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arXiv:2408.00934 · Physical Review A

Impact of chaos on the excited-state quantum phase transition of the Kerr parametric oscillator

Ignacio García-Mata, Miguel A. Prado Reynoso, Rodrigo G. Cortiñas, Jorge Chávez-Carlos, Víctor S. Batista, Léa Ferreira dos Santos, Diego A. Wisniacki

Published Mar 4, 2025• 4 citations
arXivHTMLPDF

Abstract

The Kerr parametric oscillator is a key platform for superconducting-qubit-based quantum technologies. This work helps pave the way for the development of more robust and reliable quantum devices by identifying the safe parameter landscape to avoid chaos and the breakdown of the excited-state quantum phase transition (ESQPT), which is a key feature for state stabilization.

DOI
10.1103/physreva.111.l031502

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The Kerr parametric oscillator is a key platform for superconducting-qubit-based quantum technologies. This work helps pave the way for the development of more robust and reliable quantum devices by identifying the safe parameter landscape to avoid chaos and the breakdown of the excited-state quantum phase transition (ESQPT), which is a key feature for state stabilization.
Quantum Kerr parametric oscillators (KPOs) are systems out of equilibrium with a wide range of applications in quantum computing, quantum sensing, and fundamental research. They have been realized in superconducting circuits and photonic platforms. In this work, we explore the onset of ground-state and excited-state quantum phase transitions in KPOs, focusing on the role of the phase-space rotational symmetry when the driving frequency is $\ensuremath{\mu}$ times the oscillator's natural frequency, specifically for $\ensuremath{\mu}=1,2,3,4$. These cases are experimentally accessible in superconducting circuits, where the Floquet quasienergy spectrum can also be studied as a function of tunable control parameters. Using the classical Hamiltonian of the system, we identify the stationary points associated with quantum phase transitions and analyze the emergence of both real and avoided level crossings, examining their influence on the energy spectrum and tunneling dynamics. Our findings provide insights into the engineering of robust quantum states, quantum dynamics control, and onset of quantum phase transitions with implications for critical quantum sensing.
Excited-state quantum phase transitions (ESQPTs) generalize the concept of quantum phase transitions to excited levels. Here we investigate how such ESQPTs can emerge in Kerr nonlinear oscillators, where a bosonic mode with a Kerr nonlinearity is subject to both coherent (one-photon) and parametric (two-photon) driving. We determine the structure and properties of the complete phase diagram by defining proper dimensionless parameters. Rich phases and phase transitions exist in the phase diagram, including phases with two or four critical energies above the ground-state level and first-order quantum phase transitions. We characterize the ESQPTs by singularities in the density of states, which show universal logarithmic divergence or discontinuity at the critical energies. Furthermore, we find that observables such as the photon number also exhibit singular behaviors at the critical energies and obey scaling laws. These results may extend our understanding of the driven Kerr oscillator and ESQPTs in finite-component systems.
Quantum metrology and quantum sensing aim to use quantum properties to enhance measurement precision beyond what could be classically achieved. Here, we demonstrate how the analysis of the phase space structure of the classical limit of Kerr parametric oscillators can be used for determining control parameters values that lead to the squeezing of the uncertainty in position and the amplification of the quantum Fisher information. We also explore how quantum sensing can benefit from excited-state quantum phase transitions, even in the absence of a conventional quantum phase transition. The system that we consider models exciton-polariton condensates and superconducting circuits, making our study relevant for potential experimental applications.
Abstract Kerr parametric oscillators are potential building blocks for fault-tolerant quantum computers. They can stabilize Kerr-cat qubits, which offer advantages toward the encoding and manipulation of error-protected quantum information. The recent realization of Kerr-cat qubits made use of the nonlinearity of transmon superconducting circuits and a squeezing drive. Increasing nonlinearities can enable faster gate times, but, as shown here, can also induce chaos and melt the qubit away. We determine the region of validity of the Kerr-cat qubit and discuss how its disintegration could be experimentally detected. The danger zone for parametric quantum computation is also a potential playground for investigating quantum chaos with driven superconducting circuits.
We study the quantum quench dynamics in an extended version of the Dicke model where an additional parameter allows a smooth transition to the integrable Tavis-Cummings regime. We focus on the influence of various quantum phases and excited-state quantum phase transitions (ESQPTs) on the survival probability of the initial state. We show that, depending on the quench protocol, an ESQPT can either stabilize the initial state or, on the contrary, speed up its decay to the equilibrated regime. Quantum chaos smears out the manifestations of ESQPTs in quench dynamics, therefore significant effects can only be observed in integrable or weakly chaotic settings. Similar features are present also in the postquench dynamics of some observables.
A Kerr-nonlinear parametric oscillator (KPO) can generate a quantum superposition of two oscillating states, known as a Schr\"odinger cat state, via quantum adiabatic evolution and can be used as a qubit for gate-based quantum computing and quantum annealing. In this work, we investigate complex dynamics, i.e., chaos, in two coupled nondissipative KPOs at a few-photon level. After showing that a classical model for this system is nonintegrable and consequently exhibits chaotic behavior, we provide quantum counterparts for the classical results, which are quantum versions of the Poincar\'e surface of section and its lower-dimensional version defined with time integrals of the Wigner and Husimi functions and also the initial and long-term behavior of out-of-time-ordered correlators. We conclude that some of them can be regarded as quantum signatures of chaos, together with energy-level spacing statistics (conventional signature). Thus, the system of coupled KPOs is expected to offer not only an alternative approach to quantum computing but also a promising platform for the study on quantum chaos.