Explore the vast range of titles available.

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.

Quantum computation and simulation rely on long-lived qubits with controllable interactions. Trapped polar molecules have been proposed as a promising quantum computing platform, offering scalability and single-particle addressability while still leveraging inherent complexity and strong couplings of molecules 1 , 2 , 3 , 4 – 5 . Recent progress in the single quantum state preparation and coherence of the hyperfine-rotational states of individually trapped molecules allows them to serve as promising qubits 6 , 7 , 8 , 9 , 10 – 11 , with intermolecular dipolar interactions creating entanglement 12 , 13 . However, universal two-qubit gates have not been demonstrated with molecules. Here we harness intrinsic molecular resources to implement a two-qubit iSWAP gate using individually trapped X 1 Σ + NaCs molecules. By allowing the molecules to interact for 664 μs at a distance of 1.9 μm, we create a maximally entangled Bell state with a fidelity of 94(3)% in trials in which both molecules are present. Using motion–rotation coupling, we measure residual excitation of the lowest few motional states along the axial trapping direction and find them to be the primary source of decoherence. Finally, we identify two non-interacting hyperfine states within the ground rotational level in which we encode a qubit. The interaction is toggled by transferring between interacting and non-interacting states to realize an iSWAP gate. We verify the gate performance by measuring its logical truth table. Intrinsic molecular resources are used to implement a two-qubit iSWAP gate using individually trapped X 1 Σ + NaCs molecules.

In conventional Bardeen–Cooper–Schrieffer superconductors 1 , electrons with opposite momenta bind into Cooper pairs due to an attractive interaction mediated by phonons in the material. Although superconductivity naturally emerges at thermal equilibrium, it can also emerge out of equilibrium when the system parameters are abruptly changed 2 – 8 . The resulting out-of-equilibrium phases are predicted to occur in real materials and ultracold fermionic atoms, but not all have yet been directly observed. Here we realize an alternative way to generate the proposed dynamical phases using cavity quantum electrodynamics (QED). Our system encodes the presence or absence of a Cooper pair in a long-lived electronic transition in 88 Sr atoms coupled to an optical cavity and represents interactions between electrons as photon-mediated interactions through the cavity 9 , 10 . To fully explore the phase diagram, we manipulate the ratio between the single-particle dispersion and the interactions after a quench and perform real-time tracking of the subsequent dynamics of the superconducting order parameter using nondestructive measurements. We observe regimes in which the order parameter decays to zero (phase I) 3 , 4 , assumes a non-equilibrium steady-state value (phase II) 2 , 3 or exhibits persistent oscillations (phase III) 2 , 3 . This opens up exciting prospects for quantum simulation, including the potential to engineer unconventional superconductors and to probe beyond mean-field effects like the spectral form factor 11 , 12 , and for increasing the coherence time for quantum sensing. The dynamical phases of out-of-equilibrium Bardeen–Cooper–Schrieffer superconductors have been simulated using cold atoms levitated inside an optical cavity.

The dynamics of one-dimensional quantum many-body systems is often numerically simulated with matrix-product states (MPSs). The computational complexity of MPS methods is known to be related to the growth of entropies of reduced density matrices for bipartitions of the chain. While for closed systems the entropy relevant for the complexity is uniquely defined by the entanglement entropy, for open systems it depends on the choice of the representation. Here, we systematically compare the growth of different entropies relevant to the complexity of matrix-product representations in open-system simulations. We simulate an XXZ spin-1/2 chain in the presence of spontaneous emission and absorption, and dephasing. We compare simulations using a representation of the full density matrix as a matrix-product density operator (MPDO) with a quantum trajectory unraveling, where each trajectory is itself represented by an MPS (QT+MPS). We show that the bipartite entropy in the MPDO description (operator entanglement, OE) generally scales more favorably with time than the entropy in QT+MPS (trajectory entanglement, TE): i) For spontaneous emission and absorption the OE vanishes while the TE grows and reaches a constant value for large dissipative rates and sufficiently long times; ii) for dephasing the OE exhibits only logarithmic growth while the TE grows polynomially. Although QT+MPS requires a smaller local state space, the more favorable entropy growth can thus make MPDO simulations fundamentally more efficient than QT+MPS. Furthermore, MPDO simulations allow for easier exploitation of higher-order Trotter decompositions and translational invariance, allowing for larger time steps and system sizes.

