Entangling two transportable neutral atoms via local spin exchange

Fast quantum interference of a nanoparticle via optical potential control

We introduce and theoretically analyze a scheme to prepare and detect non-Gaussian quantum states of an optically levitated particle via the interaction with light pulses that generate cubic and inverted potentials. We show that this approach allows to operate on sufficiently short time- and length scales to beat decoherence in a regime accessible in state-of-the-art experiments. Specifically, we predict the observation of single-particle interference of a nanoparticle with a mass above 108 atomic mass units delocalized by several nanometers, on timescales of milliseconds. The proposed experiment uses only optical and electrostatic control, and can be performed at about 10-10 mbar and at room temperature. We discuss the prospect of this method for coherently splitting the wavepacket of massive dielectric objects without using either projective measurements or an internal level structure.

Macroscopic Quantum Superpositions via Dynamics in a Wide Double-Well Potential

We present an experimental proposal for the rapid preparation of the center of mass of a levitated particle in a macroscopic quantum state, that is a state delocalized over a length scale much larger than its zero-point motion and that has no classical analog. This state is prepared by letting the particle evolve in a static double-well potential after a sudden switchoff of the harmonic trap, following initial center-of-mass cooling to a sufficiently pure quantum state. We provide a thorough analysis of the noise and decoherence that is relevant to current experiments with levitated nano- and microparticles. In this context, we highlight the possibility of using two particles, one evolving in each potential well, to mitigate the impact of collective sources of noise and decoherence. The generality and scalability of our proposal make it suitable for implementation with a wide range of systems, including single atoms, ions, and Bose-Einstein condensates. Our results have the potential to enable the generation of macroscopic quantum states at unprecedented scales of length and mass, thereby paving the way for experimental exploration of the gravitational field generated by a source mass in a delocalized quantum state.

Achromatic, planar Fresnel-reflector for a single-beam magneto-optical trap

We present a novel achromatic, planar, periodic mirror structure for single-beam magneto-optical trapping and demonstrate its use in the first- and second-stage cooling and trapping for different isotopes of strontium. We refer to it as a Fresnel magneto-optical trap (MOT) as the structure is inspired by Fresnel lenses. By design, it avoids many of the problems that arise for multi-color cooling using planar structures based on diffraction gratings, which have been the dominant planar structures to be used for single-beam trapping thus far. In addition to a complex design process and cost-intensive fabrication, diffraction gratings suffer from their inherent chromaticity, which causes different axial displacements of trap volumes for different wavelengths and necessitates trade-offs in their diffraction properties and achievable trap depths. In contrast, the Fresnel-reflector structure presented here is a versatile, easy-to-manufacture device that combines achromatic beam steering with the advantages of a planar architecture. It enables miniaturizing trapping systems for alkaline-earth-like atoms with multiple cooling transitions as well as multi-species trapping in the ideal tetrahedral configuration and within the same volume above the structure. Our design presents a novel approach for the miniaturization of cold-atom systems based on single-beam MOTs and enables the widespread adoption of these systems.

Floquet-tailored Rydberg interactions

The Rydberg blockade is a key ingredient for entangling atoms in arrays. However, it requires atoms to be spaced well within the blockade radius, which limits the range of local quantum gates. Here we break this constraint using Floquet frequency modulation, with which we demonstrate Rydberg-blockade entanglement beyond the traditional blockade radius and show how the enlarged entanglement range improves qubit connectivity in a neutral atom array. Further, we find that the coherence of entangled states can be extended under Floquet frequency modulation. Finally, we realize Rydberg anti-blockade states for two sodium Rydberg atoms within the blockade radius. Such Rydberg anti-blockade states for atoms at close range enables the robust preparation of strongly-interacting, long-lived Rydberg states, yet their steady-state population cannot be achieved with only the conventional static drive. Our work transforms between the paradigmatic regimes of Rydberg blockade versus anti-blockade and paves the way for realizing more connected, coherent, and tunable neutral atom quantum processors with a single approach.

Fermionic Correlation Functions from Randomized Measurements in Programmable Atomic Quantum Devices

We provide an efficient randomized measurement protocol to estimate two- and four-point fermionic correlations in ultracold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical landscapes, with high-resolution imaging systems such as quantum gas microscopes. We illustrate our results in the context of the variational quantum eigensolver algorithm for solving quantum chemistry problems.

