Search

The asymptotic quantum trajectory of weak continuous measurement for the magnetometer is investigated. The magnetometer refers to a setup where the field-to-estimate and the measured moment are orthogonal, and the quantum state is governed by the stochastic master equation which, in addition to a deterministic part, depends on the measurement outcomes. We find that the asymptotic behavior is insensitive to the initial state in the following sense: given one realization, the quantum trajectories starting from arbitrary initial states asymptotically converge to the {\em same} realization-specific {\em pure} state. For single-qubit systems, we are able to prove this statement within the framework of Probability Theory by deriving and analyzing an effective one-dimensional stochastic equation. Numerical simulations strongly indicate that the same statement holds for multi-qubit systems. Built upon this conclusion, we consider the problem of real-time parameter estimation whose feasibility hinges on the insensitivity to the initial state, and explicitly propose and test a scheme where the quantum state and the field-to-estimate are updated simultaneously., Comment: 6 figures

Optimal control theory, also known as Pontryagin's Maximum Principle, is applied to the quantum parameter estimation in the presence of decoherence. An efficient procedure is devised to compute the gradient of quantum Fisher information with respect to the control parameters and is used to construct the optimal control protocol. The proposed procedure keeps the control problem in the time-invariant form so that both first-order and second-order optimality conditions derived from Pontryagin's Maximum Principle apply; the second-order condition turns out to be crucial when the optimal control contains singular arcs. Concretely we look for the optimal control that maximizes quantum Fisher information for "twist and turn" problem. We find that the optimal control is singular without dissipation but can become unbounded once the quantum decoherence is introduced. An amplitude constraint is needed to guarantee a bounded solution. With quantum decoherence, the maximum quantum Fisher information happens at a finite time due to the decoherence, and the asymptotic value depends on the specific decoherence channel and the control of consideration., Comment: 4 figures

Quantum metrology comprises a set of techniques and protocols that utilize quantum features for parameter estimation which can in principle outperform any procedure based on classical physics. We formulate the quantum metrology in terms of an optimal control problem and apply Pontryagin's Maximum Principle to determine the optimal protocol that maximizes the quantum Fisher information for a given evolution time. As the quantum Fisher information involves a derivative with respect to the parameter which one wants to estimate, we devise an augmented dynamical system that explicitly includes gradients of the quantum Fisher information. The necessary conditions derived from Pontryagin's Maximum Principle are used to quantify the quality of the numerical solution. The proposed formalism is generalized to problems with control constraints, and can also be used to maximize the classical Fisher information for a chosen measurement., Comment: 10 pages, single column, 4 figures

A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing the density matrix. Specifically, the proper dynamical update rules are presented for the stochastic costate variables introduced by Pontryagin's maximum principle and restrictions on the form of the terminal cost function are discussed. The proposed procedure is confirmed by comparing the results to those obtained from optimal control on Lindbladian dynamics. Numerically, the proposed formalism becomes time and memory efficient for large systems, and it can be generalized to describe non-Markovian dynamics., Comment: 4 figures

A formalism based on Pontryagin's maximum principle is applied to determine the time-optimal protocol that drives a general initial state to a target state by a Hamiltonian with limited control, i.e., there is a single control field with bounded amplitude. The coupling between the bath and the qubit is modeled by a Lindblad master equation. Dissipation typically drives the system to the maximally mixed state; consequently, there generally exists an optimal evolution time beyond which the decoherence prevents the system from getting closer to the target state. For some specific dissipation channel, however, the optimal control can keep the system from the maximum entropy state for infinitely long. The conditions under which this specific situation arises are discussed in detail. The numerical procedure to construct the time-optimal protocol is described. In particular, the formalism adopted here can efficiently evaluate the time-dependent singular control which turns out to be crucial in controlling either an isolated or a dissipative qubit., Comment: 7 figures

