Rajesh Dutta - Academia.edu (original) (raw)
Papers by Rajesh Dutta
arXiv: Statistical Mechanics, 2016
We study excitation transfer dynamics in a lattice of two level systems characterized by dynamic ... more We study excitation transfer dynamics in a lattice of two level systems characterized by dynamic disorder. The diagonal and off-diagonal energy disorders arise from the coupling of system and bath. We consider both the same and the independent bath limits. In case of independent bath all diagonal and off-diagonal bath coupling elements fluctuate independently of each other and the dynamics is complicated. We obtain the time dependent population distribution by solving quantum stochastic Liouville equation (QSLE) derived by Kubo. The main result of our study is both the population transfer dynamics and the mean square displacement of the exciton behave the similar way in the same and independent bath cases in the Markovian limit. However, these two baths can give rise to markedly different behavior in the non-Markovian limit where coherent transport becomes important. There are also several additional new results as follows. (i) Exciton migration remains coherent all the time for an ...
arXiv: Statistical Mechanics, 2018
The presence of static off-diagonal disorder promotes coherent exciton transport while diffusive ... more The presence of static off-diagonal disorder promotes coherent exciton transport while diffusive motion can be recovered in the presence of fluctuations in the diagonal and off-diagonal elements of the Hamiltonian. Here we study the crossover induced by correlated dynamical disorder.We uncover a novel role of the excited bath states (ExBS) in dictating quantum coherence and quantum transport in dissipative quantum systems interacting with correlated bath.We solve both analytically and numerically the temperature dependent Quantum Stochastic Liouville equation (TD-QSLE) to study temperature dependence of quantum coherence in both linear chains and cyclic trimer (first three subunits of Fenna-Matthews-Olson(FMO) and also heptamer) complexes, using Haken-Strobl-Reineker Hamiltonian. In the non-Markovian limit where the lowering of temperature induces long-lasting quantum coherences, ExBSnot only determines the lifetime of coherences but also dictates the long time population distributi...
arXiv: Statistical Mechanics, 2016
We address the effects of quantum coherences on the optical line shape of an exciton in the prese... more We address the effects of quantum coherences on the optical line shape of an exciton in the presence of dynamic disorder. We consider a one-dimensional excitonic system that consists of two levels placed at regular intervals. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (K-QSLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigen functions are known analytically. This identification is particularly useful for long chains where the eigen values of TDTM help to understand crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peak increases beyond the...
The Journal of Physical Chemistry A, 2021
Several recent studies have interrogated the role of quantum coherence in affecting the transfer ... more Several recent studies have interrogated the role of quantum coherence in affecting the transfer efficiency of an optical excitation to the designated "trap" state where the energy can be used for subsequent reactions, as in photosynthesis. However, these studies invoke a Markovian approximation for the time correlation function describing the environment-induced stochastic fluctuations. Here, we employ Kubo's quantum stochastic Liouville equation (QSLE) to include memory effects. We extend the existing QSLE scheme to introduce decay of a newly created excitation due to radiative and nonradiative channels and also by desired trapping toward the targeted chromophore. We show that the theoretical formalism based on the QSLE correctly reproduces the rate equation description in the Markovian limit, with the rate constants determined by an appropriate quantum limiting procedure. We find that under certain conditions, the efficiency of excitation transfer to the trap gains from the combined presence of quantum coherence and temporally correlated stochastic fluctuations. We work out different limiting situations in order to discover and quantify the optimum conditions for the energy transfer to the trapped state. We find that maximum energy transfer efficiency is achieved in the intermediate limit between coherent and incoherent transport.
