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In this article, we investigate a growing trend in the worldwide Quantum Technology (QT) education landscape, that of the development of masters programs, intended to provide graduates with the knowledge and skills to take a job in the quantum industry, while serving a much shorter timeline than a doctoral degree. Through a global survey, we identified 86 masters programs, with substantial growth since 2021. Over time masters have become increasingly interdisciplinary, organised by multiple faculties or through joint degree programs, and offer more hands-on experiences such as internships in companies. Information from program organisers and websites suggests that the intended career destinations of their graduates are a diverse range of industries, and therefore masters programs may be a boon to the industrialisation of quantum technologies. Finally, we identify a range of national efforts to grow the quantum workforce of many countries, quantum program enhancements, which augment the content of existing study programs with quantum content. This may further contribute to the growth and viability of masters programs as a route to the quantum industry.

The field of Quantum Information Science & Technology (QIST) is booming. Due to this, many new educational courses and university programs are needed in order to prepare a workforce for the developing industry. Owing to its specialist nature, teaching approaches in this field can easily become disconnected from the substantial degree of science education research which aims to support the best approaches to teaching in Science, Technology, Engineering & Mathematics (STEM) fields. In order to connect these two communities with a pragmatic and repeatable methodology, we have synthesised this educational research into a decision-tree based theoretical model for the transformation of QIST curricula, intended to provide a didactical perspective for practitioners. The Quantum Curriculum Transformation Framework (QCTF) consists of four steps: 1. choose a topic, 2. choose one or more targeted skills, 3. choose a learning goal and 4. choose a teaching approach that achieves this goal. We show how this can be done using an example curriculum and more specifically quantum teleportation as a basic concept of quantum communication within this curriculum. By approaching curriculum creation and transformation in this way, educational goals and outcomes are more clearly defined which is in the interest of the individual and the industry alike. The framework is intended to structure the narrative of QIST teaching, and with future testing and refinement it will form a basis for further research in the didactics of QIST., Comment: 24+15 pages, 7+4 figures. S. Goorney and J. Bley contributed equally to this work and share first authorship

The GIREP community on teaching and learning quantum physics and the Education section of the Quantum flagship project of the European Union (QTEdu) have brought together different stakeholders in the field of teaching quantum physics on all levels, including outreach. The goal of QTEdu is to pave the way for the training of the future quantum workforce. To this end, it is necessary to understand the needs of the quantum technology (QT) field, make the general public aware of the existence and importance of QT, and introduce quantum physics already in high school, so that high school students can choose QT as their field of study and career. Finally, new university courses need to be established to support emerging specific profiles such as a quantum engineer. In this symposium, four QTEdu pilot projects were brought together to demonstrate how their complementary approaches have worked towards realising the above goals., Comment: 14 pages, 4 figures

The Bloch-sphere representation is a rather simple geometric model for all possible quantum states of a two-level system. In this article, we propose a simple geometric model for the time dynamics of a qubit based on the Bloch-sphere representation. The model can be applied both to time-independent and time-dependent Hamiltonians. As explicit application, we consider time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing-UP of the quantum emitter population) in the context of quantum tunneling. We show that the tunneling probability can be enhanced by orders of magnitude when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call educator-developer dialogue, an updated version of the software Quantum Composer is presented. Here it is used for educational purposes, to map the two lowest energy states of the 1D-Schr\"odinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics., Comment: 18 pages, 10 figures, submitted to European Journal of Physics

In this article, we provide an extensive overview of a wide range of quantum games and interactive tools that have been employed by the community in recent years. The paper presents selected tools, as described by their developers. The list includes Hello Quantum, Hello Qiskit, Particle in a Box, Psi and Delta, QPlayLearn, Virtual Lab by Quantum Flytrap, Quantum Odyssey, ScienceAtHome, and The Virtual Quantum Optics Laboratory. Additionally, we present events for quantum game development: hackathons, game jams, and semester projects. Furthermore, we discuss the Quantum Technologies Education for Everyone (QUTE4E) pilot project, which illustrates an effective integration of these interactive tools with quantum outreach and education activities. Finally, we aim at providing guidelines for incorporating quantum games and interactive tools in pedagogic materials to make quantum technologies more accessible for a wider population., Comment: 39 pages, 17 figures

