Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gros
s-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
Recent experimental and theoretical work has shown that the double perovskite NaLaMnWO$_6$ exhibits antiferromagnetic ordering owing to the Mn $d$ states, and computational studies further predict it to exhibit a spontaneous electric polarization due
to an improper mechanism for ferroelectricity [King textit{et al., Phys. Rev. B}, 2009, textbf{79}, 224428; Fukushima textit{et al., Phys. Chem. Chem. Phys.}, 2011, textbf{13}, 12186], which make it a candidate multiferroic material. Using first-principles density functional calculations, we investigate nine isostructural and isovalent $AA^{prime}$MnWO$_6$ double perovskites ($A$=Na, K, and Rb; $A^{prime}$=La, Nd, and Y) with the aim of articulating crystal-chemistry guidelines describing how to enhance the magnitude of the electric polarization through chemical substitution of the $A$-site while retaining long-range magnetic order. We find that the electric polarization can be enhanced by up to 150% in compounds which maximize the difference in the ionic size of the $A$ and $A^{prime}$ cations. By examining the tolerance factors, bond valences, and structural distortions (described by symmetry-adapted modes) of the nine compounds, we identify the atomic scale features that are strongly correlated with the ionic and electronic contributions to the electric polarization. We also find that each compound exhibits a purely electronic remnant polarization, even in the absence of a displacive polar mode. The analysis and design strategies presented here can be further extended to additional members of this family ($B$=Fe, Co, etc.), and the improper ferroelectric nature of the mechanism allows for the decoupling of magnetic and ferroelectric properties and the targeted design of novel multiferroics.
High-temperature electronic materials are in constant demand as the required operational range for various industries increases. Here we design $(A,A^prime)B_2$O$_6$ perovskite oxides with [111] ``rock salt $A$-site cation order and predict them to b
e potential high-temperature piezoelectric materials. By selecting bulk perovskites which have a tendency towards only out-of-phase $B$O$_6$ rotations, we avoid possible staggered ferroelectric to paraelectric phase transitions while also retaining non-centrosymmetric crystal structures necessary for ferro- and piezoelectricity. Using density functional theory calculations, we show that (La,Pr)Al$_2$O$_6$ and (Ce,Pr)Al$_2$O$_6$ display spontaneous polarizations in their polar ground state structures; we also compute the dielectric and piezoelectric constants for each phase. Additionally, we predict the critical phase transition temperatures for each material from first-principles to demonstrate that the piezoelectric responses, which are comparable to traditional lead-free piezoelectrics, should persist to high temperature. These features make the rock salt $A$-site ordered aluminates candidates for high-temperature sensors, actuators, or other electronic devices.