Formation of Ultracold Molecules by Merging Optical Tweezers

We demonstrate the formation of a single RbCs molecule during the merging of two optical tweezers, one containing a single Rb atom and the other a single Cs atom. Both atoms are initially predominantly in the motional ground states of their respective tweezers. We confirm molecule formation and establish the state of the molecule formed by measuring its binding energy. We find that the probability of molecule formation can be controlled by tuning the confinement of the traps during the merging process, in good agreement with coupled-channel calculations. We show that the conversion efficiency from atoms to molecules using this technique is comparable to magnetoassociation.

Scalable Multilayer Architecture of Assembled Single-Atom Qubit Arrays in a Three-Dimensional Talbot Tweezer Lattice

We report on the realization of a novel platform for the creation of large-scale 3D multilayer configurations of planar arrays of individual neutral-atom qubits: a microlens-generated Talbot tweezer lattice that extends 2D tweezer arrays to the third dimension at no additional costs. We demonstrate the trapping and imaging of rubidium atoms in integer and fractional Talbot planes and the assembly of defect-free atom arrays in different layers. The Talbot self-imaging effect for microlens arrays constitutes a structurally robust and wavelength-universal method for the realization of 3D atom arrays with beneficial scaling properties. With more than 750 qubit sites per 2D layer, these scaling properties imply that 10 000 qubit sites are already accessible in 3D in our current implementation. The trap topology and functionality are configurable in the micrometer regime. We use this to generate interleaved lattices with dynamic position control and parallelized sublattice addressing of spin states for immediate application in quantum science and technology.

Micro-fabricated components for cold atom sensors

Laser cooled atoms have proven transformative for precision metrology, playing a pivotal role in state-of-the-art clocks and interferometers and having the potential to provide a step-change in our modern technological capabilities. To successfully explore their full potential, laser cooling platforms must be translated from the laboratory environment and into portable, compact quantum sensors for deployment in practical applications. This transition requires the amalgamation of a wide range of components and expertise if an unambiguously chip-scale cold atom sensor is to be realized. We present recent developments in cold-atom sensor miniaturization, focusing on key components that enable laser cooling on the chip-scale. The design, fabrication, and impact of the components on sensor scalability and performance will be discussed with an outlook to the next generation of chip-scale cold atom devices.

Tunable Directional Emission and Collective Dissipation with Quantum Metasurfaces

Subwavelength atomic arrays, recently labeled as quantum metamaterials, have emerged as an exciting platform for obtaining novel quantum optical phenomena. The strong interference effects in these systems generate subradiant excitations that propagate through the atomic array with very long lifetimes. Here, we demonstrate that one can harness these excitations to obtain tunable directional emission patterns and collective dissipative couplings when placing judiciously additional atoms nearby the atomic array. For doing that, we first characterize the optimal square array geometry to obtain directional emission patterns. Then, we characterize the best atomic positions to couple efficiently to the subradiant metasurface excitations and provide several improvement strategies based on entangled atomic clusters or bilayers. Afterward, we also show how the directionality of the emission pattern can be controlled through the relative dipole orientation between the auxiliary atoms and the one of the array. Finally, we benchmark how these directional emission patterns translate into to collective, anisotropic dissipative couplings between the auxiliary atoms by studying the lifetime modification of atomic entangled states.