Grover's algorithm is one of the most famous algorithms which explicitly demonstrates how the quantum nature can be utilized to accelerate the searching process. In this work, Grover's quantum search problem is mapped to a time-optimal control problem. Resorting to Pontryagin's Minimum Principle we find that the time-optimal solution has the bang-singular-bang structure. This structure can be derived naturally, without integrating the differential equations, using the geometric control technique where Hamiltonians in the Schr\"odinger's equation are represented as vector fields. In view of optimal control, Grover's algorithm uses the bang-bang protocol to approximate the optimal protocol with a minimized number of bang-to-bang switchings to reduce the query complexity. Our work provides a concrete example how Pontryagin's Minimum Principle is connected to quantum computation, and offers insight into how a quantum algorithm can be designed., Comment: 4 figures

Predicting physical response of an artificially structured material is of particular interest for scientific and engineering applications. Here we use deep learning to predict optical response of artificially engineered nanophotonic devices. In addition to predicting forward approximation of transmission response for any given topology, this approach allows us to inversely approximate designs for a targeted optical response. Our Deep Neural Network (DNN) could design compact (2.6x2.6 {\mu}m2) silicon-on-insulator (SOI)-based 1 X 2 power splitters with various target splitting ratios in a fraction of a second. This model is trained to minimize the reflection (smaller than 20 dB) while achieving maximum transmission efficiency (above 90%) and target splitting specifications. This approach paves the way for rapid design of integrated photonic components relying on complex nanostructures.

Band alignment between two materials is of fundamental importance for multitude of applications. However, density functional theory (DFT) either underestimates the bandgap - as is the case with local density approximation (LDA) or generalized gradient approximation (GGA) - or is highly computationally demanding, as is the case with hybrid-functional methods. The latter can become prohibitive in electronic-structure calculations of supercells which describe quantum wells. We propose to apply the DFT$+U$ method, with $U$ for each atomic shell being treated as set of tuning parameters, to automatically fit the bulk bandgap and the lattice constant, and then use thus obtained $U$ parameters in large supercell calculations to determine the band alignment. We apply this procedure to InP/In$_{0.5}$Ga$_{0.5}$As, In$_{0.5}$Ga$_{0.5}$As/In$_{0.5}$Al$_{0.5}$As and InP/In$_{0.5}$Al$_{0.5}$As quantum wells, and obtain good agreement with experimental results. Although this procedure requires some experimental input, it provides both meaningful valence and conduction band offsets while, crucially, lattice relaxation is taken into account. The computational cost of this procedure is comparable to that of LDA. We believe that this is a practical procedure that can be useful for providing accurate estimate of band alignments between more complicated alloys., Comment: 16 pages, 4 figures

We examine the superconducting solution in the Holstein model, where the conduction electrons couple to the dispersionless Boson fields, using the Migdal-Eliashberg theory and Dynamical Mean Field Theory. Although different in numerical values, both methods imply the existence of an optimal Boson energy for superconductivity at a given electron-Boson coupling. This non-monotonous behavior can be understood as an interplay between the polaron and superconducting physics, as the electron-Boson coupling is the origin of the superconductor, but at the same time traps the conduction electrons making the system more insulating. Our calculation provides a simple explanation on the recent experiment on sulfur hydride (H$_2$S), where an optimal pressure for the superconductivity was observed. The validities of both methods are discussed., Comment: 5 figures, 11 pages, single column

We study the quench dynamics of an Anderson impurity model using the configuration interaction (CI) method. In particular, we focus on the relaxation behavior of the impurity occupation. The system is found to behave very differently in the weak-coupling and strong-coupling regimes. In the weak-coupling regime, the impurity occupation relaxes to a time-independent constant quickly after only a few oscillations. In the strong-coupling regime, the impurity occupation develops a fast oscillation, with a much slower relaxation. We show that it is the multi-peak structure in the many-body energy spectrum that separates these two regimes. The characteristic behavior, including the power-law decay and the period of oscillation, can also be related to certain features in the many-body energy spectrum. The respective advantages of several impurity solvers are discussed, and the convergence of different CI truncation schemes is provided., Comment: 14 pages single column