The Journal of Physical Chemistry Letters, 2017
Recent experiments [Nature, 2007, 446, 782-786] revealed the existence of surprisingly long lived... more Recent experiments [Nature, 2007, 446, 782-786] revealed the existence of surprisingly long lived quantum coherence in noisy biological environment of photosynthetic Fenna-Matthews-Olson (FMO) complex. Such coherence can clearly play important role in facilitating efficient energy transfer. The occurrence of quantum coherence in quantum transport is also implicated in excitation transport processes in conjugated polymers [Science, 2009, 323, 369-373]. Even though these systems are strongly correlated, most theoretical studies invoke Markovian approximation where the temporal correlation of bath fluctuations is neglected. We use an elegant non-perturbative method based on Kubo's quantum stochastic Liouville equation (QSLE) to study the effects of correlated non-Markovian bath fluctuations in several different limits and find the interesting result that fluctuations not only destroy coherence but under appropriate conditions can also facilitate it. We show that temperature has the most pronounced effect in the intermediate coupling limit where it can promote transition from coherent to incoherent transfer.
The Journal of Physical Chemistry Letters, 2019
Quantum coherence and entanglement in an extended interacting system where energy levels are non-... more Quantum coherence and entanglement in an extended interacting system where energy levels are non-degenerate and coupled to a dissipative environment is a common occurrence in nature, like in photosynthetic reaction systems and conjugated polymers. Temperature dependence of quantum coherence in trimer complex (first three subunits of Fenna-Matthews-Olson (FMO) complex) is studied using a temperature dependent Quantum Stochastic Liouville equation. In the non-Markovian limit, the lowering of temperature induces long-lasting quantum coherence which in turn leads to delocalization whose length grows in the non-Markovian limit. Measure of entanglement and coherence length determines the nature of dynamic localization.
Chemical Physics Letters, 2018
When density is varied at a constant temperature just above the gas-liquid critical temperature, ... more When density is varied at a constant temperature just above the gas-liquid critical temperature, the system is found to exhibit large scale density fluctuations which are often rationalized in terms of crossing of a Widom line. We use the discrete variable representation (DVR) scheme to construct the spectroscopic maps for transition frequencies and transition dipoles, and obtain the infrared spectrum of the O-H stretch in the said temperature-density region of the phase diagram. The infrared lineshape shows a crossover from Lorentzian to Gaussian as we approach the Widom line. The width of the lineshape displays a pronounced maximum.
The Journal of Chemical Physics, 2017
Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vi... more Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vibrational line shapes, through such concepts as static heterogeneity and motional narrowing. However, the theory does not properly address the effects of quantum coherences on optical line shape, especially in extended systems where a large number of eigenstates are present. In this work, we study the line shape of an exciton in a one-dimensional lattice consisting of regularly placed and equally separated optical two level systems. We consider both linear array and cyclic ring systems of different sizes. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (SLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigenfunctions are known analytically. This identification is particularly useful for long chains where the eigenvalues of TDTM help understanding crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peaks increases beyond the ones obtained from TDTM (constant off-diagonal coupling element J and no fluctuation). (ii) However, in the fast modulation limit when the bath correlation time is small, the spatial correlation is less important. In this limit, the line shape shows motional narrowing with peaks at the values predicted by TDTM (constant J and no fluctuation). (iii) Importantly, we find that the line shape can capture that quantum coherence affects in the two limits differently. (iv) In addition to linear chains of two level systems, we also consider a cyclic tetramer. The cyclic polymers can be designed for experimental verification. (v) We also build a connection between line shape and population transfer dynamics. In the fast modulation limit, both the line shape and the population relaxation, for both correlated and uncorrelated bath, show similar behavior. However, in slow modulation limit, they show profoundly different behavior. (vi) This study explains the unique role of the rate of fluctuation (inverse of the bath correlation time) in the sustenance and propagation of coherence. We also examine the effects of off-diagonal fluctuation in spectral line shape. Finally, we use Tanimura-Kubo formalism to derive a set of coupled equations to include temperature effects (partly neglected in the SLE employed here) and effects of vibrational mode in energy transfer dynamics.
