Strong Zero Research Articles

Strong Zero Modes in Integrable Quantum Circuits.

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this Letter, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

Developing a toolkit to help smaller local authorities establish strong net zero governance in the UK

IntroductionThe Skidmore Review of UK Government's net zero approach highlights a lack of a national framework which establishes local government role, responsibilities and area-based governance arrangements. Although unified political leadership agreed as part of devolution deals has helped some areas to marshal resources and support, the national delivery landscape for net zero remains patchy. This study develops a toolkit to help local areas improve local arrangements.MethodsA mixed methods research approach has been used to develop the toolkit. It incorporates a set of governance models, a method for assessing the values of good governance, a governance improvement process and an illustration of how the toolkit can be employed using three cases where the two-tier public administrative structure applies.ResultsResults from the research process suggest that although change is happening it lacks the coherence and scale needed, with non-urban multiple-tier public administrations getting left behind by their metropolitan, single-tier counterparts creating a credibility and performance gap between political rhetoric and local net zero delivery. This observed inertia highlights the need to change governance processes and practices if public administration is going to deliver its part of net zero effectively outside the UK Metropolitan areas.DiscussionThe gap in support for local government to develop net zero governance arrangements is well recognized in both this research and publicly funded research programmes. This study provides UK local authorities with a simple, effective toolkit, that could potentially help them build strong wider societal relationships that will assist them in playing their full part in the UK reaching net zero.

Novel green/red oxyfluoride phosphors with excellent optical properties for near-UV excited white light emitting diode

Novel eye-sensitive Ba3Nb2O2F12(H2O)2:Tb3+ green and Ba3Nb2O2F12(H2O)2:Mn4+ red oxyfluoride phosphors with extremely strong absorption in the UV region were designed and synthesized by simple co-precipitation strategy. Particularly, Tb3+ ions were doped in this matrix for the first time, which greatly improves their absorption efficiency in the near ultraviolet region (367 nm) and emits sharp green light (544 nm). In addition, the Ba3Nb2O2F12(H2O)2:Mn4+ red phosphors have strong zero phonon line (ZPL) emission at 625 nm, which is conducive to improving the sensitivity of human eye and color purity. Meanwhile, the optical properties of the red phosphor are significantly enhanced via doping K+ cations as charge compensators. Crystal field environment and nephelauxetic effect of the as-prepared phosphors before and after K+ cation doping were systematically analyzed. Moreover, these synthesized red/green phosphors have good thermal stability and moisture resistance. Remarkably, the as-prepared Ba3Nb2O2F12(H2O)2:5%Mn4+ or K0.9Ba2.1Nb2O2F12(H2O)2:5%Mn4+ red phosphors can be directly mixed with the as-synthesized Ba3Nb2O2F12(H2O)2:13%Tb3+ green phosphor coating on 365 nm near-ultraviolet LED chip to package WLED devices with excellent electroluminescence performance. These findings are conducive to opening an avenue for screening the unique structure of optical materials.

Strong zero modes and edge states in the interacting fermion chain without pairing

The operator of the strong zero mode for the one-dimensional system of interacting fermions without pairing is presented. It is conjectured that the strong zero mode is related to the Majorana edge eigenstate, which is shown to exist (using the exact Bethe ansatz study) in this system. The results are robust with respect to the sign randomness of hopping amplitudes (and if the pairing amplitudes are nonzero, similar results exist for equal sign randomness of hopping and pairing amplitudes).

Emergent strong zero mode through local Floquet engineering

Emergent strong zero mode through local Floquet engineering

STRONG MEASURE ZERO SETS ON FOR INACCESSIBLE

Abstract We investigate the notion of strong measure zero sets in the context of the higher Cantor space $2^\kappa $ for $\kappa $ at least inaccessible. Using an iteration of perfect tree forcings, we give two proofs of the relative consistency of $$\begin{align*}|2^\kappa| = \kappa^{++} + \forall X \subseteq 2^\kappa:\ X \textrm{ is strong measure zero if and only if } |X| \leq \kappa^+. \end{align*}$$ Furthermore, we also investigate the stronger notion of stationary strong measure zero and show that the equivalence of the two notions is undecidable in ZFC.

