arXiv subjects

Peter Kirton

Publications and source records attributed to Peter Kirton.

At least 19 recordsLinked to original sources

arXiv2026

Mott-insulating phases of the Bose-Hubbard model on quasi-1D ladder lattices

We calculate the phase diagram of the Bose-Hubbard model on a half-filled ladder lattice including the effect of finite on-site interactions. This shows that the rung-Mott insulator (RMI) phase persists to finite interaction strength, and we calculate the RMI-superfluid phase boundary in the thermodynamic limit. We show that the phases can still be distinguished using the number and parity variances, which are observables accessible in a quantum-gas microscope. Phases analogous to the RMI were found to exist in other quasi-1D lattice structures, with the lattice connectivity modifying the phase boundaries. This shows that the the presence of these phases is the result of states with one-dimensional structures being mapped onto higher dimensional systems, driven by the reduction of hopping rates along different directions.

cond-mat.quant-gas↗

arXiv2025

Collective Enhancement of Photon Blockade via Two-Photon Interactions

Analogous to Coulomb blockade for electrons, photon blockade is a key quantum optical effect in which the presence of one photon prevents the transmission of subsequent ones through a nonlinear medium. Beyond its fundamental interest, photon and multi-photon blockade are actively studied as mechanisms for generating technologically-relevant quantum states of light. Although photon blockade typically requires achieving strong light-matter coupling, increasing the number of atoms fails to enhance antibunching. Here, we analyze the optical transmission properties of a quantum resonator that embeds a two-photon-coupled ensemble of emitters, combining an approximate analytical approach with full quantum numerical simulations. We show that when light and matter are coupled via a two-photon interaction, both single- and multi-photon blockade can benefit from a collective enhancement. We propose different driving schemes in which the second or third-order correlation functions are strongly suppressed with increasing atom number. Differently from established methods, this collective enhancement of non-classical properties occurs with unitary transmission and is ultimately constrained only by decoherence. This demonstrates that collective two-photon couplings are a powerful mechanism for realizing photon blockade even in platforms where individual strong coupling is not achievable.

quant-ph↗

arXiv2025

PT-symmetry breaking phase transitions in an LMG dimer

The open Lipkin-Meshkov-Glick (LMG) model provides a prototype of a dissipative phase transition which can be analyzed using mean-field theory. By combining the physics of this model with those of a quantum analogue of a parity-time reversal symmetry breaking transition we analyze the steady state phase diagram of a pair of coupled LMG models. Their competition generates a complex phase diagram with multiple steady-state phases and emergent dynamical regimes absent from either constituent model, including chaos characterized by the maximum Lyapunov exponent. We show that the effects predicted from mean-field theory survive in the full quantum model.

quant-ph↗

arXiv2025

Quantum-gas microscopy and Talbot interferometry of the Bose-glass phase

Disordered potentials fundamentally affect transport and coherence in quantum systems, giving rise to a Bose-glass phase in interacting bosonic systems -- an insulating yet compressible phase lacking long-range coherence. Directly measuring a reduced coherence length of the Bose glass has been an outstanding challenge. We address this by employing Talbot interferometry combined with single-atom-resolved detection in a quantum-gas microscope. Using ultracold bosonic atoms in a two-dimensional lattice with site-resolved, reproducible disorder, we identify the Bose-glass phase through in-situ density distributions and particle-number fluctuations, quantified via the Edwards-Anderson parameter, and through the visibility of interference patterns after time-of-flight. By driving the system across the Bose-glass phase, we further observe signatures of non-ergodic dynamics. Our studies provide a starting point to further explore disordered systems in and out of equilibrium, and are relevant for understanding the dynamics and stability of disordered and glass-like quantum states in solid-state systems.

cond-mat.quant-gas↗

arXiv2024

Dissipative Phase Transition in the Two-Photon Dicke Model

We explore the dissipative phase transition of the two-photon Dicke model, a topic that has garnered significant attention recently. Our analysis reveals that while single-photon loss does not stabilize the intrinsic instability in the model, the inclusion of two-photon loss restores stability, leading to the emergence of superradiant states which coexist with the normal vacuum states. Using a second-order cumulant expansion for the photons, we derive an analytical description of the system in the thermodynamic limit which agrees well with the exact calculation results. Additionally, we present the Wigner function for the system, shedding light on the breaking of the Z4-symmetry inherent in the model. These findings offer valuable insights into stabilization mechanisms in open quantum systems and pave the way for exploring complex nonlinear dynamics in two-photon Dicke models.