State-of-the-art quantum algorithms routinely tune dynamically parametrized cost functionals for combinatorics, machine learning, equation-solving, or energy minimization. However, large search complexity often demands many (noisy) quantum measurements, leading to the increasing use of classical probability models to estimate which areas in the cost functional landscape are of highest interest. Introducing deep learning based modelling of the landscape, we demonstrate an order of magnitude increases in accuracy and speed over state-of-the-art Bayesian methods. Moreover, once trained the deep neural network enables the extraction of information at a much faster rate than conventional numerical simulation. This allows for on-the-fly experimental optimizations and detailed classification of complexity and navigability throughout the phase diagram of the landscape., Comment: 12 pages, 8 figures

Development of outreach skills is critical for researchers when communicating their work to non-expert audiences. However, due to the lack of formal training, researchers are typically unaware of the benefits of outreach training and often under-prioritize outreach. We present a training programme conducted with an international network of PhD students in quantum physics, which focused on developing outreach skills and an understanding of the associated professional benefits by creating an outreach portfolio consisting of a range of implementable outreach products. We describe our approach, assess the impact, and provide a list of guidelines for designing similar programmes across scientific disciplines in the future., Comment: 14 figures, 3 tables

We demonstrate the efficiency of a recent exact-gradient optimal control methodology by applying it to a challenging many-body problem, crossing the superfluid to Mott-insulator phase transition in the Bose-Hubbard model. The system size necessitates a matrix product state representation and this seamlessly integrates with the requirements of the algorithm. We observe fidelities in the range 0.99-0.9999 with associated minimal process duration estimates displaying an exponential fidelity-duration trade-off across several orders of magnitude. The corresponding optimal solutions are characterized in terms of a predominantly linear sweep across the critical point followed by bang-bang-like structure. This is quite different from the smooth and monotonic solutions identified by earlier gradient-free optimizations which are hampered in locating the higher complexity protocols in the regime of high-fidelities at low process durations. Overall, the comparison suggests significant methodological improvements also for many-body systems in the ideal open-loop setting. Acknowledging that idealized open-loop control may deteriorate in actual experiments, we discuss the merits of using such an approach in combination with closed-loop control -- in particular, high-fidelity physical insights extracted with the former can be used to formulate practical, low-dimensional search spaces for the latter., Comment: 19 pages, 9 figures. Content is partially a split revision of this V1 preprint arXiv:2005.09943v1

Making quantum mechanical equations and concepts come to life through interactive simulation and visualization are commonplace for augmenting learning and teaching. However, graphical visualizations nearly always exhibit a set of hard-coded functionalities while corresponding text-based codes offer a higher degree of flexibility at the expense of steep learning curves or time investments. We introduce Quantum Composer, which allows the user to build, expand, or explore quantum mechanical simulations by interacting with graphically connectable nodes, each corresponding to a physical concept, mathematical operation, visualization, etc. Abstracting away numerical and programming details while at the same time retaining accessibility, emphasis on understanding, and rapid feedback mechanisms, we illustrate through a series of examples its open-ended applicability in both introductory and advanced quantum mechanics courses, student projects, and for visual exploration within research environments., Comment: 29 pages, 12 figures

Efficient optimization of quantum systems is a necessity for reaching fault tolerant thresholds. A standard tool for optimizing simulated quantum dynamics is the gradient-based \textsc{grape} algorithm, which has been successfully applied in a wide range of different branches of quantum physics. In this work, we derive and implement exact $2^{\mathrm{nd}}$ order analytical derivatives of the coherent dynamics and find improvements compared to the standard of optimizing with the approximate $2^{\mathrm{nd}}$ order \textsc{bfgs}. We demonstrate performance improvements for both the best and average errors of constrained unitary gate synthesis on a circuit-\textsc{qed} system over a broad range of different gate durations., Comment: 13 pages, 5 figures

