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arXiv:2510.08820

Real-Time Instantons in Complex-Driven Qubits

Samuel N. Alperin

Published Oct 9, 2025• 0 citations
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Abstract

We consider the dynamics of the quantum Rabi model driven parametrically by a periodic modulation of a complex coupling. We show both analytically and numerically that instead of Rabi oscillations, this nonunitary coherent driving leads to a unidirectional instanton solution which mediates the rapid and deterministic one-way tunneling of any initial coherent state to the ground state, making the ground state a strong attractor in the quantum dynamics of the qubit. The timescale of this tunneling is shown to be inversely proportional to the effective resonant coupling, allowing for exceptionally fast, deterministic, and high-fidelity qubit reset through a purely coherent, PT-symmetric drive--without coupling to external dissipative baths, lossy resonators, or employing measurement-based feedback. Finally, we show how the drive can be engineered to place the strong attractor at any arbitrary point on the Bloch sphere.

DOI
10.48550/arxiv.2510.08820

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We consider the dynamics of the quantum Rabi model driven parametrically by a periodic modulation of a complex coupling. We show both analytically and numerically that instead of Rabi oscillations, this nonunitary coherent driving leads to a unidirectional instanton solution which mediates the rapid and deterministic one-way tunneling of any initial coherent state to the ground state, making the ground state a strong attractor in the quantum dynamics of the qubit. The timescale of this tunneling is shown to be inversely proportional to the effective resonant coupling, allowing for exceptionally fast, deterministic, and high-fidelity qubit reset through a purely coherent, PT-symmetric drive--without coupling to external dissipative baths, lossy resonators, or employing measurement-based feedback. Finally, we show how the drive can be engineered to place the strong attractor at any arbitrary point on the Bloch sphere.
We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achieved with a tunable coupling design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasistatic tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single-photon exchange in 6 ns. Qubit coherence times exceeding 20 μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon nonconserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80%.
We consider the quantum Rabi model as an open system that is subject to dissipation, dephasing, and sinusoidal qubit driving. One can change to an interaction picture where the qubit-driving term disappears at the expense of changing the free energy of the qubit which becomes time dependent. If the driving frequency is large with respect to the rest of the parameters with the exception of the driving strength, then one can obtain an effective Hamiltonian that accurately describes the dynamics of the system. The driving has two effects: the qubit-transition frequency is changed and the qubit has reduced dephasing. The driving strength can be chosen so that the qubit-transition frequency is reduced, made equal to zero, or even made negative so that the excited and ground states of the qubit are interchanged. Therefore, sinusoidal qubit driving offers another method to control the qubit-transition frequency and to reduce qubit dephasing. Adjusting the driving strength allows one to consider a qubit with degenerate energy levels. Not taking dissipation into account, the evolution operator of the qubit-harmonic oscillator system is given by a linear combination of the orthogonal projectors onto the eigenstates of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$ followed by the evolution operator of a forced harmonic oscillator, the harmonic oscillator can be prepared in such a way that it is always found in a Schr\"odinger cat state, and the transition probability of the qubit can exhibit a collapse-revival behavior. In addition, the Born-Markov-secular master equation is deduced and the effects of dissipation are presented. In particular, smaller ultrastrong-coupling values are preferable over larger ultrastrong-coupling values and deep strong-coupling values in order to have long-lived, easily distinguishable Schr\"odinger cat states because the decoherence rate is inversely proportional to the square of the coupling. Finally, the qubit-harmonic oscillator system can be prepared in highly entangled states that are stable under dissipation.
In this paper we discuss both analytically and numerically the rich quantum dynamics of the spin-boson model driven by a time-independent field of photon. Interestingly, we predict a new Rabi oscillation, whose period is inversely proportional to the driving amplitude. More surprisingly, some nonzero resonant peaks are found for some special values of the \emph{strong} driving regime. Moreover, for the different resonant positions, the peaks have different values. Thus, an important application of this resonance effect is to realize the precision measurement of the relative parameters in experiment. We also illustrate that this resonant effect arises from the interference of the nontrivial periodic phase factors induced by the evolution of the coherent states in two different subspaces. Our predictions may be, in principle, observed in the solid-state cavity quantum electrodynamics with the ultrastrong coupling if the driving magnitude of the photon field is sufficiently large.
A parametrically driven quantum oscillator, stabilized by a nonlinear dissipation, exhibits a spontaneous breaking of the parity symmetry. It results in the quantum bistability, corresponding to a Bloch sphere of dark states. This makes such a driven-dissipative system an attractive candidate for a qubit. The parity symmetry breaking is exact both on the classical level and within the quantum mechanical perturbation theory. Here, we show that nonperturbative quantum effects lead to the symmetry restoration and result in an exponentially small but finite qubit decoherence rate. Technically, the symmetry restoration is due to real-time instanton trajectories of the Keldysh path integral, which represents the Lindbladian evolution of the driven-dissipative oscillator.
We study the quantum dynamics of a single bosonic cavity subject to two-photon driving and two-photon dissipation in the presence of finite detuning. Exploiting a hidden time-reversal symmetry, the Wigner representation and the WKB method, we introduce an effective phase-space potential for description of the steady state. It reveals two attracting points, which are metastable due to quantum fluctuations. By employing the Keldysh real-time path integral formalism, we compute the instanton trajectory governing the quantum activation process between these attractors and establish a fundamental connection with the Wigner representation. This relation unifies the steady-state phase-space description with dynamical quantum activation processes. We also derive an analytical expression for the decoherence rate of the system. Our work provides a coherent theoretical framework for analyzing quantum bistability, metastability, and decoherence in driven-dissipative nonlinear resonators, with direct implications for the design of bosonic qubits and quantum information processing.
Recent progress on qubit manipulation allows application of periodic driving signals on qubits. In this study, a harmonic driving field is added to a Rabi dimer to engineer photon and qubit dynamics in a circuit quantum electrodynamics device. To model environmental effects, qubits in the Rabi dimer are coupled to a phonon bath with a sub-Ohmic spectral density. A nonperturbative treatment, the Dirac-Frenkel time-dependent variational principle together with the multiple Davydov D2 ansatz, is employed to explore the dynamical behavior of the tunable Rabi dimer. In the absence of the phonon bath, the amplitude damping of the photon number oscillation is greatly suppressed by the driving field, and photons can be created, thanks to the resonance between the periodic driving field and the photon frequency. In the presence of the phonon bath, one can still change the photon numbers in two resonators and indirectly alter the photon imbalance in the Rabi dimer by directly varying the driving signal in one qubit. It is shown that qubit states can be manipulated directly by the harmonic driving. The environment is found to strengthen the interqubit asymmetry induced by the external driving, opening up a new venue to engineer the qubit states.