Abstract We experimentally study quantum Zeno effects in a parity-time (PT) symmetric cold atom gas periodically coupled to a reservoir. Based on the state-of-the-art control of inter-site couplings of atoms in a momentum lattice, we implement a synthetic two-level system with passive PT symmetry over two lattice sites, where an effective dissipation is introduced through repeated couplings to the rest of the lattice. Quantum Zeno (anti-Zeno) effects manifest in our experiment as the overall dissipation of the two-level system becoming suppressed (enhanced) with increasing coupling intensity or frequency. We demonstrate that quantum Zeno regimes exist in the broken PT symmetry phase, and are bounded by exceptional points separating the PT symmetric and PT broken phases, as well as by a discrete set of critical coupling frequencies. Our experiment establishes the connection between PT-symmetry-breaking transitions and quantum Zeno effects, and is extendable to higher dimensions or to interacting regimes, thanks to the flexible control with atoms in a momentum lattice.
The decay of an unstable quantum state can be inhibited or enhanced by tailored measurements, known as quantum Zeno effect (QZE) or anti Zeno effect (QAZE). QZE(QAZE) has been intensively explored in terms of the cases of various system-environment couplings, where the time evolution can be affected either by the projective measurements, or through the dissipative couplings to the environment. A general relation between QZE(QAZE) and the dissipation, for arbitrary dissipation strength and periodicity, is yet to be developed. In this paper, we show a framework to unify the QZE(QAZE) and the parity-time (
PT) symmetry breaking transition, where the pure dissipative Hamiltonian is mapped onto a
PT symmetric non-Hermitian Hamiltonian. This method uses the
PT symmetry transitions to distinguish QZE and QAZE, and can be applied to analyze the crossover behavior between these two effects. Using a heuristic example of a two-level system which is coupled to environment by periodical dissipation, we show the relation diagram between the QZE(QAZE) and the
PT symmetry breaking transition, in which the QZE appears at an exceptional point that separates the
PT symmetric (PTS) phase and the
PT symmetry broken (PTSB) phase, and ends at the resonance point of the maximum
PT symmetry breaking; after that, QAZE exists at the rest of the PTSB phase and remains in the next PTS phase. This interesting finding reveals a hidden relation between the QZE--QAZE and PTS-PTSB phases in a non-Hermitian quantum system.
The interplay between the nonclassical features and the parity-time (
PT) symmetry (or its breaking) is studied here by considering a
PT-symmetric system consisting of two cavities with gain and loss. The conditions for
PT invariance are obtained for this system. The behavior of the average photon number corresponding to the gain and loss modes for different initial states (e.g., vacuum, NOON, coherent, and thermal states) has also been obtained. With the help of the number operators, quantum Zeno and anti-Zeno effects are studied, and the observed behavior is compared in
PT-symmetric (PTS) and
PT-symmetry-broken (PTSB) regimes. It has been observed that the relative phase of the input coherent fields plays a key role in the occurrence of these effects. Further, some nonclassicality features are witnessed using criteria based on the number operator(s). Specifically, intermodal antibunching, sum, and difference squeezing are investigated for specific input states. It is found that the various nonclassical features, including the observed quantum Zeno and anti-Zeno effects, are suppressed when one goes from the PTS to PTSB regime. In other words, the dominance of the loss or gain rate in the field modes over the coupling strength between them diminishes the nonclassical features of the system.
Non-Hermitian systems having parity-time (
PT) symmetry can undergo a transition, spontaneously breaking the symmetry. Ultracold atomic gases provide an ideal platform to study interaction effects on the transition. We consider a model system of
N bosons of two components confined in a tight trap. Radio-frequency and laser fields are coupled to the bosons such that the single-particle Non-Hermitian Hamiltonian ${h}_{\mathcal{P}T}=\ensuremath{-}i\mathrm{\ensuremath{\Gamma}}{\ensuremath{\sigma}}_{z}+J{\ensuremath{\sigma}}_{x}$, which has
PT symmetry, can be simulated in a passive way, namely, in the physical system there is only incurred atom loss but no gain. We show that when interatomic interactions are tuned to maintain the symmetry, the
PT-symmetry-breaking transition is affected only by the SU(2) variant part of the interatomic interactions. We find that the transition point ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{tr}}$ decreases as the strength of this interaction part or
N increases; in the strong strength limit for this interaction part, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{tr}}$ scales as the strength to the power of $\ensuremath{-}(N\ensuremath{-}1)$. We also give signatures of the
PT-symmetric and the symmetry-breaking phases for the interacting bosons in experiment.
The effect of \mathcal{PT} 𝒫 𝒯 -symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. However, it is still an unsolved problem how to generalize the concept of \mathcal{PT} 𝒫 𝒯 symmetry to the quantum domain, where the conventional definition in terms of non-Hermitian Hamiltonians is not applicable. Here we introduce a symmetry relation for Liouville operators that describe the dissipative evolution of arbitrary open quantum systems. Specifically, we show that the invariance of the Liouvillian under this symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected \mathcal{PT} 𝒫 𝒯 -symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe \mathcal{PT} 𝒫 𝒯 -symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.
We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a Hermitian Fermi gas. The fermionic Green's function decays in a power law fashion for large distances, as expected from gapless excitations, although the exponent is reduced from -1 due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-Hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT symmetry, respectively. Our results challenge the concept of universality in non-Hermitian systems, where quantum criticality can be masked due to non-Hermiticity.