Accurate derivatives are important for efficiently locally traversing and converging in quantum optimization landscapes. By deriving analytically exact control derivatives (gradient and Hessian) for unitary control tasks, we show here that the computational feasibility of meeting this accuracy requirement depends on the choice of propagation scheme and problem representation. Even when exact propagation is sufficiently cheap it is, perhaps surprisingly, much more efficient to optimize the (appropriately) approximate propagators: approximations in the dynamics are traded off for significant complexity reductions in the exact derivative calculations. Importantly, past the initial analytical considerations, only standard numerical techniques are explicitly required with straightforward application to realistic systems. These results are numerically verified for two concrete problems of increasing Hilbert space dimensionality. The best schemes obtain unit fidelity to machine precision whereas the results for other schemes are separated consistently by orders of magnitude in computation time and in worst case 10 orders of magnitude in achievable fidelity. Since these gaps continually increase with system size and complexity, this methodology allows numerically efficient optimization of very high-dimensional dynamics, e.g. in many-body contexts, operating in the high-fidelity regime which will be published separately., Comment: 20 pages, 4 figures. V2 and onwards has had content moved to another preprint here: arXiv:2008.06076

Citizen science methodologies have over the past decade been applied with great success to help solve highly complex numerical challenges. Here, we take early steps in the quantum physics arena by introducing a citizen science game, Quantum Moves 2, and compare the performance of different optimization methods across three different quantum optimal control problems of varying difficulty. Inside the game, players can apply a gradient-based algorithm (running locally on their device) to optimize their solutions and we find that these results perform roughly on par with the best of the tested standard optimization methods performed on a computer cluster. In addition, cluster-optimized player seeds was the only method to exhibit roughly optimal performance across all three challenges. This highlights the potential for crowdsourcing the solution of future quantum research problems., Comment: 15 figures

We discuss the commonly encountered problem when optimizing NMR pulses using optimal control that the otherwise very precise NMR theory does not provide as excellent agreement with experiments. We hypothesize that this disagreement is due to phase transients in the pulse due to abrupt phase- and amplitude changes resulting in a large bandwidth. We apply the GROUP algorithm that gives high fidelity pulses with a low bandwidth compared to the typical GRAPE pulses. Our results obtain a better agreement between experiment and simulations supporting our hypothesis and solution to the problem., Comment: Accepted by J. Chem. Phys

We demonstrate a method to determine the position of single atoms in a three-dimensional optical lattice. Atoms are sparsely loaded from a far-off-resonant optical tweezer into a few vertical planes of a cubic optical lattice positioned near a high-resolution microscope objective. In a single realization of the experiment, we pin the atoms in deep lattices and then acquire multiple fluorescence images with single-site resolution. The objective is translated between images, bringing different lattice planes of the lattice into focus. The applicability of our method is assessed using simulated fluorescence images, where the atomic filling fraction in the lattice is varied. This opens up the possibility of extending the domain of quantum simulation using quantum gas microscopes from two to three dimensions., Comment: 8 pages, 5 figures

Dries Sels and Allan Gr{\o}nlund have demonstrated numerical algorithms that outperform the players of our Quantum Moves game and they call the conclusions of our article Exploring the Quantum Speed Limit with Computer Games, Nature, 532, 210 (2016)] 'untenable'. Sels and Gr{\o}nlund ignore that our article already emphasizes that the players do not solve the quantum optimization challenge to any desired accuracy. Our key finding is that player solutions can be employed either as seeds for numerical optimization algorithms or as guidance towards low-dimensional representations of the solutions., Comment: A recent review of old numerical code revealed an error of implementation. An updated note will soon describe this and the implications for our work. We will also put up a description of recent much more thorough comparison of different algorithms and player solutions across a range of challenges with varying complexity to highlight strengths and weaknesses of player and algorithmic seeding

We use quantum optimal control to identify fast collision-based two-qubit $\sqrt{\text{SWAP}}$ gates in ultracold atoms. We show that a significant speed up can be achieved by optimizing the full gate instead of separately optimizing the merge-wait-separate sequence of the trapping potentials. Our optimal strategy does not rely on the atoms populating the lowest eigenstates of the merged potential, and it crucially includes accumulation of quantum phases before the potentials are fully merged. Our analyses transcend the particular trapping geometry, but to compare with previous works, we present systematic results for an optical lattice and find greatly improved gate durations and fidelities., Comment: 15 pages, 13 figures, animations at https://www.quatomic.com/quatomic_publications/

