arXiv subjects

Mark T. Mitchison

Publications and source records attributed to Mark T. Mitchison.

At least 37 records · Page 2Linked to original sources

arXiv2025

Rapid optimal work extraction from a quantum-dot information engine

The conversion of thermal energy into work is usually more efficient in the slow-driving regime, where the power output is vanishingly small. Efficient work extraction for fast driving protocols remains an outstanding challenge at the nanoscale, where fluctuations play a significant role. In this Letter, we use a quantum-dot Szilard engine to extract work from thermal fluctuations with maximum efficiency over two decades of driving speed. We design and implement a family of optimised protocols ranging from the slow- to the fast-driving regime, and measure the engine's efficiency as well as the mean and variance of its power output in each case. These optimised protocols exhibit significant improvements in power and efficiency compared to the naive approach. Our results also show that, when optimising for efficiency, boosting the power output of a Szilard engine inevitably comes at the cost of increased power fluctuations.

quant-ph↗

arXiv2025

Quantum master equation from the eigenstate thermalization hypothesis

We use the eigenstate thermalization hypothesis to derive a quantum master equation for a system weakly coupled to a chaotic finite-sized bath prepared in a pure state. We show that the emergence of Markovianity is controlled by the spectral function of the ETH and that local detailed balance emerges in the Markovian regime for a broad class of pure bath states. We numerically verify this result by comparing the master equation to dynamics computed using exact diagonalization of a chaotic Hamiltonian. We also compare the master equation to exact dynamics for an integrable bath and find that at finite size they strongly disagree. Our work puts forward eigenstate thermalization as a foundation for open quantum systems theory, thus extending it beyond ensemble bath preparations to chaotic many-body environments in generic pure states.

quant-ph↗

arXiv2025

Correlated decoherence and thermometry with mobile impurities in a 1D Fermi gas

We theoretically investigate the correlated decoherence dynamics of two mobile impurities trapped within a gas of ultracold fermionic atoms. We use a mean-field approximation to self-consistently describe the effect of impurity-gas collisions on impurity motion, while decoherence of the impurities' internal state is computed exactly within a functional determinant approach. At equilibrium, we find that the impurities undergo bath-induced localisation as the impurity-gas interaction strength is increased. We then study the non-equilibrium dynamics induced by a sudden change of the impurities' internal state, which can be experimentally probed by Ramsey interferometry. Our theoretical approach allows us to investigate the effect of impurity motion on decoherence dynamics, finding strong deviations from the universal behaviour associated with Anderson's orthogonality catastrophe when the mass imbalance between impurity and gas atoms is small. Finally, we show that mobile impurities can be used as thermometers of their environment and that bath-mediated correlations can be beneficial for thermometric performance at low temperatures, even in the presence of non-trivial impurity motion. Our results showcase the interesting open quantum dynamics of mobile impurities dephasing in a common environment, and could help provide more precise temperature estimates of ultracold fermionic mixtures.

cond-mat.quant-gas↗

arXiv2025

Quantum stochastic thermodynamics in the mesoscopic-leads formulation

We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response regime. Our method exploits the mesoscopic-leads formulation, where macroscopic reservoirs are modeled by a finite collection of modes that are continuously damped toward thermal equilibrium by an appropriate Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on non-interacting fermionic systems, we access the time-resolved full counting statistics through a trajectory unraveling of the master equation. We show that the integral fluctuation theorems for the total entropy production, as well as the martingale and uncertainty entropy production, hold. Furthermore, we investigate the fluctuations of the dissipated heat in finite-time information erasure. Conceptually, our approach extends the continuous-time trajectory description of quantum stochastic thermodynamics beyond the regime of weak system-environment coupling.

quant-ph↗

arXiv2025

Current-based metrology with two-terminal mesoscopic conductors

The traditional approach to quantum parameter estimation focuses on the quantum state, deriving fundamental bounds on precision through the quantum Fisher information. In most experimental settings, however, performing arbitrary quantum measurements is highly unfeasible. In open quantum systems, an alternative approach to metrology involves the measurement of stochastic currents flowing from the system to its environment. However, the present understanding of current-based metrology is mostly limited to Markovian master equations. Considering a parameter estimation problem in a two-terminal mesoscopic conductor, we identify the key elements that determine estimation precision within the Landauer-Büttiker formalism. Crucially, this approach allows us to address arbitrary coupling and temperature regimes. Furthermore, we obtain analytical results for the precision in linear-response and zero-temperature regimes. For the specific parameter estimation task that we consider, we demonstrate that the boxcar transmission function is optimal for current-based metrology in all parameter regimes.

