Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal transverse modes. Such a demultiplexing procedure, however, must be perfectly calibrated to the transverse profile of the incoming light as any misalignment of the modes effectively restores the diffraction limit for small source separations. We study by how much can one mitigate such an effect at the level of measurement which, after being imperfectly demultiplexed due to inevitable misalignment, may still be partially corrected by linearly transforming the relevant dominating transverse modes. We consider two complementary tasks: the estimation of the separation between the two sources and the discrimination between one and two incoherent point sources. We show that, although one cannot fully restore super-resolving powers even when the value of the misalignment is perfectly known its negative impact on the ultimate sensitivity can be significantly reduced. In the case of estimation we analytically determine the exact relation between the minimal resolvable separation as a function of misalignment whereas for discrimination we analytically determine the relation between misalignment and the probability of error, as well as numerically determine how the latter scales in the limit of long interrogation times.

%B Physical Review A %V 103 %8 Jan-02-2021 %U https://link.aps.org/doi/10.1103/PhysRevA.103.022406http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevA.103.022406/fulltexthttps://link.aps.org/article/10.1103/PhysRevA.103.022406 %! Phys. Rev. A %R 10.1103/PhysRevA.103.022406 %0 Journal Article %J Physical Review Letters %D 2016 %T Entanglement and Coherence in Quantum State Merging %A Streltsov, A. %A Chitambar, E. %A Rana, S. %A Bera, N. %A Winter, A. %A Lewenstein, M. %B Physical Review Letters %V 116 %8 Jan-06-2016 %U http://link.aps.org/doi/10.1103/PhysRevLett.116.240405http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevLett.116.240405/fulltexthttp://link.aps.org/accepted/10.1103/PhysRevLett.116.240405http://link.aps.org/article/10.1103/PhysRevLett.116.240405 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.116.240405 %0 Journal Article %J Physical Review Letters %D 2012 %T Entanglement Spectrum, Critical Exponents, and Order Parameters in Quantum Spin Chains %A De Chiara, G. %A Lepori, L. %A Lewenstein, M. %A Sanpera, A. %X We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix λ1, λ2, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter. %B Physical Review Letters %V 109 %8 12/2012 %N 23 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.109.237208 %0 Journal Article %J Physical Review Letters %D 2012 %T Quantum Memory Assisted Probing of Dynamical Spin Correlations %A O. Romero-Isart %A Rizzi, M. %A Muschik, C. A. %A Polzik, E. S. %A Lewenstein, M. %A Sanpera, A. %X We propose a method to probe time-dependent correlations of nontrivial observables in many-body ultracold lattice gases. The scheme uses a quantum nondemolition matter-light interface, first to map the observable of interest on the many-body system into the light and then to store coherently such information into an external system acting as a quantum memory. Correlations of the observable at two (or more) instances of time are retrieved with a single final measurement that includes the readout of the quantum memory. Such a method brings to reach the study of dynamics of many-body systems in and out of equilibrium by means of quantum memories in the field of quantum simulators. %B Physical Review Letters %V 108 %8 2/2012 %N 6 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.108.065302 %0 Journal Article %J Physical Review B %D 2011 %T Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect %A De Chiara, G. %A Lewenstein, M. %A Sanpera, A. %X The Heisenberg model for spin-1 bosons in one dimension presents many different quantum phases, including the famous topological Haldane phase. Here we study the robustness of such phases in front of a SU(2) symmetry-breaking field as well as the emergence of unique phases. Previous studies have analyzed