arXiv subjects

Bijay Kumar Agarwalla

Publications and source records attributed to Bijay Kumar Agarwalla.

At least 55 records · Page 3Linked to original sources

arXiv2022

Filling an empty lattice by local injection of quantum particles

We study the quantum dynamics of filling an empty lattice of size $L$, by connecting it locally with an equilibrium thermal bath that injects non-interacting bosons or fermions. We adopt four different approaches, namely (i) direct exact numerics, (ii) Redfield equation, (iii) Lindblad equation, and (iv) quantum Langevin equation -- which are unique in their ways for solving the time dynamics and the steady-state. Our setup offers a simplistic platform to understand fundamental aspects of dynamics and approach to thermalization. The quantities of interest that we consider are the spatial density profile and the total number of bosons/fermions in the lattice. The spatial spread is ballistic in nature and the local occupation eventually settles down owing to equilibration. The ballistic spread of local density admits a universal scaling form. We show that this universality is only seen when the condition of detailed balance is satisfied by the baths. The difference between bosons and fermions shows up in the early time growth rate and the saturation values of the profile. The techniques developed here are applicable to systems in arbitrary dimensions and for arbitrary geometries.

quant-ph↗

arXiv2022

Read-out of Quasi-periodic Systems using Qubits

We develop a theoretical scheme to perform a read-out of the properties of a quasi-periodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a 1D quasi-periodic system with a potential given by the André-Aubry-Harper (AAH) model and its generalized versions (GAAH model) is sensitive to the nature of the single particle eigenstates (SPEs). More specifically, we can use the non-markovianity of the qubit dynamics as quantified by the backflow of information to clearly distinguish the localized, delocalized, and mixed regimes with a mobility edge of the AAH and GAAH model and evidence the transition between them. By attaching two qubits at distinct sites of the system, we demonstrate that the transport property of the quasi-periodic system is encoded in the scaling of the threshold time to develop correlations between the qubits with the distance between the qubits. This scaling can also be used to distinguish and infer different regimes of transport such as ballistic, diffusive and no transport engendered by SPEs that are delocalized, critical and localized respectively. When there is a mobility edge allowing the coexistence of different kinds of SPEs in the spectrum, such as the coexistence of localized and delocalized states in the GAAH models, we find that the transport behaviour and the scaling of the threshold time with qubit separation is governed by the fastest spreading states.

cond-mat.mes-hall↗

arXiv2022

Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes

Quasi-periodic lattice systems offer diverse transport properties. In this work, we investigate the environment induced effects on transport properties for quasi-periodic systems, namely the one-dimensional Aubry-André-Harper (AAH) lattice chain and its generalized version (GAAH) by considering the Büttiker probe approach. We first consider voltage probe situation and study the electrical conductance properties in the linear response regime. At zero temperature, we observe enhancement in conductance at all the no-transport regimes, located both inside and outside of the band of the original system, for small probe coupling strength $γ$ with a power-law scaling $γ^4$. Whereas, for large probe coupling strengths, the conductance at all Fermi energies is the same and decays as a power-law with scaling $1/γ^4$. This particular scaling survives even in the finite-temperature limit. Interestingly, this scaling result is different from the one recently predicted following the local Lindblad master equation approach. The transport eventually becomes diffusive for all energy ranges and in all regimes of the original model for a sufficiently strong coupling with the probes. We further extend our study and consider voltage-temperature probes to analyze the thermoelectric performance of the chain in terms of the figure of merit. We also demonstrate the validity of two recently obtained bounds on thermoelectric efficiency that are tighter than the seminal Carnot bound and express the same in terms of the Onsager's transport coefficients.