The Journal of Chemical Physics, 2016
We study excitation transfer and migration in a one-dimensional lattice characterized by dynamic ... more We study excitation transfer and migration in a one-dimensional lattice characterized by dynamic disorder. The diagonal and off-diagonal energy disorders arise from the coupling of system and bath. We consider both same bath (when baths are spatially correlated) and independent bath (when baths are completely uncorrelated) limits. In the latter case, all diagonal and off-diagonal bath coupling elements fluctuate independently of each other and the dynamics is complicated. We obtain time dependent population distribution by solving Kubo's quantum stochastic Liouville equation. In the Markovian limit, both energy transfer dynamics and mean square displacement of the exciton behave the similar way in same and independent bath cases. However, these two baths can give rise to a markedly different behavior in the non-Markovian limit. We note that previously only the same bath case has been studied in the non-Markovian limit. The other main results of our study include the following. (i) For an average, non-zero off-diagonal coupling value J, exciton migration remains coherent in same bath case even at long times while it becomes incoherent in independent bath case in the Markovian limit. (ii) Coherent transfer is manifested in an oscillatory behavior of the energy transfer dynamics accompanied by faster-than diffusive spread of the exciton from the original position. (iii) Agreement with available analytical expression of mean squared displacement is good in Markovian limit for independent bath (off-diagonal fluctuation) case but only qualitative in non-Markovian limit for which no complete analytical solution is available. (iv) We observe transition from coherent to incoherent transport in independent bath (diagonal fluctuation) case when the bath is made progressively more Markovian. We present an analytical study that shows coherence to propagate through excited bath states. (v) The correlation time of the bath plays a unique role in dictating the diffusive spread that is not anticipated in a Markovian treatment.
Physical Review Letters
We present inelastic neutron scattering measurements of magnetic excitations in stripe ordered Pr... more We present inelastic neutron scattering measurements of magnetic excitations in stripe ordered Pr 3=2 Sr 1=2 NiO 4 at T ∼ 10 K. For the observed magnetic incommensurability ϵ ¼ 0.4, we have incorporated a stripe discommensuration model in our linear spin wave calculation and obtained best agreement with the measured spin wave dispersion, especially to explain the symmetrical outward shift of the magnetic peaks from Néel ordered zone center in energy range 35 to 45 meV. Our study indicates the prerequisite to consider a discommensurated spin stripe unit with proper out-of-plane and in-plane exchange interactions in between Ni 2þ spins to describe the observed spin wave characteristics in Pr 3=2 Sr 1=2 NiO 4 .
arXiv: Statistical Mechanics, 2016
We study excitation transfer dynamics in a lattice of two level systems characterized by dynamic ... more We study excitation transfer dynamics in a lattice of two level systems characterized by dynamic disorder. The diagonal and off-diagonal energy disorders arise from the coupling of system and bath. We consider both the same and the independent bath limits. In case of independent bath all diagonal and off-diagonal bath coupling elements fluctuate independently of each other and the dynamics is complicated. We obtain the time dependent population distribution by solving quantum stochastic Liouville equation (QSLE) derived by Kubo. The main result of our study is both the population transfer dynamics and the mean square displacement of the exciton behave the similar way in the same and independent bath cases in the Markovian limit. However, these two baths can give rise to markedly different behavior in the non-Markovian limit where coherent transport becomes important. There are also several additional new results as follows. (i) Exciton migration remains coherent all the time for an ...
arXiv: Statistical Mechanics, 2018
The presence of static off-diagonal disorder promotes coherent exciton transport while diffusive ... more The presence of static off-diagonal disorder promotes coherent exciton transport while diffusive motion can be recovered in the presence of fluctuations in the diagonal and off-diagonal elements of the Hamiltonian. Here we study the crossover induced by correlated dynamical disorder.We uncover a novel role of the excited bath states (ExBS) in dictating quantum coherence and quantum transport in dissipative quantum systems interacting with correlated bath.We solve both analytically and numerically the temperature dependent Quantum Stochastic Liouville equation (TD-QSLE) to study temperature dependence of quantum coherence in both linear chains and cyclic trimer (first three subunits of Fenna-Matthews-Olson(FMO) and also heptamer) complexes, using Haken-Strobl-Reineker Hamiltonian. In the non-Markovian limit where the lowering of temperature induces long-lasting quantum coherences, ExBSnot only determines the lifetime of coherences but also dictates the long time population distributi...
arXiv: Statistical Mechanics, 2016
We address the effects of quantum coherences on the optical line shape of an exciton in the prese... more We address the effects of quantum coherences on the optical line shape of an exciton in the presence of dynamic disorder. We consider a one-dimensional excitonic system that consists of two levels placed at regular intervals. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (K-QSLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigen functions are known analytically. This identification is particularly useful for long chains where the eigen values of TDTM help to understand crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peak increases beyond the...
