This website uses cookies to ensure you get the best experience on our websitePhys. Rev. A 93, 16) - Quantum-state transfer in staggered coupled-cavity arrays
We consider a coupled-cavity array, where each cavity interacts with an atom under the rotating-wave approximation. For a staggered pattern of intercavity couplings, a pair of field normal modes, each bilocalized at the two array ends, arises. A rich structure of dynamical regimes can hence be addressed, depending on which resonance condition is set between the atom and the field modes. We show that this can be harnessed to carry out high-fidelity quantum-state transfer (QST) of photonic, atomic, or polaritonic states. Moreover, by partitioning the array into coupled modules of shorter length, the QST time can be substantially shortened without significantly affecting the fidelity.DOI:https://doi.org/10.1103/PhysRevA.93.032310(C)2016 American Physical SocietyAuthors & Affiliations
1,*, 2, 2,3, and 11Departamento de Física, Universidade Federal de Sergipe,
S?o Cristóv?o, Brazil2NEST, Istituto Nanoscienze-CNR and Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, via Archirafi 36, I-90123 Palermo, Italy3Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom*Article Text (Subscription Required)
Click to ExpandReferences (Subscription Required)
Authorization RequiredOther OptionsDownload & ShareImagesFigure 1Sketch of a CCA with a staggered pattern of hopping rates, where J1=(1+η)J and J2=(1-η)J. The protected mode of each cavity can be coupled to a two-level atom at rate g.Figure 2(a) Single-excitation spectrum of Hamiltonian () (in units of J). Δω is the gap between the pair of bands corresponding to unbound states, while δω=ωb--ωb+ (inset) is the energy gap between the localized bound states [cf. Eq. ()]. (b) Spatial profile of |αb±?. Plots were obtained by exact numerical diagonalization of Eq. () for η=-0.25 and N=50 [comparison with perturbation theory, Eqs. () and (), is found to be excellent].Figure 3End-to-end amplitude |?αb±|a?1+a?N|αb±?| vs J1/J2 for several values of N (in increasing order from top to bottom) in the case of (a) a staggered array described by Hamiltonian () and (b) a uniform bulk described by Hamiltonian (). Note that J1/J2 decreases from right to left. Each plot was obtained from an exact numerical diagonalization of the Hamiltonian.Figure 4Full-array end-to-end (a, b) amplitude |?a?1+a?L?| and (c, d) energy-gap gain δωm,N/δω1,L vs Jmod/J for different values of N in the case of a modularized staggered CCA. (a, c) Two-module array (m=2); (b, d) three-module array (m=3). For each setup, we have set the intramodule distortion to η=-0.5 (about J1/J2=0.33).Figure 5Maximum achievable average QST fidelity F [cf. Eq. ()] after one Rabi-like oscillation period, that is, τ=2π/δωm,N, vs Jmod/J. We have set L=24, J1=0.3J, and J2=J and considered different modularization schemes (each specified by the value of m). Inset: Transfer time τ (in units of J-1) vs Jmod/J on a log-lin scale. For the unmodularized array (m=1), the maximum fidelity and transfer time are, respectively, F?0.98 and τ?3×106J-1.Figure 6Maximum achievable average QST fidelity F [cf. Eq. ()] after one Rabi-like oscillation period, that is, τ=2π/δωm,N, vs Jmod/J. We have set L=102 and η=-0.8 (about J1/J2=0.11) using the modularization scheme m=17, the length of each module thus being N=6. Inset: Transfer time τ (in units of J-1) vs Jmod/J on a log-lin scale. For the corresponding unmodularized CCA, the transfer time is infinite for all practical purposes.Figure 7Time evolution of (a) the photonic and (b) the atomic excitation and (c) of the transition amplitude across a 10-cavity staggered CCA for an initial state |Ψ(0)?=|e1?. In (a) [(b)], we display the probability of finding the photonic [atomic] excitation in the first cavity (thin black line), in the last one (thick red line), and in the bulk sites 2≤x≤N-1 (dashed blue line). Plots were obtained from an exact numerical diagonalization of Eq. () for η=-0.5 and g=10-6J.Figure 8Time evolution of the transition amplitude for an initial symmetric polariton set in the first cavity in the case of a staggered 30-cavity array for (a) η=0, (b) η=-0.25, and (c) η=-0.5 (solid black line). (d) The case of a modularized CCA for m=3 with Jmod=0.1J (dotted red line) and m=5 with Jmod=0.3J (thick gray line). Note that Jmod was slightly increased in order to assure the formation of bilocalized states (cf. Sec. ). The intramodular distortion parameter was fixed at η=-0.5. We set g=0.01J and ωa=0 throughout. Plots were obtained from an exact diagonalization of Eq. () [with H?hop being replaced with H?mod in (d)].AuthorsRefereesLibrariansStudentsAPS MembersISSN
(print). (C)2016
All rights reserved. Physical Review A(TM) is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. The APS Physics logo and Physics logo are trademarks of the American Physical Society. Information about registration may be found .
