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Significant efforts are being directed towards developing a quantum annealer capable of solving combinatorial optimization problems. The challenges are Hamiltonian programming and large-scale implementations. Here we report quantum annealing demonstration of Ising Hamiltonians programmed with up to $N=22$ spins mapped on various Cayley tree graphs. Experiments are performed with a Rydberg-atom quantum simulator, in which rubidium single atoms are arranged in three dimensional space in such a way that their Rydberg atoms and blockaded strong couplings respectively represent the nodes and edges of each graph. Three different Cayley-tree graphs of $Z=3$ neighbors and of up to $S=4$ shells are constructed, and their ground-state phases and N\'{e}el's order formations are probed. In good agreement with model calculations, the anti-ferromagnetic phase in regular Cayley trees and frustrated competing ground-states in a dual-center Cayley tree are directly observed. This demonstrates the possibilities of high-dimensional qubit connection programming in quantum simulators., Comment: 7 pages,5 figures

Rydberg-atom quantum simulators are of keen interest because of their possibilities towards high-dimensional qubit architectures. Here we report three-dimensional conformation spectra of quantum-Ising Hamiltonian systems with programmed qubit connections. With a Rydberg-atom quantum simulator, various connected graphs, in which vertices and edges represent atoms and blockaded couplings, respectively, are constructed in two or three-dimensional space and their eigenenergies are probed during their topological transformations. Star, complete, cyclic, and diamond graphs, and their geometric intermediates, are tested for four atoms and antiprism structures for six atoms. Spectroscopic resolution (dE/E) less than 10% is achieved and the observed energy level shifts and merges through structural transformations are in good agreement with the model few-body quantum-Ising Hamiltonian., Comment: 8 pages, 4 figures

We present an entanglement scheme for Rydberg atoms using the van der Waals interaction phase induced by Ramsey-type pulsed interactions. This scheme realizes not only controlled phase operations between atoms at a distance larger than Rydberg blockade distance, but also various counter-intuitive entanglement examples, including two-atom entanglement in the presence of a closer third atom and $W$-state generation for partially-blockaded three atoms. Experimental realization is conducted with single rubidium atoms loaded in an array of optical tweezer dipole traps, to demonstrate the proposed entanglement generations and measurements., Comment: 5 pages, 4 figures

Extremely fast qubit controls can greatly reduce the calculation time in quantum computation, and potentially resolve the finite-time decoherence issues in many physical systems. Here, we propose and experimentally demonstrate pico-second time-scale controls of atomic clock state qubits, using Berry-phase gates implemented with a pair of chirped laser pulses. While conventional methods of microwave or Raman transitions do not allow atomic qubit controls within a time faster than the hyperfine free evolution period, our approach of ultrafast Berry-phase gates accomplishes fast clock-state operations. We also achieves operational robustness against laser parametric noises, since geometric phases are determined by adiabatic evolution pathway only, without being affected by any dynamic details. The experimental implementation is conducted with two linearly polarized, chirped ultrafast optical pulses, interacting with five single rubidium atoms in an array of optical tweezer dipole traps, to demonstrate the proposed ultrafast clock-state gates and their operational robustness., Comment: 9 pages, 5 figures

Experimentally observed quantum few-body dynamics of neutral atoms excited to a Rydberg state are numerically analyzed with Lindblad master equation formalism. For this, up to five rubidium atoms are trapped with optical tweezers, arranged in various two-dimensional configurations, and excited to Rydberg 67S state in the nearest-neighbor blockade regime. Their coherent evolutions are measured with time-varying ground-state projections. The experimental results are analyzed with a model Lindblad equation with the homogeneous and inhomogeneous dampings determined by systematic and statistical error analysis. The coherent evolutions of the entangled systems are successfully reproduced by the resulting model analysis for the experimental results with optimal parameters in consistent with external calibrations., Comment: 7 pages, 4 figures, 1 table

We consider the leakage suppression problem of a three-level system in which the first two levels are the qubit system and the third, weakly-coupled to the second, is the leakage state. We show that phase- and amplitude-controlled two (three) pulses are sufficient for arbitrary qubit controls from the ground (an arbitrary) initial state, with leakage suppressed up to the first order of perturbation without additional pulse-area cost. A proof-of-principle experiment was performed with shaped femtosecond optical pulses and atomic rubidium showing a good agreement with the theory., Comment: 6 pages, 4 figures

We demonstrate subpicosecond-time-scale population transfer between the pair of hyperfine ground states of atomic rubidium using a single laser-pulse. Our scheme utilizes the geometric and dynamic phases induced during Rabi oscillation through the fine-structure excited state in order to construct an $X$ rotation gate for the hyperfine-state qubit system. Experiment performed with a femtosecond laser and cold rubidium atoms, in a magneto-optical trap, shows over 98\% maximal population transfer between the clock states., Comment: 5 pages, 5 figures