While a large number of algorithms for optimizing quantum dynamics for different objectives have been developed, a common limitation is the reliance on good initial guesses, being either random or based on heuristics and intuitions. Here we implement a tabula rasa deep quantum exploration version of the Deepmind AlphaZero algorithm for systematically averting this limitation. AlphaZero employs a deep neural network in conjunction with deep lookahead in a guided tree search, which allows for predictive hidden variable approximation of the quantum parameter landscape. To emphasize transferability, we apply and benchmark the algorithm on three classes of control problems using only a single common set of algorithmic hyperparameters. AlphaZero achieves substantial improvements in both the quality and quantity of good solution clusters compared to earlier methods. It is able to spontaneously learn unexpected hidden structure and global symmetry in the solutions, going beyond even human heuristics., Comment: 11 pages, 6 figures

We propose that weak continuous probing may be exploited to determine and define quantum phases of complex many-body systems based on the measurement record alone. We test the resulting phase criterion in numerical simulations of measurements on the Bose-Hubbard model and the quantum Ising chain. This yields a phase transition point in reasonable agreement with the quantum phase transition in the ground state of the closed system in the thermodynamic limit, despite the system being highly excited through the measurement dynamics. At high measurement strengths, the system's response enters a Zeno regime suppressing transitions between eigenstates of the measurement operator., Comment: 15 pages, 9 figures

We present the first version of the QEngine, an open-source C++ library for simulating and controlling ultracold quantum systems using optimal control theory (OCT). The most notable systems presented here are Bose-Einstein condensates, many-body systems described by Bose-Hubbard type models, and two interacting particles. These systems can all be realized experimentally using ultracold atoms in various trapping geometries including optical lattices. In addition we provide a number of optimal control algorithms including the recently introduced GROUP method. The QEngine library has a strong focus on accessibility and performance. We provide several examples of how to prepare simulations of the physical systems and apply optimal control.

We introduce an efficient iterative method to prepare a target state in Hilbert spaces with high dimensionality using a combination of unitary evolution, measurements, and quantum Zeno dynamics. The latter confines the evolution within Zeno subspaces of decreasing size. This gives an exponential speed up relative to the case of states evolving in the full Hilbert space between projective measurements. We demonstrate our approach on the control problem of rapidly transferring a superfluid into the Mott insulator in the Bose-Hubbard model. We discuss the general applicability of the method by preparing arbitrary superpositions with random Hamiltonians.

We propose a Global-Local optimization algorithm for quantum control that combines standard local search methodologies with evolutionary algorithms. This allows us to find faster solutions to a set of problems relating to ultracold control of Bose-Einstein condensates.

We discuss quantum optimal control of Bose-Einstein condensates trapped in magnetic microtraps. The objective is to transfer a condensate from the ground state to the first-excited state. This type of control problem is typically solved using derivative-based methods in a high-dimensional control space such as gradient-ascent pulse engineering (GRAPE) and Krotov's method or derivative-free methods in a reduced control space such as Nelder-Mead with a chopped random basis (CRAB). We discuss how these methods can be combined in gradient optimization using parametrization (GROUP) including the finite bandwidth of the control electronics. We compare these methods and find that GROUP converges much faster than Nelder-Mead with CRAB and achieves better results than GRAPE and Krotov's method on the control problem presented here.

