arXiv subjects

Neill Lambert

Publications and source records attributed to Neill Lambert.

At least 19 recordsLinked to original sources

arXiv2026

Quantum transport in Cooper pair splitters using hierarchical equations of motion

We investigate charge transport in Cooper pair splitters beyond the weak-coupling and Markovian limits. To this end, we employ hierarchical equations of motion (HEOM), which can capture the combined effects of strong coupling to the leads, nonperturbative interactions, and finite voltage and temperature differences. Within this framework, we compute the electric currents as functions of the level positions of a Cooper pair splitter for various voltage and temperature configurations. In the large-bias regime, our results reduce to analytical expressions obtained from a Markovian Lindblad equation. However, recent experiments were conducted with finite voltage or temperature differences, where a Markovian description may not suffice. In this regime, HEOM yield quantitative agreement with the measured currents. We can also account for an experimentally observed thermoelectric effect in Cooper pair splitters. Our results show that HEOM provide a useful framework for describing nonequilibrium quantum transport in Cooper pair splitters and related hybrid devices.

cond-mat.mes-hall↗

arXiv2026

Photon-energy-programmable subnanometric electron birth-site control

Optical control of electron-generation sites has broadly enabled ultrafast nanoscale imaging, spectroscopy, and functional control. Existing approaches achieve nanoscale site selectivity by shaping localised optical fields around nanostructures, thereby limiting independent site selectivity within the same local-field hotspot. Here, using a single-molecule electron emitter, we show that site selectivity can instead be encoded in the electronic excitation pathway, enabling subnanometric control of electron birth sites within the same local-field hotspot. By tuning the photon energy, we selectively access molecular states of different spatial symmetry and reversibly switch the electron birth site between distinct locations in the same emitter, with the change read out directly in the far-field emission pattern. The switching depends on photon energy alone and is absent under variations in intensity or polarisation. Our results establish optical birth-site selectivity that is not dictated by the local-field distribution, opening a route to electron birth-site control through the electronic excitation pathway.

cond-mat.mes-hall↗

arXiv2026

Strongly-coupled non-Markovian waveguide QED with input-output HEOM

We consider the problem of modeling a single qubit in contact with a one-dimensional waveguide beyond the standard perturbative and Markovian approximations. Using the recently developed input-output hierarchical equations of motion (io-HEOM), we investigate multiple examples of such waveguides, characterized by different spectral densities. Our examples highlight that the io-HEOM method can accurately capture non-Markovianity in waveguide QED from two distinct origins. The first source of non-Markovianity is spatially non-local coupling between the qubit and the waveguide. By examining two examples with non-local coupling, we show how the coupling function affects the steady-state bound photons, and demonstrate the release of these photons when the qubit energy is quenched. The second source of non-Markovianity is non-linear dispersion. We illustrate this scenario using the example of a cavity array with point-like coupling, where the non-linear dispersion leads to persistent oscillations due to Van Hove singularities in the spectral density.

quant-ph↗

arXiv2026

RC-HEOM Hybrid Method for Non-Perturbative Open System Dynamics

The Hierarchical equations of motion (HEOM) method is an important non-perturbative technique, allowing numerically exact treatment of open quantum systems with strong coupling and non-Markovian memory. However, its encoding of bath memory into auxiliary density operators often limits direct access to detailed bath information. In contrast, the reaction-coordinate (RC) mapping allows direct and transparent access to the dominant collective bath mode, but its perturbative and often Markovian treatment of the residual bath restricts its reliability. In this work, we introduce RC-HEOM, a hybrid method that unifies the strengths of both approaches by combining RC mapping with a fully non-perturbative HEOM description of the residual bath. RC-HEOM simultaneously retains exact non-Markovian memory and access to the RC mode, which enables analysis of system-RC information. Applying this method to the Anderson impurity models, we directly track the emergence of the Kondo singlet from the growth of the Kondo resonance and uncover a nontrivial RC-mediated coherence revival. These results demonstrate that RC-HEOM is a promising method for characterizing open quantum systems in regimes that are difficult to access with conventional master-equation methods.

quant-ph↗

arXiv2025

Resource efficient certification of system environment entanglement solely from reduced system dynamics

