arXiv subjects

Brendon W. Lovett

Publications and source records attributed to Brendon W. Lovett.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics and spectra of open quantum systems coupled to anharmonic environments

In open quantum systems, the environment is typically modelled as a collection of harmonic oscillators, whereas realistic environments often exhibit unique non-Markovian effects due to the anharmonicity of the environment. Here we present a framework for modelling anharmonic environments in open quantum systems numerically exactly, in which, via a matching criterion, we map the anharmonic environment onto an effective harmonic one. This results in an effective spectral density that is a collection of shifted bare spectra arising from the non-equidistant energy gaps of the anharmonic environment, along with a unique zero-frequency term that effectively acts as static disorder on the system. This is due to the non-zero variance of the diagonal of the bath coupling operator. In tandem, we develop a framework for investigating the effects of environments comprising a few damped anharmonic modes where the matching criterion fails to work due to the non-Gaussianity of the environment. For both continuous and discrete damped anharmonic environments, this work investigates their unique influence on the system's dynamics, including enhanced non-Markovianity compared to a harmonic approximation, novel effects in the absorption spectrum, and the potential for anharmonic environments to enhance energy transport.

quant-ph↗

arXiv2026

Tensor network methods for non-perturbative dynamics of open quantum systems

The description of open quantum system dynamics beyond the perturbative treatment (usually associated with Markovian master equations) is a computationally challenging task due to the unfavorable exponential scaling of memory kernels. Developed over recent decades in the context of quantum information and condensed matter, tensor networks provide both a new formalism and a toolbox for overcoming previous computational bottlenecks. This framework enables the formulation of non-perturbative, numerically exact methods for describing the dynamics of open quantum systems to controllable numerical accuracy. In this review, we present these methods and discuss their commonalities and differences to paint a comprehensive view of the field.

quant-ph↗

arXiv2026

Coherent room-temperature dipole synchronization in nanocavity sheets

Plasmonic nanocavities enable the synchronization of spatially distant emissive dipoles through strong near-field coupling in sub-nm gaps. We report formation of a room-temperature synchronized dipole state in locally-ordered plasmonic nanogap 2D arrays under non-resonant continuous-wave pumping. Unlike lasers, photonic Bose-Einstein condensates, or exciton-polariton condensates, this system exhibits spatial coherence across the dipoles, while rapid radiative and non-radiative emission suppresses temporal photon coherence. A change of behaviour is observed with increasing pumping, marked by the spatial spread of g(1) coherence, but without spectral narrowing or directional emission. This driven-dissipative system exhibits fast temporal coherence decay and complex spatial correlations, offering a new platform for studying synchronization at room temperature. Combining ultralow mode volumes, high Purcell enhancement, and scalable ambient operation, it opens pathways for novel photonic and quantum technologies.

cond-mat.mes-hall↗

arXiv2026

Efficient construction of time-invariant process tensors for simulating high-dimensional non-Markovian open quantum systems

Numerical methods for obtaining exact dynamics of non-Markovian open quantum systems are mostly limited to either small systems or to short-time evolution only. Here, we propose a new algorithm for computing process tensors--matrix product operator (MPO) representations that capture the environment influence--which achieves greatly enhanced computational scalings with system size, while maintaining linear scaling with simulation length. We build on recent developments in the field which allow for long-time evolutions through process tensors which have a time-translational invariance. These can be built for general Gaussian environments and generic coupling operators with the system using infinite time-evolving block decimation (iTEBD). We introduce a modified iTEBD algorithm using intermediate compression steps which bring down the computation time scaling with system size $d$ from $\mathcal{O}(d^8)$ to $\mathcal{O}(d^4)$, as well as significantly lowering the required memory. To illustrate the power of this method, we apply it to the problem of dispersive qubit readout in circuit QED, which was previously out-of-reach numerically. The full treatment of the measurement resonator, which requires a large system space, combined with the long simulation times precipitated by the separation of timescales between the measurement drive and the environment dissipation, is now possible. The algorithm we introduce not only allows for capturing non-Markovian dynamics in large open quantum systems, but also further extends all the existing capabilities of process tensors, for example in quantum optimal control, or in computation of multi-time correlations or of steady states, to more complex systems with tens of levels.