Quantum state preparation is vital to quantum computation and quantum information processing tasks. In adiabatic state preparation, the target state is theoretically obtained with nearly perfect fidelity if the control parameter is tuned slowly enough. As this, however, leads to slow dynamics, it is often desirable to be able to do processes faster. In this work, we employ two global optimization methods to estimate the quantum speed limit for few-fermion systems confined in a one-dimensional harmonic trap. Such systems can be produced experimentally in a well controlled manner. We determine the optimized control fields and achieve a reduction in the ramping time of more than a factor of four compared to linear ramping. We also investigate how robust the fidelity is to small variations of the control fields away from the optimized shapes., Comment: 8 pages, 5 figures, 1 table

We propose an efficient strategy to find optimal control functions for state-to-state quantum control problems. Our procedure first chooses an input state trajectory, that can realize the desired transformation by adiabatic variation of the system Hamiltonian. The shortcut-to-adiabaticity (STA) formalism then provides a control Hamiltonian that realizes the reference trajectory exactly but on a finite time scale. As the final state is achieved with certainty, we define a cost functional that incorporates the resource requirements and a perturbative expression for robustness. We optimize this functional by systematically varying the reference trajectory. We demonstrate the method by application to population transfer in a laser driven three-level {\Lambda}-system, where we find solutions that are fast and robust against perturbations while maintaining a low peak laser power.

We introduce a novel remote interface to control and optimize the experimental production of Bose-Einstein condensates (BECs) and find improved solutions using two distinct implementations. First, a team of theoreticians employed a Remote version of their dCRAB optimization algorithm (RedCRAB), and second a gamified interface allowed 600 citizen scientists from around the world to participate in real-time optimization. Quantitative studies of player search behavior demonstrated that they collectively engage in a combination of local and global search. This form of adaptive search prevents premature convergence by the explorative behavior of low-performing players while high-performing players locally refine their solutions. In addition, many successful citizen science games have relied on a problem representation that directly engaged the visual or experiential intuition of the players. Here we demonstrate that citizen scientists can also be successful in an entirely abstract problem visualization. This gives encouragement that a much wider range of challenges could potentially be open to gamification in the future., Comment: 8 pages, 3 figures and 12 pages, 7 figures supplementary information

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 $N \sim 5 \times 10^6$ atoms, we achieve a precision more than a factor of two below the atom shot noise level., Comment: 10 pages, 8 figures

We demonstrate how dispersive atom number measurements during evaporative cooling can be used for enhanced determination of the parameter dependence of the transition to a Bose-Einstein condensate (BEC). In this way shot-to-shot fluctuations in initial conditions are detected and the information extracted per experimental realization is increased. We furthermore calibrate in-situ images from dispersive probing of a BEC with corresponding absorption images in time-of-flight. This allows for the determination of the transition point in a single experimental realization by applying multiple dispersive measurements. Finally, we explore the continuous probing of several consecutive phase transition crossings using the periodic addition of a focused "dimple" potential., Comment: 9 pages, 7 figures; M. G. Bason and R. Heck contributed equally to this work

We investigate the potential for controlling a non-interacting Bose-Einstein condensate loaded into a one-dimensional optical superlattice. Our control strategy combines Bloch oscillations originating from accelerating the lattice and from time-dependent control of the superlattice parameters. We investigate two experimentally viable scenarios, very low and very high potential depths. We are able to exhibit a wide range of control over energy band populations using the superlattice control parameters. With this analysis we consider several examples of quantum state preparation in the superlattice structure that may be difficult to achieve in a regular lattice., Comment: 9 pages, 11 figures. Updated version as an artist's work is never finished, and due to publication. DOI & journal ref added

We prepare number stabilized ultracold clouds through the real-time analysis of non-destructive images and the application of feedback. In our experiments, the atom number ${N\sim10^6}$ is determined by high precision Faraday imaging with uncertainty $\Delta_N$ below the shot noise level, i.e., $\Delta_N <\sqrt{N}$. 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., Comment: Main text: 4 Figures, 4 pages. Supplemental Information: 4 figures, 5 pages

We develop a Gaussian state treatment that allows a transparent quantum description of the continuous, nondestructive imaging of and feedback on a Bose-Einstein condensate. We have previously demonstrated [Phys. Rev. Lett. \textbf{115}, 060401 (2015)] that the measurement back action of stroboscopic imaging leads to selective squeezing and entanglement of quantized density oscillations. Here, we investigate how the squeezing and entanglement are affected by the finite spatial resolution and geometry of the probe laser beam and of the detector and how they can be optimized.

