non-Hermitian Quantum Systems Research Articles

Enhancement of vibrationally assisted energy transfer by proximity to exceptional points, probed by fluorescence-detected vibrational spectroscopy

Emulation of energy transfer processes in natural systems on quantum platforms can further our understanding of complex dynamics in nature. One notable example is the demonstration of vibrationally assisted energy transfer (VAET) on a trapped-ion quantum emulator, which offers insights for the energetics of light harvesting. In this work, we expand the study of VAET simulation with trapped ions to a non-Hermitian quantum system comprising a PT-symmetric chromophore dimer weakly coupled to a vibrational mode. We first characterize exceptional points (EPs) and non-Hermitian features of the excitation energy transfer processes in the absence of the vibration, finding a degenerate pair of second-order EPs. Exploring the non-Hermitian dynamics of the whole system including vibrations, we find that energy transfer accompanied by absorption of phonons from a vibrational mode can be significantly enhanced near such a degenerate EP. Our calculations reveal a unique spectral feature accompanying the coalescing of eigenstates and eigenenergies that provides a unique approach to probe the degenerate EP by fluorescence-detected vibrational spectroscopy. Enhancement of the VAET process near the EP is found to be due to maximal favorability of phonon absorption at the degenerate EP, enabling multiple simultaneous excitations. Our work on improving VAET processes in non-Hermitian quantum systems paves the way for leveraging non-Hermiticity in quantum dynamics related to excitation energy transfer. Published by the American Physical Society 2024

Thin film sensing near exceptional point utilizing terahertz plasmonic metasurfaces

Non-Hermitian quantum systems along with engineered metasurfaces enable a versatile podium for sensor designs from industrial to medical sectors. The singularity points known as exceptional points (EPs) can be realized in such non-Hermitian systems. EP demonstrates a square root topology on minute perturbations, hence promising to be a potential candidate to sense external parameters, such as temperature, thermal fluctuations, refractive index, and biomolecules. Hence, in this work, through numerical and analytical investigations, we explore the sensing capabilities in the vicinity of EP utilizing suitably designed terahertz metasurfaces. Here, we propose a non-Hermitian metasystem comprising two orthogonally twisted square split ring resonators coupled by near-field Electromagnetic interactions that can exhibit dark-bright modes. In such a system, the presence of an active (photo-doped) material in the split gap of one of the resonators opens up an effective avenue to introduce controllable asymmetric losses, ultimately leading to the emergence of EPs in the polarization space. Hence, thin film sensing at the proximity of the emerged EP is investigated for different refractive indices by coating with an overlayer atop the metasurface. In such a configuration, the sensitivities of the eigenstates are calculated in terms of the refractive index unit, which turns out to be −0.044 THz RIU−1 and −0.063 THz RIU−1 when the system is perturbed near EP. Our proposed metasurface-inspired EP-based sensing strategy can open up novel ways to sense the refractive index of unknown materials besides other physical parameters.

Experimental Investigation of Lee–Yang Criticality Using Non-Hermitian Quantum System

Lee–Yang theory clearly demonstrates where the phase transition of many-body systems occurs and the asymptotic behavior near the phase transition using the partition function under complex parameters. The complex parameters make the direct investigation of Lee–Yang theory in practical systems challenging. Here we construct a non-Hermitian quantum system that can correspond to the one-dimensional Ising model with imaginary parameters through the equality of partition functions. By adjusting the non-Hermitian parameter, we successfully obtain the partition function under different imaginary magnetic fields and observe the Lee–Yang zeros. We also observe the critical behavior of free energy in vicinity of Lee–Yang zero that is consistent with theoretical prediction. Our work provides a protocol to study Lee–Yang zeros of the one-dimensional Ising model using a single-qubit non-Hermitian system.

Dynamics of 2 × 2 matrix non-Hermitian quantum systems on Bloch sphere

By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely, the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken PT non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point (EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.

Entanglement dynamics of two non-Hermitian qubits

The evolution of entanglement in a non-Hermitian quantum system may behave differently compared to its Hermitian counterpart. In this paper, we investigate the entanglement dynamics of two coupled and driven non-Hermitian qubits. Through calculating the concurrence of the system, we find that the evolution of the bipartite entanglement manifests two distinct patterns in the parameter space. In the low non-Hermiticity regime, the concurrence oscillates significantly, while in the opposite regime the same quantity would trend to a stable value. We attribute this phenomenon to parity-time ( PT ) symmetry phase transition. We also study the effect of decoherence on the entanglement dynamics. Our work provides a method to stabilize entanglement by exploiting non-Hermiticity.

Complex semiclassical theory for non-Hermitian quantum systems

Complex semiclassical theory for non-Hermitian quantum systems

Generalised quantum speed limit for arbitrary time-continuous evolution

The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e. the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.