cond-mat.mes-hall↗

arXiv2022

Counting statistics of energy transport across squeezed thermal reservoirs

A general formalism for computing the full counting statistics of energy exchanged between 'N' squeezed thermal photon reservoirs weakly coupled to a cavity with 'M' photon modes is presented. The formalism is based on the two-point measurement scheme and is applied to two simple special cases, the relaxation dynamics of a single mode cavity in contact with a single squeezed thermal photon reservoir and the steady-state energy transport between two squeezed thermal photon reservoirs coupled to a single cavity mode. Using analytical results, it is found that the short time statistics is significantly affected by noncommutivity of the initial energy measurements with the reservoirs squeezed states, and may lead to negative probabilities if not accounted properly. Furthermore, it is found that for the single reservoir setup, generically there is no transient or steady-state fluctuation theorems for energy transport. In contrast, for the two reservoir case, although there is no generic transient fluctuation theorem, steady-state fluctuation theorem with a non-universal affinity is found to be valid. Statistics of energy currents are further discussed.

cond-mat.stat-mech↗

arXiv2021

Quantum Regression theorem for multi-time correlators : A detailed analysis in the Heisenberg Picture

Quantum regression theorem is a very useful result in open quantum system and extensively used for computing multi-point correlation functions. Traditionally it is derived for two-time correlators in the Markovian limit employing the Schrödinger picture. In this paper we make use of the Heisenberg picture to derive quantum regression theorems for multi-time correlation functions which in the special limit reduce to the well known two-time regression theorem. For multi-time correlation function we find that the regression theorem takes the same form as it takes for two-time correlation function with a mild restriction that one of the times should be greater than all the other time variables. Interestingly, the Heisenberg picture also allows us to derive analogue of regression theorem for out-of-time-ordered correlators (OTOCs). We further extend our study for the case of non-Markovian dynamics and report the modifications to the standard quantum regression theorem. We illustrate all of the above results using the paradigmatic dissipative spin-boson model.

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

Universal bounds on fluctuations for machines with broken time-reversal symmetry

For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the corresponding relative fluctuation of the sum of input currents. This bound is received when the same operating condition, for example, engine, refrigerator or pump, is imposed in both the forward and the reversed processes. As a consequence, universal upper and lower bounds for the ratio of fluctuations between the output and the input current is obtained. Furthermore, we establish an important connection between our results and the recently obtained generalized thermodynamic uncertainty relation for time-reversal symmetry broken systems. We illustrate these findings for two different types of machines: (i) a steady-state three-terminal quantum thermoelectric setup in presence of an external magnetic field, and (ii) a periodically driven classical Brownian heat engine.

cond-mat.stat-mech↗

arXiv2021

Universal bounds on cooling power and cooling efficiency for autonomous absorption refrigerators

For steady-state autonomous absorption refrigerators operating in the linear response regime, we show that there exists a hierarchy between the relative fluctuation of currents for cold, hot, and work terminals. Our proof requires the Onsager's reciprocity relation along with the refrigeration condition that sets the direction of the mean currents for each terminal. As a consequence, the universal bounds on the mean cooling power, obtained following the thermodynamic uncertainty relations, receive a hierarchy. Interestingly, within this hierarchy, the tightest bound is given in terms of the work current fluctuation. Furthermore, the relative uncertainty hierarchy hands over additional bounds that can be tighter than the bounds obtained from the thermodynamic uncertainty relations. Interestingly, all of these bounds saturate in the tight-coupling limit. We test the validity of our results for two paradigmatic absorption refrigerator models: (i) a four-level working fluid and (ii) a two-level working fluid, operating, respectively, in the weak (additive) and in the strong (multiplicative) system-bath interaction regime.

cond-mat.stat-mech↗

arXiv2021

Bounds on fluctuations for finite-time quantum Otto cycle

For finite-time quantum Otto heat engine with working fluid consisting of either a (i) qubit or (ii) a harmonic oscillator, we show that the relative fluctuation of output work is always greater than the corresponding relative fluctuation of input heat absorbed from the hot bath. As a result, the ratio between the work fluctuation and the input heat fluctuation receives a lower bound in terms of the square value of the average efficiency of the engine. The saturation of the lower bound is received in the quasi-static limit of the engine and can be shown for a class of working fluids that follow a scale-invariant energy eigenspectra under driving.

cond-mat.stat-mech↗

arXiv2021

Universal Bounds on Fluctuations in Continuous Thermal Machines

We study bounds on ratios of fluctuations in steady-state time-reversal heat engines controlled by multi affinities. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower-bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.

