Minimum uncertainty and entanglement

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

MINIMUM UNCERTAINTY AND ENTANGLEMENT

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS

This paper deals with the Schrodinger equation i partial derivative(s)u(z, t; s) - Lu(z, t; s) = 0; where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies vertical bar f(z, t)vertical bar less than or similar to q(alpha)(z, t), where q(s) is the heat kernel associated to L. If in addition vertical bar u(z, t; s(0))vertical bar less than or similar to q(beta)(z, t), for some s(0) is an element of R \textbackslash {0}, then we prove that u(z, t; s) = 0 for all s is an element of R whenever alpha beta < s(0)(2). This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.

Quantum simulation using fidelity-profile optimization

Experimental quantum simulation of a Hamiltonian H requires unitary operator decomposition (UOD) of its evolution unitary U = exp(-iHt) in terms of native unitary operators of the experimental system. Here, using a genetic algorithm, we numerically evaluate the most generic UOD (valid over a continuous range of Hamiltonian parameters) of the unitary operator U, termed fidelity-profile optimization. The optimization is obtained by systematically evaluating the functional dependence of experimental unitary operators (such as single-qubit rotations and time-evolution unitaries of the system interactions) to the Hamiltonian (H) parameters. Using this technique, we have solved the experimental unitary decomposition of a controlled-phase gate (for any phase value), the evolution unitary of the Heisenberg XY interaction, and simulation of the Dzyaloshinskii-Moriya (DM) interaction in the presence of the Heisenberg XY interaction. Using these decompositions, we studied the entanglement dynamics of a Bell state in the DM interaction and experimentally verified the entanglement preservation procedure of Hou et al. Ann. Phys. (N.Y.) 327, 292 (2012)] in a nuclear magnetic resonance quantum information processor.

Octahedral distortion induced magnetic anomalies in LaMn0.5Co0.5O3 single crystals

Single crystals of LaMn0.5Co0.5O3 belonging to the ferromagnetic-insulator and distorted perovskite class were grown using a four-mirror optical float zone furnace. The as-grown crystal crystallizes into an orthorhombic Pbnm structure. The spatially resolved 2D Raman scan reveals a strain-induced distribution of transition metal (TM)-oxygen (O) octahedral deformation in the as-grown crystal. A rigorous annealing process releases the strain, thereby generating homogeneous octahedral distortion. The octahedra tilt by reducing the bond angle TM-O-TM, resulting in a decline of the exchange energy in the annealed crystal. The critical behavior is investigated from the bulk magnetization. It is found that the ground state magnetic behavior assigned to the strain-free LaMn0.5Co0.5O3 crystal is of the 3D Heisenberg kind. Strain induces mean field-like interaction in some sites, and consequently, the critical exponents deviate from the 3D Heisenberg class in the as-grown crystal. The temperature-dependent Raman scattering study reveals strong spin-phonon coupling and the existence of two magnetic ground states in the same crystal. (C) 2014 AIP Publishing LLC.

Super-Resolution Reconstruction in Frequency-Domain Optical-Coherence Tomography Using the Finite-Rate-of-Innovation Principle

The standard approach to signal reconstruction in frequency-domain optical-coherence tomography (FDOCT) is to apply the inverse Fourier transform to the measurements. This technique offers limited resolution (due to Heisenberg's uncertainty principle). We propose a new super-resolution reconstruction method based on a parametric representation. We consider multilayer specimens, wherein each layer has a constant refractive index and show that the backscattered signal from such a specimen fits accurately in to the framework of finite-rate-of-innovation (FRI) signal model and is represented by a finite number of free parameters. We deploy the high-resolution Prony method and show that high-quality, super-resolved reconstruction is possible with fewer measurements (about one-fourth of the number required for the standard Fourier technique). To further improve robustness to noise in practical scenarios, we take advantage of an iterated singular-value decomposition algorithm (Cadzow denoiser). We present results of Monte Carlo analyses, and assess statistical efficiency of the reconstruction techniques by comparing their performance against the Cramer-Rao bound. Reconstruction results on experimental data obtained from technical as well as biological specimens show a distinct improvement in resolution and signal-to-reconstruction noise offered by the proposed method in comparison with the standard approach.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

Evidence for 3D isotropic long range spin-spin interaction near the ferromagnetic transition in bulk and thin film SrRuO3

In the case of metallic ferromagnets there has always been a controversy, i.e. whether the magnetic interaction is itinerant or localized. For example SrRuO3 is known to be an itinerant ferromagnet where the spin-spin interaction is expected to be mean field in nature. However, it is reported to behave like Ising, Heisenberg or mean field by different groups. Despite several theoretical and experimental studies and the importance of strongly correlated systems, the experimental conclusion regarding the type of spin-spin interaction in SrRuO3 is lacking. To resolve this issue, we have investigated the critical behaviour in the vicinity of the paramagnetic-ferromagnetic phase transition using various techniques on polycrystalline as well as (001) oriented SrRuO3 films. Our analysis reveals that the application of a scaling law in the field-cooled magnetization data extracts the value of the critical exponent only when it is measured at H -> 0. To substantiate the actual nature without any ambiguity, the critical behavior is studied across the phase transition using the modified Arrott plot, Kouvel-Fisher plot and M-H isotherms. The critical analysis yields self-consistent beta, gamma and delta values and the spin interaction follows the long-range mean field model. Further the directional dependence of the critical exponent is studied in thin films and it reveals the isotropic nature. It is elucidated that the different experimental protocols followed by different groups are the reason for the ambiguity in determining the critical exponents in SrRuO3.

Evidence for 3D isotropic long range spin-spin interaction near the ferromagnetic transition in bulk and thin film SrRuO3

In the case of metallic ferromagnets there has always been a controversy, i.e. whether the magnetic interaction is itinerant or localized. For example SrRuO3 is known to be an itinerant ferromagnet where the spin-spin interaction is expected to be mean field in nature. However, it is reported to behave like Ising, Heisenberg or mean field by different groups. Despite several theoretical and experimental studies and the importance of strongly correlated systems, the experimental conclusion regarding the type of spin-spin interaction in SrRuO3 is lacking. To resolve this issue, we have investigated the critical behaviour in the vicinity of the paramagnetic-ferromagnetic phase transition using various techniques on polycrystalline as well as (001) oriented SrRuO3 films. Our analysis reveals that the application of a scaling law in the field-cooled magnetization data extracts the value of the critical exponent only when it is measured at H -> 0. To substantiate the actual nature without any ambiguity, the critical behavior is studied across the phase transition using the modified Arrott plot, Kouvel-Fisher plot and M-H isotherms. The critical analysis yields self-consistent beta, gamma and delta values and the spin interaction follows the long-range mean field model. Further the directional dependence of the critical exponent is studied in thin films and it reveals the isotropic nature. It is elucidated that the different experimental protocols followed by different groups are the reason for the ambiguity in determining the critical exponents in SrRuO3.