quant-ph↗

arXiv2025

Quantum detectors as autonomous machines: assessing the nonequilibrium thermodynamics of information acquisition

We formulate a minimal model of a quantum particle detector as an autonomous quantum thermal machine. Our goal is to establish how entropy production, which is needed to maintain the detector out of equilibrium, is linked to the quality of the measurement process. Using our model, we perform a detailed investigation of the detector's key performance characteristics: namely, detection efficiency, gain, jitter, dead time, and dark counts. We find that entropy production constrains both the efficiency and temporal precision of the detection process, in the sense that improved performance generally requires more dissipation. We also find that reducing either the detection jitter or dead time unavoidably increases the rate of dark counts. Our work establishes a quantitative connection between entropy production and the quality of the irreversible detection process, highlights fundamental tradeoffs in the performance of particle detectors, and provides a framework for further investigations of the non-equilibrium thermodynamics of quantum measurement and amplification.

quant-ph↗

arXiv2025

Optimal time estimation and the clock uncertainty relation for stochastic processes

Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organisation of everyday life. Many biological processes also depend on time estimation by nanoscale clocks, whose performance can be significantly impacted by random fluctuations. In this work, we formulate the problem of optimal time estimation for Markovian stochastic processes, and present its general solution in the asymptotic (long-time) limit. Specifically, we obtain a tight upper bound on the precision of any time estimate constructed from sustained observations of a classical, Markovian jump process. This bound is controlled by the mean residual time, i.e. the expected wait before the first jump is observed. As a consequence, we obtain a universal bound on the signal-to-noise ratio of arbitrary currents and counting observables in the steady state. This bound is similar in spirit to the kinetic uncertainty relation but provably tighter, and we explicitly construct the counting observables that saturate it. Our results establish ultimate precision limits for an important class of observables in non-equilibrium systems, and demonstrate that the mean residual time, not the dynamical activity, is the measure of freneticity that tightly constrains fluctuations far from equilibrium.

cond-mat.stat-mech↗

arXiv2025

Precision bounds for multiple currents in open quantum systems

Thermodynamic (TUR) and kinetic (KUR) uncertainty relations are fundamental bounds constraining the fluctuations of current observables in classical, non-equilibrium systems. Several works have verified, however, violations of these classical bounds in open quantum systems, motivating the derivation of new quantum TURs and KURs that account for the role of quantum coherence. Here, we go one step further by deriving multidimensional KUR and TUR for multiple observables in open quantum systems undergoing Markovian dynamics. Our derivation exploits a multi-parameter metrology approach, in which the Fisher information matrix plays a central role. Crucially, our bounds are tighter than previously derived quantum TURs and KURs for single observables, precisely because they incorporate correlations between multiple observables. We also find an intriguing quantum signature of correlations that is captured by the off-diagonal element of the Fisher information matrix, which vanishes for classical stochastic dynamics. By considering two examples, namely a coherently driven qubit system and the three-level maser, we demonstrate that the multidimensional quantum KUR bound can even be saturated when the observables are perfectly correlated.

quant-ph↗

arXiv2025

Quantum many-body attractors

Complex dynamics when occurring autonomously, i.e. without external driving, is usually associated with everyday length scales and classical physics, e.g. living organisms. This dynamics is \emph{not} quantum coherent. Quantum coherent dynamics is, by contrast, assumed to be either simple periodic oscillation in particular when autonomous, e.g. spin precession, or random quantum fluctuations. Combining autonomous complex and quantum coherent dynamics on microscopic length-scales could allow for novel coherent quantum machines working without external time-dependent driving. Motivated by this, here we provide an exact theoretical condition for a system to display complex quantum coherent dynamics on both microscopic and macroscopic length scales that we call a \emph{dynamical quantum algebraic thread} (D-QAT). Due to D-QATs our autonomous quantum coherent dynamics is robust to realistic imperfections (including low-doped disorder) and present for generic initial states, allowing for potential realisations in experiments. We give an example of a \emph{spin lace} model structurally similar to magnetic azurite and certain recently experimentally realized large single-molecular magnets with long coherence times. Our work opens the possibility for many potential applications including ultra-dense storage and manipulation of quantum memories, creating \emph{giant} quantum coherent qubits, or microscopic quantum mechanism perform complicated motion.