cond-mat.stat-mech↗

arXiv2021

Harmonic chains and the thermal diode effect

Harmonic oscillator chains connecting two harmonic reservoirs at different constant temperatures cannot act as thermal diodes, irrespective of structural asymmetry. However, here we prove that perfectly harmonic junctions can rectify heat once the reservoirs (described by white Langevin noise) are placed under temperature gradients, which are asymmetric at the two sides, an effect that we term "temperature-gradient harmonic oscillator diodes". This nonlinear diode effect results from the additional constraint -- the imposed thermal gradient at the boundaries. We demonstrate the rectification behavior based on the exact analytical formulation of steady state heat transport in harmonic systems coupled to Langevin baths, which can describe quantum and classical transport, both regimes realizing the diode effect under the involved boundary conditions. Our study shows that asymmetric harmonic systems, such as room-temperature hydrocarbon molecules with varying side groups and end groups, or a linear lattice of trapped ions may rectify heat by going beyond simple boundary conditions.

quant-ph↗

arXiv2020

On the definitions and simulations of vibrational heat transport in nanojunctions

Thermal transport through nanosystems is central to numerous processes in chemistry, material sciences, electrical and mechanical engineering, with classical molecular dynamics as the key simulation tool. Here we focus on thermal junctions with a molecule bridging two solids that are maintained at different temperatures. The classical steady state heat current in this system can be simulated in different ways, either at the interfaces with the solids, which are represented by thermostats, or between atoms within the conducting molecule. We show that while the latter, intramolecular definition feasibly converges to the correct limit, the molecule-thermostat interface definition is more challenging to converge to the correct result. The problem with the interface definition is demonstrated by simulating heat transport in harmonic and anharmonic one-dimensional chains illustrating unphysical effects such as thermal rectification in harmonic junctions.

cond-mat.mes-hall↗

arXiv2020

Thermodynamic uncertainty relation for energy transport in transient regime -- Model study

We investigate transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy production. We explore this relation in the context of energy transport in a bipartite setting for three exactly solvable toy model systems (two coupled harmonic oscillators, two coupled qubits and a hybrid coupled oscillator-qubit system) and analyze the role played by the underlying statistics of the transport carriers in TUR. Interestingly, for all these models, depending on the statistics, the TUR ratio can be expressed as a sum or a difference of an universal term which is always greater or equal to 2 and a corresponding entropy production term. We find that the generalized version of the TUR, originating from the universal fluctuation symmetry is always satisfied. However, interestingly, the specialized TUR, a tighter bound, is always satisfied for the coupled harmonic oscillator system obeying Bose-Einstein statistics. Whereas, for both the coupled qubit, obeying Fermi-like statistics and the hybrid qubit-oscillator system with mixed Fermi-Bose statistics, violation of tighter bound is observed in certain parameter regimes. We have provided conditions for such violations. We also provide a rigorous proof following the non-equilibrium Green's function approach that the tighter bound is always satisfied in the weak-coupling regime for generic bipartite systems.

cond-mat.stat-mech↗

arXiv2020

Thermodynamic uncertainty relation in atomic-scale quantum conductors

The thermodynamic uncertainty relation (TUR) is expected to hold in nanoscale electronic conductors, when the electron transport process is quantum coherent and the transmission probability is constant (energy and voltage independent). We present measurements of the electron current and its noise in gold atomic-scale junctions and confirm the validity of the TUR for electron transport in realistic quantum coherent conductors. Furthermore, we show that it is beneficial to present the current and its noise as a TUR ratio in order to identify deviations from noninteracting-electron coherent dynamics.