Arbitrary rotation of a qubit can be performed with a three-pulse sequence; for example, ZYZ rotations. However, this requires precise control of the relative phase and timing between the pulses, making it technically challenging in optical implementation in a short time scale. Here we show any ZYZ rotations can be implemented with a single laser-pulse, that is {\it a chirped pulse with a temporal hole}. The hole of this shaped pulse induces a non-adiabatic interaction in the middle of the adiabatic evolution of the chirped pulse, converting the central part of an otherwise simple Z-rotation to a Y rotation, constructing ZYZ rotations. The result of our experiment performed with shaped femtosecond laser pulses and cold rubidium atoms shows strong agreement with the theory., Comment: 5 pages 4 figures

The chirped-pulse interaction in the adiabatic coupling regime induces cyclic permutations of the energy states of a three-level system in the $V$-type configuration, which process is known as the three-level chirped rapid adiabatic passage. Here we show that a spectral hole in a chirped pulse can turn on and off one of the two adiabatic crossing points of this process, reducing the system to an effective two-level system. The given hybrid adiabatic-nonadiabatic transition results in selective excitation of the three-level system, controlled by the laser intensity and spectral position of the hole as well as the sign of the chirp parameter. Experiments are performed with shaped femtosecond laser pulses and the three lowest energy-levels (5S$_{1/2}$, 5P$_{1/2}$, and 5P$_{3/2}$) of atomic rubidium ($^{85}$Rb), of which the result shows good agreement with the theoretically analyzed dynamics. The result indicates that our method, being combined with the ordinary chirped-RAP, implements an adiabatic transitions between the two excited states. Furthermore the laser intensity-dependent control may have applications including selective excitations of atoms or ions arranged in space when being used in conjunction with laser beam profile programming., Comment: 7 pages, 5 figures

Cooling and trapping of atoms by light has enabled one to build and manipulate quantum systems at the single atom level. Such a bottom-up approach becomes one of the fascinating challenges toward scalable and highly controllable quantum systems, e.g., a large-scale quantum information machine. Their implementation requires crucial pre-requisites: scalablity, site distinguishability, and reliable single-atom loading into sites. The widely adopted methods satisfies the two former conditions relatively well, but the last condition, filling single atoms onto individual sites, relies mostly on the probabilistic loading, implying that loading a pre-defined set of atoms in given positions will be hampered exponentially. Two approaches are readily thinkable to overcome this issue: increasing the single-atom loading efficiency and relocating abundant atoms into unfilled positions. Realizing the relocation is directly related to how many atoms can be transportable in a designer way. Here, we demonstrate a dynamic holographic single-atom tweezers with unprecedented degrees of freedom of 2N. In a proof-of-principle experiment conducted with cold rubidium atoms, simultaneous rearrangements of N=9 single atoms are successfully performed. This method may be further applicable to deterministic N single-atom loading, coherent transport, and controlled collisions., Comment: 6 pages. 4 figures

It is well known that area pulses make Rabi oscillation and chirped pulses in the adiabatic interaction regime induce complete population inversion of a two-state system. Here we show that chirped zero-area pulses could engineer an interplay between the adiabatic evolution and Rabi-like oscillations. In a proof-of-principle experiment utilizing spectral chirping of femtosecond laser pulses with a resonant spectral hole, we demonstrate that the chirped zero-area pulses could induce, for example, complete population inversion and return of the cold rubidium atom two-state system. Experimental result agrees well with the theoretically considered overall dynamics, which could be approximately modeled to a Ramsey-like three-pulse interaction, where the $x$- and $z$- rotations are respectively driven by the hole and the main pulse., Comment: 7 pages, 4 figures

We present an experimental investigation of ultrafast-laser driven Rabi oscillations of atomic rubidium. Since the broadband spectrum of an ultrafast laser pulse simultaneously couples all the electronic hyperfine transitions between the excited and ground states, the complex excitation linkages involved with the D1 or D2 transition are energy degenerate. Here, by applying the Morris-Shore transformation, it is shown that this multi-state system is reduced to a set of independent two-state systems and dark states. In experiments performed by ultrafast laser interactions of atomic rubidium in the strong interaction regime, we demonstrate that the ultrafast dynamics of the considered multi-state system is governed by a sum of at most two decoupled Rabi oscillations when this system interacts with ultrafast laser pulses of any polarization state. We further show the implication of this result to possible controls of photo-electron polarizations., Comment: 7 pages, 4 figures