quant-ph↗

arXiv2026

Theory of dynamical superradiance in organic materials

We develop the theory of dynamical superradiance -- the collective exchange of energy between an ensemble of initially excited emitters and a single-mode cavity -- for organic materials where electronic states are coupled to vibrational modes. We consider two models to capture the vibrational effects: first, vibrations treated as a Markovian bath for two-level emitters, via a pure dephasing term in the Lindblad master equation for the system; second, vibrational modes directly included in the system via the Holstein--Tavis--Cummings Hamiltonian. By exploiting the permutation symmetry of the emitters and weak U(1) symmetry, we develop a numerical method capable of exactly solving the Tavis-Cummings model with local dissipation for up to 140 emitters. Using the exact method, we validate mean-field and second-order cumulant approximations and use them to describe macroscopic numbers of emitters. We analyse the dynamics of the average cavity photon number, electronic coherence, and Bloch vector length, and show that the effect of vibrational mode coupling goes beyond simple dephasing. Our results show that superradiance is possible in the presence of vibrational mode coupling; for negative cavity detunings, the vibrational coupling may even enhance superradiance. We identify asymmetry of the photon number rise time as a function of the detuning of the cavity frequency as an experimentally accessible signature of such vibrationally assisted superradiance.

quant-ph↗

arXiv2025

Fermionic versus Spin Baths in non-Interacting Transport Models

We investigate how fermionic anticommutation shapes transport in a noninteracting resonant-level model where a single central site is coupled to an environment. To this end, we compare a fermionic reservoir with a bath of spin-half modes using exact diagonalization and a perturbative expansion of the master equation to identify the differences. Notably, we find different reduced dynamics for the spin and fermionic baths even though the particles remain noninteracting and both models enforce local Pauli blocking. These differences originate from higher-order terms in the system-bath coupling, where fermionic anticommutation introduces exchange signs in higher-order correlations. By contrast, all second-order contributions, set solely by two-point correlators, coincide. Deviations are largest for small to intermediate bath sizes, fading in the effectively Markovian regime where higher-order corrections are negligible. These results identify when spin baths can be a substitute for fermionic reservoirs and vice versa.

quant-ph↗

arXiv2025

Non-Markovian effects in long-range polariton-mediated energy transfer

Intramolecular energy transfer driven by near-field effects plays an important role in applications ranging from biophysics and chemistry to nano-optics and quantum communications. Advances in strong light-matter coupling in molecular systems have opened new possibilities to control energy transfer. In particular, long-distance energy transfer between molecules has been reported as the result of their mutual coupling to cavity photon modes, and the formation of hybrid polariton states. In addition to strong coupling to light, molecular systems also show strong interactions between electronic and vibrational modes. The latter can act as a reservoir for energy to facilitate off-resonant transitions, and thus energy relaxation between polaritonic states at different energies. However, the non-Markovian nature of those modes makes it challenging to accurately simulate these effects. Here we capture them via process tensor matrix product operator (PT-MPO) methods, to describe exactly the vibrational environment of the molecules combined with a mean-field treatment of the light-matter interaction. In particular, we study the emission dynamics of a system consisting of two spatially separated layers of different species of molecules coupled to a common photon mode, and show that the strength of coupling to the vibrational bath plays a crucial role in governing the dynamics of the energy of the emitted light; at strong vibrational coupling this dynamics shows strongly non-Markovian effects, eventually leading to polaron formation. Our results shed light on polaritonic long-range energy transfer, and provide further understanding of the role of vibrational modes of relevance to the growing field of molecular polaritonics.

cond-mat.mes-hall↗

arXiv2025

Connectivity matters: Impact of bath modes ordering and geometry in open quantum system simulation with Tensor Network States

Being able to study the dynamics of quantum systems interacting with several environments is important in many settings ranging from quantum chemistry to quantum thermodynamics, through out-of-equilibrium systems. For such problems tensor network-based methods are state-of-the-art approaches for performing numerically exact simulations. However, to be used efficiently in this multi-environment and non-perturbative context, these methods require an optimized choice of the topology of the wave-function Ansätze. This is often done by analysing cross-correlations between different system and environment degrees of freedom. Here, we show for canonical model Hamiltonians that simple orderings of bosonic environmental modes, which enable the joint {System + Environments} state to be written as a matrix product state, considerably reduce the bond dimension required for convergence despite introducing long-ranged interactions. These results suggest that complex correlation analyses for tweaking tensor networks topology (e.g. entanglement renormalization) are usually not necessary and that tree tensor network states are sub-optimal compared to simple matrix product states in many important models of physical open systems.

