Distinct non-Hermitian dynamics has demonstrated its advantages in improving measurement precision over traditional sensing protocols. Multi-mode non-Hermitian lattice dynamics can provide exponentially-enhanced quantum sensing where the quantum Fisher information (QFI) per photon increases exponentially with the lattice size. However, somewhat surprisingly, it was also shown that the quintessential non-Hermitian skin effect does not provide any true advantage. In this paper, we demonstrate the importance of optimizing the phase of the coherent drive, and the position of the injection and detection in multi-mode non-Hermitian quantum sensing. The QFI per photon can be exponentially-enhanced or exponentially-reduced depending on parameters of the drive and detection. Specifically, it is demonstrated that for large amplification by choosing appropriate coherent drive parameters, the non-Hermitian skin effect can provide exponentially-enhanced quantum sensing. Moreover, in the regime beyond linear response, skin-effect can also provide a dramatic advantage as compared to the local perturbation, and the proposed protocol is robust in tuning the amplification factor.
We study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the so-called non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a $\mathbb{Z}_2$ symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effec…
In the Hermitian regime, a Berry phase is always the real number. It may be imaginary for a non-Hermitian system, which leads to amplitude amplification or attenuation of an evolved quantum state. We study the dynamics of the non-Hermitian Rice-Mele model driven by a time-dependent external field. The exact results show that it can have full real spectrum for any value of the field. Several rigorous results are presented for the Berry phase with respect to the varying field. We show that the Berry phase is the same complex constant for any initial state in a single sub-band. Numerical simulati…
We study the quantum phase transition (QPT) in a non-Hermitian Tavis-Cummings (TC) model of experimentally accessible parameters, which is engineered with two drive fields applied to an ensemble of two-level systems (TLSs) and a cavity, respectively. When the two drive fields satisfy a given parameter-matching condition, the coupled cavity-TLS ensemble system can be described by an effective standard TC Hamiltonian in the rotating frame. In this ideal Hermitian case, the engineered TC model can exhibit the super-radiant QPT with spin conservation at an experimentally accessible critical coupli…
One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phases to non-Hermitian systems, a finite system in a non-trivial topological phase displays surface states with exponentially long life times. In this work we explore the possibility of exploiting such non-Hermitian topological phases to enhance the quantum coherence of a fiducial qubit embedded in a dissipative environment. We first show that a network of qubits interacting with lossy cavities can be represented, in a suitable super-one-par…
A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in non-Hermitian PT-symmetric Ising model, which is driven by a staggered complex transverse field. Exact solution shows that the Laplacian of the groundstate energy density, with respect to real and imaginary components of the transverse field, diverges on the boundary in the complex plane. The phase diagram indicate that the imaginary transverse field has the effect of shrinkin…
We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time-dependent transformation operator has to be $PT$ symmetric and non-unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of non-Hermitian Hamiltonian. We obtain analytically the wave functions and associated non-adiabatic Berry phase $γ_{n}$ for the $n$th eigenstate. The classical version of the non-Hermiti…
We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schrödinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a scheme to construct the non-Hermitian invariant with a $PT$-symmetric but non-unitary transformation operator. The eigenstates of invariant and its complex conjugate form a bi-orthogonal basis to formulate the exact solution. We obtain the non-adiabatic Berry phase, which reduces to the adia…
Physics and computation: An insight from non-Hermitian quantum computing
College of Science, Liaoning Petrochemical University（辽宁石油化工大学理学院）；Liaoning Provincial Key Laboratory of Novel Micro-Nano Functional Materials（辽宁省新型微纳功能材料重点实验室）；International Center for Quantum Materials, Peking University（北京大学量子材料中心）；Wilczek Quantum Center, Shanghai Institute for Advanced Studies（上海高等研究院斐兹克量子中心）；Hefei National Laboratory（合肥国家实验室）
We study the quantum dynamics of a non-interacting spin ensemble under the effect of a reservoir by applying the framework of the non-Hermitian Hamiltonian operators. Theoretically, the two-level model describes the quantum spin system and the Bloch vector to establish the dynamical evolution. Experimentally, phosphorous ($^{31}$P) nuclei with spin $I=1/2$ are used to represent the two-level system and the magnetization evolution is measured and used to compare with the theoretical prediction. At room temperature, the composite dynamics of the radio-frequency pulse plus field inhomogeneities (…
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the sy…
Non-Hermitian skin effect induced by spatial noncommutativity
Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院先进量子研究中心）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）
The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet operator may become all real. This possibility can emerge for a continuous range of system parameters with subtle domain boundaries. It is further shown that the issue of stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of lattice Hamiltonians. As an application, we show how to use the stability of driven …
The hybrid tensor network approach allows us to perform calculations on systems larger than the scale of a quantum computer. However, when calculating transition amplitudes, there is a problem that the number of terms to be measured increases exponentially with that of contracted operators. The problem is caused by the fact that the contracted operators are represented as non-Hermitian operators. In this study, we propose a method for the hybrid tensor network calculation that contracts non-Hermitian operators without the exponential increase of the number of terms. In the proposed method, cal…
Non-Hermitian dynamics has been widely studied to enhance the precision of quantum sensing; and non-reciprocity can be a powerful resource for non-Hermitian quantum sensing, as non-reciprocity allows to arbitrarily exceed the fundamental bound on the measurement rate of any reciprocal sensors. Here we establish fundamental limits on signal-to-noise ratio for reciprocal and non-reciprocal non-Hermitian quantum sensing. In particular, for two-mode linear systems with two coherent drives, an approximately attainable uniform bound on the best possible measurement rate per photon is derived for bot…