Synthesis, optical characteristics and thermal stability of Mn4+-doped Na3GaF6 red-emitting phosphor for high-performance warm WLED

Nowadays, Mn4+-activated fluoride red phosphors with high color purity, strong zero phonon line emission and relatively short decay time are crucial for improving the optical performance of WLED and emerging applications. In this work, a series of red-emitting Mn4+-activated fluoride phosphors in consideration of the non-equivalent substitution of Mn4+ for Ga3+ in the Na3GaF6 host are synthesized via the coprecipitation method at room temperature. The use of different reaction solvents successfully regulates the morphology, size and luminescence intensity of the phosphor. Under blue light excitation, Na3GaF6:Mn4+ sample shows a bright narrow-band red emission with exceptional correlated color temperature (4029 K). Moreover, the emission of strong zero phonon line induces the outstanding color purity of red light (93%). In addition, the critical concentration of Mn4+ is determined to be 0.04 and the concentration quenching mechanism is also systematically discussed. Noticeably, when Na3GaF6:Mn4+ phosphor achieves maximum fluorescence emission, its fluorescence lifetime value is only 3.48 ms. Additionally, the theoretical calculated results demonstrate that Na3GaF6 host can provide strong crystal field strength for Mn4+, and the Racah parameters (B and C) and nephelauxetic ratio (β1) are used to evaluate the nephelauxetic effect of Mn4+, which is compared with other types of Mn4+-activated phosphors. The activation energy, chromaticity shift and chromaticity coordinate variation are systematically calculated to analyze the thermal stability of Na3GaF6:Mn4+ red phosphor. Meanwhile, by employing the as-prepared phosphor Na3GaF6:Mn4+ as a red component, a high-performance warm WLED shows a full spectrum emission, and the corresponding cold white light emission is also transformed into the warm white light emission (CCT = 4224 K, Ra = 89.1 and LE = 111.72 lm/W). Moreover, under high driving current, such WLED exhibits stable output light efficiency. These results suggest that Na3GaF6:Mn4+ as red phosphor has a stupendous potential for warm WLED in indoor lighting.

Some observations on a clopen version of the Rothberger property

In this paper, we prove that a clopen version $S_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})$ of the Rothberger property and Borel strong measure zeroness are independent. For a zero-dimensional metric space $(X,d)$, $X$ satisfies $S_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})$ if, and only if, $X$ has Borel strong measure zero with respect to each metric which has the same topology as $d$ has. In a zero-dimensional space, the game $G_1(\mathcal{O}, \mathcal{O})$ is equivalent to the game $G_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})$ and the point-open game is equivalent to the point-clopen game. Using reflections, we obtain that the game $G_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})$ and the point-clopen game are strategically and Markov dual. An example is given for a space on which the game $G_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})$ is undetermined.

Fragmentation-induced localization and boundary charges in dimensions two and above

We study higher dimensional models with symmetric correlated hoppings, which generalize a one-dimensional model introduced in the context of dipole-conserving dynamics. We prove rigorously that whenever the local configuration space takes its smallest non-trivial value, these models exhibit localized behavior due to fragmentation, in any dimension. For the same class of models, we then construct a hierarchy of conserved quantities that are power-law localized at the boundary of the system with increasing powers. Combining these with Mazur’s bound, we prove that boundary correlations are infinitely long lived, even when the bulk is not localized. We use our results to construct quantum Hamiltonians that exhibit the analogues of strong zero modes in two and higher dimensions.

Stochastic strong zero modes and their dynamical manifestations.

Strong zero modes (SZMs) are conserved operators localized at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyze analogous operators in one-dimensional classical stochastic systems. For concreteness, we focus on chains with single occupancy and nearest-neighbor transitions, in particular particle hopping and pair creation and annihilation. For integrable choices of parameters we find the exact form of the SZM operators. Being in general nondiagonal in the classical basis, the dynamical consequences of stochastic SZMs are very different from those of their quantum counterparts. We show that the presence of a stochastic SZM is manifested through a class of exact relations between time-correlation functions, absent in the same system with periodic boundaries.

Quantum Emitters with Narrow Band and High Debye-Waller Factor in Aluminum Nitride Written by Femtosecond Laser.

Solid-state quantum emitters (QEs) are central components for photonic-based quantum information processing. Recently, bright QEs in III-nitride semiconductors, such as aluminum nitride (AlN), have attracted increasing interest because of the mature commercial application of the nitrides. However, the reported QEs in AlN suffer from broad phonon side bands (PSBs) and low Debye-Waller factors. Meanwhile, there is also a need for more reliable fabrication methods of AlN QEs for integrated quantum photonics. Here, we demonstrate that laser-induced QEs in AlN exhibit robust emission with a strong zero phonon line, narrow line width, and weak PSB. The creation yield of a single QE could be more than 50%. More importantly, they have a high Debye-Waller factor (>65%) at room temperature, which is the highest result among reported AlN QEs. Our results illustrate the potential of laser writing to create high-quality QEs for quantum technologies and provide further insight into laser writing defects in relevant materials.

