Interacting Quantum Systems Research Articles

Holographic Einstein ring of a charged AdS black hole

Taking into account that the real quantum materials are engineered generically at a finite chemical potential, we investigate the Einstein ring structure for the lensed response of the complex scalar field as a probe wave on the charged AdS black hole in the context of AdS/CFT. On the one hand, we find that the resulting Einstein ring radius has no variation with the chemical potential, which is similar to the behavior for the weakly interacting quantum system. On the other hand, not only can such a ring exist well within the screen, but also the temperature dependence of its radius exhibits a distinct feature in the sense that it displays an appreciable increase at low temperatures while the ring keeps unchanged right at the edge of the screen for the weakly interacting system. Note that such a Einstein ring emerges in the large frequencies and can be well captured by the photon sphere away from the black hole horizon in the geometric optics approximation, thus such a distinct feature may be regarded as a universal behavior associated with the high energy modes of the strongly coupled system which has a gravity dual.

Many-body Hilbert space scarring on a superconducting processor

Quantum many-body scarring (QMBS) -- a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems -- presents opportunities for mitigating thermalization-induced decoherence in quantum information processsing. However, the existing experimental realizations of QMBS are based on kinetically-constrained systems where an emergent dynamical symmetry "shields" such states from the thermalizing bulk of the spectrum. Here, we experimentally realize a distinct kind of QMBS phenomena by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and tunable couplings, we realize Hilbert space scarring in a non-constrained model in different geometries, including a linear chain as well as a quasi-one-dimensional comb geometry. By performing full quantum state tomography on 4-qubit subsystems, we provide strong evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy following a quench from initial product states. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology.

Statistical complexity and the road to equilibrium in many-body chaotic quantum systems.

In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how they adhere to the predictions of the Eigenstate Thermalization Hypothesis, we focus on the equilibration process itself, i.e., the road to equilibrium. Along the road to equilibrium the diagonal ensembles obey an emergent form of the second law of thermodynamics and we provide an information theoretic proof of this fact. With this proof at hand we show that the road to equilibrium is nothing but a hierarchy in time of diagonal ensembles. Furthermore, introducing the notions of statistical complexity and the entropy-complexity plane, we investigate the uniqueness of the road to equilibrium in a generic many-body system by comparing its trajectories in the entropy-complexity plane to those generated by a random Hamiltonian. Finally, by treating the random Hamiltonian as a perturbation we analyzed the stability of entropy-complexity trajectories associated with the road to equilibrium for a chaotic Hamiltonian and different types of initial states.

Four‐mode Squeezed States in de Sitter Space: A Study With Two Field Interacting Quantum System

AbstractIn this paper we study the application of four‐mode squeezed states in the cosmological context, studying two weakly coupled scalar fields in the planar patch of the de Sitter space. We construct the four‐mode squeezed state formalism and connect this concept with the Hamiltonian of the two coupled inverted harmonic oscillators having a time‐dependent effective frequency in the planar patch of the de Sitter space. Further, the corresponding evolution operator for the quantum Euclidean vacuum state has been constructed, which captures its dynamics. Using the Heisenberg picture coupled differential equations describing the time evolution for all squeezing parameters (amplitude, phase and angle) have been obtained, for the weakly coupled two scalar field model. With the help of these evolutions for the coupled system, we simulate the dynamics of the squeezing parameters in terms of conformal time. From our analysis, we observe interesting dynamics, which helps us to explore various underlying physical implications of the weakly coupled two scalar field system in the planar patch of the de Sitter cosmological background.

Entropy fluctuation and correlation transfer in tunable discrete-time quantum walk with fractional Gaussian noise.

We study the time correlation in the von Neumann entropy fluctuation of the tunable discrete-time quantum walk in one dimension, induced by the coin disorder arising from the temporal fractional Gaussian noise (fGn). The fGn is characterized by the Hurst exponent H, which provides three different correlation scenarios, namely antipersistent (0<H<0.5), memoryless (H=0.5), and persistent (0.5<H<1). We show the correlation of fGn is transferred to the coin's degree of entanglement and eventually transpires in the time correlation of the von Neumann entropy fluctuation. This study hints at the potential of using noise correlation as a resource to sustain information backflow via the interaction of quantum system with the noisy environment.

Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction

Many-body localization (MBL) is a novel prototype of ergodicity breaking due to the emergence of local integrals of motion (LIOMs) in a disordered interacting quantum system. To better understand the role played by the existence of such macroscopically LIOMs, we explore and study some of their structural properties across the MBL transition. We first, consider a one-dimensional XXZ spin chain in a disordered magnetic field and introduce and implement a non-perturbative, fast, and accurate method of constructing LIOMs. In contrast to already existing methods, our scheme allows obtaining LIOMs not only in the deep MBL phase but rather, near the transition point too. Then, we take the matrix representation of LIOM operators as an adjacency matrix of a directed graph whose elements describe the connectivity of ordered eigenbasis in the Hilbert-space. Our cluster size analysis for this graph shows that the MBL transition coincides with a percolation transition in the Hilbert-space. By performing finite-size scaling, we compare the critical disorder and correlation exponent $\nu$ both in the presence and absence of interaction. Finally, we also discuss how the distribution of diagonal elements of LIOM operators in a typical cluster signals the transition.

Perturbative Diagonalization for Time-Dependent Strong Interactions

We present a systematic method to implement a perturbative Hamiltonian diagonalization based on the time-dependent Schrieffer-Wolff transformation. Applying our method to strong parametric interactions we show how, even in the dispersive regime, full Rabi model physics is essential to describe the dressed spectrum. Our results unveil several qualitatively different results, including realization of large energy-level shifts, tunable in magnitude and sign with the frequency and amplitude of the pump mediating the parametric interaction. Crucially, Bloch-Siegert shifts, typically thought to be important only in the ultrastrong or deep-strong coupling regimes, can be rendered large even for weak dispersive interactions to realize points of exact cancelation of dressed shifts (``blind spots'') at specific pump frequencies. The framework developed here highlights the rich physics accessible with time-dependent interactions and serves to significantly expand the functionalities for control and readout of strongly interacting quantum systems.

Multipartite entanglement in the random Ising chain

Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ensuremath{\ell}$ separated by a distance $r=\ensuremath{\alpha}\ensuremath{\ell}$ and quantify their entanglement negativity ($\mathcal{E}$) and mutual information ($\mathcal{I}$) in critical random Ising chains. We find universal constant $\mathcal{E}(\ensuremath{\alpha})$ and $\mathcal{I}(\ensuremath{\alpha})$ over any distances, using the asymptotically exact strong disorder renormalization group method. Our results are qualitatively different from both those in the clean Ising model and random spin chains of a singlet ground state, like the spin-$\frac{1}{2}$ random Heisenberg chain and the random XX chain. While for random singlet states $\mathcal{I}(\ensuremath{\alpha})/\mathcal{E}(\ensuremath{\alpha})=2$, in the random Ising chain this universal ratio is strongly $\ensuremath{\alpha}$ dependent. This deviation between systems contrasts with the behavior of the entanglement entropy of a single subsystem, for which the various random critical chains and clean models give the same qualitative behavior. The reason is that $\mathcal{E}$ and $\mathcal{I}$ are sensitive to higher order correlations in the ground-state structure. Therefore, studying multipartite entanglement provides additional universal information in random quantum systems, beyond what we can learn from a single subsystem.

Eigenstate Thermalization in Long-Range Interacting Systems.

Motivated by recent ion experiments on tunable long-range interacting quantum systems [Neyenhuis etal., Sci. Adv. 3, e1700672 (2017)SACDAF2375-254810.1126/sciadv.1700672], we test the strong eigenstate thermalization hypothesis for systems with power-law interactions ∼1/r^{α}. We numerically demonstrate that the strong eigenstate thermalization hypothesis typically holds, at least for systems with α≥0.6, which include Coulomb, monopole-dipole, and dipole-dipole interactions. Compared with short-range interacting systems, the eigenstate expectation value of a generic local observable is shown to deviate significantly from its microcanonical ensemble average for long-range interacting systems. We find that Srednicki's ansatz breaks down for α≲1.0, at least for relatively large system sizes.

Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems.

The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given.

Markovian repeated interaction quantum systems

We study a class of dynamical semigroups [Formula: see text] that emerge, by a Feynman–Kac type formalism, from a random quantum dynamical system [Formula: see text] driven by a Markov chain [Formula: see text]. We show that the almost sure large time behavior of the system can be extracted from the large [Formula: see text] asymptotics of the semigroup, which is in turn directly related to the spectral properties of the generator [Formula: see text]. As a physical application, we consider the case where the [Formula: see text]’s are the reduced dynamical maps describing the repeated interactions of a system [Formula: see text] with thermal probes [Formula: see text]. We study the full statistics of the entropy in this system and derive a fluctuation theorem for the heat exchanges and the associated linear response formulas.