Nontrivial worldline winding in non-Hermitian quantum systems

Nontrivial worldline winding in non-Hermitian quantum systems

Role of losses and coupling in bright-dark metasurfaces mimicking non-Hermitian parity-time symmetric systems

All real systems are essentially non-conservative in nature, which is non-Hermitian in the fundamental premises of the quantum realm. Such open systems obeying parity-time (PT) symmetry can offer intriguing physics, which has sparked much attention in recent years. The thoughtful interplay of loss and gain in PT-symmetric systems can tune the eigenstates from real to complex space passing through a singular point known as an exceptional point (EP) with concurrently coalescing the discrete eigenstates. In this regard, artificially engineered near-field coupled metasurfaces provide a remarkable podium to introduce as well as control loss and coupling strength simultaneously, manifesting a practical channel to attain EP. Motivated by this notion, we have theoretically explored near-field coupled dark-bright-mode assisted terahertz metasurfaces imitating a typical non-Hermitian PT-symmetric system. Structurally, such metasurfaces are realized by utilizing a pair of orthogonally twisted near-field coupled split-ring resonators (bright-dark-resonators). We have meticulously examined such a system with two distinctive approaches, i.e., the loss parameter and inter-resonator coupling strength. Eventually, our exploration demonstrates that judicious modulation of the loss parameter can invoke an undemanding route to approach the other wisely elusive exceptional point. We believe that this comprehensive study of non-Hermitian quantum systems in a photonic context can lead to the development of accurate and precise ultra-sensitive sensors besides other futuristic photonic devices.

Continuous phase transition induced by non-Hermiticity in the quantum contact process model

Non-Hermitian (NH) quantum system recently have attracted a lots of attentions theoretically and experimentally. However, the results based on the single-particle picture may not apply to understand the property of NH many-body system. How the property of quantum many-body system especially the phase transition will be affected by the non-Hermiticity remains unclear. Here we study NH quantum contact process (QCP) model, whose effective Hamiltonian is derived from Lindbladian master equation. We show that there is a continuous phase transition induced by the non-Hermiticity in QCP. We also determine the critical exponents β of order parameter, γ of susceptibility and study the correlation and entanglement near phase transition point. We observe that the order parameter and susceptibility display infinitely singularity even for finite size system, since non-Hermiticity endow many-body system with different singular behavior from classical phase transition. Moreover our results show that the phase transition have no counterpart in Hermitian case and belongs to completely different universality class.

Scrambling and operator entanglement in local non-Hermitian quantum systems

Scrambling and operator entanglement in local non-Hermitian quantum systems

Statistical mechanics for non-Hermitian quantum systems

Statistical mechanics for non-Hermitian quantum systems

Relating non-Hermitian and Hermitian quantum systems at criticality

We demonstrate three types of transformations that establish connections between Hermitian and non-Hermitian quantum systems at criticality, which can be described by conformal field theories (CFTs). For the transformation preserving both the energy and the entanglement spectra, the corresponding central charges obtained from the logarithmic scaling of the entanglement entropy are identical for both Hermitian and non-Hermitian systems. The second transformation, while preserving the energy spectrum, does not perserve the entanglement spectrum. This leads to different entanglement entropy scalings and results in different central charges for the two types of systems. We demonstrate this transformation using the dilation method applied to the free fermion case. Through this method, we show that a non-Hermitian system with central charge c = -4c=−4 can be mapped to a Hermitian system with central charge c = 2c=2. Lastly, we investigate the Galois conjugation in the Fibonacci model with the parameter \phi \to - 1/\phiϕ→−1/ϕ, in which the transformation does not preserve both energy and entanglement spectra. We demonstrate the Fibonacci model and its Galois conjugation relate the tricritical Ising model/3-state Potts model and the Lee-Yang model with negative central charges from the scaling property of the entanglement entropy.

Speeding Up Entanglement Generation by Proximity to Higher-Order Exceptional Points.

Entanglement is a key resource for quantum information technologies ranging from quantum sensing to quantum computing. Conventionally, the entanglement between two coupled qubits is established at the timescale of the inverse of the coupling strength. In this Letter, we study two weakly coupled non-Hermitian qubits and observe entanglement generation at a significantly shorter timescale by proximity to a higher-order exceptional point. We establish a non-Hermitian perturbation theory based on constructing a biorthogonal complete basis and further identify the optimal condition to obtain the maximally entangled state. Our study of speeding up entanglement generation in non-Hermitian quantum systems opens new avenues for harnessing coherent nonunitary dissipation for quantum technologies.

