arXiv subjects

J. Ankerhold

Publications and source records attributed to J. Ankerhold.

At least 19 recordsLinked to original sources

arXiv2026

Markovian Embeddings of Non-Markovian Open System Dynamics

Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations, where the dynamics of the extended space can be governed by multiple distinct Markovian equations. We show that these distinct embeddings arise from different unravelings of Gaussian bath self-energies, generating a family of deterministic, time-local equations for the extended system. Using the Brownian-oscillator spectral density as an illustrative example, we clarify the relationships among existing approaches, including the Hierarchical Equations of Motion (HEOM) and the Lindblad--pseudomode formalism, and demonstrate how this framework enables numerically stable and efficient simulations. This work provides both a transparent theoretical foundation for embedding techniques and a flexible platform for developing new methods to simulate non-Markovian quantum dynamics.

quant-ph↗

arXiv2026

Simulating Non-Markovian Dynamics in Open Quantum Systems

Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects (non-Markovianity), system-environment hybridization, and the necessity for accuracy beyond the Born-Markov approximation form particular challenges. Approaches to meet these challenges have been introduced, originating from different fields, such as hierarchical equations of motion, Lindblad-pseudomode formulas, chain-mapping approaches, quantum Brownian motion master equations, stochastic unravelings, and refined quantum master equations. This diversity, while indicative of the field's relevance, has inadvertently led to a fragmentation that hinders cohesive advances and their effective cross-community application to current problems for complex systems. How are different approaches related to each other? What are their strengths and limitations? Here we give a systematic overview and concise discussion addressing these questions. We make use of a unified framework which very conveniently allows to link different schemes and, this way, may also catalyze further progress. In line with the state of the art, this framework is formulated not in a fully reduced space of the system but in an extended state space which in a minimal fashion includes effective reservoir modes. This in turn offers a comprehensive understanding of existing methods, elucidating their physical interpretations, interconnections, and applicability.

quant-ph↗

arXiv2025

Nonlinear response theory for lossy superconducting quantum circuits

We introduce a numerically exact and computationally feasible nonlinear-response theory developed for lossy superconducting quantum circuits based on a framework of quantum dissipation in a minimally extended state space. Starting from the Feynman--Vernon path integral formalism for open quantum systems with the system degrees of freedom being the nonlinear elements of the circuit, we eliminate the temporally non-local influence functional of all linear elements by introducing auxiliary harmonic modes with complex-valued frequencies coupled to the nonlinear elements. In our work, we propose a concept of time-averaged observables, inspired by experiment, and provide an explicit formula for producing their quasiprobability distribution. We illustrate the consistency of our formalism with the well-established Markovian input-output theory by applying them the dispersive readout of a superconducting transmon qubit. For an important demonstration of our approach beyond weak coupling, we analyze the low-frequency linear response of a capacitively and resistively shunted Josephson junction and observe signatures of a much-debated quantum phase transition at a finite temperature. The developed framework enables a comprehensive fully quantum-mechanical treatment of nonlinear quantum circuits coupled to their environment, without the limitations of typical approaches to weak dissipation, high temperature, and weak drive. This versatile tool paves the way for accurate models of quantum devices and increased fundamental understanding of quanutm mechanics such as that of the quantum measurement.

quant-ph↗

arXiv2024

Environment-Mediated Long-Ranged Correlations in Many-Body System

Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation become thus unavoidable but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed Quantum Dissipation with Minimally Extended State Space (QD-MESS) approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveal a rich pattern of dynamical phases including dissipative induced phase transitions and spatiotemporal correlations.

cond-mat.stat-mech↗

arXiv2024

Ultrafast excitonic dynamics in DNA: Bridging correlated quantum dynamics and sequence dependence

After photo-excitation of DNA, the excited electron (in the LUMO) and the remaining hole (in the HOMO) localized on the same DNA base form a bound pair, called the Frenkel exciton, due to their mutual Coulomb interaction. In this study, we demonstrate that a tight-binding (TB) approach, parametrized by ab initio data, allows to correlate relaxation properties, average charge separation, and dipole moments to a large ensemble of double-stranded DNA sequences (all 16,384 possible sequences with 14 nucleobases). This way, we are able to identify a relatively small sub-ensemble of sequences responsible for long-lived excited states, high average charge separation, and high dipole moment. Further analysis shows that these sequences are particularly T-rich. By systematically screening the impact of electron-hole interaction (Coulomb forces), we verify that these correlations are relatively robust against finite-size variations of the interaction parameter, not directly accessible experimentally. This methodology combines simulation methods from quantum physics and physical chemistry with statistical analysis known from genetics and epigenetics, thus representing a powerful bridge to combine information from both fields.

