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Observation of $\mathcal{PT}$-symmetry and exceptional point in ion trap

Weichen Wang, Pin-xing Chen

Published Jun 30, 2020• 0 citations
OpenAlex

Abstract

The theory of parity time $(\mathcal{PT})$ symmetry has been quite successful in classical system. And classical $\mathcal{PT}$-symmetric systems exhibited many interesting features. However, $\mathcal{PT}$-symmetric experiments of quantum systems are progressing more slowly than $\mathcal{PT}$-symmetric experiments of classical systems. Hence, we constructed a passive quantum $\mathcal{PT}$-symmetric system by using the internal states of $ ^{40}Ca^{+}$ ion. Comparing with other systems, the experimental setup of single ion trap is easy to implement, meanwhile our single ion trap is a real quantum system and has a long coherence time. In this paper, we show the phenomenon of $\mathcal{PT}$-symmetry-breaking transions by controlling the dissipation factor of states, which is achieved through adjusting the power of laser beam. Moreover, we also investigated the quantum phase transition near exceptional point (EP) of $\mathcal{PT}$-symmetric system. The experimental results enable ion trap to be a successful device for investigating quantum $\mathcal{PT}$-symmetry.

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Observation of PT\mathcal{PT}PT-symmetry and exceptional point in ion trap
The theory of parity time (PT)(\mathcal{PT})(PT) symmetry has been quite successful in classical system. And classical PT\mathcal{PT}PT-symmetric systems exhibited many interesting features. However, PT\mathcal{PT}PT-symmetric experiments of quantum systems are progressing more slowly than PT\mathcal{PT}PT-symmetric experiments of classical systems. Hence, we constructed a passive quantum PT\mathcal{PT}PT-symmetric system by using the internal states of 40Ca+ ^{40}Ca^{+}40Ca+ ion. Comparing with other systems, the experimental setup of single ion trap is easy to implement, meanwhile our single ion trap is a real quantum system and has a long coherence time. In this paper, we show the phenomenon of PT\mathcal{PT}PT-symmetry-breaking transions by controlling the dissipation factor of states, which is achieved through adjusting the power of laser beam. Moreover, we also investigated the quantum phase transition near exceptional point (EP) of PT\mathcal{PT}PT-symmetric system. The experimental results enable ion trap to be a successful device for investigating quantum PT\mathcal{PT}PT-symmetry.
Parity-time (PT\mathcal{PT}PT)-symmetric systems, featuring real eigenvalues despite their non-Hermitian nature, undergo spontaneous PT\mathcal{PT}PT symmetry breaking at the exceptional point (EP). The phase transition from PT\mathcal{PT}PT symmetry to PT\mathcal{PT}PT symmetry breaking has shown exotic functionalities in the classical realm, such as loss-induced transparency or lasing revival. This transition is also expected to produce a more unconventional effect in pure quantum PT\mathcal{PT}PT devices. Here, we report experimental evidences of spontaneous PT\mathcal{PT}PT symmetry breaking in a single cold 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion and, more importantly, a counterintuitive effect of perfect quantum coherence occurring at the EP. Excellent agreement between experimental results and theoretical predictions is identified. In view of the versatile role of cold ions in building a quantum memory or processor, our experiment provides an alternative platform to explore PT\mathcal{PT}PT-symmetric physics and utilize pure quantum EP effects.
Exceptional points (EPs) of a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry have the potential to drastically enhance the capabilities of metrology and sensing through their power-law growing sensitivity to external perturbation. With the ability of generating and tuning dissipation in a single trapped ion system, we observe rich dynamics and detailed quantum phase transitions from the PT-symmetric phase to the symmetry-breaking phase. In this single qubit full quantum system, we develop a method to precisely determine the location of EP without any fitting parameter, and extract the eigenvalues in a unified way through all parameter regions. We can also obtain the full density matrix by quantum state tomography. Finally, we suggest from theoretical analysis that the periodically driving PT-symmetric non-Hermitian system can be used to measure the magnitude, frequency, and phase of time-dependent perturbation with EP enhancement.
