Steady-state Coherence Research Articles

Memory effects in the efficiency control of energy transfer under incoherent light excitation in noisy environments.

Fluctuations in energy gap and coupling constants between chromophores can play an important role in absorption and energy transfer across a collection of two-level systems. In photosynthesis, light-induced quantum coherence can affect the efficiency of energy transfer to the designated "trap" state. Theoretically, the interplay between fluctuations and coherence has been studied often, employing either a Markovian or a perturbative approximation. In this study, we depart from these approaches to incorporate memory effects by using Kubo's quantum stochastic Liouville equation. We introduce the effects of decay of the created excitation (to the ground state) on the desired propagation and trapping that provides a direction of flow of the excitation. In the presence of light-induced pumping, we establish a relation between the efficiency, the mean survival time, and the correlation decay time of the bath-induced fluctuations. A decrease in the steady-state coherence during the transition from the non-Markovian regime to the Markovian limit results in a decrease in efficiency. As in the well-known Haken-Strobl model, the ratio of the square of fluctuation strength to the rate plays a critical role in determining the mechanism of energy transfer and in shaping the characteristics of the efficiency profile. We recover a connection between the transfer flux and the imaginary part of coherences in both equilibrium and excited bath states, in both correlated and uncorrelated bath models. We uncover a non-monotonic dependence of efficiency on site energy heterogeneity for both correlated and uncorrelated bath models.

Protecting the Quantum Coherence of Two Atoms Inside an Optical Cavity by Quantum Feedback Control Combined with Noise-Assisted Preparation

We propose a theoretical scheme to enhance quantum coherence and obtain steady-state coherence by combining quantum feedback control and noise-assisted preparation. We investigate the effects of quantum-jump-based feedback control and noise field on the quantum coherence and excited-state population between two atoms inside an optical cavity where a noise field drives one, and the other is under quantum feedback control. It is found that steady quantum coherence can be achieved by adding an external noise field, and the quantum feedback can prolong the coherence time with partial suppression of the spontaneous emission of atoms. In addition, we study the influence of the joint action of quantum feedback and noise-assisted preparation on quantum coherence and show that the combined action of feedback control and noise-assisted preparation is more effective in enhancing steady coherence. The findings of our research offer some general guidelines for improving the steady-state coherence of coupled qubit systems and have the potential to be applied in the realm of quantum information technology.

Steady-state coherence of spin-boson model in a general non-Markovian environment

Based on the quantum coherence theory, we employ the [Formula: see text]-norm measure to explore the steady-state coherence (SSC) in the spin-boson model. In this model, the environment is a non-Markovian bosonic bath with Ohmic-like spectral density. More generally, the interaction coupling between the qubit and the environment is a linear superposition of pure dephasing and pure damping coupling. Governed by the non-Markovian dynamics, some compact expressions of the SSC have been obtained at both zero temperature and high temperature. It shows that the hybrid coupling significantly affects the SSC. Moreover, a comprehensive analysis has been conducted to investigate the effects of various crucial factors, including the temperature of the bosonic bath, the qubit’s tunneling and the Ohmicity parameter. This analysis provides an effective approach for maintaining a relatively high SSC by manipulating system parameters.

Steady state coherence and entanglement in a dissipative two-qubit system and its application for decision making

Quantum decision theory was recently established based on the mathematics of Hilbert spaces to formalize the key concepts of quantum mechanics such as uncertainty and superposition that particularly manifest in cognitive processes. We aim to address how a two-qubit system interacting with a global squeezed vacuum field reservoir can be exploited as a black box model for quantum decision-making. To do so, we encode the input of the black box into the density matrix of the two-qubit system. The global reservoir drives the system towards its steady state via the decoherence process. The outcome of the black box can be obtained by performing measurement on the stationary state of the two-qubit system. We reveal that the squeezed reservoir can be used to control the coherence and entanglement of the black box’s output. Interestingly, it is shown that the steady state entanglement and coherence between two qubits, which have the same value, can be obtained by measuring the output state of the black box. Besides, we examine the potential application of the considered model for entanglement decision-making.

