arXiv subjects

Archak Purkayastha

Publications and source records attributed to Archak Purkayastha.

At least 37 records · Page 2Linked to original sources

arXiv2022

Periodically refreshed quantum thermal machines

We introduce unique class of cyclic quantum thermal machines (QTMs) which can maximize their performance at the finite value of cycle duration $τ$ where they are most irreversible. These QTMs are based on single-stroke thermodynamic cycles realized by the non-equilibrium steady state (NESS) of the so-called Periodically Refreshed Baths (PReB) process. We find that such QTMs can interpolate between standard collisional QTMs, which consider repeated interactions with single-site environments, and autonomous QTMs operated by simultaneous coupling to multiple macroscopic baths. We discuss the physical realization of such processes and show that their implementation requires a finite number of copies of the baths. Interestingly, maximizing performance by operating in the most irreversible point as a function of $τ$ comes at the cost of increasing the complexity of realizing such a regime, the latter quantified by the increase in the number of copies of baths required. We demonstrate this physics considering a simple example. We also introduce an elegant description of the PReB process for Gaussian systems in terms of a discrete-time Lyapunov equation. Further, our analysis also reveals interesting connections with Zeno and anti-Zeno effects.

quant-ph↗

arXiv2022

Lyapunov equation in open quantum systems and non-Hermitian physics

The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic Hamiltonian, linear equations of motion) open quantum systems, typically from quantum master equations. Despite this, the Lyapunov equation is seldom considered a fundamental formalism for linear open quantum systems. In this work we aim to change that. We establish the Lyapunov equation as a fundamental and efficient formalism for linear open quantum systems that can go beyond the limitations of various standard quantum master equation descriptions, while remaining of much less complexity than general exact formalisms. This also provides valuable insights for non-Hermitian quantum physics. In particular, we derive the Lyapunov equation for the most general number conserving linear system in a lattice of arbitrary dimension and geometry, connected to an arbitrary number of baths at different temperatures and chemical potentials. Three slightly different forms of the Lyapunov equation are derived via an equation of motion approach, by making increasing levels of controlled approximations, without reference to any quantum master equation. Then we discuss their relation with quantum master equations, positivity, accuracy and additivity issues, the possibility of describing dark states, general perturbative solutions in terms of single-particle eigenvectors and eigenvalues of the system, and quantum regression formulas. Our derivation gives a clear understanding of the origin of the non-Hermitian Hamiltonian describing the dynamics and separates it from the effects of quantum and thermal fluctuations. Many of these results would have been hard to obtain via standard quantum master equation approaches.

quant-ph↗

arXiv2022

Dephasing-enhanced performance in quasiperiodic thermal machines

Understanding and controlling quantum transport in low-dimensional systems is pivotal for heat management at the nanoscale. One promising strategy to obtain the desired transport properties is to engineer particular spectral structures. In this work we are interested in quasiperiodic disorder - incommensurate with the underlying periodicity of the lattice - which induces fractality in the energy spectrum. A well known example is the Fibonacci model which, despite being non-interacting, yields anomalous diffusion with a continuously varying dynamical exponent smoothly crossing over from superdiffusive to subdiffusive regime as a function of potential strength. We study the finite-temperature electric and heat transport of this model in linear response in the absence and in the presence of dephasing noise due to inelastic scattering. The dephasing causes both thermal and electric transport to become diffusive, thereby making thermal and electrical conductivities finite in the thermodynamic limit. Thus, in the subdiffusive regime it leads to enhancement of transport. We find that the thermal and electric conductivities have multiple peaks as a function of dephasing strength. Remarkably, we observe that the thermal and electrical conductivities are not proportional to each other, a clear violation of Wiedemann-Franz law, and the position of their maxima can differ. We argue that this feature can be utilized to enhance performance of quantum thermal machines. In particular, we show that by tuning the strength of the dephasing noise we can enhance the performance of the device in regimes where it acts as an autonomous refrigerator.