We investigate the x-ray photoelectron spectroscopy (XPS) of nominally $d^1$ and $n$-doped $d^0$ transition metal oxides including NbO$_2$, SrVO$_3$, and LaTiO$_3$ (nominally $d^1$), as well as $n$-doped SrTiO$_3$ (nominally $d^0$). In the case of single phase $d^1$ oxides, we find that the XPS spectra (specifically photoelectrons from Nb $3d$, V $2p$, Ti $2p$ core levels) all display at least two, and sometimes three distinct components, which can be consistently identified as $d^0$, $d^1$, and $d^2$ oxidation states (with decreasing order in binding energy). Electron doping increases the $d^2$ component but decreases the $d^0$ component, whereas hole doping reverses this trend; a single $d^1$ peak is never observed, and the $d^0$ peak is always present even in phase-pure samples. In the case of $n$-doped SrTiO$_3$, the $d^1$ component appears as a weak shoulder with respect to the main $d^0$ peak. We argue that these multiple peaks should be understood as being due to the final-state effect and are intrinsic to the materials. Their presence does not necessarily imply the existence of spatially localized ions of different oxidation states nor of separate phases. A simple model is provided to illustrate this interpretation, and several experiments are discussed accordingly. The key parameter to determine the relative importance between the initial-state and final-state effects is also pointed out., Comment: 11 figures, single column, Supplementary Materials included in the same file

Oxygen vacancies are an important type of defect in transition metal oxides. In SrTiO$_3$ they are believed to be the main donors in an otherwise intrinsic crystal. At the same time, a relatively deep gap state associated with the vacancy is widely reported. To explain this inconsistency we investigate the effect of electron correlation in an oxygen vacancy (OV) in SrTiO$_3$. When taking correlation into account, we find that the OV-induced localized level can at most trap one electron, while the second electron occupies the conduction band. Our results offer a natural explanation of how the OV in SrTiO$_3$ can produce a deep in-gap level (about 1 eV below the conduction band bottom) in photoemission, and at the same time be an electron donor. Our analysis implies an OV in SrTiO$_3$ should be fundamentally regarded as a magnetic impurity, whose deep level is always partially occupied due to the strong Coulomb repulsion. An OV-based Anderson impurity model is derived, and its implications are discussed., Comment: 8 pages, 4 figures, double spaced

Within the framework of exact diagonalization (ED), we compute the ground state of Anderson impurity problem using the variational approach based on the configuration interaction (CI) expansion. We demonstrate that an accurate ground state can be obtained by iteratively diagonalizing a matrix with the dimension that is less than 10$%$ of the full Hamiltonian. The efficiency of the CI expansion for different problems is analyzed. By way of example, we apply this method to the single-site dynamical mean field theory using ED as the impurity solver. Specifically, to demonstrate the usefulness of this approach, we solve the attractive Hubbard model in the grand-canonical ensemble, where the s-wave superconducting solution is explicitly obtained., Comment: 16 pages, one column, double spaced, 2 figures, http://link.aps.org/doi/10.1103/PhysRevB.88.035123

An intersection between one-dimensional chiral acts as a topological current splitter. We find that the splitting of a chiral zero-line mode obeys very simple, yet highly counterintuitive, partition laws which relate current paths to the geometry of the intersection. Our results have far reaching implications for device proposals based on chiral zero-line transport in the design of electron beam splitters and interferometers, and for understanding transport properties in systems where multiple topological domains lead to a statistical network of chiral channels.

We investigate the electronic structure induced by wedge-disclinations (conical singularities) in a honeycomb lattice model realizing Chern numbers $\gamma=\pm 1$. We establish a correspondence between the bound state of (i) an isolated $\Phi_0/2$-flux, (ii) an isolated pentagon $(n=1)$ or heptagon $(n=-1)$ defect with an external flux of magnitude $n\gamma \Phi_0/4$ through the center and (iii) an isolated square or octagon defect without external flux, where $\Phi_0=h/e$ is the flux quantum. Due to the above correspondence, the existence of isolated electronic states bound to the disclinations is robust against various perturbations. These results are also generalized to graphene-based time-reversal invariant topological insulators., Comment: 5+4 pages, 4+3 figures, revised introduction and Fig. 4

