Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms

Entanglement transport and a nanophotonic interface for atoms in optical tweezers

The realization of an efficient quantum optical interface for multi-qubit systems is an outstanding challenge in science and engineering. Using two atoms in individually-controlled optical tweezers coupled to a nanofabricated photonic crystal cavity, we demonstrate entanglement generation, fast non-destructive readout, and full quantum control of atomic qubits. The entangled state is verified in free space after being transported away from the cavity by encoding the qubits into long-lived states and using dynamical decoupling. Our approach bridges quantum operations at an optical link and in free space by a coherent one-way transport, potentially enabling an integrated optical interface for atomic quantum processors.

Collectively Encoded Rydberg Qubit

We demonstrate a collectively encoded qubit based on a single Rydberg excitation stored in an ensemble of N entangled atoms. Qubit rotations are performed by applying microwave fields that drive excitations between Rydberg states. Coherent readout is performed by mapping the excitation into a single photon. Ramsey interferometry is used to probe the coherence of the qubit, as well as to test the robustness to external perturbations. We show that qubit coherence is preserved even as we lose atoms from the polariton mode, preserving Ramsey fringe visibility. We show that dephasing due to electric field noise scales as the fourth power of field amplitude. These results show that robust quantum information processing can be achieved via collective encoding using Rydberg polaritons, and hence this system could provide an attractive alternative coding strategy for quantum computation and networking.

Fast Preparation and Detection of a Rydberg Qubit Using Atomic Ensembles

We demonstrate a new approach for fast preparation, manipulation, and collective readout of an atomic Rydberg-state qubit. By making use of Rydberg blockade inside a small atomic ensemble, we prepare a single qubit within 3  μs with a success probability of F_{p}=0.93±0.02, rotate it, and read out its state in 6  μs with a single-shot fidelity of F_{d}=0.92±0.04. The ensemble-assisted detection is 10^{3} times faster than imaging of a single atom with the same optical resolution, and enables fast repeated nondestructive measurement. We observe qubit coherence times of 15  μs, much longer than the π rotation time of 90 ns. Potential applications ranging from faster quantum information processing in atom arrays to efficient implementation of quantum error correction are discussed.

Spatial Bloch Oscillations of a Quantum Gas in a "Beat-Note" Superlattice

We report the experimental realization of a new kind of optical lattice for ultracold atoms where arbitrarily large separation between the sites can be achieved without renouncing to the stability of ordinary lattices. Two collinear lasers, with slightly different commensurate wavelengths and retroreflected on a mirror, generate a superlattice potential with a periodic "beat-note" profile where the regions with large amplitude modulation provide the effective potential minima for the atoms. To prove the analogy with a standard large spacing optical lattice we study Bloch oscillations of a Bose Einstein condensate with negligible interactions in the presence of a small force. The observed dynamics between sites separated by ten microns for times exceeding one second proves the high stability of the potential. This novel lattice is the ideal candidate for the coherent manipulation of atomic samples at large spatial separations and might find direct application in atom-based technologies like trapped-atom interferometers and quantum simulators.

Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms

Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail¹. Many platforms are being developed towards this goal, in particular based on trapped ions^2-4, superconducting circuits^5-7, neutral atoms^8-11 or molecules^12,13. All of these platforms face two key challenges: scaling up the ensemble size while retaining high-quality control over the parameters, and validating the outputs for these large systems. Here we use programmable arrays of individual atoms trapped in optical tweezers, with interactions controlled by laser excitation to Rydberg states¹¹, to implement an iconic many-body problem-the antiferromagnetic two-dimensional transverse-field Ising model. We push this platform to a regime with up to 196 atoms manipulated with high fidelity and probe the antiferromagnetic order by dynamically tuning the parameters of the Hamiltonian. We illustrate the versatility of our platform by exploring various system sizes on two qualitatively different geometries-square and triangular arrays. We obtain good agreement with numerical calculations up to a computationally feasible size (approximately 100 particles). This work demonstrates that our platform can be readily used to address open questions in many-body physics.

Quantum phases of matter on a 256-atom programmable quantum simulator

Motivated by far-reaching applications ranging from quantum simulations of complex processes in physics and chemistry to quantum information processing¹, a broad effort is currently underway to build large-scale programmable quantum systems. Such systems provide insights into strongly correlated quantum matter^2-6, while at the same time enabling new methods for computation^7-10 and metrology¹¹. Here we demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms, featuring strong interactions controlled by coherent atomic excitation into Rydberg states¹². Using this approach, we realize a quantum spin model with tunable interactions for system sizes ranging from 64 to 256 qubits. We benchmark the system by characterizing high-fidelity antiferromagnetically ordered states and demonstrating quantum critical dynamics consistent with an Ising quantum phase transition in (2 + 1) dimensions¹³. We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation¹⁴, experimentally map the phase diagram and investigate the role of quantum fluctuations. Offering a new lens into the study of complex quantum matter, these observations pave the way for investigations of exotic quantum phases, non-equilibrium entanglement dynamics and hardware-efficient realization of quantum algorithms.

