Deterministic reordering of 40Ca+ ions in a linear segmented Paul trap

In the endeavour to scale up the number of qubits in an ion-based quantum computer several groups have started to develop miniaturized ion traps for extended spatial control and manipulation of the ions. Shuttling and separation of ion strings have been the foremost issues in linear-trap arrangements and some prototypes of junctions have been demonstrated for the extension of ion motion to two dimensions (2D). While junctions require complex trap structures, small extensions to the 1D motion can be accomplished in simple linear trap arrangements. Here, control of the extended field in a planar, linear chip trap is used to shuttle ions in 2D. With this approach, the order of ions in a string is deterministically reversed. Optimized potentials are theoretically derived and simulations show that the reordering can be carried out adiabatically. The control over individual ion positions in a linear trap presents a new tool for ion-trap quantum computing. The method is also expected to work with mixed crystals of different ion species and as such could have applications for sympathetic cooling of an ion string.Comment: 18 pages, 9 figures. Added section on possibility of adiabatic turn. Added appendix on point charge model. Other minor alterations/clarifications. Version now published (http://www.iop.org/EJ/abstract/1367-2630/11/10/103008

Trapping and coherent manipulation of a Rydberg atom on a microfabricated device: a proposal

We propose to apply atom-chip techniques to the trapping of a single atom in a circular Rydberg state. The small size of microfabricated structures will allow for trap geometries with microwave cut-off frequencies high enough to inhibit the spontaneous emission of the Rydberg atom, paving the way to complete control of both external and internal degrees of freedom over very long times. Trapping is achieved using carefully designed electric fields, created by a simple pattern of electrodes. We show that it is possible to excite, and then trap, one and only one Rydberg atom from a cloud of ground state atoms confined on a magnetic atom chip, itself integrated with the Rydberg trap. Distinct internal states of the atom are simultaneously trapped, providing us with a two-level system extremely attractive for atom-surface and atom-atom interaction studies. We describe a method for reducing by three orders of magnitude dephasing due to Stark shifts, induced by the trapping field, of the internal transition frequency. This allows for, in combination with spin-echo techniques, maintenance of an internal coherence over times in the second range. This method operates via a controlled light shift rendering the two internal states' Stark shifts almost identical. We thoroughly identify and account for sources of imperfection in order to verify at each step the realism of our proposal.Comment: Accepted in EPJ

Wave function recombination instability in cold atom interferometers

Cold atom interferometers use guiding potentials that split the wave function of the Bose-Einstein condensate and then recombine it. We present theoretical analysis of the wave function recombination instability that is due to the weak nonlinearity of the condensate. It is most pronounced when the accumulated phase difference between the arms of the interferometer is close to an odd multiple of PI and consists in exponential amplification of the weak ground state mode by the strong first excited mode. The instability exists for both trapped-atom and beam interferometers.Comment: 4 pages, 5 figure

Taxing interacting externalities of ocean acidification, global warming, and eutrophication

We model a stylized economy dependent on agriculture and fisheries to study optimal environmental policy in the face of interacting external effects of ocean acidification, global warming, and eutrophication. This allows us to capture some of the latest insights from research on ocean acidification. Using a static two-sector general equilibrium model we derive optimal rules for national taxes on (Formula presented.) emissions and agricultural run-off and show how they depend on both isolated and interacting damage effects. In addition, we derive a second-best rule for a tax on agricultural run-off of fertilizers for the realistic case that effective internalization of (Formula presented.) externalities is lacking. The results contribute to a better understanding of the social costs of ocean acidification in coastal economies when there is interaction with other environmental stressors. Recommendations for Resource Managers: Marginal environmental damages from (Formula presented.) emissions should be internalized by a tax on (Formula presented.) emissions that is high enough to not only reflect marginal damages from temperature increases, but also marginal damages from ocean acidification and the interaction of both with regional sources of acidification like nutrient run-off from agriculture. In the absence of serious national policies that fully internalize externalities, a sufficiently high tax on regional nutrient run-off of fertilizers used in agricultural production can limit not only marginal environmental damages from nutrient run-off but also account for unregulated carbon emissions. Putting such regional policies in place that consider multiple important drivers of environmental change will be of particular importance for developing coastal economies that are likely to suffer the most from ocean acidification. © 2021 The Authors. Natural Resource Modeling published by Wiley Periodicals LLC