quant-ph↗

arXiv2024

Entanglement signature in quantum work statistics in the slow-driving regime

In slowly driven classical systems, work is a stochastic quantity and its probability distribution is known to satisfy the work fluctuation-dissipation relation, which states that the mean and variance of the dissipated work are linearly related. Recently, it was shown that generation of quantum coherence in the instantaneous energy eigenbasis leads to a correction to this linear relation in the slow-driving regime. Here, we go even further by investigating nonclassical features of work fluctuations in setups with more than one system. To do this, we first generalize slow control protocols to encompass multipartite systems, allowing for the generation of quantum correlations during the driving process. Then, focussing on two-qubit systems, we show that entanglement generation leads to a positive contribution to the dissipated work, which is distinct from the quantum correction due to local coherence generation known from previous work. Our results show that entanglement generated during slow control protocols, e.g. as an unavoidable consequence of qubit crosstalk, comes at the cost of increased dissipation.

quant-ph↗

arXiv2024

Entropy production in the mesoscopic-leads formulation of quantum thermodynamics

Understanding the entropy production of systems strongly coupled to thermal baths is a core problem of both quantum thermodynamics and mesoscopic physics. While there exist many techniques to accurately study entropy production in such systems, they typically require a microscopic description of the baths, which can become numerically intractable to study for large systems. Alternatively an open-systems approach can be employed with all the nuances associated with various levels of approximation. Recently, the mesoscopic leads approach has emerged as a powerful method for studying such quantum systems strongly coupled to multiple thermal baths. In this method, a set of discretised lead modes, each locally damped, provide a Markovian embedding. Here we show that this method proves extremely useful to describe entropy production of a strongly coupled open quantum system. We show numerically, for both non-interacting and interacting setups, that a system coupled to a single bath exhibits a thermal fixed point at the level of the embedding. This allows us to use various results from the thermodynamics of quantum dynamical semi-groups to infer the non-equilibrium thermodynamics of the strongly coupled, non-Markovian central systems. In particular, we show that the entropy production in the transient regime recovers the well established microscopic definitions of entropy production with a correction that can be computed explicitly for both the single- and multiple-lead cases.

quant-ph↗

arXiv2024

Powering an autonomous clock with quantum electromechanics

We theoretically analyse an autonomous clock comprising a nanoelectromechanical system, which undergoes self-oscillations driven by electron tunnelling. The periodic mechanical motion behaves as the clockwork, similar to the swinging of a pendulum, while induced oscillations in the electrical current can be used to read out the ticks. We simulate the dynamics of the system in the quasi-adiabatic limit of slow mechanical motion, allowing us to infer statistical properties of the clock's ticks from the current auto-correlation function. The distribution of individual ticks exhibits a tradeoff between accuracy, resolution, and dissipation, as expected from previous literature. Going beyond the distribution of individual ticks, we investigate how clock accuracy varies over different integration times by computing the Allan variance. We observe non-monotonic features in the Allan variance as a function of time and applied voltage, which can be explained by the presence of temporal correlations between ticks. These correlations are shown to yield a precision advantage for timekeeping over the timescales that the correlations persist. Our results illustrate the non-trivial features of the tick series produced by nanoscale clocks, and pave the way for experimental investigation of clock thermodynamics using nanoelectromechanical systems.

quant-ph↗

arXiv2024

Thermometry by correlated dephasing of impurities in a 1D Fermi gas

We theoretically investigate the pure dephasing dynamics of two static impurity qubits embedded within a common environment of ultracold fermionic atoms, which are confined to one spatial dimension. Our goal is to understand how bath-mediated interactions between impurities affect their performance as nonequilibrium quantum thermometers. By solving the dynamics exactly using a functional determinant approach, we show that the impurities become correlated via retarded interactions of the Ruderman-Kittel-Kasuya-Yosida type. Moreover, we demonstrate that these correlations can provide a metrological advantage, enhancing the sensitivity of the two-qubit thermometer beyond that of two independent impurities. This enhancement is most prominent in the limit of low temperature and weak collisional coupling between the impurities and the gas. We show that this precision advantage can be exploited using standard Ramsey interferometry, with no need to prepare correlated initial states nor to individually manipulate or measure the impurities. We also quantitatively assess the impact of ignoring these correlations when constructing a temperature estimate, finding that acceptable precision can still be achieved from a simplified model of independent impurities. Our results demonstrate the rich nonequilibrium physics of impurities dephasing in a common Fermi gas, and may help to provide better temperature estimates at ultralow temperatures.