Deterministic Fast Scrambling with Neutral Atom Arrays

Fast scramblers are dynamical quantum systems that produce many-body entanglement on a timescale that grows logarithmically with the system size N. We propose and investigate a family of deterministic, fast scrambling quantum circuits realizable in near-term experiments with arrays of neutral atoms. We show that three experimental tools-nearest-neighbor Rydberg interactions, global single-qubit rotations, and shuffling operations facilitated by an auxiliary tweezer array-are sufficient to generate nonlocal interaction graphs capable of scrambling quantum information using only O(logN) parallel applications of nearest-neighbor gates. These tools enable direct experimental access to fast scrambling dynamics in a highly controlled and programmable way and can be harnessed to produce highly entangled states with varied applications.

Gaussian soft control-based quantum fan-out gate in ground-state manifolds of neutral atoms

We propose a reliable scheme for one-step synthesizing of a quantum fan-out gate in a system of neutral atoms. By introducing the off-resonant driving fields with Gaussian temporal modulation, the dynamics of the system is strictly restricted to the ground-state subspace on the basis of unconventional Rydberg pumping, which exhibits more robustness than the constant driving method against the fluctuation of system parameters, such as operating time and environment noise. As a direct application of this quantum fan-out gate, we discuss in detail the preparation of multipartite Greenberger-Horne-Zeilinger (GHZ) state for neutral atoms. The result shows that a high fidelity better than 99% can be obtained within the state-of-the-art experiments.

Efficient Tensor Network Ansatz for High-Dimensional Quantum Many-Body Problems

We introduce a novel tensor network structure augmenting the well-established tree tensor network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently manipulatable and scalable. We benchmark this novel approach against paradigmatic two-dimensional spin models demonstrating unprecedented precision and system sizes. Finally, we compute the ground state phase diagram of two-dimensional lattice Rydberg atoms in optical tweezers observing nontrivial phases and quantum phase transitions, providing realistic benchmarks for current and future two-dimensional quantum simulations.

A quantum-logic gate between distant quantum-network modules

The big challenge in quantum computing is to realize scalable multi-qubit systems with cross-talk-free addressability and efficient coupling of arbitrarily selected qubits. Quantum networks promise a solution by integrating smaller qubit modules to a larger computing cluster. Such a distributed architecture, however, requires the capability to execute quantum-logic gates between distant qubits. Here we experimentally realize such a gate over a distance of 60 meters. We employ an ancillary photon that we successively reflect from two remote qubit modules, followed by a heralding photon detection, which triggers a final qubit rotation. We use the gate for remote entanglement creation of all four Bell states. Our nonlocal quantum-logic gate could be extended both to multiple qubits and many modules for a tailor-made multi-qubit computing register.

Half-minute-scale atomic coherence and high relative stability in a tweezer clock

The preparation of large, low-entropy, highly coherent ensembles of identical quantum systems is fundamental for many studies in quantum metrology¹, simulation² and information³. However, the simultaneous realization of these properties remains a central challenge in quantum science across atomic and condensed-matter systems^2,4-7. Here we leverage the favourable properties of tweezer-trapped alkaline-earth (strontium-88) atoms^8-10, and introduce a hybrid approach to tailoring optical potentials that balances scalability, high-fidelity state preparation, site-resolved readout and preservation of atomic coherence. With this approach, we achieve trapping and optical-clock excited-state lifetimes exceeding 40 seconds in ensembles of approximately 150 atoms. This leads to half-minute-scale atomic coherence on an optical-clock transition, corresponding to quality factors well in excess of 10¹⁶. These coherence times and atom numbers reduce the effect of quantum projection noise to a level that is comparable with that of leading atomic systems, which use optical lattices to interrogate many thousands of atoms in parallel^11,12. The result is a relative fractional frequency stability of 5.2(3) × 10^-17τ^-1/2 (where τ is the averaging time in seconds) for synchronous clock comparisons between sub-ensembles within the tweezer array. When further combined with the microscopic control and readout that are available in this system, these results pave the way towards long-lived engineered entanglement on an optical-clock transition¹³ in tailored atom arrays.

Prospects and challenges for squeezing-enhanced optical atomic clocks

Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.

