Quantum systems engineering

Abstract:

We use state-of-the-art density matrix renormalization group calculations in the canonical ensemble to determine the phase diagram of the dipolar Bose-Hubbard model on a finite cylinder. We consider several observables that are accessible in typical optical lattice setups and assess how well these quantities perform as order parameters. We find that, especially for small systems, the occupation imbalance is less susceptible to boundary effects than the structure factor in uncovering the presence of a periodic density modulation. By analyzing the nonlocal correlations, we find that the appearance of supersolid order is very sensitive to boundary effects, which may render it difficult to observe in quantum gas lattice experiments with a few tens of particles. Finally, we show that density measurements readily obtainable on a quantum gas microscope allow distinguishing between superfluid and solid phases using unsupervised machine-learning techniques.

Abstract:

We show that nonlinear problems including nonlinear partial di↵erential equations can be e- ciently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities eciently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr¨odinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more ecient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.

Abstract:

Nonstationary longtime dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, M. Landini, K. Kroeger, L. Hruby, T. Donner, and T. Esslinger, arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in the thermodynamic limit and show that this system is always dynamically unstable—even when mean-field theory predicts stability. Instabilities always occur in higher-order correlation functions leading to squeezing and entanglement induced by cavity dissipation. The dynamics may be understood as the formation of a dissipative time crystal. We use perturbation theory for finite system sizes to confirm the nonstationary behavior.

Abstract:

In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying symmetry-based conditions which, when satisfied, guarantee completely synchronous, entangled limit cycles between the individual constituents of a generic open quantum system - no restrictions are placed on its microscopic details. We describe these systems as posssessing a strong dynamical symmetry and we prove that, to first order, they are completely robust to symmetry-breaking perturbations. Using these ideas we identify two central examples where synchronisation arises via this qualitatively new mechanism: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases, due to their dynamical symmetries, perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their non-linear responses elicit long-lived signatures of both phase and frequency-locking.

Abstract:

We simulate the current-voltage relation of short layered superconductors, which we model as stacks of capacitively coupled Josephson junctions. The system is driven by external laser fields, in order to optically control the voltage drop across the junction. We identify parameter regimes in which supercurrents can be stabilized against thermally induced phase slips, thus reducing the effective voltage across the superconductor. Furthermore, single driven Josephson junctions are known to exhibit phase-locked states, where the superconducting phase is locked to the driving field. We numerically observe their persistence in the presence of thermal fluctuations and capacitive coupling between adjacent Josephson junctions. Our results indicate how macroscopic material properties can be manipulated by exploiting the large optical nonlinearities of Josephson plasmons.