Quantum Leap Unlocks New Control over Light-Based Computing Components

Researchers are increasingly investigating exceptional points within non-Hermitian quantum systems to uncover novel quantum phenomena. Pei-Rong Han from Longyan University, Tian-Le Yang and Wen Ning from Fuzhou University, et al., demonstrate a previously unobserved quantum phase transition driven by Liouvillian exceptional points within a driven-dissipative Kerr-cat qubit. This work is significant because it extends the understanding of exceptional-point-induced transitions to continuous-variable systems and reveals a shift from underdamped oscillations to overdamped relaxations at the exceptional point, evidenced by Wigner functions and Bloch sphere trajectories. The negativity of the Wigner function confirms genuine quantum coherence, and a newly defined phase difference parameter quantifies this transition, establishing the Kerr-cat qubit as a promising platform for exploring dissipative quantum criticality and non-Hermitian physics.

This work details the construction and investigation of a Liouvillian exceptional structure, revealing a critical point where quantum behaviour shifts dramatically from sustained oscillations to rapid decay.

Numerical simulations, visualised through Wigner functions and Bloch sphere trajectories, demonstrate this transition occurring at a Liouvillian exceptional point. The negativity of the Wigner function serves as a definitive indicator of genuine quantum coherence, a characteristic absent in conventional non-Hermitian systems.
Researchers introduced a novel parameter, the phase difference between off-diagonal elements of the Liouvillian eigenmatrices, to precisely quantify this transition. The study centres on a single driven-dissipative Kerr-cat qubit, leveraging parity-symmetric cat states to encode quantum information. This encoding utilizes the naturally noise-biased qubit subspace arising from the degenerate eigenstates of a Kerr-nonlinear resonator under two-photon driving.

By manipulating the detuning between the drive frequency and the resonator frequency, the team observed a distinct change in dynamical behaviour near the exceptional point. Specifically, the system undergoes a phase transition characterised by a shift from underdamped oscillations, where energy gradually dissipates, to overdamped relaxations, where oscillations are immediately suppressed.

At the critical point, critical damping occurs, resulting in the fastest possible convergence to a stable state. The Liouvillian superoperator, incorporating both coherent rotations and quantum jumps induced by single-photon loss, governs the system’s dynamics. This dissipation channel acts as a bidirectional quantum jump between parity states, analogous to a sigma-x operator in a standard qubit.

This research establishes the Kerr-cat qubit as a promising setting for investigating dissipative quantum criticality and the intrinsic properties of non-Hermitian systems. The findings build upon recent advances extending explorations of exceptional-point-induced quantum phase transitions from discrete-variable to continuous-variable quantum systems, while addressing a gap in understanding LEPs within continuous-variable platforms. The work’s implications extend to the broader field of quantum information processing, potentially enabling the development of robust and coherent quantum technologies.

Liouvillian exceptional points and quantum coherence in a driven-dissipative Kerr-oscillator reveal novel sensitivity properties

A driven-dissipative Kerr- oscillator served as the central platform for investigating Liouvillian exceptional points (LEPs) and associated quantum phase transitions. Numerical simulations were performed to model the system’s dynamics, focusing on the behaviour around the LEP. The Kerr- oscillator was subjected to continuous driving and dissipation, creating a non-Hermitian system where exceptional points could emerge.

Wigner functions and Bloch sphere trajectories were employed to visualise the dynamical behaviour of the system, revealing a transition from underdamped oscillations to overdamped relaxations at the LEP. The negativity of the Wigner function was specifically used as a direct indicator of genuine quantum coherence, a feature unattainable in conventional non-Hermitian systems.

This measurement confirms the non-classical nature of the observed phenomena and distinguishes it from purely classical behaviour. To quantify the phase transition, researchers introduced the phase difference between the off-diagonal elements of the Liouvillian eigenmatrices as a novel parameter. This parameter provided a sensitive measure of the system’s state as it traversed the LEP, allowing for precise characterisation of the transition.

The study leveraged the Kerr- oscillator to establish a novel continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics. By carefully controlling the driving and dissipation parameters, the researchers were able to engineer a system exhibiting LEPs and observe the associated quantum phase transition. This approach offers a promising avenue for investigating fundamental aspects of non-Hermitian quantum mechanics and developing new quantum technologies.

Liouvillian exceptional points define a quantum phase transition in a driven-dissipative Kerr-cat qubit system

A sudden change in dynamical behaviour from underdamped oscillations to overdamped relaxations was revealed through numerical simulations of a driven-dissipative Kerr-cat qubit. The research establishes a Liouvillian exceptional structure, demonstrating a quantum phase transition occurring at the Liouvillian exceptional point.

Wigner functions and Bloch sphere trajectories visually confirmed this transition, highlighting a shift in system dynamics as the detuning parameter varied. Notably, the negativity of the Wigner function served as a direct signature of genuine quantum coherence, a characteristic unattainable in conventional single-qubit non-Hermitian systems.

This negativity confirms the non-classical nature of the observed quantum behaviour. Furthermore, a novel parameter, the phase difference between the off-diagonal elements of the Liouvillian eigenmatrices, was introduced to quantify the observed transition. This parameter provides a precise measure of the system’s evolution through the phase transition.

The study focused on a Kerr-nonlinear resonator with a two-photon driving, where the Hamiltonian includes a detuning term ∆, a Kerr coefficient K, and a driving amplitude P. Simulations were conducted assuming a Kerr coefficient and driving amplitude were positive and real, resulting in a real value for α.

Single-photon loss at a rate κ and pure dephasing at a rate κφ were incorporated into the Lindblad master equation governing the system’s dynamics. Specifically, the system exhibited critical damping at the Liouvillian exceptional point, leading to the fastest convergence to the steady state. For detunings greater than ∆LEP2, damped oscillations with exponential envelopes were observed in the time evolution of ⟨X⟩ and ⟨Y⟩.

Conversely, when detunings were less than ∆LEP2, the system became overdamped, exhibiting no oscillation. These results establish the Kerr-cat qubit as a novel continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics.

Liouvillian exceptional points define a dissipative quantum phase transition in Kerr-cat qubits characterized by non-Hermitian dynamics

Researchers have demonstrated a quantum phase transition within a driven-dissipative Kerr-cat qubit, induced by a Liouvillian exceptional point. Numerical simulations reveal a shift in dynamical behaviour from underdamped oscillations to overdamped relaxations at this exceptional point, a change readily visualised using Wigner functions and Bloch sphere trajectories.

The negativity of the Wigner function confirms the presence of genuine quantum coherence, a property not found in standard non-Hermitian systems. This work introduces a novel parameter, the phase difference between off-diagonal elements of the Liouvillian eigenmatrices, to quantify the observed transition.

The findings establish the Kerr-cat qubit as a promising continuous-variable platform for investigating dissipative quantum criticality and the intrinsic physics of non-Hermitian systems, potentially bridging bosonic encoding with the study of open quantum phase transitions. The authors acknowledge that minor deviations in fidelity arise from a detuning term not fully accounted for in the Liouvillian approximation, which can cause leakage from the encoded subspace. Future research may focus on mitigating these effects and further exploring the potential of this system for fault-tolerant quantum computation and the investigation of more complex non-Hermitian phenomena.