Atom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States

As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of $\rho_{ss}$, is more natural. In the preceding paper we concentrated upon whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy $\chi$ of the bosons in the laser mode, and the excess phase noise $\nu$. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit ($\nu=\chi=0$), the most robust states are coherent states. As the phase noise $\nu$ or phase dispersion $\chi$ is increased, the most robust states become increasingly amplitude-squeezed. We find scaling laws for these states. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR states having a well-defined coherent amplitude. This lends support to the idea that robust PR ensembles are the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.Comment: 16 pages, 9 figures included. To be published in Phys. Rev. A, as Part II of a two-part paper. The original version of quant-ph/9906125 is shortly to be replaced by a new version which is Part I of the two-part paper. This paper (Part II) also contains some material from the original version of quant-ph/990612

Removal of a single photon by adaptive absorption

We present a method to remove, using only linear optics, exactly one photon from a field-mode. This is achieved by putting the system in contact with an absorbing environment which is under continuous monitoring. A feedback mechanism then decouples the system from the environment as soon as the first photon is absorbed. We propose a possible scheme to implement this process and provide the theoretical tools to describe it

Robust unravelings for resonance fluorescence

Monitoring the fluorescent radiation of an atom unravels the master equation evolution by collapsing the atomic state into a pure state which evolves stochastically. A robust unraveling is one that gives pure states that, on average, are relatively unaffected by the master equation evolution (which applies once the monitoring ceases). The ensemble of pure states arising from the maximally robust unraveling has been suggested to be the most natural way of representing the system [H.M. Wiseman and J.A. Vaccaro, Phys. Lett. A {\bf 250}, 241 (1998)]. We find that the maximally robust unraveling of a resonantly driven atom requires an adaptive interferometric measurement proposed by Wiseman and Toombes [Phys. Rev. A {\bf 60}, 2474 (1999)]. The resultant ensemble consists of just two pure states which, in the high driving limit, are close to the eigenstates of the driving Hamiltonian $\Omega\sigma_{x}/2$. This ensemble is the closest thing to a classical limit for a strongly driven atom. We also find that it is possible to reasonably approximate this ensemble using just homodyne detection, an example of a continuous Markovian unraveling. This has implications for other systems, for which it may be necessary in practice to consider only continuous Markovian unravelings.Comment: 12 pages including 5 .eps figures, plus one .jpg figur

Entanglement and purity of two-mode Gaussian states in noisy channels

We study the evolution of purity, entanglement and total correlations of general two--mode Gaussian states of continuous variable systems in arbitrary uncorrelated Gaussian environments. The time evolution of purity, Von Neumann entropy, logarithmic negativity and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.Comment: 10 pages, 8 figure

An experience on natural sciences augmented reality contents for preschoolers

[EN] Early education is a key element for the future success of students in the education system. This work analyzes the feasibility of using augmented reality contents with preschool students (four and five years old) as a tool for improving their learning process. A quasi experimental design based on a nonequivalent groups posttest-only design was used. A didactic unit has been developed around the topic animals by the participant teachers. The control group followed all the didactic activities defined in the developed didactic materials, while the experimental group was provided in addition with some augmented reality contents. Results show improved learning outcomes in the experimental group with respect to the control group.The Spanish Ministry Economy and Competitiveness partially supported this work (Project ref. TIN2010-21296-C02-01).Cascales, A.; Laguna, I.; Pérez López, DC.; Perona Ruiz, PD.; Contero, M. (2013). An experience on natural sciences augmented reality contents for preschoolers. Lecture Notes in Computer Science. 8022:103-112. https://doi.org/10.1007/978-3-642-39420-1_12S1031128022Barnett, W.S.: Effectiveness of Early Educational Intervention. Science 333(6045), 975–978 (2011)OECD: Investing in high-quality early childhood education and care (ECEC). OECD Publishing, http://www.oecd.org/dataoecd/0/28/48980282.pdf (retrieved)Campos, P., Pessanha, S.: Designing Augmented Reality Tangible Interfaces for Kindergarten Children. In: Shumaker, R. (ed.) Virtual and Mixed Reality, HCII 2011, Part I. LNCS, vol. 6773, pp. 12–19. Springer, Heidelberg (2011)Lim, J., Kim, S.: A Study on Markerless AR-based Infant Education System using CBIR. Communications in Computer and Information Science 78, 52–58 (2010)Chen, C.H., Su, C.C., Lee, P.Y., Wu, F.G.: Augmented Interface for Children Chinese Learning Technologies. In: 7th IEEE International Conference on Advanced Learning Technologies, pp. 268–270. IEEE Press, New York (2007)Azuma, R.: A Survey of Augmented Reality. Presence: Teleoperators and Virtual Environments 6(1), 355–385 (1997)Winkler, T., Herczeg, M., Kritzenberger, H.: Mixed Reality Environments as Collaborative and Constructive Learning Spaces for Elementary School Children. In: Barker, P., Rebelsky, S. (eds.) Proceedings of World Conference on Educational Multimedia, Hypermedia and Telecommunications 2002, pp. 1034–1039. AACE, Chesapeake (2002)Hsieh, M.C., Lee, J.S.: AR Marker Capacity Increasing for Kindergarten English Learning. In: International Multi Conference of Engineers and Computer Scientists, vol. 1, pp. 663–666 (2008)Hsieh, M.C., Lin, H.C.K.: Interaction Design Based on Augmented Reality Technologies for English Vocabulary Learning. In: Wong, S.L., et al. (eds.) Proceedings of the 18th International Conference on Computers in Education, vol. 1, pp. 663–666. Asia-Pacific Society for Computers in Education (2010)Lee, H., Lee, J.: Mathematical Education Game Based on Augmented Reality. Technologies for E-Learning and Digital Entertainment, 442–450 (2008)Hyun, E., Choi, K., Kim, G.J., Han, J., Jo, M., Kim, N.: Delphi Survey on the Use of Robot Projector based Augmented Reality in Dramatic Activity for Young Children. International Journal of Digital Content Technology and its Applications 5(11), 272–282 (2011)Kim, H.M., Song, T.H., Jung, S.M., Kwon, K.H., Jeon, J.W.: Virtual Storyteller Using Marker Based AR and FPGA. In: IEEE 54th International Midwest Symposium on Circuits and Systems, pp. 1–4. IEEE Press, New York (2011)Dunleavy, M., Dede, C., Mitchell, R.: Affordances and Limitations of Immersive Participatory Augmented Reality Simulations for Teaching and Learning. Journal of Science Education and Technology 18, 7–22 (2009)Martín-Gutiérrez, J., Saorín, J.L., Contero, M., Alcañiz, M., Pérez-López, D., Ortega, M.: Design and validation of an augmented book for spatial abilities development in engineering students. Computers & Graphics 34(1), 77–91 (2010)Cook, T.D., Campbell, D.T., Day, A.: Quasi-experimentation: Design and Analysis Issues for Field Settings, pp. 19–21. Houghton Mifflin, Boston (1979)Buendía, L., Colás, P., Hernández-Pina, F.: Métodos de Investigación en Psicopedagogía. McGraw Hill, Madrid (1997

