C. Yuce, A. Kurt, A. Kucukaslan
$PT$ symmetric quantum mechanics for a particle trapped by the generalized non-Hermitian harmonic oscillator potential is studied. It is shown that energy and the expectation value of the position operator $x$ can not be real simultaneously, if the particle is trapped. Non-vanishing boundary conditions for the trapped particle in $PT$ symmetric theory are also discussed.
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We propose a method of manipulating selectively the symmetric Dicke subspace in the internal degrees of freedom of N trapped ions. We show that the direct access to ionic-motional subspaces, based on a suitable tuning of motion-dependent AC Stark shifts, induces a two-level dynamics involving previously selected ionic Dicke states. In this manner, it is possible to produce, sequentially and unitarily, ionic Dicke states with increasing excitation number. Moreover, we propose a probabilistic technique to produce directly any ionic Dicke state assuming suitable initial conditions.
We present a new and simplified two-qubit randomized benchmarking procedure that operates only in the symmetric subspace of a pair of qubits and is well suited for benchmarking trapped-ion systems. By performing benchmarking only in the symmetric subspace, we drastically reduce the experimental complexity, number of gates required, and run time. The protocol is demonstrated on trapped ions using collective single-qubit rotations and the Molmer-Sorenson (MS) interaction to estimate an entangling gate error of $2(1) \times 10^{-3}$. We analyze the expected errors in the MS gate and find that pop…
Quantum simulation of a general anti-PT-symmetric Hamiltonian with a trapped ion qubit
本研究针对单量子系统中反PT对称性难以观测的问题，利用囚禁离子通过微波与光脉冲序列实现单比特反PT对称哈密顿量，表征了相变并获取完整量子态，为非厄米特性用于量子信息处理铺路。
We propose a method for generating a spin-squeezed state that is a symmetric Dicke state, with trapped ions using only global access. The eigenstates of the ions under a strong dressing field become symmetric Dicke states and the M$ø$lmer--S$ø$rensen interaction selectively couples one of them to an initially populated auxiliary state. A $\mid D_{2n}^n>$ state, which is maximally spin squeezed, can be generated with high fidelity using only square pulses. Using an adiabatic technique, the ideal maximally spin-squeezed state is generated.
We propose the quantum simulation of a fermion and an antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add-up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Ultracold atoms provide clues to an important many-body problem regarding the dependence of Bose-Einstein condensation (BEC) transition temperature $T_c$ on interactions. However, cold atoms are trapped in harmonic potentials and theoretical evaluations of the $T_c$ shift of trapped interacting Bose gases are challenging. While previous predictions of the leading-order shift have been confirmed, more recent experiments exhibit higher-order corrections beyond available mean-field theories. By implementing two large-N based theories with the local density approximation (LDA), we extract next-ord…
Test of Causal Non-Linear Quantum Mechanics by Ramsey Interferometry on the Vibrational Mode of a Trapped Ion
针对因果非线性量子力学难以通过常规光谱学检验的问题，利用谐势阱中$^{40}$Ca$^+$离子振动模式的叠加态，通过Ramsey干涉测量对因果非线性扰动的无量纲标度因子设定了严格上限。
Quantum field theories describe a wide variety of fundamental phenomena in physics. However, their study often involves cumbersome numerical simulations. Quantum simulators, on the other hand, may outperform classical computational capacities due to their potential scalability. Here, we report an experimental realization of a quantum simulation of fermion-antifermion scattering mediated by bosonic modes, using a multilevel trapped ion, which is a simplified model of fermion scattering in both perturbative and nonperturbative quantum electrodynamics. The simulated model exhibits prototypical fe…
Spin-orbit coupling mediated photon-like resonance for a single atom trapped in a symmetric double well
本文通过周期调制拉曼激光强度，结合光子辅助隧穿与自旋轨道耦合，实现对称双阱中单原子的光子类共振，可诱导拉比振荡、抑制隧穿及自旋翻转，四能级模型解析结果与数值精确解高度吻合。
We present a feasible scheme to use trapped ions Cavity QED system to implement optimal $1\to N$ cloning machine of coherent state. In present scheme, as the ouput of the clone machine, the copies of the cavity mode emerge at the vibrational modes and cavity modes is acted as the ancilla mode in the implementation of the cloning. We further show that such system can be used to generated multimodes quantum state, which can realize optimum symmetric $1\to N$ telecloning of coherent state of distant cavity.