One-step implementation of Toffoli gate for neutral atoms based on unconventional Rydberg pumping

Compared with the idea of universal quantum computation, a direct synthesis of a multiqubit logic gate can greatly improve the efficiency of quantum information processing tasks. Here we propose an efficient scheme to implement a three-qubit controlled-not (Toffoli) gate of neutral atoms based on unconventional Rydberg pumping. By adjusting the strengths of Rabi frequencies of driving fields, the Toffoli gate can be achieved within one step, which is also insensitive to the fluctuation of the Rydberg-Rydberg interaction. Considering different atom alignments, we can obtain a high-fidelity Toffoli gate at the same operation time ∼7 μs. In addition, our scheme can be further extended to the four-qubit case without altering the operating time.

Controlling Exciton-Phonon Interactions via Electromagnetically Induced Transparency

Highly excited Rydberg states of excitons in Cu_{2}O semiconductors provide a promising approach to explore and control strong particle interactions in a solid-state environment. A major obstacle has been the substantial absorption background that stems from exciton-phonon coupling and lies under the Rydberg excitation spectrum, weakening the effects of exciton interactions. Here, we demonstrate that two-photon excitation of Rydberg excitons under conditions of electromagnetically induced transparency (EIT) can be used to control this background. Based on a microscopic theory that describes the known single-photon absorption spectrum, we analyze the conditions under which two-photon EIT permits separating the optical Rydberg excitation from the phonon-induced absorption background, and even suppressing it entir7ely. Our findings thereby pave the way for the exploitation of Rydberg blockade with Cu_{2}O excitons in nonlinear optics and other applications.

Phase Matching in Lower Dimensions

Phase matching refers to a process in which atom-field interactions lead to the creation of an output field that propagates coherently through the interaction volume. By studying light scattering from arrays of cold atoms, we show that conditions for phase matching change as the dimensionality of the system decreases. In particular, for a single atomic chain, there is phase-matched reflective scattering in a cone about the symmetry axis of the array that scales as the square of the number of atoms in the chain. For two chains of atoms, the phase-matched reflective scattering can be enhanced or diminished as a result of Bragg scattering. Such scattering can be used for mapping collective states within an array of neutral atoms onto propagating light fields and for establishing quantum links between separated arrays.

Reduction of laser intensity noise over 1 MHz band for single atom trapping

We reduce the intensity noise of laser light by using an electro-optic modulator and acousto-optic modulator in series. The electro-optic modulator reduces noise at high frequency (10 kHz to 1 MHz), while the acousto-optic modulator sets the average power of the light and reduces noise at low frequency (up to 10 kHz). The light is then used to trap single sodium atoms in an optical tweezer, where the lifetime of the atoms is limited by parametric heating due to laser noise at twice the trapping frequency. With our noise eater, the noise is reduced by up to 15 dB at these frequencies and the lifetime of the atom in the optical tweezer is increased by an order of magnitude to around 6 seconds. Our technique is general and acts directly on the laser beam, expanding laser options for sensitive optical trapping applications.

Mean field theory of weakly-interacting Rydberg polaritons in the EIT system based on the nearest-neighbor distribution

The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.

Balanced Coherence Times of Atomic Qubits of Different Species in a Dual 3×3 Magic-Intensity Optical Dipole Trap Array

We construct a polarization-mediated magic-intensity (MI) optical dipole trap (ODT) array, in which the detrimental effects of light shifts on the mixed-species qubits are efficiently mitigated so that the coherence times of the mixed-species qubits are both substantially enhanced and balanced for the first time. This mixed-species magic trapping technique relies on the tunability of the coefficient of the third-order cross term and ground state hyperpolarizability, which are inherently dependent on the degree of circular polarization of the trapping laser. Experimentally, polarization of the ODT array for ^{85}Rb qubits is finely adjusted to a definite value so that its working magnetic field required for magic trapping amounts to the one required for magically trapping ^{87}Rb qubits in another ODT array with fully circular polarization. Ultimately, in such a polarization-mediated MI-ODT array, the coherence times of ^{87}Rb and ^{85}Rb qubits are, respectively, enhanced up to 891±47  ms and 943±35  ms. Moreover, we reveal that the noise of the elliptic polarization causes dephasing effect on the ^{85}Rb qubits but it could be efficiently mitigated by choosing the dynamical range of active polarization device. We also show that light shifts seen by qubits in an elliptically polarized MI-ODT can be more efficiently compensated due to the decrease in the ground state hyperpolarizability. It is anticipated that the novel mixed-species MI-ODT array is a versatile platform for building scalable quantum computers with neutral atoms.