Active control of localized mode and transmission in topological phononic waveguides by non-Hermitian modulation

We demonstrate the switching behavioral differences between lossy and nearly lossless edge-mode propagation by non-Hermitian modulation based on the phononic band design of a C 3v symmetric, two-dimensional phononic crystal with a unit cell composed of three air-filled circular holes in polydimethylsiloxane. We numerically show that strong loss effects lead to the extinction of the localized modes. This mechanism is analogous to the bound-to-unbound transition in non-Hermitian quantum systems. This result suggests that large variations in non-Hermitian modulation can be used for the active control of edge-mode propagation along topological interfaces.

Semiclassical Husimi Distributions of Schur Vectors in Non-Hermitian Quantum Systems.

We construct a semiclassical phase-space density of Schur vectors in non-Hermitian quantum systems. Each Schur vector is associated to a single Planck cell. The Schur states are organized according to a classical norm landscape on phase space-a classical manifestation of the lifetimes which are characteristic of non-Hermitian systems. To demonstrate the generality of this construction we apply it to a highly nontrivial example: a PT-symmetric kicked rotor in the regimes of mixed and chaotic classical dynamics.

Spin transport in non-Hermitian quantum systems

Transport in non-Hermitian quantum systems is studied. The goal is a better understanding of transport in non-Hermitian systems like the Lieb lattice due to its flat bands and the integrability of the Ising chain which allows transport in that model to be computed analytically. This is a very special feature that is not present in a generic non-Hermitian system. We obtain the behaviour of the spin conductivity as a function of the non-Hermitian parameters of each system with aim to verify the influence of variation them on conductivity. For all models analyzed: Ising model as well as noninteracting fermion models, we obtain a little influence of the non-Hermitian parameters on conductivity and thus, a small effect over transport coefficients. Furthermore, we obtain an influence of opening of the gap in the spectrum in these models on longitudinal conductivity as well.

Asynchronous locking in metamaterials of fluids of light and sound

Lattices of exciton-polariton condensates represent an attractive platform for the study and implementation of non-Hermitian bosonic quantum systems with strong non-linear interactions. The possibility to actuate on them with a time dependent drive could provide for example the means to induce resonant inter-level transitions, or to perform Floquet engineering or Landau-Zener-Stückelberg state preparation. Here, we introduce polaromechanical metamaterials, two-dimensional arrays of μm-sized traps confining zero-dimensional light-matter polariton fluids and GHz phonons. A strong exciton-mediated polariton-phonon interaction induces a time-dependent inter-site polariton coupling J(t) with remarkable consequences for the dynamics. When locally perturbed by continuous wave optical excitation, a mechanical self-oscillation sets-in and polaritons respond by locking the energy detuning between neighbor sites at integer multiples of the phonon energy, evidencing asynchronous locking involving the polariton and phonon fields. These results open the path for the coherent control of dissipative quantum light fluids with hypersound in a scalable platform.

Practical quantum simulation of small-scale non-Hermitian dynamics

Non-Hermitian quantum systems have recently attracted considerable attention due to their exotic properties. Though many experimental realizations of non-Hermitian systems have been reported, the non-Hermiticity usually resorts to the hard-to-control environments and cannot last for too long times. An alternative approach is to use quantum simulation with the closed system, whereas how to simulate non-Hermitian Hamiltonian dynamics remains a great challenge. To tackle this problem, we propose a protocol which combines a dilation method with the variational quantum algorithm. The dilation method is used to transform a non-Hermitian Hamiltonian into a Hermitian one through an exquisite quantum circuit, while the variational quantum algorithm is for efficiently approximating the complex entangled gates in this circuit. As a demonstration, we apply our protocol to simulate the dynamics of an Ising chain with nonlocal non-Hermitian perturbations, which is an important model to study quantum phase transition at nonzero temperatures. The numerical simulation results are highly consistent with the theoretical predictions, revealing the effectiveness of our protocol. The presented protocol paves the way for practically simulating small-scale non-Hermitian dynamics.

Theoretical investigation of dynamics and concurrence of entangled {{mathcal {P}}}{{mathcal {T}}} and anti-{{mathcal {P}}}{{mathcal {T}}} symmetric polarized photons

Non-Hermitian systems with parity-time mathcal {(PT)} symmetry and anti-parity-time mathcal {(APT)} symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for {{mathcal {P}}}{{mathcal {T}}} symmetry and mathcal {APT}-symmetry systems have been proposed and realized. Both two-qubits mathcal {APT}-mathcal {APT} and {{mathcal {P}}}{{mathcal {T}}}-{{mathcal {P}}}{{mathcal {T}}} symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} symmetric system. We investigate the {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in {{mathcal {P}}}{{mathcal {T}}}-{{mathcal {P}}}{{mathcal {T}}}, mathcal {APT}-mathcal {APT} and {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the {{mathcal {P}}}{{mathcal {T}}}-{{mathcal {P}}}{{mathcal {T}}} symmetrical system, mathcal {APT}-mathcal {APT} symmetrical system, and {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a {{mathcal {P}}}{{mathcal {T}}}-mathcal {APT} symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.