Dynamical Regimes of Two Qubits Coupled through a Transmission Line

• URL: http://arxiv.org/abs/2604.21463v1
• Date: Thu, 23 Apr 2026 09:17:09 GMT
• Title: Dynamical Regimes of Two Qubits Coupled through a Transmission Line
• Abstract summary: We investigate the reduced dynamics of two identical superconducting qubits capacitively coupled through a finite-length transmission line.<n>In the long-line limit, each sector is described by a Drude-Lorentz spectral density and the dynamics is solved with the hierarchical equations of motion.<n>In the short-line limit, the continuum description breaks down and the dynamics becomes respectively multimode or single-mode.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the reduced dynamics of two identical superconducting qubits capacitively coupled through a finite-length transmission line. Starting from circuit quantization, we derive a circuit Hamiltonian that naturally separates the line modes into even- and odd-parity sectors coupled to collective qubit operators. Depending on the hierarchy between the qubit frequency $ω_q$, the mode spacing $ω_{TL}$, and the coupling scale $ω_g$, the line acts either as a structured reservoir or as a discrete few-mode coupler. In the long-line continuum limit, each sector is described by a Drude--Lorentz spectral density and the dynamics is solved with the hierarchical equations of motion. Using the Breuer--Laine--Piilo measure, we identify the parameter region in which the reduced dynamics exhibits non-Markovian relaxation. In the short-line limit, the continuum description breaks down and the dynamics becomes respectively multimode or single-mode. This establishes a unified cQED picture of the dynamical regimes of finite-length transmission lines in superconducting-circuit architectures.

Related papers

• Dynamical Phase Transitions Across Slow and Fast Regimes in a Two-Tone Driven Duffing Resonator [36.94429692322632]
  We study a Duffing resonator under bichromatic excitation and identify a competition between the two drives.<n>In the slow-beating regime, where the tones are closely spaced, the secondary drive acts as a modulation that induces dynamical phase transitions.<n>Our results provide a framework for controlling driven nonlinear systems, enabling state manipulation, and sensing in nanomechanical, optical, and superconducting circuit platforms.
  arXiv  Detail & Related papers  (2025-11-03T19:00:24Z)
• Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories [103.95523007319937]
  Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena.<n>Here, we investigate the dynamics of local excitations in a $mathZ$ LGT using a two-dimensional lattice of superconducting qubits.<n>Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes.
  arXiv  Detail & Related papers  (2024-09-25T17:59:05Z)
• Nonlinear dynamical Casimir effect and Unruh entanglement in waveguide QED with parametrically modulated coupling [83.88591755871734]
  We study theoretically an array of two-level qubits moving relative to a one-dimensional waveguide. When the frequency of this motion approaches twice the qubit resonance frequency, it induces parametric generation of photons and excitation of the qubits. We develop a comprehensive general theoretical framework that incorporates both perturbative diagrammatic techniques and a rigorous master-equation approach.
  arXiv  Detail & Related papers  (2024-08-30T15:54:33Z)
• Circuit QED theory of direct and dual Shapiro steps with finite-size transmission line resonators [0.0]
  We investigate the occurrence of direct and dual Shapiro steps for a Josephson junction coupled to a finite-size transmission line resonator. For the dual case, we do not assume the (approximate) charge-phase duality, but include the full multi-band dynamics for the Josephson junction. We show how the dual steps are very sensitive to these fluctuations and identify the key physical parameters for the junction and the transmission line.
  arXiv  Detail & Related papers  (2024-05-21T17:06:06Z)
• Longitudinal (curvature) couplings of an $N$-level qudit to a superconducting resonator at the adiabatic limit and beyond [0.0]
  We investigate the coupling between a multi-level system, or qudit, and a superconducting (SC) resonator's electromagnetic field. For the first time, we derive Hamiltonians describing the longitudinal multi-level interactions in a general dispersive regime. We provide examples illustrating the transition from adiabatic to dispersive coupling in different qubit systems.
  arXiv  Detail & Related papers  (2023-12-05T20:33:59Z)
• A $\delta$-free approach to quantization of transmission lines connected to lumped circuits [0.0]
  We introduce a $delta$-free Lagrangian formulation for a transmission line coupled to a lumped circuit without the need for a discretization of the transmission line or mode expansions. We apply our approach to an analytically solvable network consisting of a semi-infinite transmission line capacitively coupled to a LC circuit.
  arXiv  Detail & Related papers  (2023-11-16T13:50:21Z)
• Mediated interactions beyond the nearest neighbor in an array of superconducting qubits [0.0]
  We consider mediated interactions in an array of floating transmons, where each qubit capacitor consists of two superconducting pads galvanically isolated from ground. extraneous modes can generate coupling between the qubit modes that extends beyond the nearest neighbor.
  arXiv  Detail & Related papers  (2021-10-04T20:14:39Z)
• Superconducting coupler with exponentially large on-off ratio [68.8204255655161]
  Tunable two-qubit couplers offer an avenue to mitigate errors in multiqubit superconducting quantum processors. Most couplers operate in a narrow frequency band and target specific couplings, such as the spurious $ZZ$ interaction. We introduce a superconducting coupler that alleviates these limitations by suppressing all two-qubit interactions with an exponentially large on-off ratio.
  arXiv  Detail & Related papers  (2021-07-21T03:03:13Z)
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space [62.997667081978825]
  We investigate a quantum system simultaneously exposed to two structured reservoirs. We employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian interplay between discrete photonic feedback and structured acoustic phononovian modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.
  arXiv  Detail & Related papers  (2020-11-10T12:38:35Z)
• Universal non-adiabatic control of small-gap superconducting qubits [47.187609203210705]
  We introduce a superconducting composite qubit formed from two capacitively coupled transmon qubits. We control this low-frequency CQB using solely baseband pulses, non-adiabatic transitions, and coherent Landau-Zener interference. This work demonstrates that universal non-adiabatic control of low-frequency qubits is feasible using solely baseband pulses.
  arXiv  Detail & Related papers  (2020-03-29T22:48:34Z)
• Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks [55.41644538483948]
  We report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in neural networks. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations.
  arXiv  Detail & Related papers  (2020-01-07T02:16:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.