Hermiticity in quantum mechanics ensures the reality of energies, while parity-time symmetry offers an alternative route. Interestingly, in a three-level system, parity-time symmetry-breaking can lead to third-order exceptional points with distinctive topological properties. Experimentally implementing this in open quantum systems requires two well-controlled loss channels, resulting in dynamics that challenges a pure non-Hermitian description. Here we address the challenge by employing two approaches to eliminate the effects of quantum jump terms, ensuring pure non-Hermitian dynamics in a dissipative trapped ion. Based on this, we experimentally observe a parity-time symmetry-breaking-induced third-order exceptional point through non-Hermitian absorption spectroscopy. Quantum state tomography further demonstrates the coalescence of three eigenstates into a single eigenstate at the exceptional point. Finally, we identify an intrinsic third-order Liouvillian exceptional point via quench dynamics. Our experiments can be extended to observe other non-Hermitian phenomena involving multiple dissipative levels and potentially find applications in quantum information technology. Parity-time symmetry breaking and related non-Hermitian phenomena, such as high-order exceptional points, have attracted significant interest across various experimental platforms. Here the authors demonstrate a third-order exceptional point induced by parity-time symmetry breaking in a dissipative trapped ion.
Trapped ions are an ideal platform to implement quantum simulation. Previously, the parity-time (PT\mathcal{PT}PT)-reversal symmetry-breaking transition in the paradigmatic non-Hermitian Hamiltonian ${h}_{\mathcal{PT}}=J{\ensuremath{\sigma}}_{x}\ensuremath{-}i\mathrm{\ensuremath{\Gamma}}{\ensuremath{\sigma}}_{z}$ was observed in a single-ion experiment in a passive way. In this work we propose to study the interaction effects on the PT\mathcal{PT}PT-symmetry-breaking transition in a chain of NNN trapped interacting ions. We consider an effective Ising interaction ${H}_{\text{int}}^{\text{Ising}\phantom{\rule{4.pt}{0ex}}x}={\ensuremath{\sum}}_{j<k}{U}_{jk}{\ensuremath{\sigma}}_{x}^{j}{\ensuremath{\sigma}}_{x}^{k}$ between the ions on top of hPT{h}_{\mathcal{PT}}hPT​. We find that sufficiently strong interaction strength can enhance the PT\mathcal{PT}PT-symmetric phase for even NNN, while the phase is suppressed in all the other cases. In particular, the suppression can be so strong that even infinitesimal dissipation, quantified by $\mathrm{\ensuremath{\Gamma}}$, can turn the system into the PT\mathcal{PT}PT-symmetry-breaking phase. In addition, we assess the convolved effects due to the coupling and the spin phase shifts. Our findings can be readily tested in ion chain experiments.
Non-Hermitian systems satisfying parity-time (PT) symmetry have aroused considerable interest owing to their exotic features. Anti-PT symmetry is an important counterpart of the PT symmetry, and has been studied in various classical systems. Although a Hamiltonian with anti-PT symmetry only differs from its PT-symmetric counterpart in a global ±i phase, the information and energy exchange between systems and environment are different under them. It is also suggested theoretically that anti-PT symmetry is a useful concept in the context of quantum information storage with qubits coupled to a bosonic bath. So far, the observation of anti-PT symmetry in individual quantum systems remains elusive. Here, we implement an anti-PT-symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence. We characterize the anti-PTphase transition by mapping out the eigenvalues at different ratios between coupling strengths and dissipation rates. The full information of the quantum state is also obtained by quantum state tomography. Our work allows quantum simulation of genuine open-system feature of an anti-PT-symmetric system, which paves the way for utilizing non-Hermitian properties for quantum information processing.
Non-Hermitian systems with parity-time reversal (PT\mathcal{PT}PT) or anti-PT\mathcal{PT}PT symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. One of the most extraordinary features is the presence of an exceptional point, across which a phase transition with spontaneously broken PT\mathcal{PT}PT symmetry takes place. We implement a Floquet Hamiltonian of a single qubit with anti-PT\mathcal{PT}PT symmetry by periodically driving a dissipative quantum system of a single trapped ion. With stroboscopic emission and quantum state tomography, we obtain the time evolution of density matrix for an arbitrary initial state, and directly demonstrate information retrieval, eigenstate coalescence, and topological energy spectra as unique features of non-Hermitian systems.