quant-ph↗

arXiv2025

Extracting Coupling-Mode Spectral Densities with Two-Dimensional Electronic Spectroscopy

Methods for reconstructing the spectral density of a vibrational environment from experimental data can yield key insights into the impact of the environment on molecular function. Although such experimental methods exist, they generally only access vibrational modes that couple diagonally to the electron system. Here we present a method for extracting the spectral density of modes that couple to the transition between electronic states, using two-dimensional electronic spectroscopy. To demonstrate this, we use a process-tensor method that can simulate two-dimensional electronic spectroscopy measurements in a numerically exact way. To explain how the extraction works, we also derive an approximate analytical solution, which illustrates that the non-Markovianity of the environment plays an essential role in the existence of the simulated signal.

physics.chem-ph↗

arXiv2024

Tree-like process tensor contraction for automated compression of environments

The algorithm "automated compression of environments" (ACE) [Nat. Phys. 18, 662 (2022)] provides a versatile way of simulating an extremely broad class of open quantum systems. This is achieved by encapsulating the influence of the environment, which is determined by the interaction Hamiltonian(s) and initial states, into compact process tensor matrix product operator (PT-MPO) representations. The generality of the ACE method comes at high numerical cost. Here, we demonstrate that orders-of-magnitude improvement of ACE is possible by changing the order of PT-MPO contraction from a sequential to a tree-like scheme. The problem of combining two partial PT-MPOs with large inner bonds is solved by a preselection approach. The drawbacks of the preselection approach are that the MPO compression is suboptimal and that it is more prone to error accumulation than sequential combination and compression. We therefore also identify strategies to mitigate these disadvantages by fine-tuning compression parameters. This results in a scheme that is similar in compression efficiency and accuracy to the original ACE algorithm, yet is significantly faster. Our numerical experiments reach similar conclusions for bosonic and fermionic test cases, suggesting that our findings are characteristic of the combination of PT-MPOs more generally.

quant-ph↗

arXiv2024

Process tensor approaches to modeling two-dimensional spectroscopy

Problems in the field of open quantum systems often involve an environment that strongly influences the dynamics of excited states. Here we present a numerical method to model optical spectra of non-Markovian open quantum systems. The method employs a process tensor framework to efficiently compute multi-time correlations in a numerically exact way. To demonstrate the efficacy of our method, we compare 2D electronic spectroscopy simulations produced through our method to Markovian master equation simulations in three different system-bath coupling regimes.

quant-ph↗

arXiv2024

OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors

Non-Markovian dynamics arising from the strong coupling of a system to a structured environment is essential in many applications of quantum mechanics and emerging technologies. Deriving an accurate description of general quantum dynamics including memory effects is however a demanding task, prohibitive to standard analytical or direct numerical approaches. We present a major release of our open source software package, OQuPy (Open Quantum System in Python), which provides several recently developed numerical methods that address this challenging task. It utilizes the process tensor approach to open quantum systems in which a single map, the process tensor, captures all possible effects of an environment on the system. The representation of the process tensor in a tensor network form allows an exact yet highly efficient description of non-Markovian open quantum systems (NM-OQS). The OQuPy package provides methods to (1) compute the dynamics and multi-time correlations of quantum systems coupled to single and multiple environments, (2) optimize control protocols for NM-OQS, (3) simulate interacting chains of NM-OQS, and (4) compute the mean-field dynamics of an ensemble of NM-OQS coupled to a common central system. Our aim is to provide an easily accessible and extensible tool for researchers of open quantum systems in fields such as quantum chemistry, quantum sensing, and quantum information.

