Experimental demonstration of coherence flow in PT- and anti-PT-symmetric systems

Abstract

Non-Hermitian parity-time ($${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T ) and anti-parity-time ($${{{{{{{\mathcal{APT}}}}}}}}$$ APT )-symmetric systems exhibit novel quantum properties and have attracted increasing interest. Although many counterintuitive phenomena in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems were previously studied, coherence flow has been rarely investigated. Here, we experimentally demonstrate single-qubit coherence flow in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems using an optical setup. In the symmetry unbroken regime, we observe different periodic oscillations of coherence. Particularly, we observe two complete coherence backflows in one period in the $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T -symmetric system, while only one backflow in the $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric system. Moreover, in the symmetry broken regime, we observe the phenomenon of stable value of coherence flow. We derive the analytic proofs of these phenomena and show that most experimental data agree with theoretical results within one standard deviation. This work opens avenues for future study on the dynamics of coherence in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems.

Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor

“…8 where (a), (b) and (c) depict the dynamics of various types of quantum coherences in the unbroken phase and (d), (e) and (f) depict the dynamics of various types of quantum coherence in the broken phase. Similar patterns of coherence dynamics are observed as in the case of the optics setup [24]. Our results in Fig.…”

“…A single qubit coherence flow in PT-symmetric and anti-PT-symmetric systems was demonstrated experimentally using an optical setup and it was observed that coherence flow oscillates back and forth in the unbroken PT-symmetric and anti-PT-symmetric regimes while in broken phase, coherence flow attains a stable value in both PT-symmetric and anti-symmetric systems [24]. We investigated the dynamics of quantum coherence (total, local and global coherence) in the maximally entangled (Bell) state, when one qubit of the Bell state is acted upon by the PT-symmetric Hamiltonian at r = 0.6 (unbroken phase) and at r = 1.4 (broken phase).…”

“…Recently, it has been shown that quantum coherence is increased in a single-qubit system under PT-symmetric Hamiltonian and maximal quantum coherence is observed at the exceptional point [22,23]. The flow of quantum coherence of a single qubit under PT-symmetric and anti-PTsymmetric Hamiltonians has been demonstrated on an optics system [24].…”

Quantum simulation of a general anti-PT-symmetric Hamiltonian with a trapped ion qubit

“…Note that in the experiment, the constructed Hamiltonian is exactly (1), which is anti-PTsymmetric, there is no need to remove the iΓI term artificially as is done when simulating PT -symmetric systems [4][5][6]. Although H APT and H PT = ±iH APT have similar eigensystem structures, a recent work [25] suggests that they behave differently in the context of coherence flow between the system and environment. When taking the phonon degrees of freedom into account, evolutions under H APT might decohere more slowly than those under H PT , as studied in [27].…”

“…The information and energy exchange between anti-PT -symmetric systems and environment are different from the PT -symmetric counterpart. These result in different information-exchange scheme, e.g., coherence flow [25], between anti-PTsymmetric systems and the PT -symmetric counterpart. Interestingly, recent theoretical works [26,27] studied the evolution of qubits under H APT when coupled to a bosonic bath, and claim that these qubits decohere more slowly compared to those under Hermitian or PTsymmetric Hamiltonians.…”