Certifying nonclassical correlations typically requires access to all subsystems, presenting a major challenge in open quantum systems coupled to inaccessible environments. Recent works have shown that, in autonomous pure dephasing scenarios, quantum discord with the environment can be certified from system-only dynamics via the Hamiltonian ensemble formulation. However, this approach leaves open whether stronger correlations, such as entanglement, can be certified. Moreover, its reliance on Fourier analysis requires full-time dynamics, which is experimentally resource-intensive and provides limited information about when such correlations are established during evolution. In this work, we present a method that enables the certification of system-environment quantum entanglement solely from the reduced dynamics of the system. The method is based on the theory of mixed-unitary channels and applies to general non-autonomous pure dephasing scenarios. Crucially, it relaxes the need for full-time dynamics, offering a resource-efficient approach that also reveals the precise timing of entanglement generation. We experimentally validate this method on a Quantinuum trapped-ion quantum processor with a controlled-dephasing model. Finally, we highlight its potential as a tool for certifying gravitationally induced entanglement.

quant-ph↗

arXiv2025

Exact description of fermionic reservoirs via purified damped ancillary fermions

We present a method for the modeling of fermionic reservoirs using a new class of ancillary damped fermions, dubbed purified pseudofermions, which exhibit unusual free correlations. We show that this key feature, when combined with existing efficient decomposition algorithms for the reservoir correlation functions, enables the development of an easily implementable and accurate scheme for constructing effective models of fermionic reservoirs. We numerically demonstrate the validity, accuracy, efficiency and potential use of our method by studying the particle transport of spinless fermions in a one-dimensional chain. Beyond its utility as a quantum impurity solver, our method holds promise for addressing a wide range of problems involving extended systems in fields like quantum transport, quantum thermodynamics, thermal engines and nonequilibrium phase transitions.

cond-mat.str-el↗

arXiv2025

Purified pseudomode model for nonlinear system-bath interactions

The theory of purified pseudomodes [arXiv:2412.04264 (2024)] was recently developed to provide a numerical tool for the analysis of the properties of a quantum system and the environment it couples to via linear system-bath interactions. Here we extend this theory to allow for the description of general nonlinear system-bath interactions. We demonstrate the validity of our method by considering the spontaneous decay of a two-level atom placed inside a single-mode lossy cavity and furthermore, its potential application to nanophotonics by calculating the resonance fluorescence spectrum of a quantum dot in the presence of a phonon environment. Our method provides a useful tool for the study of phonon-assisted emission in quantum dots and holds the the promise for broad applications in fields like quantum biology, nonlinear phononics, and nanophotonics.

quant-ph↗

arXiv2025

Experimental simulation of postselected closed timelike curves for decoding scrambled quantum information

Quantum information scrambling (QIS) describes the rapid spread of initially localized information across an entire quantum many-body system through entanglement generation. Once scrambled, the original local information becomes encoded globally, inaccessible from any single subsystem. In this work, we introduce a circuit-based decoding protocol. By utilizing the concept of postselected closed timelike curves (PCTCs), we demonstrate how postselection allows us to interpret an ordinary quantum experiment as an example of a paradox-free trajectory, simulating a consistent time loop and reliable information recovery. Specifically, when conditioned on a final postselected outcome, this experiment can be interpreted as decoding the scrambled information even before the original information is generated. Furthermore, the success probability of the PCTC is governed by out-of-time-ordered correlations, which is a standard measure of QIS. We experimentally implement our protocol on cloud-based Quantinuum and IBM quantum processors. Our approach illuminates a unique quantum task under postselection: the causally consistent simulation of future-to-past scrambled information retrieval.

quant-ph↗

arXiv2024

QuTiP 5: The Quantum Toolbox in Python

QuTiP, the Quantum Toolbox in Python, has been at the forefront of open-source quantum software for the past 13 years. It is used as a research, teaching, and industrial tool, and has been downloaded millions of times by users around the world. Here we introduce the latest developments in QuTiP v5, which are set to have a large impact on the future of QuTiP and enable it to be a modern, continuously developed and popular tool for another decade and more. We summarize the code design and fundamental data layer changes as well as efficiency improvements, new solvers, applications to quantum circuits with QuTiP-QIP, and new quantum control tools with QuTiP-QOC. Additional flexibility in the data layer underlying all ``quantum objects'' in QuTiP allows us to harness the power of state-of-the-art data formats and packages like JAX, CuPy, and more. We explain these new features with a series of both well-known and new examples. The code for these examples is available in a static form on GitHub and as continuously updated and documented notebooks in the qutip-tutorials package.

quant-ph↗

arXiv2024

A purified input-output pseudomode model for structured open quantum systems

A full understanding of open quantum systems requires the characterization of both system and environmental properties. However, the complexity of the environmental statistics in the presence of strong system-bath hybridization and long memory effects usually prevents effective non-perturbative methods from going beyond the analysis of the reduced system dynamics. Here we present a model consisting of purified auxiliary bosonic modes to describe, alongside properties of the system, the dynamics of environmental observables for bosonic baths prepared in non-Gaussian initial states. We numerically exemplify this method by simulating non-Markovian multi-photon transfer processes on a coupled cavity waveguide system in the large time delay regime.

