Probing BEC phase fluctuations with atomic quantum dots

We consider the dephasing of two internal states |0> and |1> of a trapped impurity atom, a so-called atomic quantum dot (AQD), where only state |1> couples to a Bose-Einstein condensate (BEC). A direct relation between the dephasing of the internal states of the AQD and the temporal phase fluctuations of the BEC is established. Based on this relation we suggest a scheme to probe BEC phase fluctuations nondestructively via dephasing measurements of the AQD. In particular, the scheme allows to trace the dependence of the phase fluctuations on the trapping geometry of the BEC.Comment: 11 pages, 3 figure

Out-of-equilibrium Correlated Systems : Bipartite Entanglement as a Probe of Thermalization

Thermalization play a central role in out-of-equilibrium physics of ultracold atoms or electronic transport phenomena. On the other hand, entanglement concepts have proven to be extremely useful to investigate quantum phases of matter. Here, it is argued that **bipartite** entanglement measures provide key information on out-of-equilibrium states and might therefore offer stringent thermalization criteria. This is illustrated by considering a global quench in an (extended) XXZ spin-1/2 chain across its (zero-temperature) quantum critical point. A non-local **bipartition** of the chain **preserving translation symmetry** is proposed. The time-evolution after the quench of the **reduced** density matrix of the half-system is computed and its associated (time-dependent) entanglement spectrum is analyzed. Generically, the corresponding entanglement entropy quickly reaches a "plateau" after a short transient regime. However, in the case of the integrable XXZ chain, the low-energy entanglement spectrum still reveals strong time-fluctuations. In addition, its infinite-time average shows strong deviations from the spectrum of a Boltzmann thermal density matrix. In contrast, when the integrability of the model is broken (by small next-nearest neighbor couplings), the entanglement spectra of the time-average and thermal density matrices become remarkably similar.Comment: extended version: 15 pages, 9 figure

Thermometry of ultracold atoms via non-equilibrium work distributions

Estimating the temperature of a cold quantum system is difficult. Usually, one measures a well-understood thermal state and uses that prior knowledge to infer its temperature. In contrast, we introduce a method of thermometry that assumes minimal knowledge of the state of a system and is potentially non-destructive. Our method uses a universal temperature-dependence of the quench dynamics of an initially thermal system coupled to a qubit probe that follows from the Tasaki-Crooks theorem for non-equilibrium work distributions. We provide examples for a cold-atom system, in which our thermometry protocol may retain accuracy and precision at subnanokelvin temperatures.Comment: Updated to published version. 6 pages plus 11 pages of supplemental material, and some numerical dat

An explicit unconditionally stable numerical method for solving damped nonlinear Schr\"{o}dinger equations with a focusing nonlinearity

This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schr\"{o}dinger equations (NLS). The method is explicit, unconditionally stable and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing nonlinear Schr\"{o}dinger equations in 2d with a linear, cubic or a quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter \dt is larger than a threshold value \dt_{\rm th}. We note that our method can also be applied to solve the 3d Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC).Comment: SIAM Journal on Numerical Analysis, to appea

Dissipation Induced Nonstationarity in a Quantum Gas

Non-stationary long-time dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, et al. arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in the thermodynamic limit and show that this system is always dynamically unstable -- even when mean-field theory predicts stability. Instabilities always occur in higher-order correlation functions leading to squeezing and entanglement induced by cavity dissipation. The dynamics may be understood as the formation of a dissipative time crystal. We use perturbation theory for finite system sizes to confirm the non-stationary behaviour.Comment: Main text: 5 pages, 3 figures and Supplemental material: 6 pages, 2 figures. Version as accepted by Phys. Rev. Let

High field fractional quantum Hall effect in optical lattices

We consider interacting bosonic atoms in an optical lattice subject to a large simulated magnetic field. We develop a model similar to a bilayer fractional quantum Hall system valid near simple rational numbers of magnetic flux quanta per lattice cell. Then we calculate its ground state, magnetic lengths, fractional fillings, and find unexpected sign changes in the Hall current. Finally we study methods for detecting these novel features via shot noise and Hall current measurements.Comment: 4 pages, 4 figures, accepted by PR

Multipartite entanglement detection in bosons

We propose a simple quantum network to detect multipartite entangled states of bosons, and show how to implement this network for neutral atoms stored in an optical lattice. We investigate the special properties of cluster states, multipartite entangled states and superpositions of distinct macroscopic quantum states that can be identified by the network.Comment: 4 pages, 2 figure

Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms

We present a detailed analysis of the dynamical response of ultra-cold bosonic atoms in a one-dimensional optical lattice subjected to a periodic modulation of the lattice depth. Following the experimental realization by Stoferle et al [Phys. Rev. Lett. 92, 130403 (2004)] we study the excitation spectrum of the system as revealed by the response of the total energy as a function of the modulation frequency Omega. By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator to the superfluid regime. Our results produce many of the features seen in the experiment, namely a broad response in the superfluid regime, and narrow discrete resonances in the Mott-insulator regime. We identify several signatures of the superfluid-Mott insulator transition that are manifested in the spectrum as it evolves from one limit to the other.Comment: 18 pages and 12 figures; Some improved results and additional references. To appear in a special issue of New J. Phy

The Optical Excitation of Zigzag Carbon Nanotubes with Photons Guided in Nanofibers

We consider the excitation of electrons in semiconducting carbon nanotubes by photons from the evanescent field created by a subwavelength-diameter optical fiber. The strongly changing evanescent field of such nanofibers requires dropping the dipole approximation. We show that this leads to novel effects, especially a high dependence of the photon absorption on the relative orientation and geometry of the nanotube-nanofiber setup in the optical and near infrared domain. In particular, we calculate photon absorption probabilities for a straight nanotube and nanofiber depending on their relative angle. Nanotubes orthogonal to the fiber are found to perform much better than parallel nanotubes when they are short. As the nanotube gets longer the absorption of parallel nanotubes is found to exceed the orthogonal nanotubes and approach 100% for extremely long nanotubes. In addition, we show that if the nanotube is wrapped around the fiber in an appropriate way the absorption is enhanced. We find that optical and near infrared photons could be converted to excitations with efficiencies that may exceed 90%. This may provide opportunities for future photodetectors and we discuss possible setups.Comment: 14 pages, 14 figure