We model quantum transport, described by continuous-time quantum walks (CTQW), on deterministic Sierpinski fractals, differentiating between Sierpinski gaskets and Sierpinski carpets, along with their dual structures. The transport efficiencies are defined in terms of the exact and the average return probabilities, as well as by the mean survival probability when absorbing traps are present. In the case of gaskets, localization can be identified already for small networks (generations). For carpets, our numerical results indicate a trend towards localization, but only for relatively large structures. The comparison of gaskets and carpets further implies that, distinct from the corresponding classical continuous-time random walk, the spectral dimension does not fully determine the evolution of the CTQW.

We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability as in percolation. We treat this problem in a strong noise limit. We focus on the case when the time interval between subsequent changes of the graph tends to zero. We derive explicit formulae for the general evolution in this limit. We find that the percolation in this limit causes an effective time rescaling. Independently of the graph and the initial state of the walk, the time is rescaled by the probability of keeping an edge. Both the individual trajectories for a single system and average properties with a superoperator formalism are discussed. We give an analytical proof for our theorem and we also present results from numerical simulations of the phenomena for different graphs. We also analyze the effect of finite step-size on the evolution.

We propose a definition for the Pólya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, the higher-dimensional integer lattices, and a number of other graphs, and we calculate their Pólya number. For the timing of the measurements, a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.

We show how the vibrational modes of a nanowire may be coherently manipulated with a Bose-Einstein condensate of ultracold atoms. We consider the magnetomechanical coupling between paramagnetic atoms and a suspended nanowire carrying a dc current. Atomic spin flips produce a backaction onto the wire vibrations, which can lead to mechanical mode amplification. In contrast to systems considered before, the condensate has a finite energy bandwidth in the range of the chemical potential and we explore the consequences of this on the parametric drive. Applying the resolvent method, we determine the threshold coupling and we also find a significant frequency shift of the vibration due to magnetomechanical dressing.

Given a source of two coherent state superpositions with small separation in a traveling wave optical setting, we show that by interference and balanced homodyne measurement it is possible to conditionally prepare a symmetrically placed superposition of coherent states around the origo of the phase space. The separation of the coherent states in the superposition will be amplified during the process.

Bose-Einstein condensates of ultracold atoms can be used to sense fluctuations of the magnetic field by means of transitions into untrapped hyperfine states. It has been shown recently that counting the outcoupled atoms can yield the power spectrum of the magnetic noise. We calculate the spectral resolution function, which characterizes the condensate as a noise measurement device in this scheme. We use the description of the radio-frequency outcoupling scheme of an atom laser, which takes into account the gravitational acceleration. Employing both an intuitive and the exact three-dimensional and fully quantum mechanical approach, we derive the position-dependent spectral resolution function for condensates of different size and shape.

We propose a scheme to prepare optical Schrödinger-cat states in a traveling wave setting. Two states are similarly prepared via the self-Kerr effect and after mixing them, one mode is measured by homodyne detection. In the other mode a superposition of coherent states is conditionally prepared. The advantage of the scheme is that assuming a small Kerr effect one can prepare with high probability one from a set of Schrödinger-cat states. The measured value of the quadrature provides the information, which state from the set is actually prepared.

We report on the spectral analysis and the local measurement of intensity correlations of microwave fields using ultra cold quantum gases. The fluctuations of the electromagnetic field induce spin flips in a magnetically trapped quantum gas and generate a multi-mode atomlaser. The output of the atomlaser is measured with high temporal resolution on the single atom level, from which the spectrum and intensity correlations of the generating microwave field are reconstructed. We give a theoretical description of the atomlaser output and its correlations in response to resonant microwave fields and verify the model with measurements on an atom chip. The measurement technique is applicable for the local analysis of classical and quantum noise of electromagnetic fields, for example on chips, in the vicinity of quantum electronic circuits. [5], are well characterized by the electron counting statistics and the corresponding field noise. This becomes especially important, as novel materials such as artificial honeycomb crystals [6] predict quantum effects in the electron transport even at room temperature, due to the formation of topological protected states [7]. Such quantum transport phenomena might be measured by means of a recently proposed quantum galvanometer [8], in which the low frequency current noise of a nano-device is coherently coupled to an atomic quantum gas and analyzed via state selective single atom detection.Here, we demonstrate the basic operation of the quantum galvanometer and extend it to quantum correlation measurements. Using a Bose-Einstein condensate, we coherently probe artificial, low frequency magnetic field fluctuations (noise) by shifting them electronically into the microwave (mw) regime, close to an atomic resonance. These fluctuations, generate a multi-mode atomlaser, with an output directly connected to the original field fluctuations. Using a sensitive detector, we analyze this output on the single atom level and show, how the power spectral density and the intensity correlations of the microwave field can be reconstructed. We give a theoretical description for the output of the multi-mode atomlaser, including decoherence effects.Experimental setup: The experiment is illustrated in Fig. 1a. Using an atom-chip based cold atom apparatus[9], we prepare Bose-Einstein condensates and thermal ensembles of 87 Rb atoms in the 5S 1/2 , F = 2, m F = 2 ground state. The atoms are magnetically trapped in a harmonic configuration with trap frequencies ω (x,y,z) = 2π × (85, 70, 16)Hz and offset field B z,off ≈ 0.93G. If this cloud is exposed to resonant microwave radiation, spin flips to the anti-trapped 5S 1/2 , F = 1, m F = 1 state occur. Here, we irradiate microwaves of various spectra to demonstrate the measurement of noise spectra and correlations. In particular, we apply amplitude modulation to a microwave carrier at ω c ≈ 2π × 6.834GHz with a variable function A (t) in the kHz regime. Here, A(t) mimics the low frequency field noise, which in the quantum galvanometer case is intrinsically (...