Use of the American Physical Society websites and journals implies that
the user has read and agrees to our
and any applicable
Log In Article LookupPaste a citation or DOIEnter a citationJournal: Phys. Rev. Lett.
Phys. Rev. X
Rev. Mod. Phys.
Phys. Rev. A
Phys. Rev. B
Phys. Rev. C
Phys. Rev. D
Phys. Rev. E
Phys. Rev. Applied
Phys. Rev. Fluids
Phys. Rev. Accel. Beams
Phys. Rev. Phys. Educ. Res.
Phys. Rev.
Phys. Rev. (Series I)
Volume: Article:OALib Journal期刊
费用：600人民币/ 99美元
查看量下载量
Operational Risks in Financial Sectors
A new risk was born in the mid-1990s known as operational risk. Though its application varied by institutions—Basel II for banks and Solvency II for insurance companies—the idea stays the same. Firms are interested in operational risk because exposure can be fatal. Hence, it has become one of the major risks of the financial sector. In this study, we are going to define operational risk in addition to its applications regarding banks and insurance companies. Moreover, we will discuss the different measurement criteria related to some examples and applications that explain how things work in real life. 1. Introduction Operational risk existed longer than we know, but its concept was not interpreted until after the year 1995 when one of the oldest banks in London, Barings bank, collapsed because of Nick Leeson, one of the traders, due to unauthorized speculations. A wide variety of definitions are used to describe operational risk of which the following is just a sample (cf. Moosa [1, pages 87-88]). (i)All types of risk other than credit and market risk. (ii)The risk of loss due to human error or deficiencies in systems or controls. (iii)The risk that a firm’s internal practices, policies, and systems are not rigorous or sophisticated enough to cope with unexpected market conditions or human or technological errors. (iv)The risk of loss resulting from errors in the processing of transactions, breakdown in controls, and errors or failures in system support. The Basel II Committee, however, defined operational risk as the risk of loss resulting from inadequate or failed internal processes, people and systems, or from external events (cf. BCBS, Definition of Operational Risk [2]). For example, an operational risk could be losses due to an IT external events like a flood, an earthquake, or a fire such as the one at Crédit Lyonnais in May 1996 which resulted in extreme losses. Currently, the lack of operational risk loss data is a major issue on hand but once the data sources become available, a collection of methods will be progressively implemented. In 2001, the Basel Committee started a series of surveys and statistics regarding operational risks that most banks encounter. The idea was to develop and correct measurements and calculation methods. Additionally, the European Commission also started preparing for the new Solvency II Accord, taking into consideration the operational risk for insurance and reinsurance companies. As so, and since Basel and Solvency accords set forth many calculation criteria, our interest in this
References
[]&&I. A. Moosa, Quantification of Operational Risk Under Basel II: The Good, Bad and Ugly, Palgrave Macmillan, New York, NY, USA, 2008.
[]&&Basel Committee on Banking Supervision, Operational risk, Consultative Document, 2001, http://www.bis.org/publ/bcbsca07.pdf.
[]&&D. D. Lambrigger, P. V. Shevchenko, and M. V. Wüuthrich, “Data combination under Basel II and solvency 2: operational risk goes Bayesian,” Fran？ais d'Actuariat, vol. 8, no. 16, pp. 4–13, 2008.