physics.chem-ph↗

arXiv2023

A Universal Framework for Quantum Dissipation:Minimally Extended State Space and Exact Time-Local Dynamics

The dynamics of open quantum systems is formulated in a minimally extended state space comprising the degrees of freedom of a system of interest and a finite set of non-unitary, pure-state reservoir modes. This formal structure, derived from the Feynman-Vernon path integral for the reduced density, is shown to lead to an exact time-local evolution equation in a mixed Liouville-Fock space. The crucial ingredient is a mathematically consistent decomposition of the reservoir auto-correlation in terms of harmonic modes with complex-valued frequencies and amplitudes, which are obtained from any given spectral noise power of the physical reservoir. This formulation provides a universal framework to obtain a family of equivalent representations which are directly related to new and established schemes for efficient numerical simulations. By restricting some of the complex-valued mode parameters and performing linear transformations, we make connections to previous approaches, whose auxiliary degrees of freedom are thus revealed as restricted versions of the minimally extended state space presented here. From a practical perspective, the new framework offers a computational tool which combines numerical efficiency and accuracy with long time stability and broad applicability over the whole temperature range and also for strongly structured reservoir mode densities. It can thus deliver high precision data with modest computational resources and simulation times for actual quantum technological devices.

quant-ph↗

arXiv2023

Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model

The hierarchical equations of motion (HEOM) approach is an accurate method to simulate open system quantum dynamics, which allows for systematic convergence to numerically exact results. To represent the effects of the bath, the reservoir correlation functions are usually decomposed into the summation of multiple exponential terms in the HEOM method. Since the reservoir correlation functions become highly non-Markovian at low temperatures or when the bath has complex band structures, a present challenge is to obtain accurate exponential decompositions that allow efficient simulation with the HEOM. In this work, we employ the barycentric representation to approximate the Fermi function and hybridization functions in the frequency domain. The new method, by approximating these functions with optimized rational decomposition, greatly reduces the number of basis functions in decomposing the reservoir correlation functions, which further allows the HEOM method to be applied to ultra-low temperature and general bath structures. We demonstrate the efficiency, accuracy, and long-time stability of the new decomposition scheme by applying it to the Anderson impurity model (AIM) in the low-temperature regime with the Lorentzian and tight-binding hybridization functions.

cond-mat.str-el↗

arXiv2022

Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems

The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems that are embedded in thermal environments. However, its applicability is restricted to specific forms of spectral reservoir distributions and relatively elevated temperatures. Here we solve this problem and introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy and long-time stability. Moreover, the technique can directly be implemented in alternative approaches such as Green's function, stochastic, and pseudo-mode formulations. As one highly non-trivial application, for the sub-ohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.

quant-ph↗

arXiv2022

Minimal quantum thermal machine in a bandgap environment: non-Markovian features and anti-Zeno advantage

A minimal model of a quantum thermal machine is analyzed, where a driven two level working medium (WM) is embedded in an environment (reservoir) whose spectrum possesses bandgaps. overlap with hot or cold reservoirs whose spectra are separated by a bandgap. Approximate and exact treatments supported by analytical considerations yield a complete characterization of this thermal machine in the deep quantum domain. For slow to moderate modulation, the spectral response of the reservoirs is close to equilibrium, exhibiting sideband (Floquet) resonances in the heat currents and power output. In contrast, for faster modulation, strong-coupling and non-Markovian features give rise to correlations between the WM and the reservoirs and between the two reservoirs. Power boost of strictly quantum origin ('quantum advantage') is then found for both continuous and segmental fast modulation that leads to the anti-Zeno effect of enhanced spectral reservoir response. Such features cannot be captured by standard Markovian treatments.

quant-ph↗

arXiv2022

Superconducting Quantum Interference at the Atomic Scale

A single spin in a Josephson junction can reverse the flow of the supercurrent. At mesoscopic length scales, such $π$-junctions are employed in various instances from finding the pairing symmetry to quantum computing. In Yu-Shiba-Rusinov (YSR) states, the atomic scale counterpart of a single spin in a superconducting tunnel junction, the supercurrent reversal so far has remained elusive. Using scanning tunneling microscopy (STM), we demonstrate such a 0 to $π$ transition of a Josephson junction through a YSR state as we continuously change the impurity-superconductor coupling. We detect the sign change in the critical current by exploiting a second transport channel as reference in analogy to a superconducting quantum interference device (SQUID), which provides the STM with the required phase sensitivity. The measured change in the Josephson current is a signature of the quantum phase transition and allows its characterization with unprecedented resolution.