The Journal of Physical Chemistry A, 2021
Several recent studies have interrogated the role of quantum coherence in affecting the transfer ... more Several recent studies have interrogated the role of quantum coherence in affecting the transfer efficiency of an optical excitation to the designated "trap" state where the energy can be used for subsequent reactions, as in photosynthesis. However, these studies invoke a Markovian approximation for the time correlation function describing the environment-induced stochastic fluctuations. Here, we employ Kubo's quantum stochastic Liouville equation (QSLE) to include memory effects. We extend the existing QSLE scheme to introduce decay of a newly created excitation due to radiative and nonradiative channels and also by desired trapping toward the targeted chromophore. We show that the theoretical formalism based on the QSLE correctly reproduces the rate equation description in the Markovian limit, with the rate constants determined by an appropriate quantum limiting procedure. We find that under certain conditions, the efficiency of excitation transfer to the trap gains from the combined presence of quantum coherence and temporally correlated stochastic fluctuations. We work out different limiting situations in order to discover and quantify the optimum conditions for the energy transfer to the trapped state. We find that maximum energy transfer efficiency is achieved in the intermediate limit between coherent and incoherent transport.
The Journal of Physical Chemistry Letters, 2017
Recent experiments [Nature, 2007, 446, 782-786] revealed the existence of surprisingly long lived... more Recent experiments [Nature, 2007, 446, 782-786] revealed the existence of surprisingly long lived quantum coherence in noisy biological environment of photosynthetic Fenna-Matthews-Olson (FMO) complex. Such coherence can clearly play important role in facilitating efficient energy transfer. The occurrence of quantum coherence in quantum transport is also implicated in excitation transport processes in conjugated polymers [Science, 2009, 323, 369-373]. Even though these systems are strongly correlated, most theoretical studies invoke Markovian approximation where the temporal correlation of bath fluctuations is neglected. We use an elegant non-perturbative method based on Kubo's quantum stochastic Liouville equation (QSLE) to study the effects of correlated non-Markovian bath fluctuations in several different limits and find the interesting result that fluctuations not only destroy coherence but under appropriate conditions can also facilitate it. We show that temperature has the most pronounced effect in the intermediate coupling limit where it can promote transition from coherent to incoherent transfer.
The Journal of Physical Chemistry Letters, 2019
Quantum coherence and entanglement in an extended interacting system where energy levels are non-... more Quantum coherence and entanglement in an extended interacting system where energy levels are non-degenerate and coupled to a dissipative environment is a common occurrence in nature, like in photosynthetic reaction systems and conjugated polymers. Temperature dependence of quantum coherence in trimer complex (first three subunits of Fenna-Matthews-Olson (FMO) complex) is studied using a temperature dependent Quantum Stochastic Liouville equation. In the non-Markovian limit, the lowering of temperature induces long-lasting quantum coherence which in turn leads to delocalization whose length grows in the non-Markovian limit. Measure of entanglement and coherence length determines the nature of dynamic localization.
Chemical Physics Letters, 2018
When density is varied at a constant temperature just above the gas-liquid critical temperature, ... more When density is varied at a constant temperature just above the gas-liquid critical temperature, the system is found to exhibit large scale density fluctuations which are often rationalized in terms of crossing of a Widom line. We use the discrete variable representation (DVR) scheme to construct the spectroscopic maps for transition frequencies and transition dipoles, and obtain the infrared spectrum of the O-H stretch in the said temperature-density region of the phase diagram. The infrared lineshape shows a crossover from Lorentzian to Gaussian as we approach the Widom line. The width of the lineshape displays a pronounced maximum.