quant-ph↗

arXiv2024

Superfluorescent upconversion nanoparticles as an emerging second generation quantum technology material

Superfluorescence (SF) in lanthanide doped upconversion nanoparticles (UCNPs) is a room-temperature quantum phenomenon, first discovered in 2022. In a SF process, the many emissive lanthanide ions within a single UCNP are coherently coupled by an ultra-short (ns or fs) high-power excitation laser pulse. This leads to a superposition of excited emissive states which decrease the emissive lifetime of the UCNP by a factor proportional to the square of the number of lanthanide ions which are coherently coupled. This results in a dramatic decrease in UCNP emission lifetime from the microsecond regime to the nanosecond regime. Thus SF offers a tantalizing prospect to achieving superior upconversion photon flux in upconversion materials, with potential applications such as imaging and sensing. This perspective article contextualizes how SF-UCNPs can be regarded as a second generation quantum technology, and notes several challenges, opportunities, and open questions for the development of SF-UCNPs.

physics.optics↗

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

A numerical approach for calculating exact non-adiabatic terms in quantum dynamics

Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on the non-adiabatic terms that arise from time dependence in the Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an appropriate basis of the AGP, which can be easily truncated to give an approximate form when the exact result is intractable. We use this approach to study the AGP obtained for the transverse field Ising model on a variety of graphs, showing how the different underlying graph structures can give rise to very different scaling for the number of terms required in the AGP.

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

Liouville Space Neural Network Representation of Density Matrices

Neural network quantum states as ansatz wavefunctions have shown a lot of promise for finding the ground state of spin models. Recently, work has been focused on extending this idea to mixed states for simulating the dynamics of open systems. Most approaches so far have used a purification ansatz where a copy of the system Hilbert space is added which when traced out gives the correct density matrix. Here, we instead present an extension of the Restricted Boltzmann Machine which directly represents the density matrix in Liouville space. This allows the compact representation of states which appear in mean-field theory. We benchmark our approach on two different version of the dissipative transverse field Ising model which show our ansatz is able to compete with other state-of-the-art approaches.

quant-ph↗

arXiv2022

Using the Environment to Understand non-Markovian Open Quantum Systems

Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where there is strong interplay between the system and environmental degrees of freedom this loss makes understanding the dynamics challenging. These dynamics, when viewed in isolation, have no time-local description: they are non-Markovian and memory effects induce complex features that are difficult to interpret. To address this problem, we here show how to use system correlations, calculated by any method, to infer any correlation function of a Gaussian environment, so long as the coupling between system and environment is linear. This not only allows reconstruction of the full dynamics of both system and environment, but also opens avenues into studying the effect of a system on its environment. In order to obtain accurate bath dynamics, we exploit a numerically exact approach to simulating the system dynamics, which is based on the construction and contraction of a tensor network that represents the process tensor of this open quantum system. Using this we are able to find any system correlation function exactly. To demonstrate the applicability of our method we show how heat moves between different modes of a bosonic bath when coupled to a two-level system that is subject to an off-resonant drive.

quant-ph↗

arXiv2022

A quantum model of lasing without inversion

Starting from a quantum description of multiple Lambda-type 3-level atoms driven with a coherent microwave field and incoherent optical pumping, we derive a microscopic model of lasing from which we move towards a consistent macroscopic picture. Our analysis applies across the range of system sizes from nanolasers to the thermodynamic limit of conventional lasing. We explore the necessary conditions to achieve lasing without inversion by calculating the non-equilibrium steady state solutions of the model at, and between, its microscopic and macroscopic limits. For the macroscopic picture, we use mean-field theory to present a thorough analysis of the lasing phase transition. In the microscopic case, we exploit the underlying permutation symmetry of the density matrix to calculate exact solutions for N 3-level systems. This allows us to show that the steady state solutions approach the thermodynamic limit as N increases, restoring the sharp non-equilibrium phase transition in this limit. We demonstrate how the lasing phase transition and degree of population inversion can be adjusted by simply varying the phase of the coherent driving field. The high level of quantum control presented by this microscopic model and the framework outlined here have applications to further understanding and developing nanophotonic technology.

quant-ph↗

arXiv2021

Exact dynamics of non-additive environments in non-Markovian open quantum systems

