Frustration and glassiness in spin models with cavity-mediated interactions

We show that the effective spin-spin interaction between three-level atoms confined in a multimode optical cavity is long-ranged and sign-changing, like the RKKY interaction; therefore, ensembles of such atoms subject to frozen-in positional randomness can realize spin systems having disordered and frustrated interactions. We argue that, whenever the atoms couple to sufficiently many cavity modes, the cavity-mediated interactions give rise to a spin glass. In addition, we show that the quantum dynamics of cavity-confined spin systems is that of a Bose-Hubbard model with strongly disordered hopping but no on-site disorder; this model exhibits a random-singlet glass phase, absent in conventional optical-lattice realizations. We briefly discuss experimental signatures of the realizable phases.Comment: 5 pages, 2 figure

Phase Diagram of the Bose-Hubbard Model with T_3 symmetry

In this paper we study the quantum phase transition between the insulating and the globally coherent superfluid phases in the Bose-Hubbard model with T_3 structure, the "dice lattice". Even in the absence of any frustration the superfluid phase is characterized by modulation of the order parameter on the different sublattices of the T_3 structure. The zero-temperature critical point as a function of a magnetic field shows the characteristic "butterfly" form. At fully frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at f=1/2, we find evidence for the existence of an intermediate insulating phase characterized by a zero superfluid stiffness but finite compressibility. In this intermediate phase bosons are localized due to the external frustration and the topology of the T_3 lattice. We name this new phase the Aharonov-Bohm (AB) insulator. In the presence of charge frustration the phase diagram acquires the typical lobe-structure. The form and hierarchy of the Mott insulating states with fractional fillings, is dictated by the particular topology of the T_3 lattice. The results presented in this paper were obtained by a variety of analytical methods: mean-field and variational techniques to approach the phase boundary from the superconducting side, and a strongly coupled expansion appropriate for the Mott insulating region. In addition we performed Quantum Monte Carlo simulations of the corresponding (2+1)D XY model to corroborate the analytical calculations with a more accurate quantitative analysis. We finally discuss experimental realization of the T_3 lattice both with optical lattices and with Josephson junction arrays.Comment: 16 pages, 17 figure

Photonic simulation of entanglement growth and engineering after a spin chain quench

The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices

Quantum Hamiltonian Complexity

Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via so-called area laws. Our aim here is to provide a computer science-oriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field. As such, we include the following in this survey: (1) The motivations and history of the field, (2) a glossary of condensed matter physics terms explained in computer-science friendly language, (3) overviews of central ideas from condensed matter physics, such as indistinguishable particles, mean field theory, tensor networks, and area laws, and (4) brief expositions of selected computer science-based results in the area. For example, as part of the latter, we provide a novel information theoretic presentation of Bravyi's polynomial time algorithm for Quantum 2-SAT.Comment: v4: published version, 127 pages, introduction expanded to include brief introduction to quantum information, brief list of some recent developments added, minor changes throughou

Numerical solution of perturbed Kepler problem using a split operator technique

An efficient geometric integrator is proposed for solving the perturbed Kepler motion. This method is stable and accurate over long integration time, which makes it appropriate for treating problems in astrophysics, like solar system simulations, and atomic and molecular physics, like classical simulations of highly excited atoms in external fields. The key idea is to decompose the hamiltonian in solvable parts and propagate the system according to each term. Two case studies, the Kepler atom in an uniform field and in a monochromatic field, are presented and the errors are analyzed.Comment: 17 pages, 5 figures, submitted to the Journal of Computational Physic