Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode

Gough, John; Van Handel, R., (2007) 'Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode', Journal of Statistical Physics 127(3) pp.575-607 RAE2008

OPEN DOORS AND OPEN MINDS: WHAT FACULTY AUTHORS CAN DO TO ENSURE OPEN ACCESS TO THEIR WORK THROUGH THEIR INSTITUTION

The Internet has brought unparalleled opportunities for expanding availability of research by bringing down economic and physical barriers to sharing. The digitally networked environment promises to democratize access, carry knowledge beyond traditional research niches, accelerate discovery, encourage new and interdisciplinary approaches to ever more complex research challenges, and enable new computational research strategies. However, despite these opportunities for increasing access to knowledge, the prices of scholarly journals have risen sharply over the past two decades, often forcing libraries to cancel subscriptions. Today even the wealthiest institutions cannot afford to sustain all of the journals needed by their faculties and students. To take advantage of the opportunities created by the Internet and to further their mission of creating, preserving, and disseminating knowledge, many academic institutions are taking steps to capture the benefits of more open research sharing. Colleges and universities have built digital repositories to preserve and distribute faculty scholarly articles and other research outputs. Many individual authors have taken steps to retain the rights they need, under copyright law, to allow their work to be made freely available on the Internet and in their institutionâ s repository. And, faculties at some institutions have adopted resolutions endorsing more open access to scholarly articles. Most recently, on February 12, 2008, the Faculty of Arts and Sciences (FAS) at Harvard University took a landmark step. The faculty voted to adopt a policy requiring that faculty authors send an electronic copy of their scholarly articles to the universityâ s digital repository and that faculty authors automatically grant copyright permission to the university to archive and to distribute these articles unless a faculty member has waived the policy for a particular article. Essentially, the faculty voted to make open access to the results of their published journal articles the default policy for the Faculty of Arts and Sciences of Harvard University. As of March 2008, a proposal is also under consideration in the University of California system by which faculty authors would commit routinely to grant copyright permission to the university to make copies of the facultyâ s scholarly work openly accessible over the Internet. Inspired by the example set by the Harvard faculty, this White Paper is addressed to the faculty and administrators of academic institutions who support equitable access to scholarly research and knowledge, and who believe that the institution can play an important role as steward of the scholarly literature produced by its faculty. This paper discusses both the motivation and the process for establishing a binding institutional policy that automatically grants a copyright license from each faculty member to permit deposit of his or her peer-reviewed scholarly articles in institutional repositories, from which the works become available for others to read and cite.

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

Small Depth Quantum Circuits

Small depth quantum circuits have proved to be unexpectedly powerful in comparison to their classical counterparts. We survey some of the recent work on this and present some open problems.

Trade & Cap: A Customer-Managed, Market-Based System for Trading Bandwidth Allowances at a Shared Link

We propose Trade & Cap (T&C), an economics-inspired mechanism that incentivizes users to voluntarily coordinate their consumption of the bandwidth of a shared resource (e.g., a DSLAM link) so as to converge on what they perceive to be an equitable allocation, while ensuring efficient resource utilization. Under T&C, rather than acting as an arbiter, an Internet Service Provider (ISP) acts as an enforcer of what the community of rational users sharing the resource decides is a fair allocation of that resource. Our T&C mechanism proceeds in two phases. In the first, software agents acting on behalf of users engage in a strategic trading game in which each user agent selfishly chooses bandwidth slots to reserve in support of primary, interactive network usage activities. In the second phase, each user is allowed to acquire additional bandwidth slots in support of presumed open-ended need for fluid bandwidth, catering to secondary applications. The acquisition of this fluid bandwidth is subject to the remaining "buying power" of each user and by prevalent "market prices" – both of which are determined by the results of the trading phase and a desirable aggregate cap on link utilization. We present analytical results that establish the underpinnings of our T&C mechanism, including game-theoretic results pertaining to the trading phase, and pricing of fluid bandwidth allocation pertaining to the capping phase. Using real network traces, we present extensive experimental results that demonstrate the benefits of our scheme, which we also show to be practical by highlighting the salient features of an efficient implementation architecture.

On the Complexity of Quantum ACC

For any q > 1, let MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by q. We show that for any q,t > 1, MOD_q is equivalent to MOD_t (up to constant depth). Based on the case q=2, Moore has shown that quantum analogs of AC^(0), ACC[q], and ACC, denoted QAC^(0)_wf, QACC[2], QACC respectively, define the same class of operators, leaving q > 2 as an open question. Our result resolves this question, implying that QAC^(0)_wf = QACC[q] = QACC for all q. We also prove the first upper bounds for QACC in terms of related language classes. We define classes of languages EQACC, NQACC (both for arbitrary complex amplitudes) and BQACC (for rational number amplitudes) and show that they are all contained in TC^(0). To do this, we show that a TC^(0) circuit can keep track of the amplitudes of the state resulting from the application of a QACC operator using a constant width polynomial size tensor sum. In order to accomplish this, we also show that TC^(0) can perform iterated addition and multiplication in certain field extensions.

