Polaronic signatures and spectral properties of graphene antidot lattices

We explore the consequences of electron-phonon (e-ph) coupling in graphene antidot lattices (graphene nanomeshes), i.e., triangular superlattices of circular holes (antidots) in a graphene sheet. They display a direct band gap whose magnitude can be controlled via the antidot size and density. The relevant coupling mechanism in these semiconducting counterparts of graphene is the modulation of the nearest-neighbor electronic hopping integrals due to lattice distortions (Peierls-type e-ph coupling). We compute the full momentum dependence of the e-ph vertex functions for a number of representative antidot lattices. Based on the latter, we discuss the origins of the previously found large conduction-band quasiparticle spectral weight due to e-ph coupling. In addition, we study the nonzero-momentum quasiparticle properties with the aid of the self-consistent Born approximation, yielding results that can be compared with future angle-resolved photoemission spectroscopy measurements. Our principal finding is a significant e-ph mass enhancement, an indication of polaronic behavior. This can be ascribed to the peculiar momentum dependence of the e-ph interaction in these narrow-band systems, which favors small phonon momentum scattering. We also discuss implications of our study for recently fabricated large-period graphene antidot lattices.Comment: published versio

Ground-state entanglement spectrum of a generic model with nonlocal excitation-phonon coupling

While the concept of the entanglement spectrum has heretofore been utilized to address various many-body systems, the models describing an itinerant spinless-fermion excitation coupled to zero-dimensional bosons (e.g. dispersionless phonons) have as yet not received much attention in this regard. To fill this gap, the ground-state entanglement spectrum of a model that includes two of the most common types of short-ranged, nonlocal excitation-phonon interaction -- the Peierls- and breathing-mode couplings -- is numerically evaluated here. This model displays a sharp, level-crossing transition at a critical coupling strength, which signifies the change from a nondegenerate ground state at the quasimomentum $K_{\textrm{gs}}=0$ to a twofold-degenerate one corresponding to a symmetric pair of nonzero quasimomenta. Another peculiarity of this model is that in the special case of equal Peierls- and breathing-mode coupling strengths the bare-excitation Bloch state with the quasimomentum $0$ or $\pi$ is its exact eigenstate. Moreover, below a critical coupling strength this state is the ground state of the model. Thus, the sharp transition between a bare excitation and a heavily phonon-dressed (polaronic) one can be thought of as a transition between vanishing and finite entanglement. It is demonstrated here that the smallest ground-state entanglement-spectrum eigenvalue to a large extent mimics the behavior of the entanglement entropy itself and vanishes in this special case of the model; by contrast, all the remaining eigenvalues diverge in this case. The implications of excitation-phonon entanglement for $W$-state engineering in superconducting and neutral-atom-based qubit arrays serving as analog simulators of this model are also discussed.Comment: 13 pages, 5 figure

Extracting spectral properties of small Holstein polarons from a transmon-based analog quantum simulator

The Holstein model, which describes purely local coupling of an itinerant excitation (electron, hole, exciton) with zero-dimensional (dispersionless) phonons, represents the paradigm for short-range excitation-phonon interactions. It is demonstrated here how spectral properties of small Holstein polarons -- heavily phonon-dressed quasiparticles, formed in the strong-coupling regime of the Holstein model -- can be extracted from an analog quantum simulator of this model. This simulator, which is meant to operate in the dispersive regime of circuit quantum electrodynamics, has the form of an array of capacitively coupled superconducting transmon qubits and microwave resonators, the latter being subject to a weak external driving. The magnitude of $XY$-type coupling between adjacent qubits in this system can be tuned through an external flux threading the SQUID loops between those qubits; this translates into an {\em in-situ} flux-tunable hopping amplitude of a fictitious itinerant spinless-fermion excitation, allowing one to access all the relevant physical regimes of the Holstein model. By employing the kernel-polynomial method, based on expanding dynamical response functions in Chebyshev polynomials of the first kind and their recurrence relation, the relevant single-particle momentum-frequency resolved spectral function of this system is computed here for a broad range of parameter values. To complement the evaluation of the spectral function, it is also explained how -- by making use of the many-body version of the Ramsey interference protocol -- this dynamical-response function can be measured in the envisioned analog simulator.Comment: 17 pages, 7 figure

Dicke-state preparation through global transverse control of Ising-coupled qubits

We consider the problem of engineering the two-excitation Dicke state $|D^{3}_{2}\rangle$ in a three-qubit system with all-to-all Ising-type qubit-qubit interaction, which is also subject to global transverse (Zeeman-type) control fields. The theoretical underpinning for our envisioned state-preparation scheme, in which $|000\rangle$ is adopted as the initial state of the system, is provided by a Lie-algebraic result that guarantees state-to-state controllability of this system for an arbitrary choice of initial- and final states that are invariant with respect to permutations of qubits. This scheme is envisaged in the form of a pulse sequence that involves three instantaneous control pulses, which are equivalent to global qubit rotations, and two Ising-interaction pulses of finite durations between consecutive control pulses. The design of this pulse sequence -- whose total duration is $T\approx 0.95\:\hbar/J$, where $J$ is the Ising-coupling strength -- leans heavily on the concept of the symmetric sector, a four-dimensional, permutationally-invariant subspace of the three-qubit Hilbert space. We demonstrate the feasibility of the proposed state-preparation scheme by carrying out a detailed numerical analysis of its robustness to systematic errors, i.e. deviations from the optimal values of the eight parameters that characterize the underlying pulse sequence. Finally, we discuss how our proposed scheme can be generalized for engineering Dicke states in systems with $N \ge 4$ qubits. For the sake of illustration, we describe the preparation of the two-excitation Dicke state $|D^{4}_{2}\rangle$ in a four-qubit system.Comment: extended version, accepted for publication in Phys. Rev.

Digital quantum simulation of scalar Yukawa coupling: Dynamics following an interaction quench on IBM Q

Motivated by the dearth of studies pertaining to the digital quantum simulation of coupled fermion-boson systems and the revitalized interest in simulating models from medium- and high-energy physics, we investigate the nonequilibrium dynamics following a Yukawa-interaction quench on IBM Q. After adopting -- due to current quantum-hardware limitations -- a single-site (zero-dimensional) version of the scalar Yukawa-coupling model as our point of departure, we design low-depth quantum circuits that emulate its dynamics with up to three bosons. In particular, using advanced circuit-optimization techniques, in the one-boson case we demonstrate circuit compression, i.e. design a shallow (constant-depth) circuit that contains only two CNOT gates, regardless of the total simulation time. In the three-boson case -- where such a compression is not possible -- we design a circuit in which one Trotter step entails 8 CNOTs, this number being far below the maximal CNOT-cost of a generic three-qubit gate. Using an analogy with the travelling salesman problem, we also provide a CNOT-cost estimate for quantum circuits emulating the system dynamics for higher boson-number truncations. Finally, based on the proposed circuits for one- and three-boson cases, we quantify the system dynamics for several different initial states by evaluating the expected fermion- and boson numbers at an arbitrary time after the quench. We validate our results by finding their good agreement with the exact ones obtained through classical benchmarking.Comment: 19 pages, 21 figure