Mach-Zehnder interferometry with interacting trapped Bose-Einstein condensates

We theoretically analyze a Mach-Zehnder interferometer with trapped condensates, and find that it is surprisingly stable against the nonlinearity induced by inter-particle interactions. The phase sensitivity, which we study for number squeezed input states, can overcome the shot noise limit and be increased up to the Heisenberg limit provided that a Bayesian or Maximum-Likelihood phase estimation strategy is used. We finally demonstrate robustness of the Mach-Zehnder interferometer in presence of interactions against condensate oscillations and a realistic atom counting error.Comment: 4 pages, 5 figures, minor revision

Optimal control of number squeezing in trapped Bose-Einstein condensates

We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms, and the multi-configurational time dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.Comment: 17 pages, 21 figures, minor correction

Atom interferometry with trapped Bose-Einstein condensates: Impact of atom-atom interactions

Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultra cold atoms can be precisely manipulated at the quantum level, held for very long times in traps, and would therefore be an ideal setting for interferometry. In this paper we discuss how the non-linearities from atom-atom interactions on one hand allow to efficiently produce squeezed states for enhanced readout, but on the other hand result in phase diffusion which limits the phase accumulation time. We find that low dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom-atom interactions. Even for time sequences generated by optimal control the achievable minimal detectable interaction energy $\Delta E^{\rm min}$ is on the order of 0.001 times the chemical potential of the BEC in the trap. From there we have to conclude that for more precise measurements with atom interferometers more sophisticated strategies, or turning off the interaction induced dephasing during the phase accumulation stage, will be necessary.Comment: 28 pages, 13 figures, extended and correcte

Shapiro effect in atomchip-based bosonic Josephson junctions

We analyze the emergence of Shapiro resonances in tunnel-coupled Bose-Einstein condensates, realizing a bosonic Josephson junction. Our analysis is based on an experimentally relevant implementation using magnetic double well potentials on an atomchip. In this configuration the potential bias (implementing the junction voltage) and the potential barrier (realizing the Josephson link) are intrinsically coupled. We show that the dynamically driven system exhibits significantly enhanced Shapiro resonances which will facilitate experimental observation. To describe the systems response to the dynamic drive we compare a single-mode Gross-Pitaevskii (GP) description, an improved two-mode (TM) model and the self-consistent multi-configurational time dependent Hartree for Bosons (MCTDHB) method. We show that in the case of significant atom-atom interactions or strong driving, the spatial dynamics of the involved modes have to be taken into account, and only the MCTDHB method allows reliable predictions.Comment: 16 pages, 4 figure

Spin entanglement using coherent light and cavity-QED

A scheme for probabilistic entanglement generation between two distant single electron doped quantum dots, each placed in a high-Q microcavity, by detecting strong coherent light which has interacted dispersively with both subsystems and experienced Faraday rotation due to the spin selective trion transitions is discussed. In order to assess the applicability of the scheme for distant entanglement generation between atomic qubits proposed by T.D. Ladd et al. [New J. Phys. 8, 184 (2006)] to two distant quantum dots, one needs to understand the limitations imposed by hyperfine interactions of the quantum dot spin with the nuclear spins of the material and by non-identical quantum dots. Feasibility is displayed by calculating the fidelity for Bell state generation analytically within an approximate framework. The fidelity is evaluated for a wide range of parameters and different pulse lengths, yielding a trade-off between signal and decoherence, as well as a set of optimal parameters. Strategies to overcome the effect of non-identical quantum dots on the fidelity are examined and the timescales imposed by the nuclear spins are discussed, showing that efficient entanglement generation is possible with distant quantum dots. In this context, effects due to light hole transitions become important and have to be included. The scheme is discussed for one- as well as for two-sided cavities, where one must be careful with reflected light which carries spin information. The validity of the approximate method is checked by a more elaborate semiclassical simulation which includes trion formation.Comment: 17 pages, 13 figures, typos corrected, reference update

