Decoherence of a Superposition of Macroscopic Current States in a SQUID

We show that fundamental conservation laws mandate parameter-free mechanisms of decoherence of quantum oscillations of the superconducting current between opposite directions in a SQUID -- emission of phonons and photons at the oscillation frequency. The corresponding rates are computed and compared with experimental findings. The decohering effects of external mechanical and magnetic noise are investigated

From Event-B models to Dafny code contracts

International audienceThe constructive approach to software correctness aims at formal modelling and verification of the structure and behaviour of a system in different levels of abstraction. In contrast, the analytical approach to software verification focuses on code level correctness and its verification. Therefore it would seem that the constructive and analytical approaches should complement each other well. To demonstrate this idea we present a case for linking two existing verification methods, Event-B (constructive) and Dafny (analytical). This approach combines the power of Event-B abstraction and its stepwise refinement with the verification capabilities of Dafny. We presented a small case study to demonstrate this approach and outline of the rules for transforming Event-B events to Dafny contracts. Finally, a tool for automatic generation of Dafny contracts from Event-B formal models is presented

Testing Broken U(1) Symmetry in a Two-Component Atomic Bose-Einstein Condensate

We present a scheme for determining if the quantum state of a small trapped Bose-Einstein condensate is a state with well defined number of atoms, a Fock state, or a state with a broken U(1) gauge symmetry, a coherent state. The proposal is based on the observation of Ramsey fringes. The population difference observed in a Ramsey fringe experiment will exhibit collapse and revivals due to the mean-field interactions. The collapse and revival times depend on the relative strength of the mean-field interactions for the two components and the initial quantum state of the condensate.Comment: 20 Pages RevTex, 3 Figure

SMT-based Model Checking for Recursive Programs

We present an SMT-based symbolic model checking algorithm for safety verification of recursive programs. The algorithm is modular and analyzes procedures individually. Unlike other SMT-based approaches, it maintains both "over-" and "under-approximations" of procedure summaries. Under-approximations are used to analyze procedure calls without inlining. Over-approximations are used to block infeasible counterexamples and detect convergence to a proof. We show that for programs and properties over a decidable theory, the algorithm is guaranteed to find a counterexample, if one exists. However, efficiency depends on an oracle for quantifier elimination (QE). For Boolean Programs, the algorithm is a polynomial decision procedure, matching the worst-case bounds of the best BDD-based algorithms. For Linear Arithmetic (integers and rationals), we give an efficient instantiation of the algorithm by applying QE "lazily". We use existing interpolation techniques to over-approximate QE and introduce "Model Based Projection" to under-approximate QE. Empirical evaluation on SV-COMP benchmarks shows that our algorithm improves significantly on the state-of-the-art.Comment: originally published as part of the proceedings of CAV 2014; fixed typos, better wording at some place

Interference between the halves of a double-well trap containing a Bose-Einstein condensate

Interference between the halves of a double-well trap containing a Bose-Einstein condensate is studied. It is found that when the atoms in the two wells are initially in the coherent state, the intensity exhibits collapses and revivals, but it does not for the initial Fock states. Whether the initial states are in the coherent states or in a Fock states, the fidelity time has nothing to do with collision. We point out that interference and its fidelity can be adjusted experimentally by properly preparing the number and initial states of the system.Comment: 10 pages, 3 figures, accepted by Phy. rev.

Finding optimal strategies for minimum-error quantum-state discrimination

We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.Comment: 4 pages, 2 figure

Optimal discrimination of mixed quantum states involving inconclusive results

We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the Helstrom one. We formulate the extremal equations for the optimal positive operator valued measure describing the discrimination device and establish a criterion for its optimality. We also devise a numerical method for efficient solving of these extremal equations.Comment: 5 pages, 1 figur

Chaos in a double driven dissipative nonlinear oscillator

We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum trajectories in quantum state diffusion approach. Quantum dynamical manifestation of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement are studied by numerical simulation of ensemble averaged Wigner function and von Neumann entropy.Comment: 9 pages, 18 figure

The Casimir force and the quantum theory of lossy optical cavities

We present a new derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are in general lossy and characterized by frequency dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the Casimir force. The force is obtained as an integral over the real frequencies, including the contribution of evanescent waves besides that of ordinary waves, and, then, as an integral over imaginary frequencies. The demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the Casimir force.Comment: 18 pages, 6 figures, minor amendment

Multipole interaction between atoms and their photonic environment

Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are determined and in particular the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielectric a dipole couples to a field that is neither the (transverse) electric nor the macroscopic displacement field. The dielectric function is different from the bulk dielectric function at the position of the dipole, so that local-field effects must be taken into account.Comment: 17 pages, to be published in Physical Review