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Physical Review A

Comment on “Thermal-light-induced dynamics: Coherence and revivals in V -type and molecular Jaynes-Cummings systems”

Amro Dodin, Paul W. Brumer

Published Jun 28, 2017• 1 citation
Publisher

Abstract

Recent numerical and analytical results have been obtained for the dynamics of a $V$-type system, and of a model molecular system, interacting with the thermal states of a cavity with a single mode or with a few discrete modes [D. Avisar and A. D. Wilson-Gordon, Phys. Rev. A 93, 033843 (2016)]. The authors speculate that these results may be relevant to excitation with natural incoherent radiation, such as sunlight, which has a continuous spectrum. We claim that this is incorrect, as are their comments about prior work on natural incoherent radiation that does properly deal with a continuous spectrum. Specifically, while their results obtained for the Jaynes-Cummings systems may be of interest for excitation by thermal states of cavities with a few modes, the discrete nature of their field modes produces dynamics that are fundamentally different from those induced by natural sunlight. Hence, we show here that the criticisms leveled in their paper regarding prior treatments that dealt with the continuous spectrum of natural incoherent radiation, as well as their speculation that excitation with continuous-mode thermal radiation can induce long-lived molecular coherences, are incorrect.

DOI
10.1103/physreva.95.067801

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Reply to “Comment on ‘Thermal-light-induced dynamics: Coherence and revivals in V -type and molecular Jaynes-Cummings systems’ ”

David Avisar, A. D. Wilson‐Gordon

We recently presented an extended Jaynes-Cummings model for the interaction of a realistic molecular system of two Born-Oppenheimer potential energy surfaces and a quantized electromagnetic field [Avisar and Wilson-Gordon, Phys. Rev. A 93, 033843 (2016)]. We studied the interaction of this molecular model, and also a prototype $V$-type system, with single-mode and multimode thermal states of the field, characterized by low and high average photon number $\overline{n}$. Among our results, we showed that the three-mode thermal state of the field induces excited-state material coherence and that a thermal state of high $\overline{n}$ can induce ``coherentlike'' collapse and revival patterns. The preceding Comment by Dodin and Brumer [Phys. Rev. A 95, 067801 (2017)] criticizes our work for allegedly drawing conclusions regarding sunlight-induced dynamics from our results, and for unjustified citation of previous work. However, we think the Comment fails to represent the contents of our paper, and we therefore reply to it. We show it is based on misinterpretation of our paper.

Physical Review A•Jun 28, 2017•0 citations

Thermal-light-induced dynamics: Coherence and revivals in V -type and molecular Jaynes-Cummings systems

David Avisar, A. D. Wilson‐Gordon

We examine the interaction of thermal light with matter with emphasis on two aspects that have not been considered before. By employing a fully quantized Jaynes-Cummings--type interaction model on a $V$-type three-level system, we show that multimode thermal light induces coherence in the excited material states. This is in contrast to previous studies that suggest thermal light cannot induce coherence in material systems. We also show that the ratio between the field detuning and the interaction constant has a significant influence on the characteristic time-dependent dynamics. In particular, for some ratio regimes, the thermal light induces dynamics with a ``coherentlike'' collapse and revivals pattern rather than the familiar pattern. We then extend the Jaynes-Cummings model to a two-state Born-Oppenheimer potential energy surface molecular system where the internal vibrational degrees of freedom are fully taken into account. The matter-field bipartite system is represented, and propagated, in the full electronic bond-coordinate Fock product space. We show that single-mode thermal light induces extensive excited-state vibrational coherence in the molecule that, when observed in coordinate space, exhibits wave-packet-like dynamics. The molecular Jaynes-Cummings model we propose is useful for cavity molecular dynamics simulations.

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Thermal-Light-Induced Coherent Dynamics in Atoms and Molecules -- an Exact Quantum Mechanical Treatment

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The question of whether sunlight induces coherent dynamics in biological systems is under debate. Here we show, on the basis of an exact fully quantum mechanical treatment, that thermal light induces excited-state coherences in matter similar to those induced by a coherent state. We demonstrate the phenomenon on a V-type model system and a two-state Born-Oppenheimer molecular system. Remarkably, wavepacket-like dynamics is induced in the excited molecular potential-energy surface.