cond-mat.dis-nn↗

arXiv2022

Taking the temperature of a pure quantum state

Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalisation in completely isolated quantum systems, such as cold-atom quantum simulators, implies that a temperature can be assigned even to individual, pure quantum states. Here, we propose a scheme to measure the temperature of such pure states through quantum interference. Our proposal involves interferometry of an auxiliary qubit probe, which is prepared in a superposition state and subsequently decoheres due to weak coupling with a closed, thermalised many-body system. Using only a few basic assumptions about chaotic quantum systems -- namely, the eigenstate thermalisation hypothesis and the emergence of hydrodynamics at long times -- we show that the qubit undergoes pure exponential decoherence at a rate that depends on the temperature of its surroundings. We verify our predictions by numerical experiments on a quantum spin chain that thermalises after absorbing energy from a periodic drive. Our work provides a general method to measure the temperature of isolated, strongly interacting systems under minimal assumptions.

quant-ph↗

arXiv2022

Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths

It is very common in the literature to write down a Markovian quantum master equation in Lindblad form to describe a system with multiple degrees of freedom and weakly connected to multiple thermal baths which can, in general, be at different temperatures and chemical potentials. However, the microscopically derived quantum master equation up to leading order in system-bath coupling is of the so-called Redfield form which is known to not preserve complete positivity in most cases. Additional approximations to the Redfield equation are required to obtain a Lindblad form. We lay down some fundamental requirements for any further approximations to Redfield equation, which, if violated, leads to physical inconsistencies like inaccuracies in the leading order populations and coherences in the energy eigenbasis, violation of thermalization, violation of local conservation laws at the non-equilibrium steady state (NESS). We argue that one or more of these conditions will generically be violated in all the weak system-bath-coupling Lindblad descriptions existing in literature to our knowledge. As an example, we study the recently derived Universal Lindblad Equation (ULE) and use these conditions to show violation of local conservation laws due to inaccurate coherences but accurate populations in energy eigenbasis. Finally, we exemplify our analytical results numerically in an interacting open quantum spin system.

quant-ph↗

arXiv2021

Sub-diffusive phases in open clean long-range systems

We show that a one-dimensional ordered fermionic lattice system with power-law-decaying hopping, when connected to two baths at its two ends with different chemical potentials at zero temperature, features two phases showing sub-diffusive scaling of conductance with system size. These phases have no analogues in the isolated system (i.e, in absence of the baths) where the transport is perfectly ballistic. In the open system scenario, interestingly, there occurs two chemical-potential-driven sub-diffusive to ballistic phase transitions at zero temperature. We discuss how these phase transitions, to our knowledge, are different from all the known non-equilibrium quantum phase transitions. We provide a clear understanding of the microscopic origin of these phases and argue that the sub-diffusive phases are robust against the presence of arbitrary number-conserving many-body interactions in the system. These phases showing sub-diffusive scaling of conductance with system size in a two-terminal set-up are therefore universal properties of all ordered one-dimensional number-conserving fermionic systems with power-law-decaying hopping at zero temperature.

cond-mat.mes-hall↗

arXiv2021

Periodically refreshed baths to simulate open quantum many-body dynamics

Obtaining dynamics of an interacting quantum many-body system connected to multiple baths initially at different, finite, temperatures and chemical potentials is a challenging problem. This is due to a combination of the prevalence of strong correlations in the system, the infinite nature of the baths and the long time to reach steady state. In this work we develop a general formalism that allows access to the full non-Markovian dynamics of such open quantum many-body systems up to the non-equilibrium steady state (NESS), provided its uniqueness. Specifically, we show how finite-time evolution in presence of finite-sized baths, whose opportune size is determined by their original spectral density, can be recursively used to faithfully reconstruct the exact dynamics without requiring any small parameter. Such a reconstruction is possible even in parameter regimes which would otherwise be inaccessible by current state-of-the-art techniques. We specifically demonstrate this by obtaining the full numerically exact non-Markovian dynamics of interacting fermionic chains in two terminal set-ups with finite temperature and voltage biases, a problem which previously remained outstanding despite its relevance in a wide range of contexts, for example, quantum heat engines and refrigerators.