Correlations in low dimensional quantum systems

In this thesis I present the work done during my PhD in the area of low dimensional quantum gases. The chapters of this thesis are self contained and represent individual projects which have been peer reviewed and accepted for publication in respected international journals. Various systems are considered, the first of which is a two particle model which possesses an exact analytical solution. I investigate the non-classical correlations that exist between the particles as a function of the tunable properties of the system. In the second work I consider the coherences and out of equilibrium dynamics of a one-dimensional Tonks-Girardeau gas. I show how the coherence of the gas can be inferred from various properties of the reduced state and how this may be observed in experiments. I then present a model which can be used to probe a one-dimensional Fermi gas by performing a measurement on an impurity which interacts with the gas. I show how this system can be used to observe the so-called orthogonality catastrophe using modern interferometry techniques. In the next chapter I present a simple scheme to create superposition states of particles with special emphasis on the NOON state. I explore the effect of inter-particle interactions in the process and then characterise the usefulness of these states for interferometry. Finally I present my contribution to a project on long distance entanglement generation in ion chains. I show how carefully tuning the environment can create decoherence-free subspaces which allows one to create and preserve entanglement.

Techniques for engineering quantum states

In this thesis I theoretically study quantum states of ultracold atoms. The majority of the Chapters focus on engineering specific quantum states of single atoms with high fidelity in experimentally realistic systems. In the sixth Chapter, I investigate the stability and dynamics of new multidimensional solitonic states that can be created in inhomogeneous atomic Bose-Einstein condensates. In Chapter three I present two papers in which I demonstrate how the coherent tunnelling by adiabatic passage (CTAP) process can be implemented in an experimentally realistic atom chip system, to coherently transfer the centre-of-mass of a single atom between two spatially distinct magnetic waveguides. In these works I also utilise GPU (Graphics Processing Unit) computing which offers a significant performance increase in the numerical simulation of the Schrödinger equation. In Chapter four I investigate the CTAP process for a linear arrangement of radio frequency traps where the centre-of-mass of both, single atoms and clouds of interacting atoms, can be coherently controlled. In Chapter five I present a theoretical study of adiabatic radio frequency potentials where I use Floquet theory to more accurately model situations where frequencies are close and/or field amplitudes are large. I also show how one can create highly versatile 2D adiabatic radio frequency potentials using multiple radio frequency fields with arbitrary field orientation and demonstrate their utility by simulating the creation of ring vortex solitons. In the sixth Chapter I discuss the stability and dynamics of a family of multidimensional solitonic states created in harmonically confined Bose-Einstein condensates. I demonstrate that these solitonic states have interesting dynamical instabilities, where a continuous collapse and revival of the initial state occurs. Through Bogoliubov analysis, I determine the modes responsible for the observed instabilities of each solitonic state and also extract information related to the time at which instability can be observed.

Pyramidal quantum dots: single and entangled photon sources and correlation studies

Practical realisation of quantum information science is a challenge being addressed by researchers employing various technologies. One of them is based on quantum dots (QD), usually referred to as artificial atoms. Being capable to emit single and polarization entangled photons, they are attractive as sources of quantum bits (qubits) which can be relatively easily integrated into photonic circuits using conventional semiconductor technologies. However, the dominant self-assembled QD systems suffer from asymmetry related problems which modify the energetic structure. The main issue is the degeneracy lifting (the fine-structure splitting, FSS) of an optically allowed neutral exciton state which participates in a polarization-entanglement realisation scheme. The FSS complicates polarization-entanglement detection unless a particular FSS manipulation technique is utilized to reduce it to vanishing values, or a careful selection of intrinsically good candidates from the vast number of QDs is carried out, preventing the possibility of constructing vast arrays of emitters on the same sample. In this work, site-controlled InGaAs QDs grown on (111)B oriented GaAs substrates prepatterned with 7.5 μm pitch tetrahedrons were studied in order to overcome QD asymmetry related problems. By exploiting an intrinsically high rotational symmetry, pyramidal QDs were shown as polarization-entangled photon sources emitting photons with the fidelity of the expected maximally entangled state as high as 0.721. It is the first site-controlled QD system of entangled photon emitters. Moreover, the density of such emitters was found to be as high as 15% in some areas: the density much higher than in any other QD system. The associated physical phenomena (e.g., carrier dynamic, QD energetic structure) were studied, as well, by different techniques: photon correlation spectroscopy, polarization-resolved microphotoluminescence and magneto-photoluminescence.