The Journal of Chemical Physics, 2017
Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vi... more Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vibrational line shapes, through such concepts as static heterogeneity and motional narrowing. However, the theory does not properly address the effects of quantum coherences on optical line shape, especially in extended systems where a large number of eigenstates are present. In this work, we study the line shape of an exciton in a one-dimensional lattice consisting of regularly placed and equally separated optical two level systems. We consider both linear array and cyclic ring systems of different sizes. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (SLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigenfunctions are known analytically. This identification is particularly useful for long chains where the eigenvalues of TDTM help understanding crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peaks increases beyond the ones obtained from TDTM (constant off-diagonal coupling element J and no fluctuation). (ii) However, in the fast modulation limit when the bath correlation time is small, the spatial correlation is less important. In this limit, the line shape shows motional narrowing with peaks at the values predicted by TDTM (constant J and no fluctuation). (iii) Importantly, we find that the line shape can capture that quantum coherence affects in the two limits differently. (iv) In addition to linear chains of two level systems, we also consider a cyclic tetramer. The cyclic polymers can be designed for experimental verification. (v) We also build a connection between line shape and population transfer dynamics. In the fast modulation limit, both the line shape and the population relaxation, for both correlated and uncorrelated bath, show similar behavior. However, in slow modulation limit, they show profoundly different behavior. (vi) This study explains the unique role of the rate of fluctuation (inverse of the bath correlation time) in the sustenance and propagation of coherence. We also examine the effects of off-diagonal fluctuation in spectral line shape. Finally, we use Tanimura-Kubo formalism to derive a set of coupled equations to include temperature effects (partly neglected in the SLE employed here) and effects of vibrational mode in energy transfer dynamics.
The Journal of Chemical Physics, 2016
We study excitation transfer and migration in a one-dimensional lattice characterized by dynamic ... more We study excitation transfer and migration in a one-dimensional lattice characterized by dynamic disorder. The diagonal and off-diagonal energy disorders arise from the coupling of system and bath. We consider both same bath (when baths are spatially correlated) and independent bath (when baths are completely uncorrelated) limits. In the latter case, all diagonal and off-diagonal bath coupling elements fluctuate independently of each other and the dynamics is complicated. We obtain time dependent population distribution by solving Kubo's quantum stochastic Liouville equation. In the Markovian limit, both energy transfer dynamics and mean square displacement of the exciton behave the similar way in same and independent bath cases. However, these two baths can give rise to a markedly different behavior in the non-Markovian limit. We note that previously only the same bath case has been studied in the non-Markovian limit. The other main results of our study include the following. (i) For an average, non-zero off-diagonal coupling value J, exciton migration remains coherent in same bath case even at long times while it becomes incoherent in independent bath case in the Markovian limit. (ii) Coherent transfer is manifested in an oscillatory behavior of the energy transfer dynamics accompanied by faster-than diffusive spread of the exciton from the original position. (iii) Agreement with available analytical expression of mean squared displacement is good in Markovian limit for independent bath (off-diagonal fluctuation) case but only qualitative in non-Markovian limit for which no complete analytical solution is available. (iv) We observe transition from coherent to incoherent transport in independent bath (diagonal fluctuation) case when the bath is made progressively more Markovian. We present an analytical study that shows coherence to propagate through excited bath states. (v) The correlation time of the bath plays a unique role in dictating the diffusive spread that is not anticipated in a Markovian treatment.
Physical Review Letters
We present inelastic neutron scattering measurements of magnetic excitations in stripe ordered Pr... more We present inelastic neutron scattering measurements of magnetic excitations in stripe ordered Pr 3=2 Sr 1=2 NiO 4 at T ∼ 10 K. For the observed magnetic incommensurability ϵ ¼ 0.4, we have incorporated a stripe discommensuration model in our linear spin wave calculation and obtained best agreement with the measured spin wave dispersion, especially to explain the symmetrical outward shift of the magnetic peaks from Néel ordered zone center in energy range 35 to 45 meV. Our study indicates the prerequisite to consider a discommensurated spin stripe unit with proper out-of-plane and in-plane exchange interactions in between Ni 2þ spins to describe the observed spin wave characteristics in Pr 3=2 Sr 1=2 NiO 4 .