A Bayesian elicitation of veterinary beliefs regarding systemic dry cow therapy: variation and importance for clinical trial design

The two key aims of this research were: (i) to conduct a probabilistic elicitation to quantify the variation in veterinarians’ beliefs regarding the efficacy of systemic antibiotics when used as an adjunct to intra-mammary dry cow therapy and (ii) to investigate (in a Bayesian statistical framework) the strength of future research evidence required (in theory) to change the beliefs of practising veterinary surgeons regarding the efficacy of systemic antibiotics, given their current clinical beliefs. The beliefs of 24 veterinarians in 5 practices in England were quantified as probability density functions. Classic multidimensional scaling revealed major variations in beliefs both within and between veterinary practices which included: confident optimism, confident pessimism and considerable uncertainty. Of the 9 veterinarians interviewed holding further cattle qualifications, 6 shared a confidently pessimistic belief in the efficacy of systemic therapy and whilst 2 were more optimistic, they were also more uncertain. A Bayesian model based on a synthetic dataset from a randomised clinical trial (showing no benefit with systemic therapy) predicted how each of the 24 veterinarians’ prior beliefs would alter as the size of the clinical trial increased, assuming that practitioners would update their beliefs rationally in accordance with Bayes’ theorem. The study demonstrated the usefulness of probabilistic elicitation for evaluating the diversity and strength of practitioners’ beliefs. The major variation in beliefs observed raises interest in the veterinary profession's approach to prescribing essential medicines. Results illustrate the importance of eliciting prior beliefs when designing clinical trials in order to increase the chance that trial data are of sufficient strength to alter the clinical beliefs of practitioners and do not merely serve to satisfy researchers

Synchronized pulse control of decoherence

We present a new strategy for multipulse control over decoherence. When a two-level system interacts with a reservoir characterized by a specific frequency, we find that the decoherence is effectively suppressed by synchronizing the pulse-train application with the dynamical motion of the reservoir.Comment: 14 pages, 8 figure

Dynamical aspects of quantum entanglement for weakly coupled kicked tops

We investigate how the dynamical production of quantum entanglement for weakly coupled, composite quantum systems is influenced by the chaotic dynamics of the corresponding classical system, using coupled kicked tops. The linear entropy for the subsystem (a kicked top) is employed as a measure of entanglement. A perturbative formula for the entanglement production rate is derived. The formula contains a correlation function that can be evaluated only from the information of uncoupled tops. Using this expression and the assumption that the correlation function decays exponentially which is plausible for chaotic tops, it is shown that {\it the increment of the strength of chaos does not enhance the production rate of entanglement} when the coupling is weak enough and the subsystems (kicked tops) are strongly chaotic. The result is confirmed by numerical experiments. The perturbative approach is also applied to a weakly chaotic region, where tori and chaotic sea coexist in the corresponding classical phase space, to reexamine a recent numerical study that suggests an intimate relationship between the linear stability of the corresponding classical trajectory and the entanglement production rate.Comment: 16 pages, 11 figures, submitted to Phys. Rev.

Spontaneous decay in the presence of dispersing and absorbing bodies: general theory and application to a spherical cavity

A formalism for studying spontaneous decay of an excited two-level atom in the presence of dispersing and absorbing dielectric bodies is developed. An integral equation, which is suitable for numerical solution, is derived for the atomic upper-state-probability amplitude. The emission pattern and the power spectrum of the emitted light are expressed in terms of the Green tensor of the dielectric-matter formation including absorption and dispersion. The theory is applied to the spontaneous decay of an excited atom at the center of a three-layered spherical cavity, with the cavity wall being modeled by a band-gap dielectric of Lorentz type. Both weak coupling and strong coupling are studied, the latter with special emphasis on the cases where the atomic transition is (i) in the normal-dispersion zone near the medium resonance and (ii) in the anomalous-dispersion zone associated with the band gap. In a single-resonance approximation, conditions of the appearance of Rabi oscillations and closed solutions to the evolution of the atomic state population are derived, which are in good agreement with the exact numerical results.Comment: 12 pages, 6 figures, typos fixed, 1 figure adde