Crowdscience games may hold unique potentials as learning opportunities compared to games made for fun or education. They are part of an actual science problem solving process: By playing, players help scientists, and thereby interact with real continuous research processes. This mixes the two worlds of play and science in new ways. During usability testing we discovered that users of the crowdscience game Quantum Dreams tended to answer questions in game terms, even when directed explicitly to give science explanations.We then examined these competing frames of understanding through a mixed correlational and grounded theory analysis. This essay presents the core ideas of crowdscience games as learning opportunities, and reports how a group of players used "game", "science" and "conceptual" frames to interpret their experience. Our results suggest that oscillating between the frames instead of sticking to just one led to the largest number of correct science interpretations, as players could participate legitimately and autonomously at multiple levels of understanding., Comment: 26 pages, 3 figures

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science exploits this ability by presenting scientific research problems to non-experts. Gamification is an effective tool for attracting citizen scientists to provide solutions to research problems. While citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, so far gamification has not been applied to problems in quantum physics. Does the fact that everyday experiences are based on classical physics hinder the use of non-expert citizen scientists in the realm of quantum mechanics? 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. Based on player strategies, we have thus developed a new, few-parameter heuristic optimization method which efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To better understand this, we have made a low-dimensional rendering of the optimization landscape. These studies show why traditional optimization methods fail near the quantum speed limit, and they bring promise that combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond., Comment: 19 pages, 7 figures, supplementary materials are included

The game Quantum Moves was designed to pit human players against computer algorithms, combining their solutions into hybrid optimization to control a scalable quantum computer. In this midstream report, we open our design process and describe the series of constitutive building stages going into a quantum physics citizen science game. We present our approach from designing a core gameplay around quantum simulations, to putting extra game elements in place in order to frame, structure, and motivate players' difficult path from curious visitors to competent science contributors. The player base is extremely diverse - for instance, two top players are a 40 year old female accountant and a male taxi driver. Among statistical predictors for retention and in-game high scores, the data from our first year suggest that people recruited based on real-world physics interest and via real-world events, but only with an intermediate science education, are more likely to become engaged and skilled contributors. Interestingly, female players tended to perform better than male players, even though men played more games per day. To understand this relationship, we explore the profiles of our top players in more depth. We discuss in-world and in-game performance factors departing in psychological theories of intrinsic and extrinsic motivation, and the implications for using real live humans to do hybrid optimization via initially simple, but ultimately very cognitively complex games., Comment: 26 pages, 15 figures

In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark., Comment: 5 pages, 3 figures, conference proceedings: Proceedings of World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education 2014 (pp. 218-222)

The dispersive interaction of atoms and a far-detuned light field allows nondestructive imaging of the density oscillations in Bose-Einstein condensates. Starting from a ground state condensate, we investigate how the measurement back action leads to squeezing and entanglement of the quantized density oscillations. In particular, we show that properly timed, stroboscopic imaging and feedback can be used to selectively address specific eigenmodes and avoid excitation of non-targeted modes of the system., Comment: 6 pages, 4 figures

We develop a scheme to prepare a desired state or subspace in high-dimensional Hilbert-spaces using repeated applications of a single static projection operator onto the desired target and fixed unitary dynamics. Benchmarks against other control schemes, performed on generic Hamiltonians and on Bose-Hubbard systems, establish the competitiveness of the method. As a concrete application of the control of mesoscopic atomic samples in optical lattices we demonstrate the near deterministic preparation of Schr\"{o}dinger cat states of all atoms residing on either the odd or the even sites., Comment: 5 pages, 4 figures, New revised version with new title, added references, corrected typos and unclarities

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., Comment: 7 pages, 4 figures

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., Comment: 5 pages, 4 figures