cond-mat.mes-hall↗

arXiv2019

Experimental study of the thermodynamic uncertainty relation

A cost-precision trade-off relationship, the so-called thermodynamic uncertainty relation (TUR), has been recently discovered in stochastic thermodynamics. It bounds certain thermodynamic observables in terms of the associated entropy production. In this work, we experimentally study the TUR in a two-qubit system using an NMR setup. Each qubit is prepared in an equilibrium state, but at different temperatures. The qubits are then coupled, allowing energy exchange (in the form of heat). Using the quantum state tomography technique we obtain the moments of heat exchange within a certain time interval and analyze the relative uncertainty of the energy exchange process. We find that generalized versions of the TUR, which are based on the fluctuation relation, are obeyed. However, the specialized TUR, a tighter bound that is valid under specific dynamics, is violated in certain regimes of operation, in excellent agreement with analytic results. Altogether, this experiment-theory study provides a deep understanding of heat exchange in quantum systems, revealing favorable noise-dissipation regimes of operation.

cond-mat.stat-mech↗

arXiv2019

Quantum entanglement and transport in non-equilibrium interacting double-dot setup: The curious role of degeneracy

We study quantum entanglement and its relation to transport in a non-equilibrium interacting double dot system connected to electronic baths. The dynamical properties in the non-interacting regime are studied using an exact numerical approach whereas the steady state properties are obtained following the well-known non-equilibrium Green's function (NEGF) approach. By means of mutual information and concurrence we explore the connection between the quantum correlations in the system and the current flowing through the dots. It is observed that entanglement between the dots is heavily influenced by the degeneracy or the lack thereof, of the dot levels. In the non-degenerate case, the concurrence falls sharply when the applied bias crosses a certain critical value. In contrast when the dot energy levels are degenerate, the concurrence reaches a very high asymptotic value of 1/2. When interactions are switched on, the degeneracy is lifted, and once again concurrence falls to zero beyond a critical value of the applied bias. Lastly it is observed that the concurrence can be made to reach almost the value of 1.0 if the chemical potential in both baths is made very large (while keeping the sign the same) provided the dot levels are kept degenerate within the non-interacting limit. A combination of NEGF method, brute-force numerics and asymptotics are employed to corroborate our findings.

cond-mat.mes-hall↗

arXiv2019

Thermodynamic uncertainty relation in thermal transport

We use the fundamental nonequilibrium steady-state fluctuation symmetry and derive a condition on the validity of the thermodynamic uncertainty relation (TUR) in thermal transport problems, classical or quantum alike. We test this condition and study the breakdown of the TUR in different thermal transport junctions of bosonic and electronic degrees of freedom. First, we prove that the TUR is valid in harmonic oscillator junctions. In contrast, in the nonequilibrium spin-boson model, which realizes many-body effects, it is satisfied in the Markovian limit, but violations arise as we tune (reduce) the cutoff frequency of the thermal baths, thus observing non-Markovian dynamics. Finally, we consider heat transport by noninteracting electrons in a tight-binding chain model. Here we show that the TUR is feasibly violated by tuning e.g. the hybridization energy of the chain to the metal leads. These results manifest that the validity of the TUR relies on the statistics of the participating carriers, their interaction, and the nature of their couplings to the macroscopic contacts (metal electrodes, phonon baths).

cond-mat.mes-hall↗

arXiv2019

Photon statistics of a double quantum dot micromaser: Quantum treatment

A semiconductor single-atom micromaser consists of a microwave cavity coupled to a gain medium, a double quantum dot driven out of equilibrium by a bias voltage. The masing threshold of this system was recently probed by measuring photon statistics in the cavity [Y-Y. Liu \textit{et al}, Phys. Rev. Lett. 119, 097702 (2017)]. In this paper, we develop an in-depth, rigorous understanding of this experiment and related works. First, we use a semiclassical theory and study transmission spectroscopy. This approach allows us to derive the masing threshold condition for arbitrary temperature and voltage bias, and expose microscopic principles required for realizing photon gain and thereby a photon amplifier. Next, by employing the quantum master equation approach we extend the Scully-Lamb quantum theory of a laser to the present setup, and investigate the statistics of emitted photons below and above the masing threshold as a function of experimentally tunable parameters. Although our focus is primarily on hybrid quantum dot circuit - quantum electrodynamics systems, our approach is adaptable to other light-matter systems where the gain medium consists of a mesoscopic structure.

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