Recursive formulation of the multiconfigurational time-dependent Hartree method for fermions, bosons and mixtures thereof in terms of one-body density operators

The multiconfigurational time-dependent Hartree method (MCTDH) [Chem. Phys. Lett. {\bf 165}, 73 (1990); J. Chem. Phys. {\bf 97}, 3199 (1992)] is celebrating nowadays entering its third decade of tackling numerically-exactly a broad range of correlated multi-dimensional non-equilibrium quantum dynamical systems. Taking in recent years particles' statistics explicitly into account, within the MCTDH for fermions (MCTDHF) and for bosons (MCTDHB), has opened up further opportunities to treat larger systems of interacting identical particles, primarily in laser-atom and cold-atom physics. With the increase of experimental capabilities to simultaneously trap mixtures of two, three, and possibly even multiple kinds of interacting composite identical particles together, we set up the stage in the present work and specify the MCTDH method for such cases. Explicitly, the MCTDH method for systems with three kinds of identical particles interacting via all combinations of two- and three-body forces is presented, and the resulting equations-of-motion are briefly discussed. All four possible mixtures of fermions and bosons are presented in a unified manner. Particular attention is paid to represent the coefficients' part of the equations-of-motion in a compact recursive form in terms of one-body density operators only. The recursion utilizes the recently proposed Combinadic-based mapping for fermionic and bosonic operators in Fock space [Phys. Rev. A {\bf 81}, 022124 (2010)] and successfully applied and implemented within MCTDHB. Our work sheds new light on the representation of the coefficients' part in MCTDHF and MCTDHB without resorting to the matrix elements of the many-body Hamiltonian with respect to the time-dependent configurations. It suggests a recipe for efficient implementation of the schemes derived here for mixtures which is suitable for parallelization.Comment: 43 page

Cerebral small vessel disease genomics and its implications across the lifespan

White matter hyperintensities (WMH) are the most common brain-imaging feature of cerebral small vessel disease (SVD), hypertension being the main known risk factor. Here, we identify 27 genome-wide loci for WMH-volume in a cohort of 50,970 older individuals, accounting for modification/confounding by hypertension. Aggregated WMH risk variants were associated with altered white matter integrity (p = 2.5×10-7) in brain images from 1,738 young healthy adults, providing insight into the lifetime impact of SVD genetic risk. Mendelian randomization suggested causal association of increasing WMH-volume with stroke, Alzheimer-type dementia, and of increasing blood pressure (BP) with larger WMH-volume, notably also in persons without clinical hypertension. Transcriptome-wide colocalization analyses showed association of WMH-volume with expression of 39 genes, of which four encode known drug targets. Finally, we provide insight into BP-independent biological pathways underlying SVD and suggest potential for genetic stratification of high-risk individuals and for genetically-informed prioritization of drug targets for prevention trials.Peer reviewe

Cerebral small vessel disease genomics and its implications across the lifespan

White matter hyperintensities (WMH) are the most common brain-imaging feature of cerebral small vessel disease (SVD), hypertension being the main known risk factor. Here, we identify 27 genome-wide loci for WMH-volume in a cohort of 50,970 older individuals, accounting for modification/confounding by hypertension. Aggregated WMH risk variants were associated with altered white matter integrity (p = 2.5×10-7) in brain images from 1,738 young healthy adults, providing insight into the lifetime impact of SVD genetic risk. Mendelian randomization suggested causal association of increasing WMH-volume with stroke, Alzheimer-type dementia, and of increasing blood pressure (BP) with larger WMH-volume, notably also in persons without clinical hypertension. Transcriptome-wide colocalization analyses showed association of WMH-volume with expression of 39 genes, of which four encode known drug targets. Finally, we provide insight into BP-independent biological pathways underlying SVD and suggest potential for genetic stratification of high-risk individuals and for genetically-informed prioritization of drug targets for prevention trials.</p

Excitation spectra of many-body systems by linear response: General theory and applications to trapped condensates

International audienc