Stabilizing correlated pair tunneling of spin-orbit-coupled bosons in a non-Hermitian driven double well
Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, and Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, School of Physics and Electronics, Hunan Normal University（湖南师范大学物理与电子学院）；School of Physics and Electronic Information Engineering, Ningxia Normal University（宁夏师范大学物理与电子信息工程学院）
We introduce and study a novel class of sensors whose sensitivity grows exponentially with the size of the device. Remarkably, this drastic enhancement does not rely on any fine-tuning, but is found to be a stable phenomenon immune to local perturbations. Specifically, the physical mechanism behind this striking phenomenon is intimately connected to the anomalous sensitivity to boundary conditions observed in non-Hermitian topological systems. We outline concrete platforms for the practical implementation of these non-Hermitian topological sensors (NTOS) ranging from classical meta-materials t…
Environment-assisted squeezing in a coherently driven non-Hermitian degenerate parametric oscillator
Adama Science and Technology University（阿达马科学与技术大学）；Khalifa University of Science and Technology（哈利法科学技术大学）；Durban University of Technology（德班理工大学）；Arba Minch University（阿尔巴明奇大学）
We study the dynamical behavior of a non-Hermitian moire superlattice system, which consists of two-coupled SSH chains with staggered imaginary on-site potentials. There are two main spatial regions, in which systems are in unbroken symmetric phases with fully real spectrum, appearing periodically along the ladder. We show that the two quantum phases are dimerized and tetramerized, which determine the distinct dynamical behaviors. Dirac probability can oscillate periodically, increase quadratically and increase exponentially, which correspond to the unbroken phase, exceptional point and the br…
The non-Hermitian skin effect (NHSE) is a phenomenon whereby certain non-Hermitian lattice Hamiltonians, particularly those with nonreciprocal couplings, can host an extensive number of eigenmodes condensed to the boundary, called skin modes. Although the NHSE has mostly been studied in the classical regime, we show that it can also manifest in quantum systems containing boson number nonconserving processes arising from uniform parametric driving. We study lattices of coupled nonlinear resonators that can function as reciprocal quantum amplifiers. A one-dimensional chain exhibiting NHSE can pe…
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency sp…
Exceptional point (EP) is exclusive for non-Hermitian system and distinct from that at a degeneracy point (DP), supporting intriguing dynamics, which can be utilized to probe quantum phase transition and prepare eigenstates in a Hermitian many-body system. In this work, we investigate the transition from DP for a Hermitian system to EP driven by non-Hermitian terms. We present a theorem on the existence of transition between DP and EP for a general system. The obtained EP is robust to the strength of non-Hermitian terms. We illustrate the theorem by an exactly solvable quasi-one-dimensional mo…
We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment.
Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on Berry's transitionless driving algorithm or on dynamical invariants. We work out the basic theory and examples described by two-level Hamiltonians: the acceleration of rapid adiabatic passage with a decaying excited level and of the dynamics of a classical particle on an expanding harmonic oscillator.
Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric systems, in which the exceptional points are driven through at finite speed which are quadratic or cubic functions of time. We identity different transmission dynamics separated by exceptional points, and derive analytical approximate formula…
This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established Hermitian and non-Hermitian critical scenarios where spectrum remains continuous across a transition. Such critical behavior, dubbed the "critical skin effect", is rather generic, occuring whenever subsystems with dissimilar non-Hermitian skin localization lengths are coupled, however weakly. Due to the existence of this criticality, the thermodynamic limit and the zero-coupling limit canno…
Quantum phase transitions are intriguing and fundamental cooperative phenomena in physics. Analyzing a superconducting nanowire with spin-dependent non-Hermitian hopping, we discover a topological quantum phase transition driven by infinitesimal cascade instability. The anomalous phase transition is complementary to the universal non-Bloch wave behavior of non-Hermitian systems. We show that an infinite small magnetic field drastically suppresses the non-Hermitian skin effect, inducing a topological phase with Majorana boundary states. Furthermore, by identifying the bulk topological invariant…
Informational Mpemba Effect for Fast State Purification in Non-Hermitian System
Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；Department of Physics, National Central University（国立中央大学物理系）；Department of Physics, National Taiwan Normal University（国立台湾师范大学物理系）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
Here we present an strategy for the derivation of a time-dependent Dyson map which ensures simultaneously the unitarity of the time evolution and the observability of a quasi-Hermitian Hamiltonian. The time-dependent Dyson map is derived through a constructed Schrödinger-like equation governed by the non-Hermitian Hamiltonian itself; despite its time-dependence our scheme ensures the time-independence of the metric operator, a necessary condition for the observability of the quasi-Hermitian Hamiltonian. As an illustrative example we consider a driven Harmonic oscillator described by a time-dep…
We study the behavior of the out-of-time-ordered correlator (OTOC) in a non-Hermitian quantum Ising system. We show that the OTOC can diagnose not only the ground state exceptional point, which hosts the Yang-Lee edge singularity, but also the \textit{dynamical} exceptional point at the excited state. We find that the evolution of the OTOC in the parity-time symmetric phase can be divided into two stages: in the short-time stage, the OTOC oscillates periodically, and when the parameter is near the ground state exceptional point, this oscillation behavior can be described by both the scaling th…
We propose a scheme to generate a persistent current in driven-dissipative systems which can be described by the generalized Gross-Pitaevskii (GP) equation. Our proposal consists of fabricating a rachet-potential shape of the loss-rate profile, which simultaneously breaks the time-reversal and parity-inversion symmetry. Unlike existing schemes to generate a current using a rachet potential in Hermitian systems, no dynamic drive is needed. The basic physics of our scheme is discussed by a simple discrete driven-dissipative GP model, and the results are also verified by a realistic continuous mo…