[]&&Basel Committee on Banking Supervision, Quantitative impact study 3 technical guidance, 2002, http://www.bis.org/bcbs/qis/qis3tech.pdf.
[]&&Basel Committee on Banking Supervision, Working paper on the regulatory treatment of operational risk, 2001, http://www.bis.org/publ/bcbs_wp8.pdf.
[]&&H. Dahen, La Quantification du Risque Opérationnel des Instituts Bancaires [Thèse de doctorat], HEC, Montréal, Canada, 2006.
[]&&F. Maurer, “Les développements récents de la mesure du risque opérationnel,” in Congrès AFFI, 2007.
[]&&A. Frachot, P. Georges, and T. Roncalli, “Loss distirbution approach for operational risk,” Groupe de Recherche Opérationnelle, Crédit Lyonnais, Lyon, France, 2001.
[]&&CEIOPS, “Advice for level 2 implementing measures on solvency II: SCR standard formula,” Article 111 (f) Operational Risk ceiops-doc-45/09, 2009.
[]&&CEIOPS, QIS5-Technical Specifications, 2010, http://www.eiopa.europa.eu.
[]&&M. Gilli and E. Kellezi, An Application of Extreme Value Theory for Measuring Risk, Department of Econometrics, University of Geneva and FAME CH1211, Geneva, Switzerland, 2003.
[]&&A. J. McNeil, R. Frey, and P. Embrechts, Quantitative Risk Management, Princeton Series in Finance, Princeton University Press, Princeton, NJ, USA, 2005.
[]&&A. Chernobai, C. Menn, S. T. Rachev, and S. Trück, “Estimation of operational value-at-risk in the presence of minimum collection thresholds,” Tech. Rep., University of California, Santa Barbara, Calif, USA, 2005.
[]&&A. Chernobai, F. Fabozzi, and S. T. Rachev, “Composite goodness-of-fit tests for left-truncated loss samples,” Tech. Rep., University of California, Santa Barbara, Calif, USA, 2005.
[]&&R. L. Smith, Measuring Risk with Extreme Value Theory, M.A.H. Dempster, 2002.
[]&&E. A. Medova and M. N. Kyriacou, Extremes in Operational Risk Management, M.A.H. Dempster, 2002.
[]&&Basel Committee on Banking Supervision, BIS(2005) Basel II: international convergence of capital measurement and capital standards: a revised framework, Bank for international settlements(BIS), 2005, http://www.bis.org/publ/bcbs118.pdf.
[]&&D. D. Lambrigger, P. V. Shevchenko, and M. V. Wüuthrich, “The quantification of operational risk using internal data, relevent external data and expert opinions,” The Journal of Operational Risk, vol. 2, no. 3, pp. 3–27, 2007.
[]&&A. Frachot and T. Roncalli, “Mixing internal and external data for managing operational risk,” Groupe de Recherche Opérationnelle, Crédit Lyonnais, Lyon, France, 2002.
[]&&H. Dahen and G. Dionne, “Scaling for the Severity and frequency of external operational loss data,” Submitted to the Conference Performance Measurment in the Financial Services Sector: Frontier Efficiency Methodologies and Other Innovative Techniques, 2008.
[]&&Basel Committee on Banking Supervision, CP3 on issues relating to the use and recognition of Insurance in the calculation of operational risk capital requirements for banks under the proposed Basel 2 capital accord, 2003, http://www.bis.org/bcbs/cp3/talbunde.pdf.
[]&&Basel Committee on Banking Supervision, Recognising the risk-mitigating impact of insurance in operational risk modelling, 2010, http://www.bis.org/publ/bcbs181.pdf.
[]&&D. Bazzarello, B. Crielaard, F. Piacenza, and A. Soprano, Modeling Insurance Miti-Gation on Operational Risk Capital, Unicredit Group, Operational Risk Management, Milan, Italy, 2006.
Please enable JavaScript to view the
&&&OALib Suggest
Live SupportAsk us anythingNews about Scitation
In December 2016 Scitation will launch with a new design, enhanced navigation and a much improved user experience.
To ensure a smooth transition, from today, we are temporarily stopping new account registration and single article purchases. If you already have an account you can continue to use the site as normal.
For help or more information please visit our .