Energy harvesting system design and optimization for wireless sensor networks

Wireless sensor networks (WSN) are becoming widely adopted for many applications including complicated tasks like building energy management. However, one major concern for WSN technologies is the short lifetime and high maintenance cost due to the limited battery energy. One of the solutions is to scavenge ambient energy, which is then rectified to power the WSN. The objective of this thesis was to investigate the feasibility of an ultra-low energy consumption power management system suitable for harvesting sub-mW photovoltaic and thermoelectric energy to power WSNs. To achieve this goal, energy harvesting system architectures have been analyzed. Detailed analysis of energy storage units (ESU) have led to an innovative ESU solution for the target applications. Battery-less, long-lifetime ESU and its associated power management circuitry, including fast-charge circuit, self-start circuit, output voltage regulation circuit and hybrid ESU, using a combination of super-capacitor and thin film battery, were developed to achieve continuous operation of energy harvester. Low start-up voltage DC/DC converters have been developed for 1mW level thermoelectric energy harvesting. The novel method of altering thermoelectric generator (TEG) configuration in order to match impedance has been verified in this work. Novel maximum power point tracking (MPPT) circuits, exploring the fractional open circuit voltage method, were particularly developed to suit the sub-1mW photovoltaic energy harvesting applications. The MPPT energy model has been developed and verified against both SPICE simulation and implemented prototypes. Both indoor light and thermoelectric energy harvesting methods proposed in this thesis have been implemented into prototype devices. The improved indoor light energy harvester prototype demonstrates 81% MPPT conversion efficiency with 0.5mW input power. This important improvement makes light energy harvesting from small energy sources (i.e. credit card size solar panel in 500lux indoor lighting conditions) a feasible approach. The 50mm × 54mm thermoelectric energy harvester prototype generates 0.95mW when placed on a 60oC heat source with 28% conversion efficiency. Both prototypes can be used to continuously power WSN for building energy management applications in typical office building environment. In addition to the hardware development, a comprehensive system energy model has been developed. This system energy model not only can be used to predict the available and consumed energy based on real-world ambient conditions, but also can be employed to optimize the system design and configuration. This energy model has been verified by indoor photovoltaic energy harvesting system prototypes in long-term deployed experiments.

Surveillance during pregnancy: methods and response rates from a hospital based pilot study of the Pregnancy Risk Assessment Monitoring System in Ireland

Background: Many European countries including Ireland lack high quality, on-going, population based estimates of maternal behaviours and experiences during pregnancy. PRAMS is a CDC surveillance program which was established in the United States in 1987 to generate high quality, population based data to reduce infant mortality rates and improve maternal and infant health. PRAMS is the only on-going population based surveillance system of maternal behaviours and experiences that occur before, during and after pregnancy worldwide.Methods: The objective of this study was to adapt, test and evaluate a modified CDC PRAMS methodology in Ireland. The birth certificate file which is the standard approach to sampling for PRAMS in the United States was not available for the PRAMS Ireland study. Consequently, delivery record books for the period between 3 and 5 months before the study start date at a large urban obstetric hospital [8,900 births per year] were used to randomly sample 124 women. Name, address, maternal age, infant sex, gestational age at delivery, delivery method, APGAR score and birth weight were manually extracted from records. Stillbirths and early neonatal deaths were excluded using APGAR scores and hospital records. Women were sent a letter of invitation to participate including option to opt out, followed by a modified PRAMS survey, a reminder letter and a final survey.Results: The response rate for the pilot was 67%. Two per cent of women refused the survey, 7% opted out of the study and 24% did not respond. Survey items were at least 88% complete for all 82 respondents. Prevalence estimates of socially undesirable behaviours such as alcohol consumption during pregnancy were high [>50%] and comparable with international estimates.Conclusion: PRAMS is a feasible and valid method of collecting information on maternal experiences and behaviours during pregnancy in Ireland. PRAMS may offer a potential solution to data deficits in maternal health behaviour indicators in Ireland with further work. This study is important to researchers in Europe and elsewhere who may be interested in new ways of tailoring an established CDC methodology to their unique settings to resolve data deficits in maternal health.

