability for returning to the origin Π_{ϵ}(0,t), decaying much slower than 1/Δx_{ϵ}(t). Correspondingly, the spatial decay of Π_{ϵ}(x,t) is far from Gaussian, being exponential or even slower. On a phenomenological level, our findings are broadly consistent with the effects of strong disorder and (fractal) Griffiths regions.

Quantum Mutual Information as a Probe for Many-Body Localization.

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal-insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from a MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.

Many-Body Localization Characterized from a One-Particle Perspective.

We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ρ) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of ρ) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.

Out of equilibrium chiral higher order topological insulator on aπ-flux square lattice.

One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventionalddimensional topological system hostsd- 1 dimensional surface modes, which are protected by non-spatial symmetries. Recently, this idea has been extended to higher order topological phases with boundary modes that are localized in lower dimensions such as in the corners or in one dimensional hinges of the system. In this work, we demonstrate that a higher order topological phase can be engineered in a nonequilibrium state when the time-independent model does not possess any symmetry protected topological states. The higher order topology is protected by an emerging chiral symmetry, which is generated through the Floquet driving. Using both the exact numerical method and an effective high-frequency Hamiltonian obtained from the Brillouin-Wigner (BW) perturbation theory, we verify the emerging topological phase on aπ-flux square lattice. We show that the localized corner modes in our model are robust against a chiral symmetry preserving perturbation and can be classified as 'extrinsic' higher order topological phase. Finally, we identify a two dimensional topological invariant from the winding number of the corresponding sublattice symmetric one dimensional model. The latter model belongs to class AIII of ten-fold symmetry classification of topological matter.