Manipulating and measuring single atoms in the Maltese cross geometry

Background: Optical microtraps at the focus of high numerical aperture (high-NA) imaging systems enable efficient collection, trapping, detection and manipulation of individual neutral atoms for quantum technology and studies of optical physics associated with super- and sub-radiant states.  The recently developed "Maltese cross" geometry (MCG) atom trap uses four in-vacuum lenses to achieve four-directional high-NA optical coupling to single trapped atoms and small atomic arrays. This article presents the first extensive characterisation of atomic behaviour in a MCG atom trap. Methods: We employ a MCG system optimised for high coupling efficiency and characterise the resulting properties of the trap and trapped atoms.  Using current best practices, we measure occupancy, loading rate, lifetime, temperature, fluorescence anti-bunching and trap frequencies. We also use the four-directional access to implement a new method to map the spatial distribution of collection efficiency from high-NA optics:  we use the two on-trap-axis lenses to produce a 1D optical lattice, the sites of which are stochastically filled and emptied by the trap loading process. The two off-trap-axis lenses are used for imaging and single-mode collection.  Correlations of single-mode and imaging fluorescence signals are then used to map the single-mode collection efficiency. Results: We observe trap characteristics comparable to what has been reported for single-atom traps with one- or two-lens optical systems. The collection efficiency distribution in the axial and transverse directions is directly observed to be in agreement with expected collection efficiency distribution from Gaussian beam optics. Conclusions: The multi-directional high-NA access provided by the Maltese cross geometry enables complex manipulations and measurements not possible in geometries  with fewer  directions of  access,  and can  be  achieved  while  preserving other trap characteristics such as lifetime, temperature, and trap size.

Quantum register of fermion pairs

Quantum control of motion is central for modern atomic clocks¹ and interferometers². It enables protocols to process and distribute quantum information^3,4, and allows the probing of entanglement in correlated states of matter⁵. However, the motional coherence of individual particles can be fragile to maintain, as external degrees of freedom couple strongly to the environment. Systems in nature with robust motional coherence instead often involve pairs of particles, from the electrons in helium, to atom pairs⁶, molecules⁷ and Cooper pairs. Here we demonstrate long-lived motional coherence and entanglement of pairs of fermionic atoms in an optical lattice array. The common and relative motion of each pair realize a robust qubit, protected by exchange symmetry. The energy difference between the two motional states is set by the atomic recoil energy, is dependent on only the mass and the lattice wavelength, and is insensitive to the noise of the confining potential. We observe quantum coherence beyond ten seconds. Modulation of the interactions between the atoms provides universal control of the motional qubit. The methods presented here will enable coherently programmable quantum simulators of many-fermion systems⁸, precision metrology based on atom pairs and molecules^9,10 and, by implementing further advances^11-13, digital quantum computation using fermion pairs¹⁴.

Super-resolved Imaging of a Single Cold Atom on a Nanosecond Timescale

In cold atomic systems, fast and high-resolution microscopy of individual atoms is crucial, since it can provide direct information on the dynamics and correlations of the system. Here, we demonstrate nanosecond-scale two-dimensional stroboscopic pictures of a single trapped ion beyond the optical diffraction limit, by combining the main idea of ground-state depletion microscopy with quantum-state transition control in cold atoms. We achieve a spatial resolution up to 175 nm using a NA=0.1 objective in the experiment, which represents a more than tenfold improvement compared with direct fluorescence imaging. To show the potential of this method, we apply it to observe the secular motion of the trapped ion; we demonstrate a temporal resolution up to 50 ns with a displacement detection sensitivity of 10 nm. Our method provides a powerful tool for probing particle positions, momenta, and correlations, as well as their dynamics in cold atomic systems.

Nano-Optical Tweezers: Methods and Applications for Trapping Single Molecules and Nanoparticles

Optical tweezers were developed in 1970 by Arthur Ashkin as a tool for the manipulation of micron-sized particles. Ashkin's original design was then adapted for a variety of purposes, such as trapping and manipulation of biological materials^[1] and the laser cooling of atoms.^[2,3] More recent development has led to nano-optical tweezers, for trapping particles on the scale of only a few nanometers, and holographic tweezers, which allow for dynamic control of multiple traps in real-time. These alternatives to conventional optical tweezers have made it possible to trap single molecules and to perform a variety of studies on them. Presented here is a review of recent developments in nano-optical tweezers and their current and future applications.

