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arXiv:2605.23413

Quantum Simulation of Energy Bifurcation and Z_2-Symmetry Restoration in Macroscopic Quantum Tunneling

Masao Hirokawa

quant-phSubmitted May 22, 2026• Announced May 25, 2026• 0 citations
v1 · May 22, 2026v2 · Jun 8, 2026
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Abstract

Macroscopic quantum tunneling (MQT), a cornerstone of Leggett's program, is deeply linked with instanton physics, yet its experimental verification remains elusive. This Perspective demonstrates that the quantum Rabi model manifests observable, instanton-like effects via quantum simulation. In the MQT regime, qubit-boson interactions drive Polyakov's energy bifurcation, governing tunneling and spontaneous symmetry breaking. Mapping the quantum Rabi model onto an effective double-well potential reveals that while tunneling suppression induces spontaneous symmetry breaking, instanton-like contributions act to restore it. This mechanism enables experimental access to the classical Euclidean action of an effective instanton-like particle, offering a route to probe non-perturbative phenomena.

Comments
13 pages, 15 figures

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Macroscopic quantum tunneling (MQT), a cornerstone of Leggett's program, is deeply linked with instanton physics, yet its experimental verification remains elusive. This Perspective demonstrates that the quantum Rabi model manifests observable, instanton-like effects via quantum simulation. In the MQT regime, qubit-boson interactions drive Polyakov's energy bifurcation, governing tunneling and spontaneous symmetry breaking. Mapping the quantum Rabi model onto an effective double-well potential reveals that while tunneling suppression induces spontaneous symmetry breaking, instanton-like contributions act to restore it. This mechanism enables experimental access to the classical Euclidean action of an effective instanton-like particle, offering a route to probe non-perturbative phenomena.
The renormalized quantum Rabi model describing a qubit-boson interaction has the transition from SUSY to its spontaneous breaking under suitable conditions. It is caused by how the X-gate coupled to the Bose field works properly between the two symmetrical wells made by the bosons coupled to a qubit. According to Polyakov's idea, there is the possibility that an instanton tunneling the barrier between those symmetrical wells appears as the classical trajectory. In this paper, therefore, under a physical condition, we show the vestige of the particle like an instanton in the expression of the ground-state energy of the quantum Rabi model.
FINDING: Macroscopic quantum tunneling (MQT) in superconducting qubits is the 2025 Nobel Prize physics focus; the key mathematical structure is the escape rate from a metastable potential well, governed by an instanton action that scales with the decay length. | MATH: The MQT rate is Γ=Aexp⁡(−Sinst/ℏ) \Gamma = A \exp(-S_{\text{inst}}/\hbar) Γ=Aexp(−Sinst​/ℏ), where Sinst S_{\text{inst}} Sinst​ is the Euclidean action. For a cubic potential V(q)=12mω02q2−λq3 V(q) = \frac{1}{2}m\omega_0^2 q^2 - \lambda q^3 V(q)=21​mω02​q2−λq3, the decay length ℓ=ℏ/2mΔU \ell = \hbar / \sqrt{2m\Delta U} ℓ=ℏ/2mΔU​ (where ΔU \Delta U ΔU is barrier height) enters as Sinst=365ΔUω0 S_{\text{inst}} = \frac{36}{5} \frac{\Delta U}{\omega_0} Sinst​=536​ω0​ΔU​. The qubit's Josephson energy ratio EJ/EC E_J/E_C EJ​/EC​ sets the effective mass; the crossover from quantum to thermal regime occurs at T∗=ℏω0/(2πkB) T^* = \hbar \omega_0 / (2\pi k_B) T∗=ℏω0​/(2πkB​). | CONNECTION: The decay length ratio ℓ/Δqzero-point \ell / \Delta q_{\text{zero-point}} ℓ/Δqzero-point​ (zero-point width Δq0=ℏ/(2mω0) \Delta q_0 = \sqrt{\hbar/(2m\omega_0)} Δq0​=ℏ/(2mω0​)​) yields \( \ell/\Delta q_0 = \sqrt{\Delta U / (\hbar \o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
The macroscopic quantum tunneling in a double-well potential with dissipation is formulated without referring to instantons. This formulation, in the domain of small dissipation, goes beyond the instanton approximation which corresponds to the two-state truncated system (or, the so-called spin-boson Hamiltonian). It is first confirmed that our formulation, when applied to the two-state truncated system, reproduces all the known results of the instanton approximation. It is then shown that the ground state is mixed with excited states by dissipative interactions and this effect tends to enhance the ground-state quantum tunneling. In the Ohmic dissipation case this enhancement factor, even for a shallow double-well potential, can be at most comparable to the suppression factor which has been known from the work by Caldeira and Leggett. In the super-Ohmic case, however, the enhancement factor generally exceeds the suppression factor and the two-state approximation fails. A salient feature in the choice of counter terms in macroscopic quantum tunneling, which is essential to the above conclusion, is emphasized.
