Quantum spin models with electrons in Penning traps

We propose a scheme to engineer an effective spin Hamiltonian starting from a system of electrons confined in micro-Penning traps. By means of appropriate sequences of electromagnetic pulses, alternated to periods of free evolution, we control the shape and strength of the spin-spin interaction. Moreover, we can modify the effective magnetic field experienced by the particle spin. This procedure enables us to reproduce notable quantum spin systems, such as Ising and XY models. Thanks to its scalability, our scheme can be applied to a fairly large number of trapped particles within the reach of near future technology.Comment: 22 pages, 1 figure, added minor changes and typos, accepted for publication in PR

Unravelling quantum carpets: a travelling wave approach

Quantum carpets are generic spacetime patterns formed in the probability distributions P(x,t) of one-dimensional quantum particles, first discovered in 1995. For the case of an infinite square well potential, these patterns are shown to have a detailed quantitative explanation in terms of a travelling-wave decomposition of P(x,t). Each wave directly yields the time-averaged structure of P(x,t) along the (quantised)spacetime direction in which the wave propagates. The decomposition leads to new predictions of locations, widths depths and shapes of carpet structures, and results are also applicable to light diffracted by a periodic grating and to the quantum rotator. A simple connection between the waves and the Wigner function of the initial state of the particle is demonstrated, and some results for more general potentials are given.Comment: Latex, 26 pages + 6 figures, submitted to J. Phys. A (connections with prior literature clarified

Wigner quasi-probability distribution for the infinite square well: energy eigenstates and time-dependent wave packets

We calculate the Wigner quasi-probability distribution for position and momentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite well potential, using both x- and p-space stationary-state solutions, as well as visualizing the results. We then evaluate the time-dependent Wigner distribution, P_W(x,p;t), for Gaussian wave packet solutions of this system, illustrating both the short-term semi-classical time dependence, as well as longer-term revival and fractional revival behavior and the structure during the collapsed state. This tool provides an excellent way of demonstrating the patterns of highly correlated Schrodinger-cat-like `mini-packets' which appear at fractional multiples of the exact revival time.Comment: 45 pages, 16 embedded, low-resolution .eps figures (higher resolution, publication quality figures are available from the authors); submitted to American Journal of Physic

Properties of finite Gaussians and the discrete-continuous transition

Weyl's formulation of quantum mechanics opened the possibility of studying the dynamics of quantum systems both in infinite-dimensional and finite-dimensional systems. Based on Weyl's approach, generalized by Schwinger, a self-consistent theoretical framework describing physical systems characterised by a finite-dimensional space of states has been created. The used mathematical formalism is further developed by adding finite-dimensional versions of some notions and results from the continuous case. Discrete versions of the continuous Gaussian functions have been defined by using the Jacobi theta functions. We continue the investigation of the properties of these finite Gaussians by following the analogy with the continuous case. We study the uncertainty relation of finite Gaussian states, the form of the associated Wigner quasi-distribution and the evolution under free-particle and quantum harmonic oscillator Hamiltonians. In all cases, a particular emphasis is put on the recovery of the known continuous-limit results when the dimension $d$ of the system increases.Comment: 21 pages, 4 figure

Robustness of spatial Penning trap modes against environment-assisted entanglement

The separability of the spatial modes of a charged particle in a Penning trap in the presence of an environment is studied by means of the positive partial transpose (PPT) criterion. Assuming a weak Markovian environment, described by linear Lindblad operators, our results strongly suggest that the environmental coupling of the axial and cyclotron degrees of freedom does not lead to entanglement at experimentally realistic temperatures. We therefore argue that, apart from unavoidable decoherence, the presence of such an environment does not alter the effectiveness of recently suggested quantum information protocols in Penning traps, which are based on the combination of a spatial mode with the spin of the particle.Comment: 11 pages, 2 figure

Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions

We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially extended condition leading to a uniform probability distribution whose width increases linearly with time, with increasing homogeneity.Comment: 4 pages, 2 figure

Describing astronomy identity of upper primary and middle school students through structural equation modeling

We describe how young students situate themselves with respect to astronomy through an identity framework that features four dimensions: interest, utility value, confidence, and conceptual knowledge. Overall, about 900 Italian students, from 5th to 9th grade (9-14 years old), were involved in the study. We tested our model using confirmatory factor analysis and structural equation modeling. Differences between girls and boys and across school levels were also investigated. Results show that interest has both a direct and an indirect effect on astronomy identity. The indirect effect of interest on identity is mediated by utility value. Moreover, confidence mediates the effect of interest on conceptual knowledge. Concerning differences between girls and boys, we found that the effect of interest on identity is greater for girls than for boys and that the utility value mediates the effect of interest on identity for boys but not for girls. Finally, our findings show also that the students' interest in astronomy and confidence in their performance decrease with age, with a potential negative impact on conceptual knowledge and future career choice in astronomy. The astronomy identity framework can be employed to examine the role of affective variables on performance and persistence in astronomy and to improve the design of teaching-learning activities that can potentially stimulate a lasting interest in astronomy

Dynamical Cooling of Trapped Gases I: One Atom Problem

We study the laser cooling of one atom in an harmonic trap beyond the Lamb-Dicke regime. By using sequences of laser pulses of different detunings we show that the atom can be confined into just one state of the trap, either the ground state or an excited state of the harmonic potential. The last can be achieved because under certain conditions an excited state becomes a dark state. We study the problem in one and two dimensions. For the latter case a new cooling mechanism is possible, based on the destructive interference between the effects of laser fields in different directions, which allows the creation of variety of dark states. For both, one and two dimensional cases, Monte Carlo simulations of the cooling dynamics are presented.Comment: LaTeX file with 8 pages, 7 eps figures. Submitted to Phys. Rev.