Sub-Doppler Cooling and Compressed Trapping of YO Molecules at μK Temperatures

Complex molecular structure demands customized solutions to laser cooling by extending its general set of principles and practices. Compared with other laser-cooled molecules, yttrium monoxide (YO) exhibits a large electron-nucleus interaction, resulting in a dominant hyperfine interaction over the electron spin-rotation coupling. The YO ground state is thus comprised of two manifolds of closely spaced states, with one of them possessing a negligible Landé g factor. This unique energy level structure favors dual-frequency dc magneto-optical trapping (MOT) and gray molasses cooling (GMC). We report exceptionally robust cooling of YO at 4 μK over a wide range of laser intensity, detunings (one- and two-photon), and magnetic field. The magnetic insensitivity enables the spatial compression of the molecular cloud by alternating GMC and MOT under the continuous operation of the quadrupole magnetic field. A combination of these techniques produces a laser-cooled molecular sample with the highest phase space density in free space.

Many-Body Entanglement in Short-Range Interacting Fermi Gases for Metrology

We explore many-body entanglement in spinful Fermi gases with short-range interactions, for metrology purposes. We characterize the emerging quantum phases via density-matrix renormalization group simulations and quantify their entanglement content for metrological usability via quantum Fisher information (QFI). Our study establishes a method, promoting QFI to be an order parameter. Short-range interactions reveal to build up metrologically promising entanglement in the XY-ferromagnetic and cluster ordering, the cluster physics being unexplored so far.

Defect-Free Assembly of 2D Clusters of More Than 100 Single-Atom Quantum Systems

We demonstrate the defect-free assembly of versatile target patterns of up 111 neutral atoms, building on a 361-site subset of a micro-optical architecture that readily provides thousands of sites for single-atom quantum systems. By performing multiple assembly cycles in rapid succession, we drastically increase achievable structure sizes and success probabilities. We implement repeated target pattern reconstruction after atom loss and deterministic transport of partial atom clusters necessary for distributing entanglement in large-scale systems. This technique will propel assembled-atom architectures beyond the threshold of quantum advantage and into a regime with abundant applications in quantum sensing and metrology, Rydberg-state mediated quantum simulation, and error-corrected quantum computation.

Thermally robust spin correlations between two 85Rb atoms in an optical microtrap

The complex collisional properties of atoms fundamentally limit investigations into a range of processes in many-atom ensembles. In contrast, the bottom-up assembly of few- and many-body systems from individual atoms offers a controlled approach to isolating and studying such collisional processes. Here, we use optical tweezers to individually assemble pairs of trapped ⁸⁵Rb atoms, and study the spin dynamics of the two-body system in a thermal state. The spin-2 atoms show strong pair correlation between magnetic sublevels on timescales exceeding one second, with measured relative number fluctuations 11.9 ± 0.3 dB below quantum shot noise, limited only by detection efficiency. Spin populations display relaxation dynamics consistent with simulations and theoretical predictions for ⁸⁵Rb spin interactions, and contrary to the coherent spin waves witnessed in finite-temperature many-body experiments and zero-temperature two-body experiments. Our experimental approach offers a versatile platform for studying two-body quantum dynamics and may provide a route to thermally robust entanglement generation.

Spin-changing atomic collisions are important for thermally robust entanglement generation with applications in quantum information. Here the authors demonstrate record high spin state correlations and long spin relaxation times in the collision of two Rb atoms at relatively warm temperatures.

Narrow-Line Cooling and Imaging of Ytterbium Atoms in an Optical Tweezer Array

Engineering controllable, strongly interacting many-body quantum systems is at the frontier of quantum simulation and quantum information processing. Arrays of laser-cooled neutral atoms in optical tweezers have emerged as a promising platform because of their flexibility and the potential for strong interactions via Rydberg states. Existing neutral atom array experiments utilize alkali atoms, but alkaline-earth atoms offer many advantages in terms of coherence and control, and also open the door to new applications in precision measurement and time keeping. In this Letter, we present a technique to trap individual alkaline-earth-like ytterbium (Yb) atoms in optical tweezer arrays. The narrow ^{1}S_{0}-^{3}P_{1} intercombination line is used for both cooling and imaging in a magic-wavelength optical tweezer at 532 nm. The low Doppler temperature allows for imaging near the saturation intensity, resulting in a very high atom detection fidelity. We demonstrate the imaging fidelity concretely by observing rare (<1 in 10^{4} images) spontaneous quantum jumps into and out of a metastable state. We also demonstrate stochastic loading of atoms into a two-dimensional, 144-site tweezer array. This platform will enable advances in quantum information processing, quantum simulation, and precision measurement. The demonstrated narrow-line Doppler imaging may also be applied in tweezer arrays or quantum gas microscopes using other atoms with similar transitions, such as erbium and dysprosium.