cond-mat.quant-gas↗

arXiv2023

The Impact of Imperfect Timekeeping on Quantum Control

In order to unitarily evolve a quantum system, an agent requires knowledge of time, a parameter which no physical clock can ever perfectly characterise. In this letter, we study how limitations on acquiring knowledge of time impact controlled quantum operations in different paradigms. We show that the quality of timekeeping an agent has access to limits the circuit complexity they are able to achieve within circuit-based quantum computation. We do this by deriving an upper bound on the average gate fidelity achievable under imperfect timekeeping for a general class of random circuits. Another area where quantum control is relevant is quantum thermodynamics. In that context, we show that cooling a qubit can be achieved using a timer of arbitrary quality for control: timekeeping error only impacts the rate of cooling and not the achievable temperature. Our analysis combines techniques from the study of autonomous quantum clocks and the theory of quantum channels to understand the effect of imperfect timekeeping on controlled quantum dynamics.

quant-ph↗

arXiv2023

Thermodynamics of decoherence

We investigate the nonequilibrium thermodynamics of pure decoherence. In a pure decoherence process, the system Hamiltonian is a constant of motion and there is no direct energy exchange between the system and its surroundings. Nevertheless, the environment's energy is not generally conserved and in this work we show that this leads to nontrivial heat dissipation as a result of decoherence alone. This heat has some very distinctive properties: it obeys an integral fluctuation relation and can be interpreted in terms of the entropy production associated with populations in the energy eigenbasis of the initial state. We show that the heat distribution for a pure decoherence process is different from the distribution of work done by the initial system-bath interaction quench. Instead, it corresponds to a mixture of work distributions of cyclical processes, each conditioned on a state of the open system. Inspired by recent experiments on impurities in ultra-cold gases, we demonstrate our general results by studying the heat generated by the decoherence of a qubit immersed within a degenerate Fermi gas in the lowest band of a species-selective optical lattice.

quant-ph↗

arXiv2023

Calculating the many-body density of states on a digital quantum computer

Quantum statistical mechanics allows us to extract thermodynamic information from a microscopic description of a many-body system. A key step is the calculation of the density of states, from which the partition function and all finite-temperature equilibrium thermodynamic quantities can be calculated. In this work, we devise and implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer which is inspired by the kernel polynomial method. Classically, the kernel polynomial method allows to sample spectral functions via a Chebyshev polynomial expansion. Our algorithm computes moments of the expansion on quantum hardware using a combination of random state preparation for stochastic trace evaluation and a controlled unitary operator. We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18 qubits. This not only represents a state-of-the-art calculation of thermal properties of a many-body system on quantum hardware, but also exploits the controlled unitary evolution of a many-qubit register on an unprecedented scale.

quant-ph↗

arXiv2022

Robust nonequilibrium surface currents in the 3D Hofstadter model

Genuinely two-dimensional robust crosscurrents -- which flow against the natural direction of heat flux -- have been missing since the discovery of their one-dimensional counterpart. We provide a setup to realize them on a cubic three-dimensional (3D) lattice hosting a Hofstadter model coupled to two heat baths with different temperatures. We show that these currents exhibit dissipative robustness: they are stable against the presence of impurities and tilting of the gauge field in certain nonequilibrium configurations. Moreover, we find protected boundary currents with genuinely 3D robustness, i.e. they are only stable if tunnelling can occur in all three spatial directions. The model also presents generic surface currents, which are robust for both bosonic and fermionic systems. We identify the underlying qualitative mechanism responsible for the robustness of the surface currents and the crucial role played by certain discrete symmetries.

cond-mat.mes-hall↗

arXiv2022

Diverging current fluctuations in critical Kerr resonators

The parametrically pumped Kerr model describes a driven-dissipative nonlinear cavity, whose nonequilibrium phase diagram features both continuous and discontinuous quantum phase transitions. We consider the consequences of these critical phenomena for the fluctuations of the photocurrent obtained via continuous weak measurements on the cavity. Considering both direct photodetection and homodyne detection schemes, we find that the current fluctuations diverge exponentially at the discontinuous phase transition. However, we find strikingly different current fluctuations for these two detection schemes near the continuous transition, a behaviour which is explained by the complementary information revealed by measurements in different bases. To obtain these results, we develop formulas to efficiently compute the diffusion coefficient -- which characterises the long-time current fluctuations -- directly from the quantum master equation, thus connecting the formalisms of full counting statistics and stochastic quantum trajectories. Our findings highlight the rich features of current fluctuations near nonequilibrium phase transitions in quantum-optical systems.

quant-ph↗