Steps towards implementing a collision based two-qubit gate in optical lattices have previously been realized by the parallel merging all pairs of atoms in a periodicity two superlattice. In contrast, we propose an architecture which allows for the merger of a selected qubit pair in a novel long-periodicity superlattice structure consisting of two optical lattices with close-lying periodicity. We numerically optimize the gate time and fidelity, including the effects on neighboring atoms, and in the presence of experimental sources of error. Furthermore, the superlattice architecture induces a differential hyperfine shift, allowing for single-qubit gates. The fastest possible single-qubit gate times, given a maximal tolerable rotation error on the remaining atoms at various values of the lattice wavelengths, are identified. We find that robust single- and two-qubit gates with gate times of a few 100~$\mu$s and with error probabilities $\sim{}10^{-3}$ are possible., Comment: 7 pages, 5 figures. Accepted in Physical Review A

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 system's dynamic behavior. This demonstrates that the method is a useful tool for the characterization of static and dynamically changing properties of ultracold atomic clouds., Comment: 8 pages, 5 figures

We present a fast scheme for arbitrary unitary control of interacting bosonic atoms in a double-well. Assuming fixed inter-well tunnelling rate and intra-well interaction strength, we control the many-atom state by a discrete sequence of shifts of the single-well energies. For strong interactions, resonant tunnelling transitions implement beam-splitter U(2) rotations among atom number eigenstates, which can be combined and, thus, permit full controllability. By numerically optimizing such sequences of couplings at avoided level crossings (CALC), we extend the realm of full controllability to a wide range of realistic interaction parameters, while we remain in the simple control space. We demonstrate the efficiency and the high achievable fidelity of our proposal with non-adiabatic population transfer, N00N-state creation, a C-NOT gate, and a transistor-like, conditional evolution of several atoms., Comment: 7 pages, 6 figures, extended version

In a double-well potential, a Bose-Einstein condensate exhibits Josephson oscillations or self-trapping, depending on its initial preparation and on the ratio of inter-particle interaction to inter-well tunneling. Here, we elucidate the role of the exchange symmetry for the dynamics with a mixture of two distinguishable species with identical physical properties, i.e. which are governed by an isospecific interaction and external potential. In the mean-field limit, the spatial population imbalance of the mixture can be described by the dynamics of a single species in an effective potential with modified properties or, equivalently, with an effective total particle number. The oscillation behavior can be tuned by populating the second species while maintaining the spatial population imbalance and all other parameters constant. In the corresponding many-body approach, the single-species description approximates the full counting statistics well also outside the realm of spin-coherent states. The method is extended to general Bose-Hubbard systems and to their classical mean-field limits, which suggests an effective single-species description of multicomponent Bose gases with weakly an-isospecific interactions., Comment: amended and expanded, accepted for Phys. Rev. A, 14 pages, 7 figures

We report on measurements of splitting Bose-Einstein condensates (BEC) by using a time-dependent optical lattice potential. First, we demonstrate the division of a BEC into a set of equally populated components by means of time dependent control of Landau-Zener tunneling in a vertical lattice potential. Next, we apply time dependent optical Bragg mirrors to a BEC oscillating in a harmonic trap. We demonstrate high-order Bragg reflection of the condensate due to multi-photon Raman transitions, where the depth of the optical lattice potential allows for a choice of the order of the transition. Finally, a combination of multiple Bragg reflections and Landau-Zener tunneling allows for the generation of macroscopic arrays of condensates with potential applications in atom optics and atom interferometry., Comment: 7 pages, 8 figures

We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits require the transport of atoms to neighboring sites. We numerically optimize the non-adiabatic transport of the atoms through the lattice and the intensity ramps of the optical tweezer in order to maximize the gate fidelities. We find overall gate times of a few 100 us, while keeping the error probability due to vibrational excitations and spontaneous scattering below 10^3. The requirements on the positioning error and intensity noise of the optical tweezer and the magnetic field stability are analyzed and we show that atoms in optical lattices could meet the requirements for fault-tolerant scalable quantum computing., Comment: 10 pages, 6 figures

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 reflection on 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 localized lattice states at a long, controllable distance of more than 100 lattice sites from the main component. This coherent control mechanism for ultra-cold atoms thus enables controlled quantum state preparation, opening exciting perspectives for quantum metrology and simulation., Comment: 5 pages, 5 figures