Process tomography of ion trap quantum gates

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude--shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates

Trapped-ion probing of light-induced charging effects on dielectrics

We use a string of confined $^{40}$Ca$^+$ ions to measure perturbations to a trapping potential which are caused by light-induced charging of an anti-reflection coated window and of insulating patches on the ion-trap electrodes. The electric fields induced at the ions' position are characterised as a function of distance to the dielectric, and as a function of the incident optical power and wavelength. The measurement of the ion-string position is sensitive to as few as $40$ elementary charges per $\sqrt{\mathrm{Hz}}$ on the dielectric at distances of order millimetres, and perturbations are observed for illumination with light of wavelengths as long as 729\,nm. This has important implications for the future of miniaturised ion-trap experiments, notably with regards to the choice of electrode material, and the optics that must be integrated in the vicinity of the ion. The method presented can be readily applied to the investigation of charging effects beyond the context of ion trap experiments.Comment: 11 pages, 5 figure

Breakdown of superfluidity of an atom laser past an obstacle

The 1D flow of a continuous beam of Bose-Einstein condensed atoms in the presence of an obstacle is studied as a function of the beam velocity and of the type of perturbing potential (representing the interaction of the obstacle with the atoms of the beam). We identify the relevant regimes: stationary/time-dependent and superfluid/dissipative; the absence of drag is used as a criterion for superfluidity. There exists a critical velocity below which the flow is superfluid. For attractive obstacles, we show that this critical velocity can reach the value predicted by Landau's approach. For penetrable obstacles, it is shown that superfluidity is recovered at large beam velocity. Finally, enormous differences in drag occur when switching from repulsive to attractive potential.Comment: 15 pages, 6 figure

Dynamics of Macroscopic Wave Packet Passing through Double Slits: Role of Gravity and Nonlinearity

Using the nonlinear Schroedinger equation (Gross-Pitaevskii equation), the dynamics of a macroscopic wave packet for Bose-Einstein condensates falling through double slits is analyzed. This problem is identified with a search for the fate of a soliton showing a head-on collision with a hard-walled obstacle of finite size. We explore the splitting of the wave packet and its reorganization to form an interference pattern. Particular attention is paid to the role of gravity (g) and repulsive nonlinearity (u_0) in the fringe pattern. The peak-to-peak distance in the fringe pattern and the number of interference peaks are found to be proportional to g^(-1/2) and u_0^(1/2)g^(1/4), respectively. We suggest a way of designing an experiment under controlled gravity and nonlinearity.Comment: 10 pages, 4 figures and 1 tabl

Coherence length of an elongated condensate: a study by matter-wave interferometry

We measure the spatial correlation function of Bose-Einstein condensates in the cross-over region between phase-coherent and strongly phase-fluctuating condensates. We observe the continuous path from a gaussian-like shape to an exponential-like shape characteristic of one-dimensional phase-fluctuations. The width of the spatial correlation function as a function of the temperature shows that the condensate coherence length undergoes no sharp transition between these two regimes.Comment: 8 pages, 6 figure, submitted to EPJ

Spatially-resolved potential measurement with ion crystals

We present a method to measure potentials over an extended region using one-dimensional ion crystals in a radio frequency (RF) ion trap. The equilibrium spacings of the ions within the crystal allow the determination of the external forces acting at each point. From this the overall potential, and also potentials due to specific trap features, are calculated. The method can be used to probe potentials near proximal objects in real time, and can be generalized to higher dimensions.Comment: 7 pages (double spaced), 3 figure