Optical demonstration of quantum fault-tolerant threshold

A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable to the output of a higher probability of correct logical qubits under the presence of errors. However, strict requirements to encode qubits and operators render the implementation of a full fault-tolerant computation challenging even for the achievable noisy intermediate-scale quantum technology. Especially the threshold for fault-tolerant computation still lacks experimental verification. Here, based on an all-optical setup, we experimentally demonstrate the existence of the threshold for the fault-tolerant protocol. Four physical qubits are represented as the spatial modes of two entangled photons, which are used to encode two logical qubits. The experimental results clearly show that when the error rate is below the threshold, the probability of correct output in the circuit, formed with fault-tolerant gates, is higher than that in the corresponding non-encoded circuit. In contrast, when the error rate is above the threshold, no advantage is observed in the fault-tolerant implementation. The developed high-accuracy optical system may provide a reliable platform to investigate error propagation in more complex circuits with fault-tolerant gates.

Amplification of quantum signals by the non-Hermitian skin effect

The non-Hermitian skin effect (NHSE) is a phenomenon whereby certain non-Hermitian lattice Hamiltonians host an extensive number of eigenmodes condensed to the boundary, called skin modes. Although the NHSE has mostly been studied in the classical or single-particle regime, it can also manifest in interacting quantum systems with boson number nonconserving processes. We show that lattices of coupled nonlinear resonators can function as reciprocal quantum amplifiers. A one-dimensional chain exhibiting the NHSE can perform strong photon amplification aided by the skin modes, which scales exponentially with the chain length and outperforms alternative lattice configurations lacking the NHSE. Moreover, two-dimensional lattices can perform directional photon amplification between different lattice corners, due to the two-dimensional NHSE. These quantum amplifiers are based on experimentally feasible lattice configurations with uniform parametric driving schemes.

Near-equilibrium approach to transport in complex Sachdev-Ye-Kitaev models

We study the non-equilibrium dynamics of a one-dimensional complex Sachdev-Ye-Kitaev chain by directly solving for the steady state Green's functions in terms of small perturbations around their equilibrium values. The model exhibits strange metal behavior without quasiparticles and features diffusive propagation of both energy and charge. We explore the thermoelectric transport properties of this system by imposing uniform temperature and chemical potential gradients. We then expand the conserved charges and their associated currents to leading order in these gradients, which we can compute numerically and analytically for different parameter regimes. This allows us to extract the full temperature and chemical potential dependence of the transport coefficients. In particular, we uncover that the diffusivity matrix takes on a simple form in various limits and leads to simplified Einstein relations. At low temperatures, we also recover a previously known result for the Wiedemann-Franz ratio. Furthermore, we establish a relationship between diffusion and quantum chaos by showing that the diffusivity eigenvalues are upper bounded by the chaos propagation rate at all temperatures. Our work showcases an important example of an analytically tractable calculation of transport properties in a strongly interacting quantum system and reveals a more general purpose method for addressing strongly coupled transport.

Interpretable machine-learning identification of the crossover from subradiance to superradiance in an atomic array

Light–matter interacting quantum systems manifest strong correlations that lead to distinct cooperative spontaneous emissions of subradiance or superradiance. To demonstrate the essence of finite-range correlations in such systems, we consider an atomic array under the resonant dipole–dipole interactions (RDDI) and apply an interpretable machine learning (ML) with the integrated gradients to identify the crossover between the subradiant and superradiant sectors. The machine shows that the next nearest-neighbor (NN) couplings in RDDI play as much as the roles of NN ones in determining the whole eigenspectrum within the training sets. Our results present the advantage of ML approach with explainable ability to reveal the underlying mechanism of correlations in quantum optical systems, which can be potentially applied to investigate many other strongly interacting quantum many-body systems.

Observing emergent hydrodynamics in a long-range quantum magnet

Identifying universal properties of nonequilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system. We experimentally probed the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain. By measuring space-time–resolved correlation functions in an infinite temperature state, we observed a whole family of hydrodynamic universality classes, ranging from normal diffusion to anomalous superdiffusion, that are described by Lévy flights. We extracted the transport coefficients of the hydrodynamic theory, reflecting the microscopic properties of the system. Our observations demonstrate the potential for engineered quantum systems to provide key insights into universal properties of nonequilibrium states of quantum matter.

Closed-System Solution of the 1D Atom from Collision Model.