Effect of the size of environment on the steady-state entanglement and coherence via collision model

Effect of the size of environment on the steady-state entanglement and coherence via collision model

Features of quantum thermodynamics induced by common environments based on collision model

The common reservoir can cause some unique effects, such as dark state and steady-state coherence, which are extensively studied in the dynamics of open quantum system. In this work, by means of collision model, we explore features of quantum thermodynamics induced by common reservoirs. We first construct general formulations of thermodynamic quantities for the system consisting of N coupling subsystems embedded in M common thermal reservoirs. We confirm the existence of nonlocal work due to simultaneous interactions of subsystems with the common reservoirs resembling what is found for nonlocal heat. With a system of two coupled qubits in a common reservoir, we show that steady-state currents could emerge even when interactions of individual subsystems and the reservoir fulfill strict energy conservation. We also exhibit the effect of dark state on the steady-state currents. We then examine relations between the work cost, the system’s nonequilibrium steady-state and the extractable work. In particular, we find that in the presence of dark state, the work cost is only related to the coherence generated in the dynamical evolution but not to the one contributed by the initial dark state of the system. We also show the possible transformation of coherence into useful work in terms of ergotropy. We finally examine the scale effect of reservoirs and show that the increase of the number of involved reservoirs need more work to be costed and meanwhile can produce more coherence so that more ergotropy can be extracted. The obtained features contribute to the understanding of thermodynamics in common reservoirs and would be useful in quantum technologies when common reservoirs are necessary.

Structure–function models for estimating retinal ganglion cell count using steady-state pattern electroretinography and optical coherence tomography in glaucoma suspects and preperimetric glaucoma: an electrophysiological pilot study

PurposeTo derive and validate structure–function models for estimating retinal ganglion cell (RGC) count using optical coherence tomography (OCT) and steady-state pattern electroretinography (ssPERG) parameters in glaucoma suspects (GS) and preperimetric glaucoma (PPG).MethodsIn this prospective cross-sectional study, 25 subjects (50 eyes) were recruited at the Manhattan Eye, Ear, and Throat Hospital. Subjects underwent comprehensive eye examinations, OCT, standard automated perimetry (SAP), and ssPERG testing. Eyes were divided into three groups based on the Global Glaucoma Staging System: healthy (N = 30), GS (N = 10), and PPG (N = 10) eyes. The combined structure–function index (CSFI), which estimates retinal ganglion cell count (eRGCCSFI) from SAP and OCT parameters, was calculated in each study subject. Two prediction formulas were derived using a generalized linear mixed model (GLMM) to predict eRGCCSFI from ssPERG parameters, age, and average retinal nerve fiber layer thickness (ARNFLT) in 30 eyes selected at random (training group). GLMM predicted values were cross-validated with the remaining 20 eyes (validation group).ResultsThe ARNFLT, ssPERG parameters magnitude (Mag) and magnitudeD (MagD), and eRGCCSFI were significantly different among study groups (ANOVA p ≤ 0.001). Pearson correlations demonstrated significant associations among ARNFLT, ssPERG parameters, and eRGCCSFI (r2 ≥ 0.31, p < 0.001). Two GLMMs predicted eRGCCSFI from Mag (eRGCMag) and MagD (eRGCMagD), respectively, with significant equations (F(3,18), F(3,19) ≥ 58.37, R2 = 0.90, p < 0.001). eRGCMag and eRGCMagD in the validation group (R2 = 0.89) correlated with eRGCCSFI similarly to the training group. Multivariate pairwise comparisons revealed that eRGCMag and eRGCMagD distinguished between healthy, GS, and PPG eyes (p ≤ 0.035), whereas independent Mag, MagD, and ARNFLT measures did not distinguish between GS and PPG eyes.ConclusionThis pilot study offers the first combined structure–function models for estimating RGC count using ssPERG parameters. RGC counts estimated with these models were generalizable, strongly associated with CSFI estimates, and performed better than individual ssPERG and OCT measures in distinguishing healthy, GS, and PPG eyes.