Temperature-dependent photoluminescence properties of single defects in AlGaN micropillars

Single-photon emitters (SPEs) are attractive as integrated platforms for quantum applications in technologically mature wide-bandgap semiconductors since their stable operation at room temperature or even at high temperatures. In this study, we systematically studied the temperature dependence of the SPE in AlGaN micropillar by experiment. The photoluminescence (PL) spectrum, PL intensity, radiative lifetime and second-order autocorrelation function measurements are investigated over the temperature range from 303 to 373 K. The point defects of AlGaN show strong zero phonon line in the wavelength range of 800–900 nm and highly antibunched photon emission even up to 373 K. Our study reveals a possible mechanism for linewidth broadening in AlGaN SPE at high temperatures. This indicates a possible key for on-chip integration applications based on this material operating at high temperatures.

Morphology controllable BaNbF5.5(OH)1.5:Mn4+ red phosphor with strong zero phonon line for WLED application

A hydroxy fluoride red phosphor BaNbF5.5(OH)1.5:Mn4+ with dual morphology was designed and manufactured by co-precipitation strategy. The crystal phase structure, controlled morphology and photoluminescence performances were systematically investigated. The Mn4+ non-equivalent doped hydroxy fluoride phosphor has similar luminescence performance to fluoride phosphors, and it is worth noting that it presents a very strong zero phonon line (ZPL) at ∼629 nm at blue light excitation and has high color purity (98.5%). Crystal field intensity (Dq), Racah parameters (B and C) and nephelauxetic effect ratio parameter β1 of the sample were calculated and analyzed, the results indicate that the BaNbF5.5(OH)1.5 matrix provides a strong crystal field environment for Mn4+. The effects of the experimental conditions on the morphology of the phosphors were analyzed, and optimal synthetic conditions were determined. Because of the short fluorescence decay lifetime (τ < 4 ms), this red phosphor may be a prospective red emitting candidate for backlight displays. Moreover, the as-prepared BaNbF5.5(OH)1.5:Mn4+ red phosphor possesses distinguished UV light-induced stability. Thermal stability and hydrophobic stability of the phosphor were analyzed. Thanks to the strong ZPL, WLED device prepared with this phosphor can produce warm white light and show remarkable photoelectric properties, with a color rendering index (CRI, Ra) of up to 92.5 and a correlated color temperature (CCT, Tc) as low as 3944 K. The results indicate that the red phosphor BaNbF5.5(OH)1.5:Mn4+ has application possibilities in WLED illumination and display backlighting.

A reverse coprecipitation route for preparing Na2WO2F4:Mn4+ phosphor with high yield

For the coprecipitation preparation of the Na2WO2F4:Mn4+ phosphor, we propose a new reverse approach, i.e., adding the precursor solution into a precipitant, which efficiently induces the precipitation of the targeted composition with much higher yield than a conventional forward approach. NaHF2 occurred as a secondary phase due to the high HF concentration in the precursor solution but was successfully avoided by varying the precipitant from alcohols to acetic acid. The as-precipitated Na2WO2F4:Mn4+ phosphor exhibits strong zero phonon line emission (ZPL) at 619 nm; the ZPL/ν6 (Stokes) intensity ratio varies from 137% to 73%, depending on the type and amount of the precipitant, the reason for which is ascribed mainly to the nonstoichiometry of Na+. This reverse coprecipitation approach could be applicable to prepare any other oxyfluoride compositions with considerable solubility.

More on generalizations of topology of uniform convergence and m-topology on C(X)

This paper conglomerates our findings on the space C(X) of all real valued continuous functions, under different generalizations of the topology of uniform convergence and the m-topology. The paper begins with answering all the questions which were left open in our previous paper on the classifications of Z-ideals of C(X) induced by the UI and the mI-topologies on C(X) [5]. Motivated by the definition of the mItopology, another generalization of the topology of uniform convergence, called UI-topology, is introduced here. Among several other results, it is established that for a convex ideal I in C(X), a necessary and sufficient condition for UI-topology to coincide with mI-topology on C(X) is the boundedness of X ? T Z[I] in X. As opposed to the case of the UI-topologies (and mI-topologies) on C(X), it is proved that each UI-topology (respectively, mI-topology) on C(X) is uniquely determined by the ideal I. In the last section, the denseness of the set of units of C(X) in CU(X) (= C(X) with the topology of uniform convergence) is shown to be equivalent to the strong zero dimensionality of the space X. Also, the space X turns out to be a weakly P-space if and only if the set of zero divisors (including 0) in C(X) is closed in CU(X). Computing the closure of CP(X) (={ f ? C(X) : the support of f ? P} where P is an ideal of closed sets in X) in CU(X) and Cm(X) (= C(X) with the m-topology), the results clUCP(X) = CP? (X) (= { f ? C(X) : ?n ? N, {x ? X : | f (x)| ? 1n } ? P}) and clmCP(X) = { f ? C(X) : f.1 ? CP? (X) for each 1 ? C(X)} are achieved.

