Miroslav Gajdacz

Exploring the quantum speed limit with computer games

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. ‘Gamification’—the application of game elements in a non-game context—is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.

Non-destructive Faraday imaging of dynamically controlled ultracold atoms

We describe an easily implementable method for non-destructive measurements of ultracold atomic clouds based on dark field imaging of spatially resolved Faraday rotation. The signal-to-noise ratio is analyzed theoretically and, in the absence of experimental imperfections, the sensitivity limit is found to be identical to other conventional dispersive imaging techniques. The dependence on laser detuning, atomic density, and temperature is characterized in a detailed comparison with theory. Due to low destructiveness, spatially resolved images of the same cloud can be acquired up to 2000 times. The technique is applied to avoid the effect of shot-to-shot fluctuations in atom number calibration, to demonstrate single-run vector magnetic field imaging and single-run spatial imaging of the systems dynamic behavior. This demonstrates that the method is a useful tool for the characterization of static and dynamically changing properties of ultracold atomic clouds.

Preparation of Ultracold Atom Clouds at the Shot Noise Level.

We prepare number stabilized ultracold atom clouds through the real-time analysis of nondestructive images and the application of feedback. In our experiments, the atom number N∼10^{6} is determined by high precision Faraday imaging with uncertainty ΔN below the shot noise level, i.e., ΔN<sqrt[N]. Based on this measurement, feedback is applied to reduce the atom number to a user-defined target, whereupon a second imaging series probes the number stabilized cloud. By this method, we show that the atom number in ultracold clouds can be prepared below the shot noise level.

Time limited optimal dynamics beyond the Quantum Speed Limit

The quantum speed limit sets the minimum time required to transfer a quantum system completely into a given target state. At shorter times the higher operation speed has to be paid with a loss of fidelity. Here we quantify the trade-off between the fidelity and the duration in a system driven by a time-varying control. The problem is addressed in the framework of Hilbert space geometry offering an intuitive interpretation of optimal control algorithms. This approach is applied to non-uniform time variations which leads to a necessary criterion for control optimality applicable as a measure of algorithm convergence. The time fidelity trade-off expressed in terms of the direct Hilbert velocity provides a robust prediction of the quantum speed limit and allows to adapt the control optimization such that it yields a predefined fidelity. The results are verified numerically in a multilevel system with a constrained Hamiltonian, and a classification scheme for the control sequences is proposed based on their optimizability.

Transparent nonlocal species-selective transport in an optical superlattice containing two interacting atom species

In an optical superlattice of triple wells, containing two mutually interacting atom species in adjacent wells, we show that one species can be transported through the positions of the other species, yet avoiding significant overlap and direct interaction. The transfer protocol is optimized to be robust against missing atoms of either species in any lattice site, as well as against lattice fluctuations. The degree and the duration of the inter-species overlap during passage can be tuned, making possible controlled large-scale interaction-induced change of internal states.

The pump?probe coupling of matter wave packets to remote lattice states

The coherent manipulation of wave packets is an important tool in many areas of physics. We demonstrate the experimental realization of quasi-free wave packets of ultra-cold atoms bound by an external harmonic trap. The wave packets are produced by modulating the intensity of an optical lattice containing a Bose–Einstein condensate. The evolution of these wave packets is monitored in situ and their six-photon reflection at a band gap is observed. In direct analogy with pump–probe spectroscopy, a probe pulse allows for the resonant de-excitation of the wave packet into states localized around selected lattice sites at a long, controllable distance of more than 100 lattice sites from the main component. This precise control mechanism for ultra-cold atoms thus enables controlled quantum state preparation and splitting for quantum dynamics, metrology and simulation.

Spin dynamics in a two-dimensional quantum gas

We have investigated spin dynamics in a 2D quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimposed angular density modulations. The density distributions depend on the applied magnetic field and are well explained by a simple Bogoliubov model. We show that the two clouds are anti-correlated in momentum space. The observed momentum correlations pave the way towards the creation of an atom source with non-local Einstein-Podolsky-Rosen entanglement.

Production and manipulation of wave packets from ultracold atoms in an optical lattice

Within the combined potential of an optical lattice and a harmonic magnetic trap, it is possible to form matter wave packets by intensity modulation of the lattice. An analysis of the production and motion of these wave packets provides a detailed understanding of the dynamical evolution of the system. The modulation technique also allows for a controllable transfer (de-excitation) of atoms from such wave packets to a state bound by the lattice. Thus, it acts as a beam splitter for matter waves that can selectively address different bands, enabling the preparation of atoms in selected localized states. The combination of wave packet creation and de-excitation closely resembles the well-known method of pump-probe spectroscopy. Here, we use the de-excitation for precision spectroscopy of the anharmonicity of the magnetic trap. Finally, we demonstrate that lattice modulation can be used to excite matter wave packets to even higher momenta, producing fast wave packets with potential applications in precision measurements.

Sub-atom shot noise Faraday imaging of ultracold atom clouds

We demonstrate that a dispersive imaging technique based on the Faraday effect can measure the atom number in a large, ultracold atom cloud with a precision below the atom shot noise level. The minimally destructive character of the technique allows us to take multiple images of the same cloud, which enables sub-atom shot noise measurement precision of the atom number and allows for an in situ determination of the measurement precision. We have developed a noise model that quantitatively describes the noise contributions due to photon shot noise in the detected light and the noise associated with single atom loss. This model contains no free parameters and is calculated through an analysis of the fluctuations in the acquired images. For clouds containing

An atomtronics transistor for quantum gates

N \sim 5 \times 10^6