We introduce an approach to scattering problems in theories with non-Hermitian Hamiltonian, usually known as PT-symmetric quantum theories, by means of the adiabatic switching of the interaction. The modifications of usual methods needed to employ time-dependent metrics are described. We argue that an analogue of the adiabatic theorem hold for time dependent metrics and that its validity forms a necessary condition for consistency of the procedure.
Quantum state discrimination in a $\mathcal{PT}$-symmetric system of a single trapped ion
本文在单个囚禁钙离子中实验验证了$\mathcal{PT}$对称非厄米哈密顿量下任意两个非正交量子比特态可经时间演化变为正交态，实现确定性判别，并优化参数实现最快正交化，展示了非厄米物理在量子信息处理中的应用前景。
Experimental demonstration of enhanced violations of Leggett-Garg inequalities in a $\mathcal{PT}$-symmetric trapped-ion qubit
本研究在$\u001a$PT$\u001b$对称囚禁离子量子比特系统中实验验证了非厄米条件下Leggett-Garg不等式的违反增强效应，揭示了耗散对时间量子关联的调控作用，为利用耗散调控量子关联与纠缠提供了新路径。
A tapered optical nanofiber simultaneously used to trap and optically interface of cold atoms through evanescent fields constitutes a new and well controllable hybrid quantum system. The atoms are trapped in two parallel 1D optical lattices generated by suitable far blue and red detuned evanescent field modes very close to opposite sides of the nanofiber surface. Collective electronic excitations (excitons) of each of the optical lattices are resonantly coupled to the second lattice forming symmetric and antisymmetric common excitons. In contrast to the inverse cube dependence of the individua…
Gauge field theories play a central role in modern physics and are at the heart of the Standard Model of elementary particles and interactions. Despite significant progress in applying classical computational techniques to simulate gauge theories, it has remained a challenging task to compute the real-time dynamics of systems described by gauge theories. An exciting possibility that has been explored in recent years is the use of highly-controlled quantum systems to simulate, in an analog fashion, properties of a target system whose dynamics are difficult to compute. Engineered atom-laser inte…
For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this paper we investigate the relationship between the values of the sum/difference angular momentums for an atomic condensate inside a magnetic trap and the associated gauge potential induced by the adiabatic approximation. Our result provides significant new insight into the vo…
Evolution time of a qubit under a Hamiltonian operation is one of the key issues in quantum control, quantum information processing and quantum computing. It has a lower bound in Hermitian system, which is limited by the coupling between two states of the qubit, while it is proposed that in a non-Hermitian system it can be made much smaller without violating the time-energy uncertainty principle. Here we have experimentally confirmed the proposal in a single dissipative qubit system and demonstrate that the evolution time of a qubit from an initial state to an arbitrary state can be controlled…
Synthetic $\mathbb{Z}_2$ gauge theories based on parametric excitations of trapped ions
该研究提出利用囚禁离子内态与运动自由度的混合编码及参数激发，构建可模拟Z2规范理论的模拟量子方案，验证最小模型并推广到格点链，同时评估实验误差与规范动力学。
We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a renormalization method for the interparticle interactions. The procedure is benchmarked with state-of-the-art numerical results for three and four symmetric fermions.