quant-ph↗

arXiv2021

Quantum dynamics in the interacting Fibonacci chain

Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultra-cold atom experiments where non trivial localised phases have been observed. One such quasiperiodic model is the so called Fibonacci model. In this tight-binding model, non-interacting particles are subject to on-site energies generated by a Fibonacci sequence. This is known to induce critical states, with a continuously varying dynamical exponent, leading to anomalous transport. In this work, we investigate whether anomalous diffusion present in the non-interacting system survives in the presence of interactions and establish connections to a possible transition towards a localized phase. We investigate the dynamics of the interacting Fibonacci model by studying real-time spread of density-density correlations at infinite temperature using the dynamical typicality approach. We also corroborate our findings by calculating the participation entropy in configuration space and investigating the expectation value of local observables in the diagonal ensemble.

cond-mat.dis-nn↗

arXiv2021

Time periodicity from randomness in quantum systems

Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the vibration of a cello string. While self-oscillation is well understood in classical non-linear systems and their quantized counterparts, the spontaneous emergence of periodicity in quantum systems without a semi-classical limit is more elusive. Here, we show that this behavior can emerge within the repeated-interaction description of open quantum systems. Specifically, we consider a many-body quantum system that undergoes dissipation due to sequential coupling with auxiliary systems at random times. We develop dynamical symmetry conditions that guarantee an oscillatory long-time state in this setting. Our rigorous results are illustrated with specific spin models, which could be implemented in trapped-ion quantum simulators.

quant-ph↗

arXiv2020

Tensor-network method to simulate strongly interacting quantum thermal machines

We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at fixed temperature and chemical potential. Our method works at finite temperature, beyond linear response and weak system-reservoir coupling, and allows for non-quadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped towards thermal equilibrium, in order to represent continuum baths and a novel tensor network algorithm to simulate the steady-state thermodynamics. Using the example of a quantum-dot heat engine, we demonstrate that our technique replicates the well known Landauer-Büttiker theory for efficiency and power. We then go beyond the quadratic limit to demonstrate the capability of our method by simulating a three-site machine with non-quadratic interactions. Remarkably, we find that such interactions lead to power enhancement, without being detrimental to the efficiency. Furthermore, we demonstrate the capability of our method to tackle complex many-body systems by extracting the super-diffusive exponent for high-temperature transport in the isotropic Heisenberg model. Finally, we discuss transport in the gapless phase of the anisotropic Heisenberg model at finite temperature and its connection to charge conjugation-parity, going beyond the predictions of single-site boundary driving configurations.

cond-mat.str-el↗

arXiv2020

Emergent $\mathcal{PT}$ symmetry in a double-quantum-dot circuit QED set-up

Open classical and quantum systems with effective parity-time ($\mathcal{PT}$) symmetry, over the past five years, have shown tremendous promise for advances in lasers, sensing, and non-reciprocal devices. And yet, how such effective $\mathcal{PT}$-symmetric non-Hermitian models emerge out of Hermitian quantum mechanics is not well understood. Here, starting from a fully Hermitian microscopic Hamiltonian description, we show that a non-Hermitian Hamiltonian emerges naturally in a double-quantum-dot-circuit-QED (DQD-circuit QED) set-up, which can be controllably tuned to the $\mathcal{PT}$-symmetric point. This effective Hamiltonian governs the dynamics of two coupled circuit-QED cavities with a voltage-biased DQD in one of them. Our analysis also reveals the effect of quantum fluctuations on the $\mathcal{PT}$ symmetric system. The $\mathcal{PT}$-transition is, then, observed both in the dynamics of cavity observables as well as via an input-output experiment. As a simple application of the $\mathcal{PT}$-transition in this set-up, we show that loss-induced enhancement of amplification and lasing can be observed in the coupled cavities. By comparing our results with two conventional local Lindblad equations, we demonstrate the utility and limitations of the latter. Our results pave the way for an on-chip realization of a potentially scalable non-Hermitian system with a gain medium in quantum regime, as well as its potential applications for quantum technology.