quant-ph↗

arXiv2024

Revealing non-Markovian Kondo transport with waiting time distributions

We investigate non-Markovian transport dynamics and signatures of the Kondo effect in a single impurity Anderson model. The model consists of a quantum dot (QD) with ultra-strong coupling to a left lead and weak coupling to a right lead acting as a detector. We calculate the waiting time distribution (WTD) of electrons tunneling into the detector using a combination of the hierarchical equations of motion approach (HEOM) and a dressed master equation. Oscillations emerge in the short-time WTD, becoming more pronounced with stronger left-lead coupling. Fourier analysis reveals a blue shift in the oscillation frequency as coupling increases, indicating enhanced system-bath hybridization. Crucially, comparison with a dressed master equation confirms that these oscillations are a direct consequence of non-Markovian system-bath correlations. We examine the Kondo effect's influence on these oscillations by varying the quantum dot's Coulomb repulsion. Increasing this interaction enhances the WTD oscillations, coinciding with the signatures of a strengthened Kondo resonance in the quantum dot's density of states. Our results demonstrate that WTD oscillations offer a valuable tool for probing non-Markovian system-bath interactions and the emergence of Kondo correlations within quantum dot systems.

cond-mat.mes-hall↗

arXiv2024

Input-Output Hierarchical Equations Of Motion

We derive an extended version of the hierarchical equations of motion (HEOM) to compute output physical properties of a bosonic environment, which is allowed to be initially prepared at an earlier time in a non-Gaussian input state and then non-perturbatively interact with a quantum system with a linear environmental operator. While spectral assumptions analogous to the ones used in the regular HEOM are imposed to compute dynamical output bath observables, they are not required to model input states or output observables at a fixed time, in this case leading to time-dependent contributions to the equations. In the Markovian limit, we use this formalism to derive an input-output Lindblad equation which can be used to extend the applicability of the regular version. For a given desired input state and output observable, the range of the indexes extending the regular HEOM is, by construction, bounded. Overall, the aim of this formalism is to take advantage of the efficiency and generality of the HEOM framework to model non-Gaussian input states and the dynamics of environmental observables in bosonic, non-Markovian open quantum systems.

quant-ph↗

arXiv2024

Non-Markovian Quantum Exceptional Points

Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators, where eigenvalues and eigenvectors coalesce. Recently, open quantum systems have been increasingly explored as EP testbeds due to their natural non-Hermitian nature. However, existing works mostly focus on the Markovian limit, leaving a gap in understanding EPs in the non-Markovian regime. In this work, we address this gap by proposing a theoretical framework based on two numerically exact descriptions of non-Markovian dynamics: the pseudomode mapping and the hierarchical equations of motion. The proposed framework enables conventional spectral analysis for EP identification, establishing direct links between EPs and dynamic manifestations in open systems, such as non-exponential decays and enhanced sensitivity to external perturbations. We unveil pure non-Markovian EPs that are unobservable in the Markovian limit. Remarkably, the EP aligns with the Markovian-to-non-Markovian transition, and the EP condition is adjustable by modifying environmental spectral properties. Moreover, we show that structured environments can elevate EP order, thereby enhancing the system's sensitivity. These findings lay a theoretical foundation and open new avenues for non-Markovian reservoir engineering and non-Hermitian physics.

quant-ph↗

arXiv2024

Lee-Yang theory of the superradiant phase transition in the open Dicke model

The Dicke model describes an ensemble of two-level atoms that are coupled to a confined light mode of an optical cavity. Above a critical coupling, the cavity becomes macroscopically occupied, and the system enters the superradiant phase. This phase transition can be observed by detecting the photons that are emitted from the cavity; however, it only becomes apparent in the limit of long observation times, while actual experiments are of a finite duration. To circumvent this problem, we here make use of recent advances in Lee-Yang theories of phase transitions to show that the superradiant phase transition can be inferred from the factorial cumulants of the photon emission statistics obtained during a finite measurement time. Specifically, from the factorial cumulants, we can determine the complex singularities of generating functions that describe the photon emission statistics, and by extrapolating their positions to the long-time limit, one can detect the superradiant phase transition. We also show that the convergence points determine the tails of the large-deviation statistics of the photon current. Our work demonstrates how phase transitions in the Dicke model and in other quantum many-body systems can be detected from measurements of a finite duration.