Sample-Based Krylov Quantum Diagonalization for the Schwinger Model on Trapped-Ion and Superconducting Quantum Processors
基于样本的Krylov量子对角化方法用于研究带有θ项的Schwinger模型，通过混合量子-经典方法有效减少希尔伯特空间，展现其在格点规范理论模拟中的应用前景。
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing…
We analyze the efficiency of quantum simulations of fermionic and bosonic models in trapped ions. In particular, we study the optimal time of entangling gates and the required number of total elementary gates. Furthermore, we exemplify these estimations in the light of quantum simulations of quantum field theories, condensed-matter physics, and quantum chemistry. Finally, we show that trapped-ion technologies are a suitable platform for implementing quantum simulations involving interacting fermionic and bosonic modes, paving the way for overcoming classical computers in the near future.
We implement direct readout of the symmetric characteristic function of quantum states of the motional oscillation of a trapped calcium ion. Using suitably chosen internal electronic state-dependent displacements based on bi-chromatic laser fields we map the expectation value of the real or imaginary part of the displacement operator to the internal states, which are subsequently read out using fluorescence detection. Combining the two readout results provides full information about the symmetric characteristic function. We characterize the performance of the technique by applying it to a rang…
Measurement-based simulation of lattice gauge theory dynamics with adaptive quantum circuits on a trapped-ion processor
研究人员利用Quantinuum H2囚禁离子处理器，首次实验实现(2+1)维Z₂规范理论实时动力学的基于测量的量子模拟，验证该架构可在现有硬件上模拟格点场论。
We consider a generalized Dicke model with U(1) symmetry, which can undergo a transition to a superradiant state that spontaneously breaks this symmetry. By exploiting the difference in timescale between atomic and cavity dynamics, one may eliminate the cavity dynamics, providing an atom-only theory. We show that the standard Redfield theory cannot describe the transition to the superradiant state, but including higher-order corrections does recover the transition. Our work reveals how the forms of effective theories must vary for models with continuous symmetry, and provides a template to dev…
Onset of thermalization of q-deformed SU(2) Yang-Mills theory on a trapped-ion quantum computer
利用囚离子量子计算机模拟q-变形SU(2)杨-米尔斯理论的热化动力学，通过F移动实现非阿贝尔融合结构的模拟。
We describe recent progress in understanding the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. Focussing on a simple non-Hermitian theory composed of one complex scalar and one complex pseudoscalar, we revisit the derivation of Noether's theorem to show that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. We illustrate the impact that this has on the consistent formulation of (Abelian) gauge theories by studying a non-Hermitian extension of scalar quantum electrodynamics. We consi…
Phases of 2d Gauge Theories and Symmetric Mass Generation
研究二维阿贝尔规范理论的动力学和相结构，探讨质量变化下的复杂相图及手征规范理论的对称质量生成机制
Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog q…
We use the Higgs mechanism to investigate connections between higher-rank symmetric $U(1)$ gauge theories and gapped fracton phases. We define two classes of rank-2 symmetric $U(1)$ gauge theories: the $(m,n)$ scalar and vector charge theories, for integer $m$ and $n$, which respect the symmetry of the square (cubic) lattice in two (three) spatial dimensions. We further provide local lattice rotor models whose low energy dynamics are described by these theories. We then describe in detail the Higgs phases obtained when the $U(1)$ gauge symmetry is spontaneously broken to a discrete subgroup. A…
We theoretically study the quantum dynamics of transverse vibrations of a one-dimensional chain of trapped ions in harmonic potentials interacting via a Reggeon-type cubic nonlinearity that is nonunitary but preserves PT symmetry. We propose the notion of quantum fragility for the dissipative structural phase transition that spontaneously breaks the PT symmetry. In the quantum fragile regime, the nonlinearity dominates the response to mechanical perturbations and the chain supports neither the ordinary quantum phonons of a Luttinger liquid, nor the supersonic solitons that arise in classical f…
Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $γ_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the mass parameter this symmetry may be either broken or unbroken. When the $\cal PT$ symmetry is unbroken, the spectrum of the quantum field theory is real. For the $\cal PT$-symmetric version of the massive Thirring model in two-dimensional space-time, which is dual to the $\cal PT$-symmetric scalar Sine-Gordon model, an exact construction of the $\cal C$ operator is given…
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