Ultracold atoms in optical lattices are a versatile tool to investigate fundamental properties of quantum many body systems. In particular, the high degree of control of experimental parameters has allowed the study of many interesting phenomena such as quantum phase transitions and quantum spin dynamics. Here we demonstrate how such control can be extended down to the most fundamental level of a single spin at a specific site of an optical lattice. Using a tightly focussed laser beam together with a microwave field, we were able to flip the spin of individual atoms in a Mott insulator with sub-diffraction-limited resolution, well below the lattice spacing. The Mott insulator provided us with a large two-dimensional array of perfectly arranged atoms, in which we created arbitrary spin patterns by sequentially addressing selected lattice sites after freezing out the atom distribution. We directly monitored the tunnelling quantum dynamics of single atoms in the lattice prepared along a single line and observed that our addressing scheme leaves the atoms in the motional ground state. Our results open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing., Comment: 8 pages, 5 figures

We present a simple and efficient scheme to reduce atom-number fluctuations in optical lattices. The interaction-energy difference for atoms in different vibrational states is used to remove excess atomic occupation. The remaining vacant sites are then filled with atoms by merging adjacent wells, for which we implement a protocol that circumvents the constraints of unitarity. The preparation of large regions with precisely one atom per lattice site is discussed for both bosons and fermions. The resulting low-entropy Mott-insulating states may serve as high-fidelity register states for quantum computing and as a starting point for investigations of many-body physics., Comment: 8 pages, 7 figures, version accepted by PRA

The reliable detection of single quantum particles has revolutionized the field of quantum optics and quantum information processing. For several years, researchers have aspired to extend such detection possibilities to larger scale strongly correlated quantum systems, in order to record in-situ images of a quantum fluid in which each underlying quantum particle is detected. Here we report on fluorescence imaging of strongly interacting bosonic Mott insulators in an optical lattice with single-atom and single-site resolution. From our images, we fully reconstruct the atom distribution on the lattice and identify individual excitations with high fidelity. A comparison of the radial density and variance distributions with theory provides a precise in-situ temperature and entropy measurement from single images. We observe Mott-insulating plateaus with near zero entropy and clearly resolve the high entropy rings separating them although their width is of the order of only a single lattice site. Furthermore, we show how a Mott insulator melts for increasing temperatures due to a proliferation of local defects. Our experiments open a new avenue for the manipulation and analysis of strongly interacting quantum gases on a lattice, as well as for quantum information processing with ultracold atoms. Using the high spatial resolution, it is now possible to directly address individual lattice sites. One could, e.g., introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes for atoms on a lattice.

We show that it is possible to generate continuous-wave fields and pulses of polarization squeezed light by sending classical, linearly polarized laser light twice through an atomic sample which causes an optical Faraday rotation of the field polarization. We characterize the performance of the process, and we show that an appreciable degree of squeezing can be obtained under realistic physical assumptions., Comment: 4 pages, 4 figures

Quantum teleportation is an important ingredient in distributed quantum networks, and can also serve as an elementary operation in quantum computers. Teleportation was first demonstrated as a transfer of a quantum state of light onto another light beam; later developments used optical relays and demonstrated entanglement swapping for continuous variables. The teleportation of a quantum state between two single material particles (trapped ions) has now also been achieved. Here we demonstrate teleportation between objects of a different nature - light and matter, which respectively represent 'flying' and 'stationary' media. A quantum state encoded in a light pulse is teleported onto a macroscopic object (an atomic ensemble containing 10^12 caesium atoms). Deterministic teleportation is achieved for sets of coherent states with mean photon number (n) up to a few hundred. The fidelities are 0.58+-0.02 for n=20 and 0.60+-0.02 for n=5 - higher than any classical state transfer can possibly achieve. Besides being of fundamental interest, teleportation using a macroscopic atomic ensemble is relevant for the practical implementation of a quantum repeater. An important factor for the implementation of quantum networks is the teleportation distance between transmitter and receiver; this is 0.5 metres in the present experiment. As our experiment uses propagating light to achieve the entanglement of light and atoms required for teleportation, the present approach should be scalable to longer distances., Comment: 23 pages, 8 figures, incl. supplementary information