Subterfuge-safe trust management for delegation of permissions in open environments

Open environments involve distributed entities interacting with each other in an open manner. Many distributed entities are unknown to each other but need to collaborate and share resources in a secure fashion. Usually resource owners alone decide who is trusted to access their resources. Since resource owners in open environments do not have a complete picture of all trusted entities, trust management frameworks are used to ensure that only authorized entities will access requested resources. Every trust management system has limitations, and the limitations can be exploited by malicious entities. One vulnerability is due to the lack of globally unique interpretation for permission specifications. This limitation means that a malicious entity which receives a permission in one domain may misuse the permission in another domain via some deceptive but apparently authorized route; this malicious behaviour is called subterfuge. This thesis develops a secure approach, Subterfuge Safe Trust Management (SSTM), that prevents subterfuge by malicious entities. SSTM employs the Subterfuge Safe Authorization Language (SSAL) which uses the idea of a local permission with a globally unique interpretation (localPermission) to resolve the misinterpretation of permissions. We model and implement SSAL with an ontology-based approach, SSALO, which provides a generic representation for knowledge related to the SSAL-based security policy. SSALO enables integration of heterogeneous security policies which is useful for secure cooperation among principals in open environments where each principal may have a different security policy with different implementation. The other advantage of an ontology-based approach is the Open World Assumption, whereby reasoning over an existing security policy is easily extended to include further security policies that might be discovered in an open distributed environment. We add two extra SSAL rules to support dynamic coalition formation and secure cooperation among coalitions. Secure federation of cloud computing platforms and secure federation of XMPP servers are presented as case studies of SSTM. The results show that SSTM provides robust accountability for the use of permissions in federation. It is also shown that SSAL is a suitable policy language to express the subterfuge-safe policy statements due to its well-defined semantics, ease of use, and integrability.

A support system for mentors of novice entrepreneurs

In this study we present online software to rapidly assess the impact of mentoring techniques on a novice entrepreneur. We have built a prototype that collects data from team members in less than five minutes and that automatically returns a diagnostic analysis to the mentor. Between 2012 and 2015 we have tested three versions of our prototype with longitudinal analyses of teams attending startup weekend competitions, to confirm that our prototype supports mentors with few and yet relevant information. The results of our studies open several avenues of research regarding rapid diagnostic of project teams, whereas, from a practical point of view, our prototype entirely done with Google Docs can be easily used by anyone interested in entrepreneurship education. Keywords: Entrepreneurship education, effectuation, mentoring, decision support, design science.

Plate-specific gain map correction for the improvement of detective quantum efficiency in computed radiography.

PURPOSE: The purpose of this work is to improve the noise power spectrum (NPS), and thus the detective quantum efficiency (DQE), of computed radiography (CR) images by correcting for spatial gain variations specific to individual imaging plates. CR devices have not traditionally employed gain-map corrections, unlike the case with flat-panel detectors, because of the multiplicity of plates used with each reader. The lack of gain-map correction has limited the DQE(f) at higher exposures with CR. This current work describes a feasible solution to generating plate-specific gain maps. METHODS: Ten high-exposure open field images were taken with an RQA5 spectrum, using a sixth generation CR plate suspended in air without a cassette. Image values were converted to exposure, the plates registered using fiducial dots on the plate, the ten images averaged, and then high-pass filtered to remove low frequency contributions from field inhomogeneity. A gain-map was then produced by converting all pixel values in the average into fractions with mean of one. The resultant gain-map of the plate was used to normalize subsequent single images to correct for spatial gain fluctuation. To validate performance, the normalized NPS (NNPS) for all images was calculated both with and without the gain-map correction. Variations in the quality of correction due to exposure levels, beam voltage/spectrum, CR reader used, and registration were investigated. RESULTS: The NNPS with plate-specific gain-map correction showed improvement over the noncorrected case over the range of frequencies from 0.15 to 2.5 mm(-1). At high exposure (40 mR), NNPS was 50%-90% better with gain-map correction than without. A small further improvement in NNPS was seen from carefully registering the gain-map with subsequent images using small fiducial dots, because of slight misregistration during scanning. Further improvement was seen in the NNPS from scaling the gain map about the mean to account for different beam spectra. CONCLUSIONS: This study demonstrates that a simple gain-map can be used to correct for the fixed-pattern noise in a given plate and thus improve the DQE of CR imaging. Such a method could easily be implemented by manufacturers because each plate has a unique bar code and the gain-map for all plates associated with a reader could be stored for future retrieval. These experiments indicated that an improvement in NPS (and hence, DQE) is possible, depending on exposure level, over a wide range of frequencies with this technique.

Independent individual addressing of multiple neutral atom qubits with a micromirror-based beam steering system

We demonstrate a scalable approach to addressing multiple atomic qubits for use in quantum information processing. Individually trapped 87Rb atoms in a linear array are selectively manipulated with a single laser guided by a microelectromechanical beam steering system. Single qubit oscillations are shown on multiple sites at frequencies of ≃3.5 MHz with negligible crosstalk to neighboring sites. Switching times between the central atom and its closest neighbor were measured to be 6-7 μs while moving between the central atom and an atom two trap sites away took 10-14 μs. © 2010 American Institute of Physics.