Completely scrambled memory for quantum superposition

Although constructing a quantum computation device with multiple qubits is arguably a difficult task, several seconds of coherence time with tens of thousands of quantum particles has been demonstrated with a trapped atomic ensemble. As a practical application, a security-enhanced quantum state memory using atoms has been demonstrated. It was shown that the quantum superposition preserved in an atomic ensemble was scrambled and faithfully descrambled; however, the scrambled phase ambiguity remained at 50%. To overcome this problem, we propose and demonstrate a scheme that achieves 100% phase ambiguity without introducing an extra Ramsey interferometer. Moreover, this scheme can be used as a direct application to keep the choice between two values secret without falsification.

Quantum Spin Dynamics of Individual Neutral Impurities Coupled to a Bose-Einstein Condensate

We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single cesium atoms are transported into a cloud of rubidium atoms and thermalize with the bath, and the ensuing spin exchange between localized impurities with quasispin F_{i}=3 and bath atoms with F_{b}=1 is resolved. Comparing our data to numerical simulations of spin dynamics, we find that, for gas densities in the Bose-Einstein condensate regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin population of impurities. Finally, we trace the coherence of impurities prepared in a coherent superposition of internal states when coupled to a gas of different densities. For our choice of states, we show that, despite high bath densities and, thus, fast thermalization rates, the impurity coherence is not affected by the bath, realizing a regime of sympathetic cooling while maintaining internal state coherence. Our work paves the way toward the nondestructive probing of quantum many-body systems via localized impurities.

Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

Measurement-Based Entanglement of Noninteracting Bosonic Atoms

We demonstrate the ability to extract a spin-entangled state of two neutral atoms via postselection based on a measurement of their spatial configuration. Typically, entangled states of neutral atoms are engineered via atom-atom interactions. In contrast, in our Letter, we use Hong-Ou-Mandel interference to postselect a spin-singlet state after overlapping two atoms in distinct spin states on an effective beam splitter. We verify the presence of entanglement and determine a bound on the postselected fidelity of a spin-singlet state of (0.62±0.03). The experiment has direct analogy to creating polarization entanglement with single photons and hence demonstrates the potential to use protocols developed for photons to create complex quantum states with noninteracting atoms.

Correlated Dynamics in a Synthetic Lattice of Momentum States

We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low-energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the added exchange energy between atoms in distinguishable momentum states leads to an effectively attractive, finite-ranged interaction between atoms in momentum space. In this Letter, we observe the onset of self-trapping driven by such interactions in a momentum-space double well, paving the way for more complex many-body studies in tailored MSLs. We consider the types of phenomena that may result from these interactions, including the formation of chiral solitons in zigzag flux lattices.

Revealing Quantum Statistics with a Pair of Distant Atoms

Quantum statistics have a profound impact on the properties of systems composed of identical particles. At the most elementary level, Bose and Fermi quantum statistics differ in the exchange phase, either 0 or π, which the wave function acquires when two identical particles are exchanged. In this Letter, we demonstrate that the exchange phase can be directly probed with a pair of massive particles by physically exchanging their positions. We present two protocols where the particles always remain spatially well separated, thus ensuring that the exchange contribution to their interaction energy is negligible and that the detected signal can only be attributed to the exchange symmetry of the wave function. We discuss possible implementations with a pair of trapped atoms or ions.

Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade

We report on the first experimental realization of the controlled-not (cnot) quantum gate and entanglement for two individual atoms of different isotopes and demonstrate a negligible cross talk between two atom qubits. The experiment is based on a strong Rydberg blockade for ^{87}Rb and ^{85}Rb atoms confined in two single-atom optical traps separated by 3.8  μm. The raw fidelities of the cnot gate and entanglement are 0.73±0.01 and 0.59±0.03, respectively, without any corrections for atom loss or trace loss. Our work has applications for simulations of many-body systems with multispecies interactions, for quantum computing, and for quantum metrology.