When a quantum system couples strongly to multiple baths then it is generally no longer possible to describe the resulting system dynamics by simply adding the individual effects of each bath. However, capturing such multi-bath system dynamics has up to now required approximations that can obscure some of the non-additive effects. Here we present a numerically-exact and efficient technique for tackling this problem that builds on the time-evolving matrix product operator (TEMPO) representation. We test the method by applying it to a simple model system that exhibits non-additive behaviour: a two-level dipole coupled to both a vibrational and an optical bath. Although not directly coupled, there is an effective interaction between the baths mediated by the system that can lead to population inversion in the matter system when the vibrational coupling is strong. We benchmark and validate multi-bath TEMPO against two approximate methods - one based on a polaron transformation, the other on an identification of a reaction coordinate - before exploring the regime of simultaneously strong vibrational and optical coupling where the approximate techniques break down. Here we uncover a new regime where the quantum Zeno effect leads to a fully mixed state of the electronic system.

quant-ph↗

arXiv2021

Phase-Space Methods for Simulating the Dissipative Many-Body Dynamics of Collective Spin Systems

We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses an extension of the truncated Wigner approximation to map the exact open system dynamics onto stochastic differential equations for the corresponding phase space distribution. This approach is most effective in the limit of very large spin quantum numbers, where exact numerical simulations and other approximation methods are no longer applicable. We benchmark this numerical technique for known superradiant decay and spin-squeezing processes and illustrate its application for the simulation of non-equilibrium phase transitions in dissipative spin lattice models.

quant-ph↗

arXiv2020

Non-equilibrium magnetic phases in spin lattices with gain and loss

We study the magnetic phases of a non-equilibrium spin chain, where coherent interactions between neighboring lattice sites compete with alternating gain and loss processes. This competition between coherent and incoherent dynamics induces transitions between magnetically aligned and highly mixed phases, across which the system changes from a low- to an effective infinite-temperature state. We show that the origin of these transitions can be traced back to the dynamical effect of parity-time-reversal symmetry breaking, which has no counterpart in the theory of equilibrium phase transitions. This mechanism also results in very atypical features and we find first-order transitions without phase co-existence and mixed-order transitions which do not break the underlying $U(1)$ symmetry, even in the appropriate thermodynamic limit. Thus, despite its simplicity, the current model considerably extends the phenomenology of non-equilibrium phase transitions beyond that commonly assumed for driven-dissipative spins and related systems.

quant-ph↗

arXiv2020

Emergence of PT-symmetry breaking in open quantum systems

The effect of PT-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. Here we generalize the definition of PT symmetry to finite-dimensional open quantum systems, which are described by a Markovian master equation. Specifically, we show that the invariance of this master equation under a certain symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected PT-symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe PT-symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.

quant-ph↗

arXiv2020

Super-correlated radiance in nonlinear photonic waveguides

We study the collective decay of two-level emitters coupled to a nonlinear waveguide, for example, a nanophotonic lattice or a superconducting resonator array with strong photon-photon interactions. Under these conditions a new decay channel into bound photon pairs emerges, through which spatial correlations between emitters are established by regular interference as well as interactions between the photons. We derive an effective Markovian theory to model the resulting decay dynamics of an arbitrary distribution of emitters and identify collective effects beyond the usual phenomena of super- and subradiance. Specifically, in the limit of many close-by emitters, we find that the system undergoes a super-correlated decay process where either all the emitters are in the excited state or in the ground state, but not in any of the intermediate states. The predicted effects can be probed in state-of-the-art waveguide QED experiments and provide a striking example of how the dynamics of open quantum systems can be modified by many-body effects in a non-harmonic environment.

quant-ph↗

arXiv2019

Exact Quantum Dynamics in Structured Environments

The dynamics of a wide range of technologically important quantum systems are dominated by their interaction with just a few environmental modes. Such highly structured environments give rise to long-lived bath correlations that induce complex dynamics which are very difficult to simulate. These difficulties are further aggravated when spatial correlations between different parts of the system are important. By modeling the dynamics of a pair of two-level quantum systems in a common, structured, environment we show that a recently developed numerical approach, the time-evolving matrix product operator, is capable of accurate simulation under exactly these conditions. We find that tuning the separation to match the wavelength of the dominant environmental modes can drastically modify the system dynamics. To further explore this behavior, we show that the full dynamics of the bath can be calculated directly from those of the system, thus allowing us to develop intuition for the complex system dynamics observed.

quant-ph↗