Path integral formulation of the tunneling dynamics of a superfluid Fermi gas in an optical potential

To describe the tunneling dynamics of a stack of two-dimensional fermionic superfluids in an optical potential, we derive an effective action functional from a path integral treatment. This effective action leads, in the saddle point approximation, to equations of motion for the density and the phase of the superfluid Fermi gas in each layer. In the strong coupling limit (where bosonic molecules are formed) these equations reduce to a discrete nonlinear Schrodinger equation, where the molecular tunneling amplitude is reduced for large binding energies. In the weak coupling (BCS) regime, we study the evolution of the stacked superfluids and derive an approximate analytical expression for the Josephson oscillation frequency in an external harmonic potential. Both in the weak and intermediate coupling regimes the detection of the Josephson oscillations described by our path integral treatment constitutes experimental evidence for the fermionic superfluid regime.Comment: 13 pages + 2 figure

The vortex state in the BEC to BCS crossover: a path-integral description

We derive a path-integral description of the vortex state of a fermionic superfluid in the crossover region between the molecular condensate (BEC) regime and the Cooper pairing (BCS) regime. This path-integral formalism, supplemented by a suitable choice for the saddle point value of the pairing field in the presence of a vortex, offers a unified description that encompasses both the BEC and BCS limits. The vortex core size is studied as a function of the tunable interaction strength between the fermionic atoms. We find that in the BEC regime, the core size is determined by the molecular healing length, whereas in the BCS regime, the core size is proportional only to the Fermi wave length. The observation of such quantized vortices in dilute Fermi gases would provide an unambiguous proof of the realization of superfluidity in these gases.Comment: 10 pages, 2 figure

A practical guide to density matrix embedding theory in quantum chemistry

Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample S$_{\text{N}}$2 reaction. The source code for the calculations in this work can be obtained from \url{https://github.com/sebwouters/qc-dmet}.Comment: 41 pages, 10 figure

Three-Fluid Description of the Sympathetic Cooling of a Boson-Fermion Mixture

We present a model for sympathetic cooling of a mixture of fermionic and bosonic atomic gases in harmonic traps, based on a three-fluid description. The model confirms the experimentally observed cooling limit of about 0.2 T_F when only bosons are pumped. We propose sequential cooling -- first pumping of bosons and afterwards fermions -- as a way to obtain lower temperatures. For this scheme, our model predicts that temperatures less than 0.1 T_F can be reached.Comment: 9 pages, 6 figure

The changing pattern of domestic cannabis cultivation in the UK and its impact on the cannabis market

With improvements in both technology and information cannabis is being increasingly grown indoors for domestic use, rather than being imported. This study examines 50 cannabis farms detected by an English police force, and examines the characteristics of the 61 suspects associated with them. The study highlights a UK pattern in domestic cultivation, that is moving away from large scale commercial cultivation, at times co-ordinated by South East Asian organised crime groups, to increased cultivation within residential premises by British citizens. Offenders range from those who have no prior criminal history to those who are serious and persistent offenders. The ramifications for law enforcement agencies and policy formers are discussed

Altimetry, gravimetry, GPS and viscoelastic modeling data for the joint inversion for glacial isostatic adjustment in Antarctica (ESA STSE Project REGINA)

The poorly known correction for the ongoing deformation of the solid Earth caused by glacial isostatic adjustment (GIA) is a major uncertainty in determining the mass balance of the Antarctic ice sheet from measurements of satellite gravimetry and to a lesser extent satellite altimetry. In the past decade, much progress has been made in consistently modeling ice sheet and solid Earth interactions; however, forward-modeling solutions of GIA in Antarctica remain uncertain due to the sparsity of constraints on the ice sheet evolution, as well as the Earth's rheological properties. An alternative approach towards estimating GIA is the joint inversion of multiple satellite data – namely, satellite gravimetry, satellite altimetry and GPS, which reflect, with different sensitivities, trends in recent glacial changes and GIA. Crucial to the success of this approach is the accuracy of the space-geodetic data sets. Here, we present reprocessed rates of surface-ice elevation change (Envisat/Ice, Cloud,and land Elevation Satellite, ICESat; 2003–2009), gravity field change (Gravity Recovery and Climate Experiment, GRACE; 2003–2009) and bedrock uplift (GPS; 1995–2013). The data analysis is complemented by the forward modeling of viscoelastic response functions to disc load forcing, allowing us to relate GIA-induced surface displacements with gravity changes for different rheological parameters of the solid Earth. The data and modeling results presented here are available in the PANGAEA database (https://doi.org/10.1594/PANGAEA.875745). The data sets are the input streams for the joint inversion estimate of present-day ice-mass change and GIA, focusing on Antarctica. However, the methods, code and data provided in this paper can be used to solve other problems, such as volume balances of the Antarctic ice sheet, or can be applied to other geographical regions in the case of the viscoelastic response functions. This paper presents the first of two contributions summarizing the work carried out within a European Space Agency funded study: Regional glacial isostatic adjustment and CryoSat elevation rate corrections in Antarctica (REGINA)

Direct magneto-optical compression of an effusive atomic beam for high-resolution focused ion beam application

An atomic rubidium beam formed in a 70 mm long two-dimensional magneto-optical trap (2D MOT), directly loaded from a collimated Knudsen source, is analyzed using laser-induced fluorescence. The longitudinal velocity distribution, the transverse temperature and the flux of the atomic beam are reported. The equivalent transverse reduced brightness of an ion beam with similar properties as the atomic beam is calculated because the beam is developed to be photoionized and applied in a focused ion beam. In a single two-dimensional magneto-optical trapping step an equivalent transverse reduced brightness of $(1.0\substack{+0.8-0.4})$ $\times 10^6$ A/(m$^2$ sr eV) was achieved with a beam flux equivalent to $(0.6\substack{+0.3-0.2})$ nA. The temperature of the beam is further reduced with an optical molasses after the 2D MOT. This increased the equivalent brightness to $(6\substack{+5-2})$$\times 10^6$ A/(m$^2$ sr eV). For currents below 10 pA, for which disorder-induced heating can be suppressed, this number is also a good estimate of the ion beam brightness that can be expected. Such an ion beam brightness would be a six times improvement over the liquid metal ion source and could improve the resolution in focused ion beam nanofabrication.Comment: 10 pages, 8 figures, 1 tabl