arXiv subjects

L. A. Williamson

Publications and source records attributed to L. A. Williamson.

11 recordsLinked to original sources

arXiv2026

Frictional work and entropy production in integrable and non-integrable spin chains

The maximum work extractable from a quantum system is achieved when the system is driven adiabatically. Frictional work $\langle W\rangle_\mathrm{fric}$ then quantifies the difference in work output between adiabatic and non-adiabatic driving. Here we show that frictional work in a non-integrable spin chain is well-characterized by the diagonal entropy production $ΔS_\mathrm{d}$ associated with the build up of quantum coherence. We show that, over a broad range of parameters, $\langle W\rangle_\mathrm{fric}\approx T_τΔS_\mathrm{d}$, with $T_τ$ the effective temperature of the final time-evolved state. The relationship breaks down for fast protocols at low temperatures, in which case frictional work is instead well-described by the quantum relative entropy between the time-evolved state and a Gibbs-state approximation of the adiabatic state. We compare our results to those obtained from an integrable spin chain, in which case the system is no longer described by a single temperature. In this case, the frictional work is described by a sum of terms for each independent subspace of the spin chain, which are at different effective temperatures. Finally, we show how integrability breaking can enhance work extraction in the adiabatic limit, but degrade work extraction in sufficiently non-adiabatic regimes.

quant-ph↗

arXiv2026

Reservoir-mediated spin entanglement in the mean-force Gibbs state

Two qubits strongly coupled to a common bosonic reservoir can become entangled with each other, despite having no direct interaction. In equilibrium, such coupling-induced coherences can be described by the mean-force Gibbs state. Here we derive approximate, analytic expressions for the two-qubit mean-force Gibbs state, and use these to characterize equilibrium qubit-qubit entanglement mediated by a thermal reservoir. Entanglement, which is highest at lowest temperatures, is a non-monotonic function of the system-reservoir coupling strength. Moreover, we find that broadening the reservoir spectral density beyond a single mode, as is realistic for typical baths, can enhance the qubit entanglement. Our results provide a comprehensive understanding of reservoir-mediated two-qubit entanglement in thermal equilibrium and provide a benchmark to compare with numerical methods, as well as demonstrating the utility of strong system-reservoir coupling as a resource.

quant-ph↗

arXiv2025

Quantum thermal machine regimes in the transverse-field Ising model

We identify and interpret the possible quantum thermal machine regimes with a transverse-field Ising model as the working substance. In general, understanding the emergence of such regimes in a many-body quantum system is challenging due to the dependence on the many energy levels in the system. By considering infinitesimal work strokes, we can understand the operation from equilibrium properties of the system. We find that infinitesimal work strokes enable both heat engine and accelerator operation, with the output and boundaries of operation described by macroscopic properties of the system, in particular the net transverse magnetization. At low temperatures, the regimes of operation and performance can be understood from quasiparticles in the system, while at high temperatures an expansion of the free energy in powers of inverse temperature describes the operation. The understanding generalises to larger work strokes when the temperature difference between the hot and cold reservoirs is large. For hot and cold reservoirs close in temperature, a sufficiently large work stroke can enable refrigerator and heater regimes. Our results and method of analysis will prove useful in understanding the possible regimes of operation of quantum many-body thermal machines more generally.

quant-ph↗

arXiv2025

Extracting work from coherence in a two-mode Bose-Einstein condensate

We show how work can be extracted from number-state coherence in a two-mode Bose-Einstein condensate. With careful tuning of parameters, a sequence of thermodynamically reversible steps transforms a Glauber coherent state into a thermal state with the same energy probability distribution. The work extracted during this process arises entirely from the removal of quantum coherence. More generally, we characterise quantum (from coherence) and classical (remaining) contributions to work output, and find that in this system the quantum contribution can be dominant over a broad range of parameters. The proportion of quantum work output can be further enhanced by squeezing the initial state. Due to the many-body nature of the system, the work from coherence can equivalently be understood as work from entanglement.

cond-mat.quant-gas↗

arXiv2025

Modified Jarzynski equality in a microcanonical ensemble

We show that the conventional Jarzynski equality does not hold for a system prepared in a microcanonical ensemble. We derive a modified equality that connects microcanonical work fluctuations to entropy production, in an analogous way to the Jarzynski equality, but with reference to an inverse temperature that depends on the path of the work protocol. For close to isothermal processes the modified equality can improve on the bound $\langle W\rangle\ge ΔF$. Our result is a special case of a general expression for the microcanonical moment-generating function for any extensive quantity, which enables calculation of the breakdown of ensemble equivalence for thermodynamic fluctuations. We demonstrate our microcanonical Jarzynski equality in a system of driven two-level spins.

cond-mat.stat-mech↗

arXiv2024

Many-body enhancement in a spin-chain quantum heat engine

We show that ferromagnetic interactions can enhance the adiabatic performance of a quantum spin chain engine at low temperatures. The enhancement in work output is particular pronounced, increasing exponentially with interaction strength. The performance enhancement occurs in the paramagnetic phase and is qualitatively explained by considering just the ground and first excited state, in which case the system exhibits bipartite entanglement. As the temperature is increased, thermal occupation of higher energy states diminishes performance. We find that these thermal fluctuations are smallest for long-range interactions, resulting in the highest efficiency. Diabatic work extraction degrades performance due to quantum friction. We identify an approximate, experimentally realisable counterdiabatic drive that can mitigate friction for weak interactions.

