The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$, we consider the problem of restoring the metric $g$ and the magnetic potential $\alpha$ from the values of the Ma\~n\'e action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Ma\~n\'e action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of $\alpha$. For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on $\alpha$. We also show injectivity and stability for $g$ and $\alpha$ in a generic class $\mathcal{G}$ including real analytic ones. For the nonlinear problem, we show rigidity for real analytic simple $g$, $\alpha$. Also, rigidity holds for metrics in a given conformal class, and locally, near any $(g,\alpha)\in \mathcal{G}$.Comment: This revised version contains a proof that 2D simple magnetic systems are boundary rigid. Some references have been adde

Mixed state geometric phases, entangled systems, and local unitary transformations

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.Comment: minor changes, journal reference adde

Bogoliubov theory of quantum correlations in the time-dependent Bose-Hubbard model

By means of an adapted mean-field expansion for large fillings $n\gg1$, we study the evolution of quantum fluctuations in the time-dependent Bose-Hubbard model, starting in the superfluid state and approaching the Mott phase by decreasing the tunneling rate or increasing the interaction strength in time. For experimentally relevant cases, we derive analytical results for the temporal behavior of the number and phase fluctuations, respectively. This allows us to calculate the growth of the quantum depletion and the decay of off-diagonal long-range order. We estimate the conditions for the observability of the time dependence in the correlation functions in the experimental setups with external trapping present. Finally, we discuss the analogy to quantum effects in the early universe during the inflationary epoch.Comment: 11 pages of RevTex4, 2 figures; significantly extended, with several analytically solvable cases added, to appear in Physical Review

Simulation study of a highly efficient, high resolution X-ry sensor based on self-organizing aluminum oxide

State of the art X-ray imaging sensors comprise a trade-off between the achievable efficiency and the spatial resolution. To overcome such limitations, the use of structured and scintillator filled aluminum oxide (AlOx) matrices has been investigated. We used Monte-Carlo (MC) X-ray simulations to determine the X-ray imaging quality of these AlOx matrices. Important factors which influence the behavior of the matrices are: filling factor (surface ratio between channels and 'closed' AlOx), channel diameter, aspect ratio, filling material etc. Therefore we modeled the porous AlOx matrix in several different ways with the MC X-ray simulation tool ROSI [1] and evaluated its properties to investigate the achievable performance at different X-ray spectra, with different filling materials (i.e. scintillators) and varying channel height and pixel readout. In this paper we focus on the quantum efficiency, the spatial resolution and image homogeneity

Effect of fluctuations on the superfluid-supersolid phase transition on the lattice

We derive a controlled expansion into mean field plus fluctuations for the extended Bose-Hubbard model, involving interactions with many neighbors on an arbitrary periodic lattice, and study the superfluid-supersolid phase transition. Near the critical point, the impact of (thermal and quantum) fluctuations on top of the mean field grows, which entails striking effects, such as negative superfluid densities and thermodynamical instability of the superfluid phase -- earlier as expected from mean-field dynamics. We also predict the existence of long-lived "supercooled" states with anomalously large quantum fluctuations.Comment: 5 pages of RevTex4; as published in Physical Review

Mean-field expansion in Bose-Einstein condensates with finite-range interactions

We present a formal derivation of the mean-field expansion for dilute Bose-Einstein condensates with two-particle interaction potentials which are weak and finite-range, but otherwise arbitrary. The expansion allows for a controlled investigation of the impact of microscopic interaction details (e.g., the scaling behavior) on the mean-field approach and the induced higher-order corrections beyond the s-wave scattering approximation.Comment: 6 pages of RevTex4; extended discussion, added reference

Optimal manipulations with qubits: Universal quantum entanglers

We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler which entangles a qubit in unknown state $|\Psi>$ with a qubit in a reference (known) state $|0>$. That is, our entangler generates the output state which is as close as possible to the pure (symmetrized) state $(|\Psi>|0> +|0>|\Psi>)$. The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e. the distance between the output and the ideally entangled -- symmetrized state) does not depend on the input and takes the constant value $F= (9+3\sqrt{2})/14\simeq 0.946$. We also analyze how to optimally generate from a single qubit initially prepared in an unknown state |\Psi\r a two qubit entangled system which is as close as possible to a Bell state $(|\Psi\r|\Psi^\perp\r+|\Psi^\perp\r|\Psi\r)$, where \l\Psi|\Psi^\perp\r =0.Comment: 11 pages, 3 eps figures, accepted for publication in Phys. Rev.

Quantum backreaction in dilute Bose-Einstein condensates

For many physical systems which can be approximated by a classical background field plus small (linearized) quantum fluctuations, a fundamental question concerns the correct description of the backreaction of the quantum fluctuations onto the dynamics of the classical background. We investigate this problem for the example of dilute atomic/molecular Bose-Einstein condensates, for which the microscopic dynamical behavior is under control. It turns out that the effective-action technique does not yield the correct result in general and that the knowledge of the pseudo-energy-momentum tensor ${<\hat T_{\mu\nu}>}$ is not sufficient to describe quantum backreaction.Comment: 8 pages of RevTex4; extended discussion with additional sections, to be published in Physical Review