We study Kosterlitz-Thouless (KT) transitions of the Larkin-Ovchinnikov (LO) phase for a two-dimensional system composed of coupled one-dimensional tubes of fermions. The LO phase here is characterized by a stripe structure (periodic in only one direction) in the order parameter. The low energy excitations involve the oscillation of the stripe and the fluctuation of the phase, which can be described by an effective theory composed of two anisotropic XY models. We compute from a microscopic model the coefficients of the XY models from which the KT transition temperatures are determined. We found the $T^{KT} \propto t_{\perp}$ for small intertube tunneling $t_{\perp}$. As $t_{\perp}$ increases the system undergoes a first-order transition to the normal phase at zero temperature. Our method can be used to determine the Goldstone excitations of any stripe order involving charge or spin degrees of freedom., Comment: one-column, 5+ pages, 4 figures

A novel class of non-local interactions between bosons is found to favor a crystalline Bose-Einstein condensation ground state. By using both low energy effective field theory and variational wavefunction method, we compare this state not only with the homogeneous superfluid, as has been done previously, but also with the normal (non-superfluid) crystalline phase and obtain the phase diagram. The key characters are: the interaction potential displays a negative minimum at finite momentum which determines the wavevector of this supersolid phase; and the wavelength corresponding to the momentum minimum needs to be greater than the mean inter-boson distance., Comment: 4 pages 3 figures, fig 1 and fig 2 updated

Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x-y$ plane) with dipoles pointing to the $z$ direction. We determine the phase diagram using two complimentary methods, the Hatree-Fock mean field theory and the linear response analysis of compressibility. Both give consistent results. In addition to the staggered ($\pi$, $\pi$) density wave, over a finite range of densities and hopping parameters, the ground state of the system first becomes nematic and then smectic, when the dipolar interaction strength is increased. Both phases are characterized by the same broken four-fold (C$_4$) rotational symmetry. The difference is that the nematic phase has a closed Fermi surface but the smectic does not. The transition from the nematic to the smectic phase is associated with a jump in the nematic order parameter. This jump is closely related to the van Hove singularities. We derive the kinetic equation for collective excitations in the normal isotropic phase and find that the zero sound mode is strongly Landau damped and thus is not a well defined excitation. Experimental implications of our results are discussed., Comment: 8 pages, 4 figures; Erratum added in the appendix

To gain insight into the physics of the metal insulator transition and the effectiveness of cluster dynamical mean field theory (DMFT) we have used one, two and four site dynamical mean field theory to solve a polaron model of electrons coupled to a classical phonon field. The cluster size dependence of the metal to polaronic insulator phase boundary is determined along with electron spectral functions and cluster correlation functions. Pronounced cluster size effects start to occur in the intermediate coupling region in which the cluster calculation leads to a gap and the single-site approximation does not. Differences (in particular a sharper band edge) persist in the strong coupling regime. A partial density of states is defined encoding a generalized nesting property of the band structure; variations in this density of states account for differences between the dynamical cluster approximation and the cellular-DMFT implementations of cluster DMFT, and for differences in behavior between the single band models appropriate for cuprates and the multiband models appropriate for manganites. A pole or strong resonance in the self energy is associated with insulating states; the momentum dependence of the pole is found to distinguish between Slater-like and Mott-like mechanisms for metal insulator transition. Implications for the theoretical treatment of doped manganites are discussed., Comment: 28 pages (single column, double space) 15 figures

A theoretical model is proposed for the (0,0,1) superlattice manganite system (LaMnO$_3$)$_n$(SrMnO$_3$)$_m$. The model includes the electron-electron, electron-phonon, and cooperative Jahn-Teller interactions. It is solved using a version of single-site the dynamical mean field approximation generalized to incorporate the cooperative Jahn-Teller effect. The phase diagram and conductivities are calculated. The behavior of the superlattice is found to a good approximation to be an average over the density-dependent properties of individual layers, with the density of each layer fixed by electrostatics., Comment: 9 figures, 22 pages

