Optimal Control of Quantum Dissipative Dynamics: Analytic solution for cooling the three level Λ\Lambda system

We study the problem of optimal control of dissipative quantum dynamics. Although under most circumstances dissipation leads to an increase in entropy (or a decrease in purity) of the system, there is an important class of problems for which dissipation with external control can decrease the entropy (or increase the purity) of the system. An important example is laser cooling. In such systems, there is an interplay of the Hamiltonian part of the dynamics, which is controllable and the dissipative part of the dynamics, which is uncontrollable. The strategy is to control the Hamiltonian portion of the evolution in such a way that the dissipation causes the purity of the system to increase rather than decrease. The goal of this paper is to find the strategy that leads to maximal purity at the final time. Under the assumption that Hamiltonian control is complete and arbitrarily fast, we provide a general framework by which to calculate optimal cooling strategies. These assumptions lead to a great simplification, in which the control problem can be reformulated in terms of the spectrum of eigenvalues of $\rho$, rather than $\rho$ itself. By combining this formulation with the Hamilton-Jacobi-Bellman theorem we are able to obtain an equation for the globaly optimal cooling strategy in terms of the spectrum of the density matrix. For the three-level $\Lambda$ system, we provide a complete analytic solution for the optimal cooling strategy. For this system it is found that the optimal strategy does not exploit system coherences and is a 'greedy' strategy, in which the purity is increased maximally at each instant.Comment: 9 pages, 3 fig

Evaluating amplified rDNA restriction analysis assay for identification of bacterial communities

Amplified ribosomal DNA restriction analysis (ARDRA) and restriction fragment length polymorphism were originally used for strain typing and for screening clone libraries to identify phylogenetic clusters within a microbial community. Here we used ARDRA as a model to examine the capacity of restriction-based techniques for clone identification, and the possibility of deriving phylogenetic information from ARDRA-based dendrograms. ARDRA was performed in silico on 48,759 sequences from the Ribosomal Database Project, and it was found that the fragmentation profiles were not necessarily unique for each sequence in the database, resulting in different species sharing fragmentation profiles. Although ARDRA-based clusters separated clones into different genera, these phylogenetic clusters did not overlap with trees constructed according to sequence alignment, calling into question the intra-genus ARDRA-based phylogeny. It is thus suggested that the prediction power of ARDRA clusters in identifying clone phylogeny be regarded with caution

Optimal control theory for unitary transformations

The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory (OCT) is used to solve the inversion problem irrespective of the initial input state. A unified formalism, based on the Krotov method is developed leading to a new scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X^1\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\Sigma^+_u$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Out of the schemes studied the square modulus scheme converges fastest. A study of the implementation of the $Q$ qubit Fourier transform in the Na$_2$ molecule was carried out for up to 5 qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.Comment: 32 pages, 6 figure

Quantum computing implementations with neutral particles

We review quantum information processing with cold neutral particles, that is, atoms or polar molecules. First, we analyze the best suited degrees of freedom of these particles for storing quantum information, and then we discuss both single- and two-qubit gate implementations. We focus our discussion mainly on collisional quantum gates, which are best suited for atom-chip-like devices, as well as on gate proposals conceived for optical lattices. Additionally, we analyze schemes both for cold atoms confined in optical cavities and hybrid approaches to entanglement generation, and we show how optimal control theory might be a powerful tool to enhance the speed up of the gate operations as well as to achieve high fidelities required for fault tolerant quantum computation.Comment: 19 pages, 12 figures; From the issue entitled "Special Issue on Neutral Particles

Speeding up the spatial adiabatic passage of matter waves in optical microtraps by optimal control

We numerically investigate the performance of atomic transport in optical microtraps via the so called spatial adiabatic passage technique. Our analysis is carried out by means of optimal control methods, which enable us to determine suitable transport control pulses. We investigate the ultimate limits of the optimal control in speeding up the transport process in a triple well configuration for both a single atomic wave packet and a Bose-Einstein condensate within a regime of experimental parameters achievable with current optical technology.Comment: 17 pages, 14 figure

Perennials but not slope aspect affect the diversity of soil bacterial communities in the northern Negev Desert, Israel

Underneath the canopy of perennials in arid regions, moderate soil temperature and evaporation, as well as plant litter create islands of higher fertility in the low-productivity landscape, known as ‘resource islands’. The sparse distribution of these resource islands is mirrored by soil microbial communities, which mediate a large number of biogeochemical transformations underneath the plants. We explored the link between the bacterial community composition and two prevalent desert shrubs, Zygophyllum dumosum and Artemisia herba-alba, on northern- and southern-facing slopes in the northern highlands of the Negev Desert (Israel), at the end of a drought winter mild rainy season. We sequenced the bacterial community and analysed the physicochemical properties of the soil under the shrub canopies and from barren soil in replicate slopes. The soil bacterial diversity was independent of slope aspect, but differed according to shrub presence or type. Links between soil bacterial community composition and their associated desert shrubs were found, enabling us to link bacterial diversity with shrub type or barren soils. Our results suggest that plants and their associated bacterial communities are connected to survival and persistence under the harsh desert conditions

Combination of the PI3K inhibitor Idelalisib with the conventional cytostatics cytarabine and dexamethasone leads to changes in pathway activation that induce anti-proliferative effects in B lymphoblastic leukaemia cell lines

Background!#!The introduction of combined conventional cytostatics and pathway-specific inhibitors has opened new treatment options for several cancer types including hematologic neoplasia such as leukaemias. As the detailed understanding of the combination-induced molecular effects is often lacking, the identification of combination-induced molecular mechanisms bears significant value for the further development of interventional approaches.!##!Methods!#!Combined application of conventional cytostatic agents (cytarabine and dexamethasone) with the PI3K-inhibitor Idelalisib was analysed on cell-biologic parameters in two acute pro-B lymphoblastic leukaemia (B-ALL) cell lines. In particular, for comparative characterisation of the molecular signatures induced by the combined and mono application, whole transcriptome sequencing was performed. Emphasis was placed on pathways and genes exclusively regulated by drug combinations.!##!Results!#!Idelalisib + cytostatics combinations changed pathway activation for, e.g., 'Retinoblastoma in cancer', 'TGF-b signalling', 'Cell cycle' and 'DNA-damage response' to a greater extent than the two cytostatics alone. Analyses of the top-20 regulated genes revealed that both combinations induce characteristic gene expression changes.!##!Conclusion!#!A specific set of genes was exclusively deregulated by the drug combinations, matching the combination-specific anti-proliferative cell-biologic effects. The addition of Idelalisib suggests minor synergistic effects which are rather to be classified as additive

House Prices and Economic Growth

Economic growth, House prices, Wealth effect, Collateral effect, Common correlated effects estimators, Long horizon predictability, E23, E24, R11,