quant-ph↗

arXiv2020

Tunable phonon induced steady state coherence in a double quantum dot

Charge qubits can be created and manipulated in solid-state double-quantum-dot (DQD) platforms. Typically, these systems are strongly affected by quantum noise stemming from coupling to substrate phonons. This is usually assumed to lead to decoherence towards steady states that are diagonal in the energy eigenbasis. In this article we show, to the contrary, that due to the presence of phonons the equilibrium steady state of the DQD charge qubit spontaneously exhibits coherence in the energy eigenbasis with high purity. The magnitude and phase of the coherence can be controlled by tuning the Hamiltonian parameters of the qubit. The coherence is also robust to presence of fermionic leads. In addition, we show that this steady-state coherence can be used to drive an auxiliary cavity mode coupled to the DQD.

cond-mat.mes-hall↗

arXiv2019

Anomalous transport through algebraically localized states in one-dimension

Localization in one-dimensional disordered or quasiperiodic non-interacting systems in presence of power-law hopping is very different from localization in short-ranged systems. Power-law hopping leads to algebraic localization as opposed to exponential localization in short-ranged systems. Exponential localization is synonymous with insulating behavior in the thermodynamic limit. Here we show that the same is not true for algebraic localization. We show, on general grounds, that depending on the strength of the algebraic decay, the algebraically localized states can be actually either conducting or insulating in thermodynamic limit. We exemplify this statement with explicit calculations on the Aubry-André-Harper model in presence of power-law hopping, with the power-law exponent $α>1$, so that the thermodynamic limit is well-defined. We find a phase of this system where there is a mobility edge separating completely delocalized and algebraically localized states, with the algebraically localized states showing signatures of super-diffusive transport. Thus, in this phase, the mobility edge separates two kinds of conducting states, ballistic and super-diffusive. We trace the occurrence of this behavior to near-resonance conditions of the on-site energies that occur due to the quasi-periodic nature of the potential.

cond-mat.dis-nn↗

arXiv2019

More current with less particles due to power-law hopping

We reveal interesting universal transport behavior of ordered one-dimensional fermionic systems with power-law hopping. We restrict ourselves to the case where the power-law decay exponent $α>1$, so that the thermodynamic limit is well-defined. We explore the quantum phase-diagram of the non-interacting model in terms of the zero temperature Drude weight, which can be analytically calculated. Most interestingly, we reveal that for $1<α<2$, there is a phase where the zero temperature Drude weight diverges as filling fraction goes to zero. Thus, in this regime, counter intuitively, reducing number of particles increases transport and is maximum for a sub-extensive number of particles. Being a statement about zero-filling, this transport behavior is immune to adding number conserving interaction terms. We have explicitly checked this using two different interacting systems. We propose that measurement of persistent current due to a flux through a mesoscopic ring with power-law hopping will give an experimental signature of this phase. In persistent current, the signature of this phase survives up to a finite temperature for a finite system. At higher temperatures, a crossover is seen. The maximum persistent current shows a power-law decay at high temperatures. This is in contrast with short ranged systems, where the persistent current decays exponentially with temperature.