cond-mat.mes-hall↗

arXiv2024

Non-Markovian skin effect

The Liouvillian skin effect and the non-Hermitian skin effect have both been used to explain the localization of eigenmodes near system boundaries, though the former is arguably more accurate in some regimes due to its incorporation of quantum jumps. However, these frameworks predominantly focus on weak Markovian interactions, neglecting the potentially crucial role of memory effects. To address this, we investigate, utilizing the powerful hierarchical equations of motion method, how a non-Markovian environment can modify the Liouvillian skin effect. We demonstrate that a non-Markovian environment can induce a ``thick skin effect", where the skin mode broadens and shifts into the bulk. {We further identify that the skin-mode quantum coherence can only be generated when the coupling contains counter-rotating terms}, leading to the coherence-delocalization and oscillatory relaxation with a characteristic linear scaling with system size. Remarkably, both the skin-mode and steady-state coherence exhibit resistance to decoherence from additional environmental noise. These findings highlight the profound impact of system-bath correlations on relaxation and localization, revealing unique phenomena beyond conventional Markovian approximations.

quant-ph↗

arXiv2024

Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics

The pseudomode framework provides an exact description of the dynamics of an open quantum system coupled to a non-Markovian environment. Using this framework, the influence of the environment on the system is studied in an equivalent model, where the open system is coupled to a finite number of unphysical pseudomodes that follow a time-local master equation. Building on the insight that this master equation does not need to conserve the hermiticity of the pseudomode state, we here ask for the most general conditions on the master equation that guarantee the correct reproduction of the system's original dynamics. We demonstrate that our generalized approach decreases the number of pseudomodes that are required to model, for example, underdamped environments at finite temperature. We also provide an unraveling of the master equation into quantum jump trajectories of non-Hermitian states, which further facilitates the utilization of the pseudomode technique for numerical calculations by enabling the use of easily parallelizable Monte Carlo simulations. Finally, we show that pseudomodes, despite their unphysical nature, provide a natural picture in which physical processes, such as the creation of system-bath correlations or the exchange of heat, can be studied. Hence, our results pave the way for future investigations of the system-environment interaction leading to a better understanding of open quantum systems far from the Markovian weak-coupling limit.

quant-ph↗

arXiv2023

Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise

The influence of a Gaussian environment on a quantum system can be described by effectively replacing the continuum with a discrete set of ancillary quantum and classical degrees of freedom. This defines a pseudomode model which can be used to classically simulate the reduced system dynamics. Here, we consider an alternative point of view and analyze the potential benefits of an analog or digital quantum simulation of the pseudomode model itself. Superficially, such a direct experimental implementation is, in general, impossible due to the unphysical properties of the effective degrees of freedom involved. However, we show that the effects of the unphysical pseudomode model can still be reproduced using measurement results over an ensemble of physical systems involving ancillary harmonic modes and an optional stochastic driving field. This is done by introducing an extrapolation technique whose efficiency is limited by stability against imprecision in the measurement data. We examine how such a simulation would allow us to (i) perform accurate quantum simulation of the effects of complex non-perturbative and non-Markovian environments in regimes that are challenging for classical simulation, (ii) conversely, mitigate potential unwanted non-Markovian noise present in quantum devices, and (iii) restructure some of some of the properties of a given physical bath, such as its temperature.

quant-ph↗

arXiv2023

Fixing detailed balance in ancilla-based dissipative state engineering

Dissipative state engineering is a general term for a protocol which prepares the ground state of a complex many-body Hamiltonian using engineered dissipation or engineered environments. Recently, it was shown that a version of this protocol, where the engineered environment consists of one or more dissipative qubit ancillas tuned to be resonant with the low-energy transitions of a many-body system, resulted in the combined system evolving to reasonable approximation to the ground state. This potentially broadens the applicability of the method beyond non-frustrated systems, to which it was previously restricted. Here we argue that this approach has an intrinsic limitation because the ancillas, seen as an effective bath by the system in the weak-coupling limit, do not give the detailed balance expected for a true zero-temperature environment. Our argument is based on the study of a similar approach employing linear coupling to bosonic ancillas. We explore overcoming this limitation using a recently developed technique from open-quantum-systems called pseudomodes. With a simple example model of a 1D quantum Ising chain, we show that detailed balance can be fixed, and a more accurate estimation of the ground state obtained, at the cost of two additional unphysical dissipative modes and the extrapolation error of implementing those modes in physical systems.

quant-ph↗