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arXiv:2609.07820

Creation and characterization of leviton excitations in tight-binding chains

Stephen R. McMillan, Thomas Frederiksen, Géza Giedke

cond-mat.mes-hallquant-phSubmitted Sep 7, 2026• Announced Sep 8, 2026

Abstract

Levitons are minimal-excitation electronic wave packets generated by Lorentzian voltage pulses and constitute a central resource for electron quantum optics. Their creation and defining properties are usually formulated in continuum scattering descriptions, whereas many candidate platforms for integrated electronic quantum circuits are finite, discrete, and strongly shaped by lattice dispersion. We study leviton generation in finite one-dimensional tight-binding chains of non-interacting fermions driven by time-dependent voltage pulses. Using the single-particle density matrix, we resolve the excitation above the initial Fermi sea and quantify its quality through the average excitation number and its fluctuations. We find that clean leviton-like states emerge only in an intermediate regime where the pulse is slow enough to be resolved by the dynamics on the lattice, but not so slow that truncation and finite-size effects distort the Lorentzian profile in the time domain. Lorentzian pulses (even if truncated) systematically outperform non-Lorentzian pulse shapes in approaching the low-noise limit with increasing system size. We further identify finite-lattice signatures associated with band filling, pulse amplitude, linear voltage-drop geometry, and residual deviations from the continuum integer-charge condition. These results establish a microscopic framework for understanding leviton formation beyond the ideal continuum limit and for evaluating lattice-based platforms for coherent few-electron transport.

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Levitons are minimal-excitation electronic wave packets generated by Lorentzian voltage pulses and constitute a central resource for electron quantum optics. Their creation and defining properties are usually formulated in continuum scattering descriptions, whereas many candidate platforms for integrated electronic quantum circuits are finite, discrete, and strongly shaped by lattice dispersion. We study leviton generation in finite one-dimensional tight-binding chains of non-interacting fermions driven by time-dependent voltage pulses. Using the single-particle density matrix, we resolve the excitation above the initial Fermi sea and quantify its quality through the average excitation number and its fluctuations. We find that clean leviton-like states emerge only in an intermediate regime where the pulse is slow enough to be resolved by the dynamics on the lattice, but not so slow that truncation and finite-size effects distort the Lorentzian profile in the time domain. Lorentzian pulses (even if truncated) systematically outperform non-Lorentzian pulse shapes in approaching the low-noise limit with increasing system size. We further identify finite-lattice signatures associated with band filling, pulse amplitude, linear voltage-drop geometry, and residual deviations from the continuum integer-charge condition. These results establish a microscopic framework for understanding leviton formation beyond the ideal continuum limit and for evaluating lattice-based platforms for coherent few-electron transport.

Reduced transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, but may also emerge from the influence of a few controllable defects. We show here how a single defect profoundly reshapes wave-function spreading on a finite and periodic tight-binding lattice. Adapting the defect technique from classical random-walk studies, we obtain exact time-resolved site-occupation probabilities and several observables of interest. Even a single defect induces remarkable nonlinear effects, including non-monotonic suppression of transport, enhanced localization at distant sites, and strong sensitivity to the initial particle position at long times. These results demonstrate that minimal perturbations can generate nontrivial long-time transport signatures, giving rise to a microscopic defect-driven mechanism of quantum localization. Although the main results presented pertain to a single isolated defect, we show that the developed formalism may naturally extend to multiple as well as to a wider class of defects.

Abstract We study the response of a degenerate Fermi sea to a time‐dependent perturbation. We find that elementary excitations in the Fermi sea are electrons and electron–hole quasiparticle pairs whose number and probability of creation depend on amplitude and shape of the drive. The excitations can be probed in a driven quantum contact at low temperature. While electronic excitations are associated to the dc voltage offset and determine the average current, the electron–hole pairs are created by the ac voltage component and give rise to the excess current noise power in a junction. We also obtain the many‐body state created by the drive. The constituent quasiparticle states can be probed by a Hong–Ou–Mandel type of correlation experiment where electrons emitted from the terminals with a relative time delay collide at the contact. The current noise power in the junction is directly related to the wave packet overlap at the contact. This is confirmed in recent experiments, demonstrating an unprecedented degree of control of elementary excitations in a coherent mesoscopic junction.

We propose to generate heat pulses in mesoscopic conductors using light fields. In contrast to single-electron excitations such as levitons, which are created by accurate voltage drives, our approach relies on modulating the temperature of an electronic reservoir. To this end, we show that the interactions with a light field can induce a controllable time-dependent temperature in an electrode. The temperature modulations generate charge-neutral heat pulses that can be emitted into a mesoscopic conductor and detected in the outputs. We illustrate our approach by evaluating the time-dependent currents and their fluctuations using a tight-binding model of two electronic reservoirs connected by a quantum point contact. Our work establishes a route towards on-demand caloritronics, where energy rather than charge carries quantum information, and it paves the way for probing time-resolved heat transport and quantum coherence in thermally driven conductors.

In this work, we develop a time-dependent mathematical model to investigate the wave packet evolution of both massive and massless Dirac fermions in a tight-binding lattice. Our study focuses on the quantum diffusion of carriers in a one-dimensional crystal, where the system Hamiltonian is represented by both the Dirac and Schrödinger equations. Interestingly, during the quantum diffusion process, we observe oscillations of the wave packet between the spinor-up and spinor-down bands in the Dirac case. In the massive fermion scenario, these oscillations between the sublattices are influenced by inertial mass effects, resulting in longer oscillation periods as the mass increases. In addition, we find a strong dependence of Dirac fermion dynamics on the Fermi velocity in the tight-binding chain.

A strategy is proposed to excite particles from a Fermi sea in a noise-free fashion by electromagnetic pulses with realistic parameters. We show that by using quantized pulses of simple form one can suppress the particle-hole pairs which are created by a generic excitation. The resulting many-body states are characterized by one or several particles excited above the Fermi surface accompanied by no disturbance below it. These excitations carry charge which is integer for noninteracting electron gas and fractional for Luttinger liquid. The operator algebra describing these excitations is derived, and a method of their detection which relies on noise measurement is proposed.

State-of-the-art quantum simulators -- ranging from ultracold atoms and trapped ions to Rydberg arrays and superconducting qubits -- have rapidly evolved into powerful platforms for investigating complex quantum many-body phenomena. In this thesis, we discuss various models and their static and non-equilibrium properties that can be realized on near-term quantum devices. We conduct comprehensive studies on the phases of these models, spanning novel symmetry-protected topological and critical gapless phases in one dimension to the non-equilibrium behavior of localized excitations in one-dimensional quantum chains and extended one-dimensional quantum objects embedded in a two-dimensional quantum magnet. On the technical side, we employ extensive tensor network simulations to validate our findings and introduce new algorithms to determine the lifetime of edge excitations emerging in the symmetry-protected topological phase of fermionic chains. Furthermore, we propose a new variational ansatz to directly search for these novel edge modes in the topological phase. By integrating analytical tools and tensor network simulations, this thesis contributes to the roadmap for establishing quantum simulators as promising tools for investigating complex quantum systems.