cond-mat.mes-hall↗

arXiv2019

Quasiperiodic quantum heat engines with a mobility edge

Steady-state thermoelectric machines convert heat into work by driving a thermally-generated charge current against a voltage gradient. In this work, we propose a new class of steady-state heat engines operating in the quantum regime, where a quasi-periodic tight-binding model that features a mobility edge forms the working medium. In particular, we focus on a generalization of the paradigmatic Aubrey-André-Harper (AAH) model, known to display a single-particle mobility edge that separates the energy spectrum into regions of completely delocalized and localized eigenstates. Remarkably, these two regions can be exploited in the context of steady-state heat engines as they correspond to ballistic and insulating transport regimes. This model also presents the advantage that the position of the mobility edge can be controlled via a single parameter in the Hamiltonian. We exploit this highly tunable energy filter, along with the peculiar spectral structure of quasiperiodic systems, to demonstrate large thermoelectric effects, exceeding existing predictions by several orders of magnitude. This opens the route to a new class of highly efficient and versatile quasi-periodic steady-state heat engines, with a possible implementation using ultracold neutral atoms in bichromatic optical lattices.

cond-mat.dis-nn↗

arXiv2019

Classifying transport behavior via current fluctuations in open quantum systems

There are two standard ways of classifying transport behavior of systems. The first is via time scaling of spread of correlations in the isolated system in thermodynamic limit. The second is via system size scaling of conductance in the steady state of the open system. We show here that these correspond to taking the thermodynamic limit and the long time limit of the integrated equilibrium current-current correlations of the open system in different order. In general, the limits may not commute leading to a conflict between the two standard ways of transport classification. Nevertheless, the full information is contained in the equilibrium current-current correlations of the open system. We show this analytically by rigorously deriving the open-system current fluctuation dissipation relations (OCFDR) starting from an extremely general open quantum set-up and then carefully taking the proper limits. We test our theory numerically on the non-trivial example of the critical Aubry-André-Harper (AAH) model, where, it has been recently shown that, the two standard classifications indeed give different results. We find that both the total current autocorrelation and the long-range local current correlations of the open system in equilibrium show signatures of diffusive transport up to a time scale. This time scale grows as square of system size. Beyond this time scale a steady state value is reached. The steady state value is conductance, which shows sub-diffusive scaling with system size.

cond-mat.stat-mech↗

arXiv2018

Anomalous transport in the Aubry-André-Harper model in isolated and open systems

We study the high temperature transport behavior of the Aubry-André-Harper (AAH) model, both in the isolated thermodynamic limit and in the open system. At the critical point of the AAH model, we find hints of super-diffusive behavior from the scaling of spread of an initially localized wavepacket. On the other hand, when connected to two baths with different chemical potentials at the two ends, we find that the critical point shows clear sub-diffusive scaling of current with system size. We provide an explanation of this by showing that the current scaling with system-size is entirely governed by the behavior of the single particle eigenfunctions at the boundary sites where baths are attached. We also look at the particle density profile in non-equilibrium steady state of the open system when the two baths are at different chemical potentials. We find that the particle density profile has distinctly different behavior in the delocalized, critical and localized phases of the AAH model.

cond-mat.mes-hall↗

arXiv2017

Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge

We investigate and map out the non-equilibrium phase diagram of a generalization of the well known Aubry-André-Harper (AAH) model. This generalized AAH (GAAH) model is known to have a single-particle mobility edge which also has an additional self-dual property akin to that of the critical point of AAH model. By calculating the imbalance, we get hints of a rich phase diagram. We find a fascinating connection between single particle wavefunctions near the mobility edge of GAAH model and the wavefunctions of the critical AAH model. By placing this model far-from-equilibrium with the aid of two baths, we investigate the open system transport via system size scaling of non-equilibrium steady state (NESS) current. Current is calculated by fully exact non-equilibrium Green's function (NEGF) formalism. The critical point of the AAH model now generalizes to a 'critical' line separating regions of ballistic and localized transport. Like critical point of AAH model, current scales sub-diffusively with system size on the 'critical' line ($I\sim N^{-2\pm0.1}$). However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model (where $I\sim N^{-1.4\pm0.05}$). All these results can be understood from the above-mentioned connection between states near mobility edge of GAAH model and those of critical AAH model. A very interesting high temperature non-equilibrium phase diagram of the GAAH model emerges from our calculations.

cond-mat.dis-nn↗