Collectively coupling molecular ensembles to a cavity has been demonstrated to modify chemical reactions akin to catalysis. Theoretically understanding this experimental finding remains to be 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 reaction 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.

Entangled spin squeezed states generated via dipolar interactions in lattice models provide unique opportunities for quantum enhanced sensing and are now within reach of current experiments. A critical question in this context is which parameter regimes offer the best prospects under realistic conditions. Light scattering in deep lattices can induce significant decoherence and strong Stark shifts, while shallow lattices face motional decoherence as a fundamental obstacle. Here we analyze the interplay between motion and spin squeezing in itinerant fermionic dipoles in one dimensional chains using exact matrix product state simulations. We demonstrate that shallow lattices can achieve more than 5dB of squeezing, outperforming deep lattices by up to more than 3dB, even in the presence of low filling, loss and decoherence. We relate this finding to SU(2)-symmetric superexchange interactions, which keep spins aligned and protect collective correlations. We show that the optimal regime is achieved for small repulsive off-site interactions, with a trade-off between maximal squeezing and optimal squeezing time.

The operator space entanglement entropy, or simply 'operator entanglement' (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial 'rise and fall' the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a \\(U(1)\\) conservation law. We argue that in an XXZ spin-model and a Bose-Hubbard model the OE grows universally as \\(\\frac{1}{4} \\log_2 t\\) at long times, and as \\(\\frac{1}{2} \\log_2 t\\) for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.

We study a simple model for photoinduced electron transfer reactions for the case of many donor-acceptor pairs that are collectively and homogeneously coupled to a photon mode of a cavity. We describe both coherent and dissipative collective effects resulting from this coupling within the framework of a quantum optics Lindblad master equation. We introduce a method to derive an effective rate equation for electron transfer, by adiabatically eliminating donor and acceptor states and the cavity mode. The resulting rate equation is valid both for weak and strong coupling to the cavity mode, and describes electronic transfer through both the cavity coupled bright states and the uncoupled dark states. We derive an analytic expression for the instantaneous electron transfer rate that depends non-trivially on the time-varying number of pairs in the ground state. We find that under proper resonance conditions, and in the presence of an incoherent drive, reaction rates can be enhanced by the cavity. This enhancement persists, and can even be largest, in the weak light-matter coupling regime. We discuss how the cavity effect is relevant for realistic experiments.

We study the temporal growth and spatial propagation of quantum correlations in a two-dimensional bilayer realising a spin-1/2 quantum XXZ model with couplings mediated by long-range and anisotropic dipolar interactions. Starting with an initial state consisting of spins with opposite magnetization in each of the layers, we predict the emergence of a momentum-dependent dynamic instability in the spin structure factor that results, at short times, in the creation of pairs of excitations at exponentially fast rates. The created pairs present a characteristic momentum distribution that can be tuned by controlling the dipolar orientation, the layer separation or the dipolar couplings. The predicted behavior remains observable at very low filling fractions, making it accessible in state-of-the-art experiments with Rydberg atoms, magnetic atoms, and polar molecule arrays.

We propose a mechanism to realize high-yield molecular formation from ultracold atoms. Atom pairs are continuously excited by a laser, and a collective decay into the molecular ground state is induced by a coupling to a lossy cavity mode. Using a combination of analytical and numerical techniques, we demonstrate that the molecular yield can be improved by simply increasing the number of atoms, and can overcome efficiencies of state-of-the-art association schemes. We discuss realistic experimental setups for diatomic polar and nonpolar molecules, opening up collective light matter interactions as a tool for quantum state engineering, enhanced molecule formation, collective dynamics, and cavity mediated chemistry.