Steady state entanglement of distant nitrogen-vacancy centers in a coherent thermal magnon bath

We investigate steady state entanglement (SSE) between two nitrogen-vacancy (NV) center defects in a diamond host on an ultrathin yttrium iron garnet (YIG) strip. We determine the dephasing and dissipative interactions of the qubits with the quanta of spin waves (magnon bath) in the YIG depending on the qubit positions on the strip. We show that the magnon's dephasing effect can be eliminated, and we can transform the bath into a multimode displaced thermal state using external magnetic fields. Entanglement dynamics of the qubits in such a displaced thermal bath have been analyzed by deriving and solving the master equation. An additional electric field is considered to engineer the magnon dispersion relation at the band edge to control the Markovian character of the open system dynamics. We determine the optimum geometrical parameters of the system of distant qubits and the YIG strip to get SSE. Furthermore, parameter regimes for which the shared displaced magnon bath can sustain significant SSE against the local dephasing and decoherence of NV centers to their nuclear spin environments have been determined. Along with SSE, we investigate the steady state coherence (SSC) and explain the physical mechanism of how delayed SSE appears following a rapid generation and sudden death of entanglement using the interplay of decoherence-free subspace states, system geometry, displacement of the thermal bath, and enhancement of the qubit dissipation near the magnon band edge. A nonmonotonic relation between bath coherence and SSE is found, and critical coherence for maximum SSE is determined. Our results illuminate the efficient use of system geometry, band edge in bath spectrum, and reservoir coherence to engineer system-reservoir interactions for robust SSE and SSC.

Steady-State Thermodynamics of a Cascaded Collision Model.

We study the steady-state thermodynamics of a cascaded collision model where two subsystems and collide successively with an environment R in the cascaded fashion. We first formulate general expressions of thermodynamics quantities and identify the nonlocal forms of work and heat that result from cascaded interactions of the system with the common environment. Focusing on a concrete system of two qubits, we then show that, to be able to unidirectionally influence the thermodynamics of , the former interaction of should not be energy conserving. We finally demonstrate that the steady-state coherence generated in the cascaded model is a kind of useful resource in extracting work, quantified by ergotropy, from the system. Our results provide a comprehensive understanding on the thermodynamics of the cascaded model and a possible way to achieve the unidirectional control on the thermodynamics process in the steady-state regime.

Non-Markovian Steady States of a Driven Two-Level System.

We show that an open quantum system in a non-Markovian environment can reach steady states that it cannot reach in a Markovian environment. As these steady states are unique for the non-Markovian regime, they could offer a simple way of detecting non-Markovianity, as no information about the system's transient dynamics is necessary. In particular, we study a driven two-level system (TLS) in a semi-infinite waveguide. Once the waveguide has been traced out, the TLS sees an environment with a distinct memory time. The memory time enters the equations as a time delay that can be varied to compare a Markovian to a non-Markovian environment. We find that some non-Markovian states show exotic behaviors such as population inversion and steady-state coherence beyond 1/sqrt[8], neither of which is possible for a driven TLS in the Markovian regime, where the time delay is neglected. Additionally, we show how the coherence of quantum interference is affected by time delays in a driven system by extracting the effective Purcell-modified decay rate of a TLS in front of a mirror.

Enhanced steady-state coherence via repeated system-bath interactions

The appearance of steady-state coherence (SSC) from system-bath interaction proves that quantum effects can appear without an external drive. Such SSC could become a resource to demonstrate quantum advantage in the applications. We predict the generation of SSC if the target system repeatedly interacts with independent and non-correlated bath elements. To describe their behavior, we use the collision model approach of system-bath interaction, where the system interacts with one bath element (initially in an incoherent state) at a time, asymptotically (in the fast-collision regime) mimicking a macroscopic Markovian bath coupled to the target system. Therefore, the SSC qualitatively appears to be the same as if the continuous Markovian bath would be used. We confirm that the presence of composite system-bath interactions under the rotating-wave approximation (RWA) is the necessary condition for the generation of SSC using thermal resources in collision models. Remarkably, we show that SSC substantially increases if the target system interacts collectively with more than one bath element at a time. Already few bath elements collectively interacting with the target system are sufficient to increase SSC at non-zero temperatures at the cost of tolerable lowering the final state purity. From the thermodynamic perspective, the SSC generation in our collision models is inevitably linked to a non zero power input (and thus heat dissipated to the bath) necessary to reach the steady-state, although such energetic cost can be lower compared to cases relying on SSC non generating interactions.