We study the quantum dynamics of supercurrents of one-dimensional Bose gases in a ring optical lattice to verify instanton methods applied to coherent macroscopic quantum tunneling (MQT). We directly simulate the real-time quantum dynamics of supercurrents, where a coherent oscillation between two macroscopically distinct current states occurs due to MQT. The tunneling rate extracted from the coherent oscillation is compared with that given by the instanton method. We find that the instanton method is quantitatively accurate when the effective Planck's constant is sufficiently small. We also find phase slips associated with the oscillations.
In this paper, macroscopic quantum tunneling (MQT) effect of Z2{Z}_{2}Z2​ topological order in the Wen-Plaquette model is studied. This kind of MQT is characterized by quantum tunneling processes of different virtual quasiparticles moving around a torus. By a high-order degenerate perturbation approach, the effective pseudospin models of the degenerate ground states are obtained. From these models, we get the energy splitting of the ground states, which are consistent with those obtained from exact diagonalization method.
Ultracold Bose gases as precise quantum simulators have emerged amongst the leaders in the current race  – a second quantum revolution  – toward the promise of unfathomable sensitivity, scope, and speed of a new era of technology. The only path leading to these advancements is through many-body descriptions, especially in regimes where interatomic interactions render many approximations incompatible with the physics. The research in this dissertation unlocks a piece of this mystery through investigations of many-body quantum tunneling of ultracold bosons in optical lattices. A key mechanism to characterizing the dynamics, matrix product state simulations equip the many-body toolbox with efficient optimization of large Hilbert spaces together with correlation and entropy measures that help clarify when semiclassical or mean-field approximations fail. In this thesis we obtain the following results. Macroscopic quantum tunneling escape of a Bose-Einstein condensate  – comprised of tens of thousands of 87Rb atoms  – from a single well, as portrayed through both experiment and theory, highlights non-exponential decay in the number of atoms trapped behind the barrier. Additionally, explicit symmetry breaking of a biperiodic optical lattice ring trap to a uniform one illustrates a critical symmetry-breaking strength at which the system transitions from a state of remembering to a state of forgetting its initial symmetry state; this symmetry memory indicates a new form of quantum dynamics that requires the quantum advantage for scaling up particle number and lattice sites. Extensive characterization of dynamical regimes in a bosonic Josephson junction  – underlaid by an optical lattice as described by the Bose-Hubbard model  – reveal substantial deviation of many body dynamics from the mean field or semiclassical predictions underlying the usual operating regime of Josephson junctions. Initial state population and phase yield insight into dynamic tunneling regimes of a quasi one-dimensional double well potential, through the Z2 spontaneous symmetry-breaking phase transition from Josephson oscillations to macroscopic self-trapping. We demonstrate that with increasing repulsive interaction strength, the U(1) superfluid-Mott insulator phase transition induces localized dynamics in the number density, such as particle-hole and soliton formation. Moreover, g^(2) correlations unveil a new dynamic regime  – the Fock flashlight. The new field of atomtronics  – or atomic circuits  – has emerged with many studies of weakly-interacting condensates. In contrast, and building on our work on many-body effects in the double wells underlying Josephson junctions, we present a proof-of-principle of a Mott-insulating atomtronic switch that requires strongly-interacting bosons. Through transient analysis, we reveal that hole conductance can be modulated via tuning interaction strength through a critical value, thus propelling the state to the next ``wedding cake'' layer of the Mott insulating structure. This critical interaction strength is a…