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arXiv:2512.10921

Qubit decoherence in dissipative two-photon resonator: real-time instantons and Wigner function

V. Yu. Mylnikov, S. O. Potashin, Alex Kamenev

quant-phSubmitted Dec 11, 2025• Announced Dec 12, 2025• 0 citations
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Abstract

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.

Comments
10 pages, 4 figures

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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.
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We analytically investigate the switching rate in a two-photon driven Kerr oscillator with finite detuning and two-photon dissipation. This system exhibits quantum bistability and supports a logical manifold for a bosonic qubit. Using Kramer's theory together with the PPP-representation, we derive an analytical expression for the bit-flip error rate within the potential-barrier approximation. The agreement is demonstrated between analytical calculations and numerical simulations obtained by diagonalization of the Liouvillian superoperator. In the purely dissipative limit, the switching rate increases monotonically with detuning, as the two metastable states approach each other in phase space. However, the exponential contribution to the bit-flip rate exhibits a nontrivial dependence on system parameters, extending beyond the naive scaling with the average photon number. In the presence of large Kerr nonlinearity, the switching rate becomes a nonmonotonic function of the detuning and reaches a minimum at a finite detuning. This effect arises because detuning lowers the activation barrier for weak nonlinearity but increases it for large ones, ensuring a minimum of the switching-rate at nonzero detuning. These results establish key conditions for optimizing the performance of critical cat qubits and are directly relevant for the design of scalable superconducting bosonic quantum architectures.
We follow the passage from complex amplitude bistability to phase bistability in the driven dissipative Jaynes-Cummings oscillator. Quasi -distribution functions in the steady state are employed, for varying qubit-cavity detuning and drive parameters, in order to track a first-order dissipative quantum phase transition up to the critical point marking a second-order transition and spontaneous symmetry breaking. We demonstrate the photon blockade breakdown in the dispersive regime, and find that the coexistence of cavity states in the regime of quantum bistability is accompanied by pronounced qubit-cavity entanglement. Focusing on the effect of quantum-activated switching for both coupled degrees of freedom, we move from a region of minimal entanglement in the dispersive regime, where we derive analytical perturbative results, to the threshold behaviour of spontaneous dressed-state polarization at resonance.
Parametrically driven Kerr nonlinear quantum oscillator plays a central role in quantum optics, superconducting circuits, and in engineered light-matter interactions. For the development of future quantum technologies, it is crucial to understand the behavior of this quantum system under realistic dissipative conditions. The objective of this thesis is to investigate the phase-space dynamics of a dissipative Kerr nonlinear oscillator under different driving regimes and corresponding dissipation channels, with a particular focus on the emergence of nonclassical features in phase space. The aim is also to understand how nonlinearity and different driving mechanisms influence quantum properties such as coherence, nonclassicality, and phase-space structure. The analysis was carried out using the Wigner phase-space formalism and numerical simulations of the Lindblad master equation. The results show that in the case of finite nonlinearity the coherence time is prolonged compared to the harmonic case. In the single photon regime, the interplay between the photon drive and nonlinearity can lead to coherence revivals after which the system relaxes into a squeezed steady state. In the two photon and dissipation regime, the system exhibits parity-protected dynamics, leading to very long coherence times.
Metastability in many-body quantum systems and its associated exponentially-long timescales have been the subject of considerable recent interest. Here, we focus on a class of driven-dissipative many-body open quantum systems described by a Lindbladian having hidden time-reversal symmetry (a form of quantum detailed balance). Examples include boundary-driven interacting spin chains, bosonic lattice models and driven-dissipative collective spin models. We suggest that for such systems, slow timescales in the vicinity of a dissipative first-order phase transition can be analytically predicted using a special purification of the non-equilibrium steady state. We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay, and a driven-dissipative nonlinear cavity model. Our results allow quantitative insights into metastability and slow dynamics for a range of systems, including cases where semiclassical or path-integral instanton approaches are intractable.
We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical, and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical analysis, we find steady-state solutions with different photon occupations in two cavities. Such states can be considered analogs of the closed system double-well symmetry-breaking states. We analyze the occurrence and properties of these localized states in the system parameter space and examine how the symmetry-breaking states, in the form of a bistable pair, are associated with the single-cavity bistable behavior. In a full quantum calculation of the master equation dynamics that includes quantum fluctuations, the symmetry-breaking states and bistability disappear due to the quantum fluctuations. In the quantum trajectory picture, we observe enhanced quantum jumps and switching, which indicate the presence of the underlying semiclassical symmetry-breaking states. Finally, we present a set of analytical solutions for the steady-state correlation functions by using the complex PPP representation and discuss its regime of validity.