Improving the steady-state coherence and entanglement of two coupled qubits via composite system-reservoir interactions

In this work, we study the improvement of steady-state coherence (SSC) and steady-state entanglement (SSE) of two coupled qubits by means of composite system-reservoir interaction constructed by a linear combination of orthogonal and parallel ones. We show that in the non-equilibrium case, the SSC and SSE can be significantly enhanced by increasing the parallel components of the interaction Hamiltonian between the system of interest and the heat reservoirs. In addition, we find that in the non-equilibrium case, increasing the parallel components can enlarge the temperature (temperature difference) region where the SSC can maintain nonzero values. In the equilibrium situation, however, the SSC and SSE are not affected by the parallel components of the composite system-reservoir interactions.

Violating the thermodynamic uncertainty relation in the three-level maser.

Nanoscale heat engines are subject to large fluctuations which affect their precision. The thermodynamic uncertainty relation (TUR) provides a trade-off between output power, fluctuations, and entropic cost. This trade-off may be overcome by systems exhibiting quantum coherence. This Letter provides a study of the TUR in a prototypical quantum heat engine, the Scovil-Schulz-DuBois maser. Comparison with a classical reference system allows us to determine the effect of quantum coherence on the performance of the heat engine. We identify analytically regions where coherence suppresses fluctuations, implying a quantum advantage, as well as regions where fluctuations are enhanced by coherence. This quantum effect cannot be anticipated from the off-diagonal elements of the density matrix. Because the fluctuations are not encoded in the steady state alone, TUR violations are a consequence of coherence that goes beyond steady-state coherence. While the system violates the conventional TUR, it adheres to a recent formulation of a quantum TUR. We further show that parameters where the engine operates close to the conventional limit are prevalent and TUR violations in the quantum model are not uncommon.

Steady-state Fano coherences in a V-type system driven by polarized incoherent light

We explore the properties of steady-state Fano coherences generated in a three-level V-system continuously pumped by polarized incoherent light in the absence of coherent driving. The ratio of the stationary coherences to excited-state populations $\mathcal{C} = (1+\frac{\Delta^2}{\gamma(r+\gamma)} )^{-1}$ is maximized when the excited-state splitting $\Delta$ is small compared to either the spontaneous decay rate $\gamma$ or the incoherent pumping rate $r$. We demonstrate that an intriguing regime exists where the $\mathcal{C}$ ratio displays a maximum as a function of the dephasing rate $\gamma_d$. We attribute the surprising dephasing-induced enhancement of stationary Fano coherences to the environmental suppression of destructive interference of individual incoherent excitations generated at different times. We identify the imaginary Fano coherence with the non-equilibrium flux across a pair of qubits coupled to two independent thermal baths, unraveling a direct connection between the seemingly unrelated phenomena of incoherent driving of multilevel quantum systems and non-equilibrium quantum transport in qubit networks. The real part of the steady-state Fano coherence is found to be proportional to the deviation of excited-state populations from their values in thermodynamic equilibrium, making it possible to observe signatures of steady-state Fano coherences in excited-state populations. We put forward an experimental proposal for observing steady-state Fano coherences by detecting the total fluorescence signal emitted by Calcium atoms excited by polarized vs. isotropic incoherent light. Our analysis paves the way toward further theoretical and experimental studies of non-equilibrium coherent steady states in thermally driven atomic and molecular systems, and for the exploration of their potential role in biological processes.

A multifunctional quantum thermal device: With and without inner coupling

A three-level system attached to three thermal baths is manipulated to be a microscopic thermal device integrating a valve, a refrigerator, an amplifier, and a thermometer in the quantum regime, via tuning the inner coupling strength of the system and the temperatures of the external baths. We discuss the role of the inner coupling as well as the steady-state quantum coherence in these thermal functions using the Redfield master equation under a partial secular approximation. A high-sensitive thermometer for the low-temperature terminal can be established without the assistance from the inner coupling of the system. Our study of this multifunctional thermal device provides a deeper insight to the underlying quantum thermodynamics associated with the quantum coherence.

Steady-State Analysis of Light-Harvesting Energy Transfer Driven by Incoherent Light: From Dimers to Networks.

