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arXiv:2412.19305

Analog quantum simulation of small-polaron physics in arrays of neutral atoms with Rydberg-dressed resonant dipole-dipole interaction

Vladimir M. Stojanović

Published Dec 26, 2024• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2412.19305

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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.
We investigate the spectral properties of polaronic excitations within the framework of an analog quantum simulator based on inductively coupled superconducting transmon qubits and microwave resonators. This system emulates a lattice model that describes a nonlocal coupling of an itinerant spinless-fermion excitation to dispersionless (Einstein-type) phonons through the Peierls and breathing-mode interaction mechanisms. The model is characterized by a sharp, level-crossing transition at a critical value of the effective excitation-phonon coupling strength; above the transition point, the ground state of this model corresponds to a heavily dressed (small-polaron) excitation. Using the kernel-polynomial method, we evaluate the momentum-frequency resolved spectral function of this system for a broad range of parameters. In particular, we underscore the ramifications of the fact that the zero-quasimomentum Bloch state of a bare excitation represents the exact eigenstate of the Hamiltonian of this system for an arbitrary excitation-phonon coupling strength. We also show that---based on the numerically evaluated spectral function and its well-known relation with the survival probability of the initial, bare-excitation Bloch state (the Loschmidt echo)---one can make predictions about the system dynamics following an excitation-phonon interaction quench. To make contact with anticipated experimental realizations, we utilize a previously proposed method for extracting dynamical-response functions in systems with local (single-qubit) addressability using the multiqubit (many-body) version of the Ramsey interference protocol.
We propose an analog superconducting quantum simulator for a one-dimensional model featuring momentum-dependent (nonlocal) electron-phonon couplings of Su-Schrieffer-Heeger and ``breathing-mode'' types. Because its corresponding coupling vertex function depends on both the electron and phonon quasimomenta, this model does not belong to the realm of validity of the Gerlach-L\"owen theorem that rules out any nonanalyticities in single-particle properties. The superconducting circuit behind the proposed simulator entails an array of transmon qubits and microwave resonators. By applying microwave driving fields to the qubits, a small-polaron Bloch state with an arbitrary quasimomentum can be prepared in this system within times several orders of magnitude shorter than the typical qubit decoherence times. We demonstrate that---by varying the externally tunable parameters---one can readily reach the critical coupling strength required for observing the sharp transition from a nondegenerate (single-particle) ground state corresponding to zero quasimomentum (Kgs=0{K}_{\mathrm{gs}}=0Kgs​=0) to a twofold-degenerate small-polaron ground state at nonzero quasimomenta Kgs{K}_{\mathrm{gs}}Kgs​ and $\ensuremath{-}{K}_{\mathrm{gs}}$. Through exact numerical diagonalization of our effective Hamiltonian, we show how this nonanalyticity is reflected in the relevant single-particle properties (ground-state energy, quasiparticle residue, average number of phonons). We also show that the proposed setup provides an ideal testbed for studying the nonequilibrium dynamics of small-polaron formation in the presence of strongly momentum-dependent electron-phonon interactions.
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.
Polarons, which arise from the self-trapping interaction between electrons and lattice distortions in a solid, have been known and extensively investigated for nearly a century. Nevertheless, the study of polarons continues to be an active and evolving field, with ongoing advancements in both fundamental understanding and practical applications. Here, we present a microscopic model that exhibits a diverse range of dynamic behavior, arising from the intricate interplay between two excitation-phonon coupling terms. The derivation of the model is based on an experimentally feasible Rydberg-dressed system with dipole-dipole interactions, making it a promising candidate for realization in a Rydberg atoms quantum simulator for excitation dynamics interacting with optical phonons. Remarkably, our analysis reveals a growing asymmetry in Bloch oscillations, leading to a macroscopic transport of nonspreading excitations under a constant force. Finally, we demonstrate the robustness of our findings against on-site random potential.
Analog quantum simulations with Rydberg atoms in optical tweezers have emerged as a powerful tool for exploring strongly correlated many-body physics. However, the range of accessible phenomena remains limited by constraints in controlling many-body interactions in these systems. Here, we propose an alternative approach to realizing tunable interactions using Rydberg dressing on Aquila, a 256-atom quantum simulator based on optical tweezer arrays. By weakly admixing a Rydberg state via off-resonant laser coupling, we generate long-range interactions with temporal control. In combination with programmable atom geometries and site-selective control, this dressing protocol enables simulation of quantum spin models with state preparation and measurement in arbitrary basis. These capabilities enable access to exciting regimes of quantum simulation, including Quantum spin liquids, XYZ lattice models and broader application of quantum reservoir computing. Our approach establish Rydberg dressing as a practical and scalable tool for expanding the class of many-body systems accessible to analog quantum simulation and provides a critical stepping stone toward quantum machine learning and hybrid analog-digital quantum simulation with neutral atoms.
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 XYXYXY-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.