- The paper presents a precise mapping of the quantum Rabi model to symmetric double-well tunneling, demonstrating how tunneling induces energy bifurcation and parity symmetry breaking.
- It employs rigorous analytical techniques to derive the classical Euclidean action of instanton-like effects, connecting measurable energy gaps to theoretical predictions.
- The study establishes quantum simulators as versatile platforms for probing non-perturbative tunneling, symmetry restoration, and spontaneous SUSY breaking in engineered quantum systems.
Quantum Simulation, Energy Bifurcation, and Z2-Symmetry Restoration in Macroscopic Quantum Tunneling
Context and Motivation
The paper systematically analyzes macroscopic quantum tunneling (MQT) within the framework of the quantum Rabi model, emphasizing the physical origins and observability of instanton-like effects and Polyakov's energy bifurcation. Building on Leggett's program in macroscopic quantum phenomena, the work thoroughly examines symmetry breaking and restoration in prototypical quantum simulators, relevant for both condensed matter and quantum information platforms.
Modelling Double-Well Systems via the Quantum Rabi Model
The quantum Rabi model is shown to encode tunneling physics in symmetric double-well potentials through a precise mapping—leveraging unitary transformations and two-level approximations. The effective Hamiltonian representation systematically captures both qubit-boson interactions and the phase acquisition at tunneling boundaries, highlighting the role of parity symmetry. The transformed Rabi Hamiltonian, incorporating both qubit and boson degrees of freedom, is rigorously connected to double-well dynamics, with the coupling strength g quantifying the separation of potential minima and governing tunneling suppression and symmetry breaking.
The analysis details how the tunneling-induced interaction term acquires a phase factor, leading to an explicit expression for the effective Hamiltonian. Importantly, this mapping reveals that the tunneling does not perturb the harmonic oscillator well shapes, but only shifts minima and adds a self-energy term.
Spontaneous Z2-Symmetry Breaking and Limits
Two limiting procedures are studied: (LMT1) where g→∞ for fixed frequencies, and (LMT2) where both qubit transition frequency and coupling strength are continuously varied via a parameter r. These limits drive the system into regimes of spontaneous Z2-symmetry breaking, mathematically justified via norm resolvent convergence. In these limits, tunneling is suppressed, leaving a degenerate ground state and breaking parity symmetry, while maintaining a robust platform for experimental realization in quantum simulators, as demonstrated in ion-trap implementations.
A key result is that, under these limiting conditions, the tunneling matrix elements vanish, corroborated by Riemann-Lebesgue-type arguments, and symmetry breaking is accompanied by the emergence of nearly degenerate eigenstates. The model's parity operator and its transformations are rigorously defined, establishing the precise symmetry character of the system for both tunneling and boson number.
Polyakov’s Energy Bifurcation and Instanton Physics
The restoration of Z2 symmetry is addressed through Polyakov’s framework: allowing finite tunneling lifts degeneracy and induces energy bifurcation. The analysis provides explicit expressions for the ground state and first excited energy levels—incorporating instanton-induced terms—which are sharply suppressed in the strong-coupling limit. The classical Euclidean action for the instanton-like particle is analytically derived, and its role in determining energy gaps is highlighted. The bifurcation occurs precisely as predicted by Polyakov, and its signatures are argued to be experimentally observable in photon emission spectra.
The paper offers a quantitative formula for extracting the classical Euclidean action from experimentally measured energy gaps, facilitating direct comparison between quantum simulation results and instanton theory predictions.
Supersymmetry and Extension to Anisotropic Rabi Models
Under resonance conditions (ωa=ωc), the model realizes N=2 supersymmetry (SUSY), with spontaneous SUSY breaking arising in strong-coupling regimes. The manuscript analyzes how deviations from balance between rotating and counter-rotating terms in anisotropic Rabi models impact symmetry breaking and mass reduction, referencing both mathematical proofs and empirical verification. This points to broader implications for exploring SUSY and its spontaneous breaking in generalized spin-boson models, including perspectives on Nambu-Goldstone fermions and mass-enhancement effects.
Implications and Prospects
This research establishes the quantum Rabi model as a paradigmatic simulator for probing non-perturbative tunneling, instanton effects, and symmetry restoration/breaking at the macroscopic scale. The explicit connection between energy bifurcation, restoration of symmetry, and instanton physics opens pathways for leveraging quantum simulators to investigate phenomena traditionally confined to quantum field theory, such as SUSY breaking and Goldstone modes.
Practically, the results are directly relevant for superconducting circuit architectures, trapped ion simulations, and platforms aiming to realize spin-boson and lattice gauge models. The precise analytical formulas derived enable the extraction of instanton action parameters from data, paving the way for experimental tests of long-standing theoretical proposals.
Theoretically, the work implies that understanding tunneling and symmetry restoration in many-body quantum systems may require explicit modeling of instanton contributions and associated bifurcations, even in engineered quantum simulators. The mathematical framework provided is extensible to more general spin-boson and field theory models, including those with dissipative environments and nontrivial topological effects.
Conclusion
The paper presents a rigorous, detailed examination of macroscopic quantum tunneling using quantum simulation via the quantum Rabi model. It substantiates the observability of Polyakov's energy bifurcation and instanton-like effects in physical quantum systems, providing explicit mathematical and empirical routes for their investigation. The interplay between spontaneous and restored Z2 symmetry, SUSY, and instanton physics is systematically articulated, supporting the extension of quantum simulation methodologies to broader non-perturbative and field-theoretical phenomena. The analytical tools and theoretical arguments developed are broadly applicable, with significant implications for both foundational studies and practical realizations in quantum technologies (2605.23413).