We compare the interaction parameters measured on LaMnO$_3$ to single site dynamical mean field estimates of the critical correlation strength needed to drive a Mott transition, finding that the total correlation strength (electron-electron plus electron-lattice) is very close to but slightly larger than the critical value, while if the electron lattice interaction is neglected the model is metallic. Our results emphasize the importance of additional physics including the buckling of the Mn-O-Mn bonds., Comment: 2 figures, 9 pages, using the bandwidth with the observed structure in this version

A comprehensive theoretical model for the bulk manganite system La$_{1-x}$(Ca,Sr)$_x$MnO$_3$ is presented. The model includes local and cooperative Jahn-Teller distortions and the on-site Coulomb and exchange interaction. The model is is solved in the single-site dynamical mean field approximation using a solver based on the semiclassical approximation. The model semi-quantitatively reproduces the observed phase diagram for the doping $0 \leq x<0.5$ and implies that the manganites are in the strong coupling region but close to Mott insulator/metal phase boundary. The results establish a formalism for use in a broader range of calculations, for example on heterostructures., Comment: 14 figures, 34 pages, using the bandwidth obtained from LDA with the observed structure, and resulting in a better fit to data.

The physics of manganites is often described within an effective two-band tight-binding (TB) model for the Mn e_g electrons, which apart from the kinetic energy includes also a local "Hund's rule" coupling to the t_{2g} core spin and a local coupling to the Jahn-Teller (JT) distortion of the oxygen octahedra. We test the validity of this model by comparing the energy dispersion calculated for the TB model with the full Kohn-Sham band-structure calculated within the local spin-density approximation (LSDA) to density functional theory. We analyze the effect of magnetic order, JT distortions, and "GdFeO_3-type" tilt-rotations of the oxygen octahedra. We show that the hopping amplitudes are independent of magnetic order and JT distortions, and that both effects can be described with a consistent set of model parameters if hopping between both nearest and next-nearest neighbors is taken into account. We determine a full set of model parameters from the density functional theory calculations, and we show that both JT distortions and Hund's rule coupling are required to obtain an insulating ground state within LSDA. Furthermore, our calculations show that the "GdFeO_3-type" rotations of the oxygen octahedra lead to a substantial reduction of the hopping amplitudes but to no significant deviation from the simple TB model., Comment: replaced with final (published) version with improved presentation

A theoretical study of [001] "double exchange" superlattices is presented. The superlattice is defined in terms of an $AB$O$_3$ perovskite crystal. Itinerant electrons hop among the B sites according to a nearest-neighbor tight binding model and are coupled to classical "core spins". The $A$ sites contain ionic charges arranged to form an [001] superlattice which forces a spatial variation of the mobile electron charge on the $B$ sites. The double-exchange interaction is treated by the dynamical mean field approximation, while the long range Coulomb interaction is taken into account by the Hartree approximation. We find the crucial parameter is the Coulomb screening length. Different types of phases are distinguished and the interfaces between them classified., Comment: 4 pages, f figures

The single-site dynamical mean field theory approximation to the double exchange model is found to exhibit a previously unnoticed instability, in which a well-defined ground state which is stable against small perturbations is found to be unstable to large-amplitude but purely local fluctuations. The instability is shown to arise either from phase separation or, in a narrow parameter regime, from the presence of a competing phase. The instability is therefore suggested as a computationally inexpensive means of locating regimes of parameter space in which phase separation occurs., Comment: 5 pages 5 figures

A model for semimetals such as $EuB_6$, in which band overlaps are controlled by magnetic order, is presented and is solved in the dynamical mean field approximation. First order phase boundaries are computed by evaluating free energies of different states. The phase diagram is determined. A specific and physically reasonable choice of parameters is found to approximately reproduce the available data on $EuB_6$. For this material, predictions are made for the location of a metamagnetic transition and its associated endpoint, and a change in the order of the magnetic transition., Comment: 6 pages, 7 figures