[Paper Review] Exceptional entanglement phenomena: non-Hermiticity meeting non-classicality

Pei‐Rong Han, Fan Wu+12 more|PubMed|Oct 10, 2022

Quantum Mechanics and Non-Hermitian Physics4 citations

TL;DR

This paper demonstrates that non-Hermitian (NH) quantum systems exhibit a unique class of entanglement phenomena—exceptional entanglement transitions—driven by exceptional points (EPs) in the eigenstates of dissipative, interacting qubit-photon systems. Using a circuit quantum electrodynamics setup with a superconducting qubit coupled to a decaying resonator, the authors experimentally map out singular entanglement behaviors in the NH eigenstates, revealing a purely quantum-mechanical signature absent in classical or Hermitian systems.

ABSTRACT

Non-Hermitian (NH) extension of quantum-mechanical Hamiltonians represents one of the most significant advancements in physics. During the past two decades, numerous captivating NH phenomena have been revealed and demonstrated, but all of which can appear in both quantum and classical systems. This leads to the fundamental question: what NH signature presents a radical departure from classical physics? The solution of this problem is indispensable for exploring genuine NH quantum mechanics, but remains experimentally untouched so far. Here, we resolve this basic issue by unveiling distinct exceptional entanglement phenomena, exemplified by an entanglement transition, occurring at the exceptional point of NH interacting quantum systems. We illustrate and demonstrate such purely quantum-mechanical NH effects with a naturally dissipative light-matter system, engineered in a circuit quantum electrodynamics architecture. Our results lay the foundation for studies of genuinely quantum-mechanical NH physics, signified by exceptional-point-enabled entanglement behaviors.

Motivation & Objective

• To identify a non-classical, genuinely quantum-mechanical signature of non-Hermitian physics that distinguishes it from classical NH phenomena.
• To resolve the fundamental question of what NH effect cannot be replicated in classical systems.
• To demonstrate that exceptional points (EPs) in interacting quantum systems induce entanglement transitions absent in both Hermitian and classical settings.
• To experimentally realize and characterize EP-induced entanglement dynamics in a naturally dissipative, circuit-QED-based quantum system.
• To establish that entanglement behaviors in NH eigenstates are universal for composite quantum systems in Markovian reservoirs, marking a new frontier in genuinely quantum non-Hermitian physics.

Proposed method

• Theoretical modeling of a qubit-resonator system governed by a non-Hermitian Hamiltonian with intrinsic decay rates for both qubit and photon modes.
• Use of the effective non-Hermitian Hamiltonian $\mathcal{H}_{\text{NH}} = \Omega(a^\dagger|g\rangle\langle e| + a|e\rangle\langle g|) - \frac{i}{2}\kappa_q|e\rangle\langle e| - \frac{i}{2}\kappa_f a^\dagger a$ to describe resonant light-matter interaction with energy dissipation.
• Engineering the system in a circuit quantum electrodynamics architecture where a superconducting qubit is coupled to a lossy resonator via ac flux modulation, enabling tunable photonic swapping at a sideband.
• Employing a density matrix post-casting method to extract weak nonclassical signals from strong noise backgrounds, enabling reconstruction of the post-selected two-qubit density matrix.
• Mapping the entanglement of the system's eigenstates via concurrence measurements, with experimental validation using state tomography and post-selection on measurement outcomes.
• Measuring the relative phase difference and spectral gap $\Delta E_1$ between the eigenstates $|\Phi_{1,\pm}\rangle$ to confirm the EP at $\eta = 1$, where the gap closes and entanglement peaks.

Experimental results

Research questions

• RQ1 What non-Hermitian signature in quantum systems is fundamentally distinct from classical physics and cannot be replicated in classical systems?
• RQ2 Can exceptional points (EPs) in non-Hermitian quantum systems induce entanglement transitions that are purely quantum and lack classical analogs?
• RQ3 How do entanglement properties of non-Hermitian eigenstates evolve across an exceptional point in a dissipative, interacting quantum system?
• RQ4 Can naturally occurring dissipation in a quantum system—without artificial reservoir engineering—give rise to observable, non-classical entanglement phenomena?
• RQ5 What is the role of the relative phase and spectral gap in identifying the EP and its associated entanglement transition in a qubit-resonator system?

Key findings

• The authors observe a sharp entanglement transition at the exceptional point (EP), where the concurrence of the eigenstates $|\Phi_{1,\pm}\rangle$ reaches a maximum, confirming the presence of a non-analytic behavior in the entanglement spectrum.
• At the EP ($\eta = 1$), the eigenstates become maximally entangled, forming the Bell state $|Y\rangle = (|g,1\rangle - i|e,0\rangle)/\sqrt{2}$, with a concurrence of 1.
• The derivative of the entanglement with respect to the rescaled coupling $\eta$ diverges at the EP, as shown by the insets in Figure 3, indicating a non-analytic transition in entanglement.
• The relative phase difference $\varphi = \varphi_+ - \varphi_-$ between the eigenstates changes abruptly across the EP, confirming the coalescence of eigenvectors.
• The spectral gap $\Delta E_1$ closes at the EP, with both real and imaginary parts vanishing, confirming the level crossing and non-adiabatic behavior.
• Experimental results for concurrence at $\eta = 5$ and $\eta = 0.5$ show excellent agreement with numerical simulations using the effective Hamiltonian, validating the theoretical model and measurement protocol.