Submicrosecond entangling gate between trapped ions via Rydberg interaction

Generating quantum entanglement in large systems on timescales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum systems¹ with low-error entanglement gates operated within tens of microseconds using the vibrational motion of few-ion crystals^2,3. To exceed the level of complexity tractable by classical computers the main challenge is to realize fast entanglement operations in crystals made up of many ions (large ion crystals)⁴. The strong dipole-dipole interactions in polar molecule⁵ and Rydberg atom^6,7 systems allow much faster entangling gates, yet stable state-independent confinement comparable with trapped ions needs to be demonstrated in these systems⁸. Here we combine the benefits of these approaches: we report a two-ion entangling gate with 700-nanosecond gate time that uses the strong dipolar interaction between trapped Rydberg ions, which we use to produce a Bell state with 78 per cent fidelity. The sources of gate error are identified and a total error of less than 0.2 per cent is predicted for experimentally achievable parameters. Furthermore, we predict that residual coupling to motional modes contributes an approximate gate error of 10^-4 in a large ion crystal of 100 ions. This provides a way to speed up and scale up trapped-ion quantum computers and simulators substantially.

High-numerical-aperture and long-working-distance objective for single-atom experiments

We present a long-working-distance objective lens with numerical apertures NA = 0.4 for single-atom experiments. The objective lens is assembled entirely by the commercial on-catalog Φ1″ singlets. The objective can correct the spherical aberrations due to the standard flat vacuum glass windows with various thicknesses. The typical working distance is 18.2 mm at the design wavelength of 852 nm with a 5-mm thick silica window. In addition, the objective can also be optimized to work at the diffraction limit at a single wavelength in the entire visible and near infrared regions by slightly tuning the distance between the first two lenses. The diffraction limited field of view is 0.61 mm, and the spatial resolution is 1.3 μm at the design wavelength. The performances are simulated by using the commercial ray-tracing software and confirmed by imaging the resolution chart and a 1.18 μm pinhole. The objective can be used for trapping and manipulating single atoms of various species.

Light reflection and transmission in planar lattices of cold atoms

Manipulation of light using atoms plays a fundamental and important role in emerging technologies such as integrated photonics, information storage, and quantum sensors. Specifically, there have been intense theoretical efforts involving large samples of cold neutral atoms for coherent control of light. Here we present a theoretical scheme that enables efficient computation of collective optical responses of mono- and bi-layer planar square lattices of dense, cold two-level atoms using classical electrodynamics of coupled dipoles in the limit of low laser intensity. The steady-state transmissivity and reflectivity are obtained at a field point far away from the atomic lattices in the regime with no Bragg reflection. While our earlier method was based on exact solution of the electrodynamics for a small-scale lattice, here we calculate the dipole moments assuming that they are the same at all lattice sites, as for an infinite lattice. Atomic lattices with effectively over one hundred times more sites than in our earlier exact computations can then be simulated numerically with fewer computational resources. We have implemented an automatic selection of the number of sites under the given convergence criteria. We compare the numerical results from both computational schemes. We also find similarities and differences of a stack of two atomic lattices from a two-atom sample. Such aspects may be exploited to engineer a stack for potential applications.

Quantum Computation Toolbox for Decoherence-Free Qubits Using Multi-Band Alkali Atoms

Protocols for designing and manipulating qubits with ultracold alkali atoms in 3D optical lattices are introduced. These qubits are formed from two-atom spin superposition states that create a decoherence-free subspace immune to stray magnetic fields, dramatically improving coherence times while still enjoying the single-site addressability and Feshbach resonance control of state-of-the-art alkali atom systems. The protocol requires no continuous driving or spin-dependent potentials, and instead relies upon the population of a higher motional band to realize naturally tunable in-site exchange and cross-site superexchange interactions. As a proof-of-principle example of their utility for entanglement generation for quantum computation, it is shown that the cross-site superexchange interactions can be used to engineer 1D cluster states. Explicit protocols for experimental preparation and manipulation of the qubits are also discussed, as well as methods for measuring more complex quantities such as out-of-time-ordered correlation functions (OTOCs).

Rydberg-Mediated Entanglement in a Two-Dimensional Neutral Atom Qubit Array

We demonstrate high fidelity two-qubit Rydberg blockade and entanglement on a pair of sites in a large two-dimensional qubit array. The qubit array is defined by a grid of blue detuned lines of light with 121 sites for trapping atomic qubits. Improved experimental methods have increased the observed Bell state fidelity to F_{Bell}=0.86(2). Accounting for errors in state preparation and measurement we infer a fidelity of F_{Bell}^{-SPAM}=0.88. Accounting for errors in single qubit operations we infer that a Bell state created with the Rydberg mediated C_{Z} gate has a fidelity of F_{Bell}^{C_{Z}}=0.89. Comparison with a detailed error model based on quantum process matrices indicates that finite atom temperature and laser noise are the dominant error sources contributing to the observed gate infidelity.