the effect of such uniaxial anisotropy in some restricted relevant points of the phase diagram. Here we extend those studies and present the complete phase diagram of the spin-1 chain with uniaxial anisotropy. To this aim, we employ the density-matrix renormalization group together with analytical approaches. The complete phase diagram can be realized using ultracold spinor gases in the Mott insulator regime under a quadratic Zeeman effect. %B Physical Review B %V 84 %8 8/2011 %U http://prb.aps.org/abstract/PRB/v84/i5/e054451 %N 5 %! Phys. Rev. B %R 10.1103/PhysRevB.84.054451 %0 Journal Article %J Phys. Rev. A %D 2010 %T Creating p-wave superfluids and topological excitations in optical lattices %A Massignan, P. %A Sanpera, A. %A Lewenstein, M. %X We propose to realize a p-wave superfluid using bosons mixed with a single species of fermions in a deep optical lattice. We analyze with a self-consistent method its excitation spectrum in presence of a vortex, and we point out the range of interaction strengths in which the zero-energy mode with topological character exists on a finite optical lattice. Lattice effects are strongest close to fermionic half filling: here the linearity of the low-lying spectrum is lost, and a new class of extended zero-energy modes with checkerboard structure and d-wave symmetry appears. %B Phys. Rev. A %I American Physical Society %V 81 %P 031607 %8 Mar/2010 %U http://link.aps.org/doi/10.1103/PhysRevA.81.031607 %R 10.1103/PhysRevA.81.031607 %0 Journal Article %J Europhysics Letters %D 2010 %T Topological superfluids on a lattice with non-Abelian gauge fields %A A. Kubasiak %A Massignan, P. %A Lewenstein, M. %B Europhysics Letters %V 92 %P 46004 %8 12/2010 %U http://arxiv.org/abs/1007.4827 %R 10.1209/0295-5075/92/46004 %0 Journal Article %J Physical Review Letters %D 2004 %T Atomic Fermi-Bose Mixtures in Inhomogeneous and Random Lattices: From Fermi Glass to Quantum Spin Glass and Quantum Percolation %A Sanpera, A. %A Kantian, A. %A Sanchez-Palencia, L. %A Zakrzewski, J. %A Lewenstein, M. %B Physical Review Letters %V 93 %G eng %U http://prl.aps.org/abstract/PRL/v93/i4/e040401 %R 10.1103/PhysRevLett.93.040401 %0 Journal Article %J Physical Review Letters %D 2004 %T Coherence Properties of Guided-Atom Interferometers %A Kreutzmann, H. %A Poulsen, U. %A Lewenstein, M. %A Dumke, R. %A Ertmer, W. %A Birkl, G. %A Sanpera, A. %B Physical Review Letters %V 92 %G eng %U http://prl.aps.org/abstract/PRL/v92/i16/e163201 %R 10.1103/PhysRevLett.92.163201 %0 Journal Article %J Physical Review A %D 2002 %T Detection of entanglement with few local measurements %A Gühne, O. %A Hyllus, P. %A Bruß, D. %A Ekert, A. %A Lewenstein, M. %A Macchiavello, C. %A Sanpera, A. %B Physical Review A %V 66 %G eng %U http://pra.aps.org/abstract/PRA/v66/i6/e062305 %R 10.1103/PhysRevA.66.062305 %0 Journal Article %J Physical Review Letters %D 2001 %T Classification of Mixed Three-Qubit States %A Acín, A. %A Bruß, D. %A Lewenstein, M. %A Sanpera, A. %B Physical Review Letters %V 87 %G eng %U http://prl.aps.org/abstract/PRL/v87/i4/e040401 %R 10.1103/PhysRevLett.87.040401 %0 Journal Article %J Science (New York, N.Y.) %D 2001 %T Feynman's path-integral approach for intense-laser-atom interactions %A Salieres, P. %A Carre, B. %A Le Deroff, L. %A Grasbon, F. %A Paulus, G. G. %A Walther, H. %A Kopold, R. %A Becker, W. %A Milosevic, D. B. %A Sanpera, A. %A Lewenstein, M. %X Atoms interacting with intense laser fields can emit electrons and photons of very high energies. An intuitive and quantitative explanation of these highly nonlinear processes can be found in terms of a generalization of classical Newtonian particle trajectories, the so-called quantum orbits. Very few quantum orbits are necessary to reproduce the experimental results. These orbits are clearly identified, thus opening the way for an efficient control as well as previously unknown applications of these processes. %B Science (New York, N.Y.) %V 292 %P 902–5 %G eng %U http://www.sciencemag.org/cgi/content/abstract/292/5518/902 %R 10.1126/science.108836