cond-mat.supr-con↗

arXiv2022

Emission of photon multiplets by a dc-biased superconducting circuit

We observe the emission of bunches of $k \geqslant 1$ photons by a circuit made of a microwave resonator in series with a voltage-biased tunable Josephson junction. The bunches are emitted at specific values $V_k$ of the bias voltage, for which each Cooper pair tunneling across the junction creates exactly k photons in the resonator. The latter is a micro-fabricated spiral coil which resonates and leaks photons at 4.4~GHz in a measurement line. Its characteristic impedance of 1.97~k$Ω$ is high enough to reach a strong junction-resonator coupling and a bright emission of the k-photon bunches. We show that a RWA treatment of the system accounts quantitatively for the observed radiation intensity, from $k=1$ to $6$, and over three orders of magnitude when varying the Josephson energy $E_J$. We also measure the second order correlation function of the radiated microwave to determine its Fano factor $F_k$, which in the low $E_J$ limit, confirms with $F_k=k$ the emission of $k$ photon bunches. At larger $E_J$, a more complex behavior is observed in quantitative agreement with numerical simulations.

cond-mat.supr-con↗

arXiv2021

Heat transport through a superconducting artificial atom

Quantum heat transfer through a generic superconducting set-up consisting of a tunable transmon qubit placed between resonators that are termined by thermal reservoirs is explored. Two types of architectures are considered, a sequential and a beam splitter setting. Applying the numerical exact hierarchical equation of motion (HEOM) approach, steady state properties are revealed, and experimentally relevant parameter sets are identified. Benchmark results are compared with predictions based on approximate treatments to demonstrate their failure in broad ranges of parameter space. These findings may allow to improve future designs for heat control in superconducting devices.

quant-ph↗

arXiv2020

Generating two continuous entangled microwave beams using a dc-biased Josephson junction

We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absence of a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions for proving entanglement up to an emission rate of 2.5 billion photon pairs per second. The experimental results are found in quantitative agreement with theory, proving that the low frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications.

cond-mat.mes-hall↗

arXiv2019

Antibunched photons emitted by a dc biased Josephson junction

We show experimentally that a dc biased Josephson junction in series with a high-enough impedance microwave resonator emits antibunched photons. Our resonator is made of a simple micro-fabricated spiral coil that resonates at 4.4 GHz and reaches a 1.97 k$Ω$ characteristic impedance. The second order correlation function of the power leaking out of the resonator drops down to 0.3 at zero delay, which demonstrates the antibunching of the photons emitted by the circuit at a rate of 6 $10^7$ photons per second. Results are found in quantitative agreement with our theoretical predictions. This simple scheme could offer an efficient and bright single-photon source in the microwave domain.

cond-mat.mes-hall↗

arXiv2017

Emission of non-classical radiation by inelastic Cooper pair tunneling

We show that a properly dc-biased Josephson junction in series with two microwave resonators of different frequencies emits photon pairs in the resonators. By measuring auto- and inter-correlations of the power leaking out of the resonators, we demonstrate two-mode amplitude squeezing below the classical limit. This non-classical microwave light emission is found to be in quantitative agreement with our theoretical predictions, up to an emission rate of 2 billion photon pairs per second.

cond-mat.mes-hall↗

arXiv2017

Multiple-period Floquet states and time-translation symmetry breaking in quantum oscillators

We study the breaking of the discrete time-translation symmetry in small periodically driven quantum systems. Such systems are intermediate between large closed systems and small dissipative systems, which both display the symmetry breaking, but have qualitatively different dynamics. As a nontrivial example we consider period tripling in a quantum nonlinear oscillator. We show that, for moderately strong driving, the period tripling is robust on an exponentially long time scale, which is further extended by an even weak decoherence.

quant-ph↗

arXiv2015

Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters including the fundamental resonance as well as higher and sub-harmonics. Observables such as the dc-Josephson current and the radiated microwave power give direct information about the underlying dynamics covering phenomena as bifurcations, irregular motion, up- and down conversion. Due to their tunability, present and future set-ups provide versatile platforms to explore the changeover from linear response to strongly nonlinear behavior in driven dissipative systems under well defined conditions.

cond-mat.mes-hall↗

arXiv2014

Moments of work in the two-point measurement protocol for a driven open quantum system

We study the distribution of work induced by the two-point measurement protocol for a driven open quantum system. We first derive a general form for the generating function of work for the total system, bearing in mind that the Hamiltonian does not necessarily commute with its time derivative. Using this result we then study the first few moments of work by using the master equation of the reduced system, invoking approximations similar to the ones made in the microscopic derivation of the reduced density matrix. Our results show that, already in the third moment of work, correction terms appear that involve commutators between the Hamiltonian and its time derivative. To demonstrate the importance of these terms, we consider a sinusoidally, weakly driven and weakly coupled open two-level quantum system, and indeed find that already in the third moment of work the correction terms are significant. We also compare our results to those obtained with the quantum jump method and find a good agreement.

quant-ph↗