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arXiv:1206.7010 · Physical Review Letters

Quantum Simulation of Small-Polaron Formation with Trapped Ions

Vladimir M. Stojanović, Tao Shi, Christoph Bruder, J. I. Cirac

Published Dec 17, 2012• 46 citations
arXivHTMLPDF

Abstract

We propose an analog quantum simulation of small-polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of microtraps, in the single-excitation case allows the realization of the antiadiabatic regime of the Holstein model. We show that the strong excitation-phonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonon-dressed excitation.

DOI
10.1103/physrevlett.109.250501

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We propose an analog quantum simulation of small-polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of microtraps, in the single-excitation case allows the realization of the antiadiabatic regime of the Holstein model. We show that the strong excitation-phonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonon-dressed excitation.
We propose an analog quantum simulator for the Holstein molecular-crystal model based on a superconducting circuit QED system in the dispersive regime. By varying the driving field on the superconducting resonators, one can access both the adiabatic and antiadiabatic regimes of this model, and the strong electron-phonon coupling required for small-polaron formation can be readily reached. We show that a small-polaron state of arbitrary quasimomentum can be generated by applying a microwave pulse to the resonators. We also show that significant squeezing in the resonator modes can be achieved in the polaron-crossover regime through a measurement-based scheme.
Recent years have seen growing interest in sharp polaronic transitions in systems with strongly momentum-dependent interactions of an itinerant excitation (electron, hole, exciton) with dispersionless phonons. This work presents a scheme for investigating such phenomena in a controllable fashion within the framework of an analog quantum simulator based on an array of neutral atoms in optical tweezers. The envisioned analog simulator, in which the atoms interact through Rydberg-dressed resonant dipole-dipole interaction, allows one to study the rich interplay of Peierls- and breathing-mode-type excitation-phonon interactions. Based on a numerically-exact treatment of one special case of this system -- namely, the case with equal Peierls- and breathing-mode coupling strengths -- a sharp small-polaron transition was shown to take place for a critical value of the effective excitation-phonon coupling strength. This transition signifies the change from a completely bare (undressed by phonons) excitation below the transition point and a strongly phonon-dressed one (small polaron) above it. This work also highlights the comparative advantages of highly-controllable Rydberg-atom-based systems to other physical platforms for simulating polaronic phenomenology, which could be exploited to study the nonequilibrium dynamics of the small-polaron formation.
Strong coupling between mobile charge carriers or excitons and lattice vibrations gives rise to polarons: quasiparticles formed by charge carriers dressed by a cloud of phonon excitations. Polaron formation determines transport properties of systems ranging from transition-metal oxides and organic semiconductors to light-harvesting complexes. In excitonic systems that admit a hard-core boson description, mapping the excitations to pseudospins provides a natural framework for studying polaron physics, including the nonperturbative regime in which hopping amplitudes, phonon energies, and coupling strengths are comparable. Here, we propose a trapped-ion blueprint for realizing spin-phonon Hamiltonians with programmable spatial coupling between excitation density and phonon displacements, encompassing local Holstein and long-range Fröhlich-type interactions. To access strongly dressed quasiparticles whose bare spectral weight is suppressed, we introduce displaced Green's functions implemented through spin-dependent phonon displacements. Their spectral response reveals the polaron band spectrum, including binding energies and phonon-excitation sidebands, while spatially resolved measurements probe the structure of the phonon dressing cloud, providing a route to polaron tomography. We further complement this spectroscopy with direct and ancilla-assisted measurements of spin-phonon correlations that track the coupled dynamics of the excitation and its environment. These approaches connect the emergent quasiparticle spectrum to the microscopic buildup of its dressing cloud, enabling controlled studies of how the spatial range of coupling shapes polaron formation and mobility.
We propose a scheme for investigating the nonequilibrium aspects of small-polaron physics using an array of superconducting qubits and microwave resonators. This system, which can be realized with transmon or gatemon qubits, serves as an analog simulator for a lattice model describing a nonlocal coupling of a quantum particle (excitation) to dispersionless phonons. We study its dynamics following an excitation-phonon (qubit-resonator) interaction quench using a numerically exact approach based on a Chebyshev-moment expansion of the time-evolution operator of the system. We thereby glean heretofore unavailable insights into the process of the small-polaron formation resulting from strongly momentum-dependent excitation-phonon interactions, most prominently about its inherent dynamical timescale. To further characterize this complex process, we evaluate the excitation-phonon entanglement entropy and show that initially prepared bare-excitation Bloch states here dynamically evolve into small-polaron states that are close to being maximally entangled. Finally, by computing the dynamical variances of the phonon position and momentum quadratures, we demonstrate a pronounced non-Gaussian character of the latter states, with a strong antisqueezing in both quadratures.
We study the quantum dynamics of small polaron formation and polaron transport through finite quantum structures in the framework of the one-dimensional Holstein model with site-dependent potentials and interactions. Combining Lanczos diagonalization with Chebyshev moment expansion of the time evolution operator, we determine how different initial states, representing stationary ground states or injected wave packets, after an electron-phonon interaction quench, develop in real space and time. Thereby, the full quantum nature and dynamics of electrons and phonons is preserved. We find that the decay out of the initial state sensitively depends on the energy and momentum of the incoming particle, the electron-phonon coupling strength, and the phonon frequency, whereupon bound polaron-phonon excited states may emerge in the strong-coupling regime. The tunneling of a Holstein polaron through a quantum wall or dot is generally accompanied by strong phonon number fluctuations due to phonon emission and reabsorption processes.