Study of Objectives

Focal length, chromatic and spherical aberration, and astigmatism testing for astronomical telescop

Neural-Network Approach to Dissipative Quantum Many-Body Dynamics

In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master equation. However, solving this master equation for quantum many-body systems, becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine learning techniques. We represent the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte-Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system

Synchronized Switching in a Josephson Junction Crystal

We consider a superconducting coplanar waveguide resonator where the central conductor is interrupted by a series of uniformly spaced Josephson junctions. The device forms an extended medium that is optically nonlinear on the single photon level with normal modes that inherit the full nonlinearity of the junctions but are nonetheless accessible via the resonator ports. For specific plasma frequencies of the junctions a set of normal modes clusters in a narrow band and eventually become entirely degenerate. Upon increasing the intensity of a red detuned drive on these modes, we observe a sharp and synchronized switching from low occupation quantum states to high occupation classical fields, accompanied by a pronounced jump from low to high output intensity.Comment: 13 pages, 5 figure

Entangling the motion of two optically trapped objects via time-modulated driving fields

We study entanglement of the motional degrees of freedom of two tethered and optically trapped microdisks inside a single cavity. By properly choosing the position of the trapped objects in the optical cavity and driving proper modes of the cavity it is possible to equip the system with linear and quadratic optomechanical couplings. We show that a parametric coupling between the fundamental vibrational modes of two tethered mircodiscs can be generated via a time modulated input laser. For a proper choice of the modulation frequency, this mechanism can drive the motion of the microdisks into an inseparable state in the long time limit via a two-mode squeezing process. We numerically confirm the performance of our scheme for current technology and briefly discuss an experimental setup which can be employed for detecting this entanglement by employing the quadratic coupling. We also comment on the perspectives for generating such entanglement between the oscillations of optically levitated nanospheres.Comment: 9 pages, 3 figure

Floquet engineering in superconducting circuits: from arbitrary spin-spin interactions to the Kitaev honeycomb model

We derive a theory for the generation of arbitrary spin-spin interactions in superconducting circuits via periodic time modulation of the individual qubits or the qubit-qubit interactions. The modulation frequencies in our approach are in the microwave or radio frequency regime so that the required fields can be generated with standard generators. Among others, our approach is suitable for generating spin lattices that exhibit quantum spin liquid behavior such as Kitaev's honeycomb model.Comment: 21 pages, 9 figure

Many Body Physics with Coupled Transmission Line Resonators

We present the Josephson junction intersected superconducting transmission line resonator. In contrast to the Josephson parametric amplifier, Josephson bifurcation amplifier and Josephson parametric converter we consider the regime of few microwave photons. We review the derivation of eigenmode frequencies and zero point fluctuations of the nonlinear transmission line resonator and the derivation of the eigenmode Kerr nonlinearities. Remarkably these nonlinearities can reach values comparable to Transmon qubits rendering the device ideal for accessing the strongly correlated regime. This is particularly interesting for investigation of quantum many-body dynamics of interacting particles under the influence of drive and dissipation. We provide current profiles for the device modes and investigate the coupling between resonators in a network of nonlinear transmission line resonators.Comment: submitted to the proceedings of the CEWQO 2012 conferenc

Low-temperature behavior of two-dimensional Gaussian Ising spin glasses

We perform Monte Carlo simulations of large two-dimensional Gaussian Ising spin glasses down to very low temperatures $\beta=1/T=50$. Equilibration is ensured by using a cluster algorithm including Monte Carlo moves consisting of flipping fundamental excitations. We study the thermodynamic behavior using the Binder cumulant, the spin-glass susceptibility, the distribution of overlaps, the overlap with the ground state and the specific heat. We confirm that $T_c=0$. All results are compatible with an algebraic divergence of the correlation length with an exponent $\nu$. We find $-1/\nu=-0.295(30)$, which is compatible with the value for the domain-wall and droplet exponent $\theta\approx-0.29$ found previously in ground-state studies. Hence the thermodynamic behavior of this model seems to be governed by one single exponent.Comment: 7 pages, 11 figure

The Circuit Quantum Electrodynamical Josephson Interferometer

Arrays of circuit cavities offer fascinating perspectives for exploring quantum many-body systems in a driven dissipative regime where excitation losses are continuously compensated by coherent input drives. Here we investigate a system consisting of three transmission line resonators, where the two outer ones are driven by coherent input sources and the central resonator interacts with a superconducting qubit. Whereas a low excitation number regime of such a device has been considered previously with a numerical integration, we here specifically address the high excitation density regime. We present analytical approximations to these regimes in the form of two methods. The first method is a Bogoliubov or linear expansion in quantum fluctuations which can be understood as an approximation for weak nonlinearities. As the second method we introduce a combination of mean-field decoupling for the photon tunneling with an exact approach to a driven Kerr nonlinearity which can be understood as an approximation for low tunneling rates. In contrast to the low excitation regime we find that for high excitation numbers the anti-bunching of output photons from the central cavity does not monotonously disappear as the tunnel coupling between the resonators is increased.Comment: revised, comparison of numerics and mean-field adde

Master equation approach for interacting slow- and stationary-light polaritons

A master equation approach for the description of dark-state polaritons in coherently driven atomic media is presented. This technique provides a description of light-matter interactions under conditions of electromagnetically induced transparency (EIT) that is well suited for the treatment of polariton losses. The master equation approach allows us to describe general polariton-polariton interactions that may be conservative, dissipative or a mixture of both. In particular, it enables us to study dissipation-induced correlations as a means for the creation of strongly correlated polariton systems. Our technique reveals a loss mechanism for stationary-light polaritons that has not been discussed so far. We find that polariton losses in level configurations with non-degenerate ground states can be a multiple of those in level schemes with degenerate ground states