Cavity Carving of Atomic Bell States

We demonstrate entanglement generation of two neutral atoms trapped inside an optical cavity. Entanglement is created from initially separable two-atom states through carving with weak photon pulses reflected from the cavity. A polarization rotation of the photons heralds the entanglement. We show the successful implementation of two different protocols and the generation of all four Bell states with a maximum fidelity of (90±2)%. The protocol works for any distance between cavity-coupled atoms, and no individual addressing is required. Our result constitutes an important step towards applications in quantum networks, e.g., for entanglement swapping in a quantum repeater.

Universality of Schmidt decomposition and particle identity

Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, its formulation for identical particles remains controversial, jeopardizing its application to analyze general many-body quantum systems. Here we prove, using a newly developed approach, a universal Schmidt decomposition which allows faithful quantification of the physical entanglement due to the identity of particles. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in separated places. For the case of two qutrits in the same place, we show that their entanglement behavior, whose physical interpretation is given, differs from that obtained before by different methods. Our results are generalizable to multiparticle systems and open the way for further developments in quantum information processing exploiting particle identity as a resource.

Atom-by-atom assembly of defect-free one-dimensional cold atom arrays

The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a platform for the deterministic preparation of regular one-dimensional arrays of individually controlled cold atoms. In our approach, a measurement and feedback procedure eliminates the entropy associated with probabilistic trap occupation and results in defect-free arrays of more than 50 atoms in less than 400 milliseconds. The technique is based on fast, real-time control of 100 optical tweezers, which we use to arrange atoms in desired geometric patterns and to maintain these configurations by replacing lost atoms with surplus atoms from a reservoir. This bottom-up approach may enable controlled engineering of scalable many-body systems for quantum information processing, quantum simulations, and precision measurements.

In situ single-atom array synthesis using dynamic holographic optical tweezers

Establishing a reliable method to form scalable neutral-atom platforms is an essential cornerstone for quantum computation, quantum simulation and quantum many-body physics. Here we demonstrate a real-time transport of single atoms using holographic microtraps controlled by a liquid-crystal spatial light modulator. For this, an analytical design approach to flicker-free microtrap movement is devised and cold rubidium atoms are simultaneously rearranged with 2N motional degrees of freedom, representing unprecedented space controllability. We also accomplish an in situ feedback control for single-atom rearrangements with the high success rate of 99% for up to 10 μm translation. We hope this proof-of-principle demonstration of high-fidelity atom-array preparations will be useful for deterministic loading of N single atoms, especially on arbitrary lattice locations, and also for real-time qubit shuttling in high-dimensional quantum computing architectures.

It would be desirable to have a reliable and scalable method to manipulate neutral-atoms for the creation of controllable quantum systems. Here the authors demonstrate real-time transport of single rubidium atoms in holographic microtraps controlled by liquid-crystal spatial light modulators.

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.

Highly uniform holographic microtrap arrays for single atom trapping using a feedback optimization of in-trap fluorescence measurements

We report on the novel optimization method to realize highly uniform microtrap arrays for single atom trapping with a spatial light modulator (SLM). This method consists of two iterative feedback loops with the measurements of both diffracted light intensities and in-trap fluorescence intensities from each microtrap. By applying this method to the single ⁸⁷Rb atom trapping, we can reduce the variance of trap depths from 20.8% to 1.7% for 4 × 4 square arrays and less than 4% for various arrays with up to 62 sites. The detection error of individual single atoms is also reduced from 1.7% to 0.0054% on average.

Quantum entanglement of identical particles by standard information-theoretic notions

Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based methods have been developed that attempt to overcome the issue. Here we introduce a state-based method which, as second quantization, does not label identical particles and presents conceptual and technical advances compared to the previous ones. It establishes the quantitative role played by arbitrary wave function overlaps, local measurements and particle nature (bosons or fermions) in assessing entanglement by notions commonly used in quantum information theory for distinguishable particles, like partial trace. Our approach furthermore shows that bringing identical particles into the same spatial location functions as an entangling gate, providing fundamental theoretical support to recent experimental observations with ultracold atoms. These results pave the way to set and interpret experiments for utilizing quantum correlations in realistic scenarios where overlap of particles can count, as in Bose-Einstein condensates, quantum dots and biological molecular aggregates.