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads
View Affiliations
Hide Affiliations
Affiliations:
a) Electronic mail:
J. Chem. Phys. 143, 034107 (Tue Jul 21 00:00:00 UTC 2015);
In previous works, we have introduced an alternative perturbation scheme to find approximate solutions of the spectral problem for the rotation-vibration molecular Hamiltonian. An important feature of our approach is that the zero order Hamiltonian is the direct product of a purely vibrational Hamiltonian with the identity on the rotational degrees of freedom. The convergence of our method for the methane vibrational ground state was very satisfactory and our predictions were quantitative. In the present article, we provide further details on the implementation of the method in the degenerate and quasi-degenerate cases. The quasi-degenerate version of the method is tested on excited polyads of methane, and the results are assessed with respect to a variational treatment. The optimal choice of the size of quasi-degenerate spaces is determined by a trade-off between speed of convergence of the perturbation series and the computational effort to obtain the effective super-Hamiltonian.
Received Thu Apr 16 00:00:00 UTC 2015
Accepted Mon Jun 29 00:00:00 UTC 2015
Published online Mon Jul 20 00:00:00 UTC 2015
Acknowledgments:
This work was supported by the GENCI Grant No. x and Grant No. CARMA ANR-12-BS01-0017. The authors acknowledge the SIGAMM Mesocentre for hosting the CONVIV code project, as well as for providing computer facilities. This work was granted access to the HPC and visualization resources of the “Centre de Calcul Interactif” hosted by University Nice Sophia Antipolis.
Article outline:
I. INTRODUCTION
II. AB INITIO EFFECTIVE ROTATIONAL SUPER-HAMILTONIAN AND DIPOLE MOMENT SUPEROPERATOR
A. Definition of effective operators
B. Case of a symmetry operator G(Y) commuting with H(X, Y)
C. Generalized perturbation theory for the effective wave operator equation
1. First order
2. Second order
3. Higher orders
III. APPLICATION TO THE TETRADECAD OF METHANE
A. Vibrational (J = 0)-calculation
B. Reference variational calculation
C. Quasi-degenerate perturbative calculations
1. Convergence with perturbation order
2. Convergence with quasi-degenerate space
3. Computational cost
IV. CONCLUSION
/content/aip/journal/jcp/143/3/10.6471
http://aip./content/aip/journal/jcp/143/3/10.6471
Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads
J. Chem. Phys. 143, 034107 (Tue Jul 21 00:00:00 UTC 2015);
/content/aip/journal/jcp/143/3/10.6471
/content/aip/journal/jcp/143/3/10.6471
Data & Media loading...
Article metrics loading...
/content/aip/journal/jcp/143/3/10.6471
/content/aip/journal/jcp/143/3/10.6471
dcterms_title,dcterms_subject,pub_keyword
-contentType:Contributor -contentType:Concept -contentType:Institution
Full text loading...
Most read this month
content/aip/journal/jcp
Most cited this month
/recommendto/jsessionid=fF5SZiCh_PDQfRmtoaIEJBxA.x-aip-live-06?webId=%2Fcontent%2Faip%2Fjournal%2Fjcp&title=The+Journal+of+Chemical+Physics&issn=&eissn=
The Journal of Chemical Physics & Recommend this title to your library
Access Key
FFree Content
OAOpen Access Content
SSubscribed Content
TFree Trial Content
This is a required field
Please enter a valid email address
Oops! This section
does not exist...Use the links on this page to find existing content.
Click here to download this PDF to your device.
752b8dbdd7fdb8b9568b5
journal.articlezxybnytfddd
Scitation: Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads
http://aip./content/aip/journal/jcp/143/3/10.6471
SEARCH_EXPAND_ITEM
/content/realmedia?fmt=ahah&adPositionList=
&advertTargetUrl=//oascentral.aip.org/RealMedia/ads/&sitePageValue=jcp.aip.org/143/3/10.6471&pageURL=http://scitation.aip.org/content/aip/journal/jcp/143/3/10.6471'
Right1,Right2,Right3,
journal/journal.article
/content/aip/journal/jcp/143/3/10.6471
jcp.aip.org/143/3/10.6471/Right1,Right2,Right3}