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We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the one-dimensional Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance r as , as well as a related class of fermionic Hamiltonians that generalize the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents , based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for , while connected correlation functions can decay with a hybrid exponential and power-law behavior, with a power that is -dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every . Along the critical lines, for all models breaking of conformal symmetry is argued at low enough . For the fermionic models we show that the edge modes, massless for , can acquire a mass for . The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.

Collectively coupling molecular ensembles to a cavity has been demonstrated to modify chemical reactions akin to catalysis. Theoretically understanding this experimental finding remains an important challenge. In particular the role of quantum effects in such setups is an open question of fundamental and practical interest. Theoretical descriptions often neglect quantum entanglement between nuclear and electro-photonic degrees of freedom, e.g., by computing Ehrenfest dynamics. Here we discover that disorder can strongly enhance the build-up of this entanglement on short timescales after incoherent photo-excitation. We find that this can have direct consequences for nuclear coordinate dynamics. We analyze this phenomenon in a disordered Holstein-Tavis-Cummings model, a minimal toy model that includes all fundamental degrees of freedom. Using a numerical technique based on matrix product states we simulate the exact quantum dynamics of more than 100 molecules. Our results highlight the importance of beyond Born-Oppenheimer theories in polaritonic chemistry. Experiments have shown that coupling ensembles of molecules to a cavity mode can modify chemical reactions, though theoretical studies have struggled to model the complexity of this many-body system. Here, matrix product states are used to study the reaction-relevant many-body quantum dynamics, revealing the importance of disorder on entanglement build-up.

The development of scalable, high-fidelity qubits is a key challenge in quantum information science. Neutral atom qubits have progressed rapidly in recent years, demonstrating programmable processors 1 , 2 and quantum simulators with scaling to hundreds of atoms 3 , 4 . Exploring new atomic species, such as alkaline earth atoms 5 – 7 , or combining multiple species 8 can provide new paths to improving coherence, control and scalability. For example, for eventual application in quantum error correction, it is advantageous to realize qubits with structured error models, such as biased Pauli errors 9 or conversion of errors into detectable erasures 10 . Here we demonstrate a new neutral atom qubit using the nuclear spin of a long-lived metastable state in 171 Yb. The long coherence time and fast excitation to the Rydberg state allow one- and two-qubit gates with fidelities of 0.9990(1) and 0.980(1), respectively. Importantly, a large fraction of all gate errors result in decays out of the qubit subspace to the ground state. By performing fast, mid-circuit detection of these errors, we convert them into erasure errors; during detection, the induced error probability on qubits remaining in the computational space is less than 10 −5 . This work establishes metastable 171 Yb as a promising platform for realizing fault-tolerant quantum computing. This study reports gates between qubits encoded in the nuclear spin state of Yb atoms trapped in optical tweezers, reaching very high fidelity and demonstrating mid-circuit conversion of errors into erasure errors.

High-rate quantum error correcting (QEC) codes with moderate overheads in qubit number and control complexity are highly desirable for achieving fault-tolerant quantum computing. Recently, quantum error correction has experienced significant progress both in code development and experimental realizations, with neutral atom qubit architecture rapidly establishing itself as a leading platform in the field. Scalable quantum computing will require processing with QEC codes that have low qubit overhead and large error suppression, and while such codes do exist, they involve a degree of non-locality that has yet to be integrated into experimental platforms. In this work, we analyze a family of high-rate Low-Density Parity-Check (LDPC) codes with limited long-range interactions and outline a near-term implementation in neutral atom registers. By means of circuit-level simulations, we find that these codes outperform surface codes in all respects when the two-qubit nearest neighbour gate error probability is below  ~ 0.1%. By using multiple laser colors, we show how these codes can be natively integrated in two-dimensional static neutral atom qubit architectures with open boundaries, where the desired long-range connectivity can be targeted via the Rydberg blockade interaction. Quantum error correction codes with low qubit overhead and error suppression capabilities are highly desirable for fault-tolerant quantum computing. Here, the authors introduce a family of high-rate Low Density Parity-Check quantum error correcting codes with moderate long-range connectivity and outline a near-term implementation in static neutral atom registers.

In the absence of frustration, interacting bosons in their ground state in one or two dimensions exist either in the superfluid or insulating phases. Superfluidity corresponds to frictionless flow of the matter field, and in optical conductivity is revealed through a distinct δ -functional peak at zero frequency with the amplitude known as the Drude weight. This characteristic low-frequency feature is instead absent in insulating phases, defined by zero static optical conductivity. Here we demonstrate that bosonic particles in disordered one dimensional chains can also exist in a conducting, non-superfluid, phase when their hopping is of the dipolar type, often viewed as short-ranged in one dimension. This phase is characterized by finite static optical conductivity, followed by a broad anti-Drude peak at finite frequencies. Off-diagonal correlations are also unconventional: they feature an integrable algebraic decay for arbitrarily large values of disorder. These results do not fit the description of any known quantum phase, and strongly suggest the existence of an unusual conducting state of bosonic matter in the ground state. Interacting bosons in one or two dimensions are expected to be in either a superfluid or an insulating ground state. Here, the authors show numerically that an experimentally relevant 1D model of disordered bosons with dipolar couplings supports an unusual metallic phase that does not fit into existing descriptions.

Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor 1 . Optical atomic clocks 2 , the current state of the art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology 3 – 6 . Augmenting tweezer-based clocks featuring microscopic control and detection 7 – 10 with the high-fidelity entangling gates developed for atom-array information processing 11 , 12 offers a promising route towards making use of highly entangled quantum states for improved optical clocks. Here we develop and use a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger–Horne–Zeilinger (GHZ) type with up to nine optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit (SQL) using GHZ states of up to four qubits. However, because of their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared with unentangled atoms 13 . Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval 14 – 17 . These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision. A family of multi-qubit Rydberg quantum gates is developed and used to generate Schrödinger cat states in an optical clock, allowing improvement in frequency measurement precision by taking advantage of entanglement.

Ultracold atomic physics offers myriad possibilities to study strongly correlated many-body systems in lower dimensions. Typically, only ground-state phases are accessible. Using a tunable quantum gas of bosonic cesium atoms, we realized and controlled in one-dimensional geometry a highly excited quantum phase that is stabilized in the presence of attractive interactions by maintaining and strengthening quantum correlations across a confinement-induced resonance. We diagnosed the crossover from repulsive to attractive interactions in terms of the stiffness and energy of the system. Our results open up the experimental study of metastable, excited, many-body phases with strong correlations and their dynamical properties.

Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, whose phase shift on the attosecond timescale is consistent with many-body correlations among Rydberg atoms beyond mean-field approximations. This coherent and ultrafast many-body dynamics is actively controlled by tuning the orbital size and population of the Rydberg state, as well as the mean atomic distance. Our approach will offer a versatile platform to observe and manipulate non-equilibrium dynamics of quantum many-body systems on the ultrafast timescale. Studying long-range interactions in the controlled environment of trapped ultracold gases can help our understanding of fundamental many-body physics. Here the authors excite a gas of Rydberg atoms with a ps laser pulse, demonstrating behaviour consistent with many-body correlations beyond mean-field.

Show of strength Fluctuations arising from Heisenberg's uncertainty principle enable quantum systems to exhibit phase transitions even at zero temperature. For example, a superfluid-to-insulator transition has been observed for weakly interacting bosonic atomic gases. Here the authors report a novel type of quantum phase transition in a strongly interacting, one-dimensional quantum gas of bosonic caesium atoms. The results open up the experimental study of ultracold gases in a new regime. Fluctuations arising from Heisenberg's uncertainty principle enable quantum systems to exhibit phase transitions even at zero temperature. For example, a superfluid-to-insulator transition has been observed for weakly interacting bosonic atomic gases. Here the authors report a novel type of quantum phase transition in a strongly interacting, one-dimensional quantum gas of bosonic caesium atoms. The results open up the experimental study of ultracold gases in a new regime. Quantum many-body systems can have phase transitions 1 even at zero temperature; fluctuations arising from Heisenberg’s uncertainty principle, as opposed to thermal effects, drive the system from one phase to another. Typically, during the transition the relative strength of two competing terms in the system’s Hamiltonian changes across a finite critical value. A well-known example is the Mott–Hubbard quantum phase transition from a superfluid to an insulating phase 2 , 3 , which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry, a novel type 4 , 5 of quantum phase transition may be induced and driven by an arbitrarily weak perturbation to the Hamiltonian. Here we observe such an effect—the sine–Gordon quantum phase transition from a superfluid Luttinger liquid to a Mott insulator 6 , 7 —in a one-dimensional quantum gas of bosonic caesium atoms with tunable interactions. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine–Gordon model 8 . We trace the phase boundary all the way to the weakly interacting regime, where we find good agreement with the predictions of the one-dimensional Bose–Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality and transport phenomena beyond Hubbard-type models in the context of ultracold gases.

The optical hybridization of the electronic states in strongly coupled molecule–cavity systems have revealed unique properties, such as lasing, room temperature polariton condensation and the modification of excited electronic landscapes involved in molecular isomerization. Here we show that molecular vibrational modes of the electronic ground state can also be coherently coupled with a microcavity mode at room temperature, given the low vibrational thermal occupation factors associated with molecular vibrations, and the collective coupling of a large ensemble of molecules immersed within the cavity-mode volume. This enables the enhancement of the collective Rabi-exchange rate with respect to the single-oscillator coupling strength. The possibility of inducing large shifts in the vibrational frequency of selected molecular bonds should have immediate consequences for chemistry. Coherent coupling of light with electronic transitions has led to phenomena such as polariton lasing and superfluidity. Shalabney et al. now couple the optical modes of micro-cavity to the vibrational modes of a molecule at room temperature and thereby alter the chemical behaviour of the molecule.