Topological order in random interacting Ising-Majorana chains stabilized by many-body localization

We numerically explore $\mathbb Z_2$-symmetric random interacting Ising-Majorana chains at high energy. A very rich phase diagram emerges with two topologically distinct many-body localization (MBL) regimes separated by a much broader thermal phase than previously found. This is a striking consequence of the avalanche theory. We further find MBL spin-glass order always associated to a many-body spectral pairing, presumably signaling a strong zero mode operator which opens fascinating perspectives for MBL-protected topological qubits.

Probing Majorana modes via local spin dynamics

We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here, the model coincides with a phase boundary of two uncoupled instances of Kitaev's model for p-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding frequencies in the two-time correlation function. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev's fermionic model, thus opening up a bulk gap whilst retaining almost degenerate modes in the mesoscopic regime, i.e., for finite system sizes. This showcases the emergence of Majorana modes in a chain of effective dimers. Here, the binding energy within each unit cell competes with the inter-dimer coupling to generate a finite size energy gap, in analogy with local energy terms in the transverse-field Ising model. These modes give rise to long coherence times of local spins located at the system edges. By breaking the local symmetry in each dimer, one can also observe a second class of Majorana modes in terms of a beating frequency in the two-time correlations function of the edge spin. Furthermore, we develop a scenario for realizing these model predictions in ion-trap quantum simulators with collective addressing of the ions.

A strong zero phonon line of Mn4+ in a red-emitting phosphor BaGaF5:Mn4+

In this paper, a single-phase red-emitting phosphor BaGaF5:Mn4+ (BGFM) was synthesized by a hydrothermal method, and its crystal structure and luminescence properties were studied in detail. The results show that the excitation spectra of BGFM samples are mainly composed of two bands located at the near-ultraviolet and blue light region, respectively, while the emission spectra show multiple peaks in the red region. Due to the defects generated with the non-equivalent occupation of Ga3+ by Mn4+, the adjacent [MnF6] octahedron is highly distorted, resulting in a strong zero-phonon line (ZPL, 627 nm) in the emission spectrum. Additionally, the materials have shown a high internal quantum efficiency (QE = 63.7%) and good color stability. Finally, a white LED was obtained by mixing BGFM and commercial Y3Al5O12:Ce3+ yellow phosphor on a blue light-emitting diode (LED) chip.

The Hankel Determinants from a Singularly Perturbed Jacobi Weight

We study the Hankel determinant generated by a singularly perturbed Jacobi weight w(x,s):=(1−x)α(1+x)βe−s1−x,x∈[−1,1],α&gt;0,β&gt;0s≥0. If s=0, it is reduced to the classical Jacobi weight. For s&gt;0, the factor e−s1−x induces an infinitely strong zero at x=1. For the finite n case, we obtain four auxiliary quantities Rn(s), rn(s), R˜n(s), and r˜n(s) by using the ladder operator approach. We show that the recurrence coefficients are expressed in terms of the four auxiliary quantities with the aid of the compatibility conditions. Furthermore, we derive a shifted Jimbo–Miwa–Okamoto σ-function of a particular Painlevé V for the logarithmic derivative of the Hankel determinant Dn(s). By variable substitution and some complicated calculations, we show that the quantity Rn(s) satisfies the four Painlevé equations. For the large n case, we show that, under a double scaling, where n tends to ∞ and s tends to 0+, such that τ:=n2s is finite, the scaled Hankel determinant can be expressed by a particular PIII′.

Anomalous quantum information scrambling for Z3 parafermion chains

Parafermions are exotic quasiparticles with non-Abelian fractional statistics that could be exploited to realize universal topological quantum computing. Here, we study the scrambling of quantum information in one-dimensional parafermionic chains, with a focus on $\mathbb{Z}_3$ parafermions in particular. We use the generalized out-of-time-ordered correlators (OTOCs) as a measure of the information scrambling and introduce an efficient method based on matrix product operators to compute them. With this method, we compute the OTOCs for $\mathbb{Z}_3$ parafermions chains up to $200$ sites for the entire early growth region. We find that, in stark contrast to the dynamics of conventional fermions or bosons, the information scrambling light cones for parafermions can be both symmetric and asymmetric, even for inversion-invariant Hamiltonians involving only hopping terms. In addition, we find a deformed light cone structure with a sharp peak at the boundary of the parafermion chains in the topological regime, which gives a unambiguous evidence of the strong zero modes at infinite temperature.