Obtaining the total wavefunction evolution of interacting quantum systems provides access to important properties, such as entanglement, shedding light on fundamental aspects, e.g., quantum energetics and thermodynamics, and guiding towards possible application in the fields of quantum computation and communication. We consider a two-level atom (qubit) coupled to the continuum of travelling modes of a field confined in a one-dimensional chiral waveguide. Originally, we treated the light-matter ensemble as a closed, isolated system. We solve its dynamics using a collision model where individual temporal modes of the field locally interact with the qubit in a sequential fashion. This approach allows us to obtain the total wavefunction of the qubit-field system, at any time, when the field starts in a coherent or a single-photon state. Our method is general and can be applied to other initial field states.

Learning a compass spin model with neural network quantum states

Neural network quantum states provide a novel representation of the many-body states of interacting quantum systems and open up a promising route to solve frustrated quantum spin models that evade other numerical approaches. Yet its capacity to describe complex magnetic orders with large unit cells has not been demonstrated, and its performance in a rugged energy landscape has been questioned. Here we apply restricted Boltzmann machines (RBMs) and stochastic gradient descent to seek the ground states of a compass spin model on the honeycomb lattice, which unifies the Kitaev model, Ising model and the quantum 120° model with a single tuning parameter. We report calculation results on the variational energy, order parameters and correlation functions. The phase diagram obtained is in good agreement with the predictions of tensor network ansatz, demonstrating the capacity of RBMs in learning the ground states of frustrated quantum spin Hamiltonians. The limitations of the calculation are discussed. A few strategies are outlined to address some of the challenges in machine learning frustrated quantum magnets.

Quarkonium dynamics inside the Quark-Gluon Plasma using open quantum systems

In recent years, a significant theoretical effort has been made towards a dynamical description of quarkonia inside the Quark-Gluon Plasma (QGP), using the open quantum systems formalism. In this framework, one can get a real-time description of a quantum system (here the quarkonium) in interaction with a thermal bath (the QGP) by integrating out the bath degrees of freedom and studying the system reduced density matrix. We investigate the real-time dynamics of a correlated heavy quark-antiquark pair inside the QGP using a quantum master equation previously derived from first QCD principles in [4]. The full equation is directly resolved in 1D to lessen computing costs and is used for the first time to gain insight on the dynamics in both a static and evolving medium following a Björken-like temperature evolution.

Vortex chains in rotating two-dimensional Bose-Einstein condensate in a harmonic plus optical lattices potential

&lt;sec&gt;Bose-Einstein condensate (BEC) is essentially a macroscopic quantum effect with quantum volatility, macroscopic quantum coherence and artificial controllability. Owing to its unique controllability, it becomes a new ideal platform for quantum simulations and studies of interacting quantum systems.&lt;/sec&gt;&lt;sec&gt;In this paper, the generation of vortices and the formation of vortex chains, as well as characteristics of vortex chains in rotating two-dimensional BEC in a potential composed of harmonic potential and optical lattice are studied numerically. Firstly, the generation of vortices, the formation and distribution of vortex chains and the effects of different physical parameters on the vortex chains in two-dimensional BEC are investigated by using the multigrid preconditioned conjugate gradient method. Secondly, the evolution of the vortex chains with time is studied by using the time-splitting spectral method. The results show that the generation of vortices in BEC trapped in the compound potential corresponds to the minimum value of the potential. When the depth of the optical lattice increases to a certain value, vortex chains are formed in the BEC. With the further increase of the depth of the optical lattice, the vortex depth in the vortex chain in the BEC decreases continuously, and finally the vortex chain disappears completely. When the interaction strength between atoms increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the interaction strength between atoms increases to a certain value, the symmetry of the vortex chains is broken. As the rotation frequency of the condensate increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the rotation frequency is close to the external trapping potential frequency, the linear alignment of the vortex chains is disrupted. It is also found that there are three stages in the evolution of the vortex chains in the BEC: in the first stage, vortex chains rotate together with the condensate, and the original chain distribution keeps unchanged; in the second stage, the phenomenon of vortex space extrusion appears, and the vortex chain is destroyed; in the third stage, the phenomenon of vortex space expansion occurs, and finally the vortex chains disappear. The results above show that the depth of the optical lattice, the interaction strength between atoms, and the rotation frequency of the condensate have important effects on the vortices and vortex chains in the condensate. By adjusting these physical quantities, the number of vortices and the shape of vortex chains in the BEC can be effectively manipulated. This may provide some theoretical reference and guidance for future experiments and applications.&lt;/sec&gt;