The question of how quantum coherence facilitates energy transfer has been intensively debated in the scientific community. Since natural and artificial light-harvesting units operate under the stationary condition, we address this question via a nonequilibrium steady-state analysis of a molecular dimer irradiated by incoherent sunlight and then generalize the key predictions to arbitrarily complex exciton networks. The central result of the steady-state analysis is the coherence-flux-efficiency relation: η = c∑i≠jFijκj = 2c∑i≠jJijIm[ρij]κj, where c is the normalization constant. In this relation, the first equality indicates that the energy transfer efficiency, η, is uniquely determined by the trapping flux, which is the product of the flux, F, and branching ratio, κ, for trapping at the reaction centers, and the second equality indicates that the energy transfer flux, F, is equivalent to the quantum coherence measured by the imaginary part of the off-diagonal density matrix, that is, Fij = 2JijIm[ρij]. Consequently, maximal steady-state coherence gives rise to optimal efficiency. The coherence-flux-efficiency relation holds rigorously and generally for any exciton network of arbitrary connectivity under the stationary condition and is not limited to incoherent radiation or incoherent pumping. For light-harvesting systems under incoherent light, the nonequilibrium energy transfer flux (i.e., steady-state coherence) is driven by the breakdown of detailed balance and by the quantum interference of light excitations and leads to the optimization of energy transfer efficiency. It should be noted that the steady-state coherence or, equivalently, efficiency is the combined result of light-induced transient coherence, inhomogeneous depletion, and the system-bath correlation and is thus not necessarily correlated with quantum beatings. These findings are generally applicable to quantum networks and have implications for quantum optics and devices.

Photon Correlation Spectroscopy as a Witness for Quantum Coherence.

The development of spectroscopic techniques able to detect and verify quantum coherence is a goal of increasing importance given the rapid progress of new quantum technologies, the advances in the field of quantum thermodynamics, and the emergence of new questions in chemistry and biology regarding the possible relevance of quantum coherence in biochemical processes. Ideally, these tools should be able to detect and verify the presence of quantum coherence in both the transient dynamics and the steady state of driven-dissipative systems, such as light-harvesting complexes driven by thermal photons in natural conditions. This requirement poses a challenge for standard laser spectroscopy methods. Here, we propose photon correlation measurements as a new tool to analyze quantum dynamics in molecular aggregates in driven-dissipative situations. We show that the photon correlation statistics of the light emitted in several models of molecular aggregates can signal the presence of coherent dynamics. Deviations from the counting statistics of independent emitters constitute a direct fingerprint of quantum coherence in the steady state. Furthermore, the analysis of frequency resolved photon correlations can signal the presence of coherent dynamics even in the absence of steady state coherence, providing direct spectroscopic access to the much sought-after site energies in molecular aggregates.

Quantum Coherence and Its Signatures in Extended Quantum Systems.

Quantum coherence controls almost every aspect of static and dynamic response of a strongly correlated quantum system, although details of this control have not been elucidated in many cases. We find that, in the presence of a significant static off-diagonal coupling, quantum coherence can survive much longer than the bath correlation time in a noisy environment. In the presence of time correlated noise (non-Markovian limit), coherence could propagate through the excited bath states, and this plays a nontrivial role in giving rise to a noncanonical temperature dependence of population distribution in an extended conjugated polymer-like system. The quantum coherence through the excited bath states vanishes in the high temperature limit, giving rise to the equilibrium Boltzmann distribution. Second, we discuss a role of quantum coherence in exciton localization that bears resemblance to Anderson localization. Calculations have been carried out not only with a chain of conjugated polymer but also with dimer and trimer subunits of the Fenna-Matthews-Olson (FMO) complex. We derive an analytical expression of the relation between steady state coherence and excitionic population distribution. We analytically showed that steady state coherence in equilibrium bath states is governed by interchromophoric coupling (J) whereas coherence in excited bath states is dictated by fluctuation strength (Vd) for the spatially correlated bath model. For the spatially uncorrelated bath model, we observe that at the low temperature limit coherence in the excited bath states dominates over coherence in equilibrium bath states and vice versa. In the study of the localization problem, we analytically show that, in the limit of a negligibly small fluctuation rate (bd), the diffusion coefficient is exactly proportional to the fluctuation rate, leading to complete breakdown of the Haken-Strobl-Silbey Markovian prediction.

Tunable phonon-induced steady-state coherence in a double-quantum-dot charge qubit

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 the 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.

Measurement Induced Synthesis of Coherent Quantum Batteries

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.