quant-ph↗

arXiv2024

From Non-Markovian Dissipation to Spatiotemporal Control of Quantum Nanodevices

Nanodevices exploiting quantum effects are critically important elements of future quantum technologies (QT), but their real-world performance is strongly limited by decoherence arising from local `environmental' interactions. Compounding this, as devices become more complex, i.e. contain multiple functional units, the `local' environments begin to overlap, creating the possibility of environmentally mediated decoherence phenomena on new time-and-length scales. Such complex and inherently non-Markovian dynamics could present a challenge for scaling up QT, but -- on the other hand -- the ability of environments to transfer `signals' and energy might also enable sophisticated spatiotemporal coordination of inter-component processes, as is suggested to happen in biological nanomachines, like enzymes and photosynthetic proteins. Exploiting numerically exact many body methods (tensor networks) we study a fully quantum model that allows us to explore how propagating environmental dynamics can instigate and direct the evolution of spatially remote, non-interacting quantum systems. We demonstrate how energy dissipated into the environment can be remotely harvested to create transient excited/reactive states, and also identify how reorganisation triggered by system excitation can qualitatively and reversibly alter the `downstream' kinetics of a `functional' quantum system. With access to complete system-environment wave functions, we elucidate the microscopic processes underlying these phenomena, providing new insight into how they could be exploited for energy efficient quantum devices.

physics.bio-ph↗

arXiv2023

Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?

The interaction between a quantum system and its environment limits our ability to control it and perform quantum operations on it. We present an efficient method to find optimal controls for quantum systems coupled to non-Markovian environments, by using the process tensor to compute the gradient of an objective function. We consider state transfer for a driven two-level system coupled to a bosonic environment, and characterize performance in terms of speed and fidelity. We thus determine the best achievable fidelity as a function of process duration. We show there is a trade-off between speed and fidelity, and that slower processes can have higher fidelity by exploiting non-Markovian effects.

quant-ph↗

arXiv2023

Determining the validity of cumulant expansions for central spin models

For a model with many-to-one connectivity it is widely expected that mean-field theory captures the exact many-particle $N\to\infty$ limit, and that higher-order cumulant expansions of the Heisenberg equations converge to this same limit whilst providing improved approximations at finite $N$. Here we show that this is in fact not always the case. Instead, whether mean-field theory correctly describes the large-$N$ limit depends on how the model parameters scale with $N$, and the convergence of cumulant expansions may be non-uniform across even and odd orders. Further, even when a higher-order cumulant expansion does recover the correct limit, the error is not monotonic with $N$ and may exceed that of mean-field theory.

cond-mat.stat-mech↗

arXiv2023

Sublinear scaling in non-Markovian open quantum systems simulations

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps $n$. Here, we introduce a numerically exact algorithm to calculate process tensors -- compact representations of environmental influences -- which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent Gaussian environments. Based on a divide-and-conquer strategy, our approach requires only $\mathcal{O}(n\log n)$ singular value decompositions for environments with infinite memory. Where the memory can be truncated after $n_c$ time steps, a scaling $\mathcal{O}(n_c\log n_c)$ is found, which is independent of $n$. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dot-phonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but also has fundamental implications for simulation complexity.

quant-ph↗

arXiv2023

Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems

We present a general method to efficiently design optimal control sequences for non-Markovian open quantum systems, and illustrate it by optimizing the shape of a laser pulse to prepare a quantum dot in a specific state. The optimization of control procedures for quantum systems with strong coupling to structured environments -- where time-local descriptions fail -- is a computationally challenging task. We modify the numerically exact time evolving matrix product operator (TEMPO) method, such that it allows the repeated computation of the time evolution of the reduced system density matrix for various sets of control parameters at very low computational cost. This method is potentially useful for studying numerous optimal control problems, in particular in solid state quantum devices where the coupling to vibrational modes is typically strong.

quant-ph↗

arXiv2023

Tensor network simulation of chains of non-Markovian open quantum systems

We introduce a general numerical method to compute dynamics and multi-time correlations of chains of quantum systems, where each system may couple strongly to a structured environment. The method combines the process tensor formalism for general (possibly non-Markovian) open quantum systems with time evolving block decimation (TEBD) for 1D chains. It systematically reduces the numerical complexity originating from system-environment correlations before integrating them into the full many-body problem, making a wide range of applications numerically feasible. We illustrate the power of this method by studying two examples. First, we study the thermalization of individual spins of a short XYZ Heisenberg chain with strongly coupled thermal leads. Our results confirm the complete thermalization of the chain when coupled to a single bath, and reveal distinct effective temperatures in low, mid, and high frequency regimes when the chain is placed between a hot and a cold bath. Second, we study the dynamics of diffusion in an longer XY chain, when each site couples to its own bath.

quant-ph↗