quant-ph↗

arXiv2024

Berezinskii-Kosterlitz-Thouless transitions in a ferromagnetic superfluid: effects of axial magnetization

An easy-plane ferromagnetic spin-1 Bose gas undergoes two Berezinskii-Kosterlitz-Thouless (BKT) transitions, associated with mass and spin superfluidity respectively. We study the effect of axial magnetization on the superfluid properties of this system. We find that nonzero axial magnetization couples mass and spin superflow, via a mechanism analogous to the Andreev-Bashkin effect present in two-component superfluids. With sufficiently large axial magnetization mass and spin superfluidity arise simultaneously. The cross-over to this phase provides a finite-temperature generalization of the zero-temperature broken-axisymmetric to easy-axis transition. We present analytic relations connecting mass and spin superfluidity with experimentally observable coherence of the three spinor components and local magnetization.

cond-mat.quant-gas↗

arXiv2023

Berezinskii-Kosterlitz-Thouless transitions in an easy-plane ferromagnetic superfluid

A two-dimensional (2D) spin-1 Bose gas exhibits two Berezenskii-Kosterlitz-Thouless (BKT) transitions in the easy-plane ferromagnetic phase. The higher temperature transition is associated with superfluidity of the mass current determined predominantly by a single spin component. The lower temperature transition is associated with superfluidity of the axial spin current, quasi-long range order of the transverse spin density and binding of polar-core spin vortices (PCVs). Above the spin BKT temperature, the component circulations that make up each PCV spatially separate, suggesting possible deconfinement analogous to quark deconfinement in high energy physics. Intercomponent interactions give rise to superfluid drag between the spin components, which we calculate analytically at zero temperature. We present the mass/spin superfluid phase diagram as a function of quadratic Zeeman energy $q$. At $q=0$ the system is in an isotropic spin phase with $\mathrm{SO}(3)$ symmetry. Here the fluid response exhibits a system size dependence, suggesting the absence of a BKT transition. Despite this, for finite systems the decay of spin correlations changes from exponential to algebraic as the temperature is decreased.

cond-mat.quant-gas↗

arXiv2020

A superatom picture of collective nonclassical light emission and dipole blockade in atom arrays

We show that two-time, second-order correlations of scattered photons from planar arrays and chains of atoms display nonclassical features that can be described by a superatom picture of the canonical single-atom $g_2(τ)$ resonance fluorescence result. For the superatom, the single-atom linewidth is replaced by the linewidth of the underlying collective low light-intensity eigenmode. Strong light-induced dipole-dipole interactions lead to a correlated response, suppressed joint photon detection events, and dipole blockade that inhibits multiple excitations of the collective atomic state. For targeted subradiant modes, nonclassical nature of emitted light can be dramatically enhanced even compared with that of a single atom.

physics.atom-ph↗

arXiv2020

Optical response of atom chains beyond the limit of low light intensity: The validity of the linear classical oscillator model

Atoms subject to weak coherent incident light can be treated as coupled classical linear oscillators, supporting subradiant and superradiant collective excitation eigenmodes. We identify the limits of validity of this \emph{linear classical oscillator model} at increasing intensities of the drive by solving the quantum many-body master equation for coherent and incoherent scattering from a chain of trapped atoms. We show that deviations from the linear classical oscillator model depend sensitively on the resonance linewidths $\upsilon_α$ of the collective eigenmodes excited by light, with the intensity at which substantial deviation occurs scaling as a powerlaw of $\upsilon_α$. The linear classical oscillator model then becomes inaccurate at much lower intensities for subradiant collective excitations than superradiant ones, with an example system of seven atoms resulting in critical incident light intensities differing by a factor of 30 between the two cases. By individually exciting eigenmodes we find that this critical intensity has a $\upsilon_α^{2.5}$ scaling for narrower resonances and more strongly interacting systems, while it approaches a $\upsilon_α^3$ scaling for broader resonances and when the dipole-dipole interactions are reduced. The $\upsilon_α^3$ scaling also corresponds to the semiclassical result whereby quantum fluctuations between the atoms have been neglected. We study both the case of perfectly mode-matched drives and the case of standing wave drives, with significant differences between the two cases appearing only at very subradiant modes and positions of Fano resonances.

physics.atom-ph↗

arXiv2019

Anomalous phase ordering of a quenched ferromagnetic superfluid

Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects. Here we show that this understanding is incomplete. We simulate the dynamics of an isolated spin-1 condensate quenched into the easy-plane ferromagnetic phase and find that the mutual annihilation of spin vortices does not take the system to the equilibrium state. A nonequilibrium background of long wavelength spin waves remain at the Berezinskii-Kosterlitz-Thouless temperature, an order of magnitude hotter than the equilibrium temperature. The coarsening continues through a second much slower scale invariant process with a length scale that grows with time as $t^{1/3}$. This second regime of coarsening is associated with spin wave energy transport from low to high wavevectors, bringing about the the eventual equilibrium state. Because the relevant spin waves are noninteracting, the transport occurs through a dynamic coupling to other degrees of freedom of the system. The transport displays features of a spin wave energy cascade, providing a potential profitable connection with the emerging field of spin wave turbulence. Strongly coupling the system to a reservoir destroys the second regime of coarsening, allowing the system to thermalise following the annihilation of vortices.

cond-mat.quant-gas↗