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Under natural conditions, excitation of biological molecules, which display nonunitary open system dynamics, occurs via incoherent processes such as temperature changes or irradiation by sunlight or moonlight. The dynamics of such processes is explored analytically in a non-Markovian generic model. Specifically, a system S in equilibrium with a thermal bath TB is subjected to an external incoherent perturbation BB (such as sunlight) or another thermal bath TB${}^{\ensuremath{'}}$, which induces time evolution in ($\text{S}+\text{TB}$). Particular focus is on (i) the extent to which the resultant dynamics is coherent, and (ii) the role of ``stationary coherences'' established in the ($\text{S}+\text{TB}$) equilibration in response to the second incoherent perturbation. Results for systems with parameters analogous to those in light-harvesting molecules in photosynthesis show that the resultant dynamical behavior is incoherent beyond a very short response to the turn on of the perturbation.

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Glauber-Lachs version of the Jaynes-Cummings interaction of a two-level atom

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The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of a radiation field prepared in a Glauber-Lachs state is investigated to study the development of seemingly chaotic oscillations of the atomic inversion from a regular collapse-and-revival phenomenon, as the field statistics is changed from the coherent state to the thermal state. The effect of thermal photons on the coherent light is shown to be striking: Both the photon distribution as well as the atomic inversion are highly sensitive to even a very small addition of thermal photons to an initially coherent radiation field. We also compare the collapse and revival occurring in the micromaser case with the Glauber-Lachs version of the Jaynes-Cummings model.

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Some aspects of cavity quantum electrodynamics

Bjørn Å Bergsjordet

We have in this thesis looked at two very different problems related to quantum optics. In Part I we have studied the Jaynes-Cummings model with cavity damping and a thermal background. To give an introduction to the field we started Chapter 2 by repeating how one in general derives the master equations for a system coupled to a reservoir. We then repeat the Jaynes-Cummings model and show extensions of the Jaynes-Cummings model where cavity-damping and a thermal background are taken into account. We proceed, in Chapter 3, by finding an analytical solution to the Jaynes-Cummings model with cavity damping in a thermal background when there is no detuning in the system, i.e. we have resonance between the energy of the photons in the cavity and the energy difference in the excited and ground state of the atom. We derive analytical expressions for P+(t), the probability of finding the atom in an excited state after some transition time t given that the atom was prepared in an excited state, and P++(t), the probability of finding the atom in an excited state after some transition time t when a previous atom was measured to be in the excited state. Both atoms where initially prepared in the excited state. We also, in Section 3.7 make use of the Poisson summation formula to rewrite the analytical solution P+(t) in terms of a Fourier series, from which we can predict the location of the revivals in the system. In Section 3.8 we derive stationary results, i.e. when the transition time t→∞, for the probabilities P+(t) and P++(t) and the mean number of photons ‹ n(t) › in the cavity. From our analytical results one is, for instance, led to believe that the probability P+(t) approaches 0 as the transitiontime increases, when it in reality approaches the value nb/(1 + 2nb). The results of our study of the extended Jaynes-Cummings model is presented in the article “Macroscopic Interference Effects in Resonant Cavities” and is published in Physica Scripta [5]. The article is reprinted as Article 1 at the end of this thesis. In Chapter 4 we present the result of a numerical solution of the Jaynes-Cummings model with cavity damping in a thermal background. Here we consider both the resonant case and also the case where detuning is present in the system. When we compare our numerical simulation with our analytical solutions we find that the correlation between the two are close to 1, at least when experimental values of Walther et al. [22] and Brune et al. [15, 16] are used. We also present some figures that show how the revival times and probabilities previously discussed is affected by detuning. In Section 4.2 we find an analytical formula for the revival time where detuning is embedded. In Chapter 4 we also, shortly, discuss how the detuning changes the effective number of photons in the cavity and what criteria should be present in order to separate the revival times.In Part II we study some aspects of quantum mechanical phase. We start, in Section 5.1, by repeating the definition and some results of the Susskind-Glogower phase operator. We then turn our attention to the Pegg-Barnett phase operator [26, 27, 28] in Section 5.4. We describe how to evaluate expectation-values and variances of the Pegg-Barnett phase. In Section 5.5 we establish an upper and lower bound on the phase based on the Pegg-Barnett phase description.In Section 5.9 we repeat some details of a new formalism of the phase which we have conveniently called the NFM-formalism after its inventors Noh, Foug`eres and Mandel [29, 30, 31]. We then describe how to find expectation-values using the Pegg-Barnett phase operator definition applied to the NFM-experiment described in Section 5.9. Our work on the quantum mechanical phase operator is presented in the paper “On the Quantum Phase Operator for Coherent States” and is published in Physica Scripta [6]. This paper is reprinted as Article II at the end of this thesis.

118•Jan 1, 2005•0 citations
Recent numerical and analytical results have been obtained for the dynamics of a VVV-type system, and of a model molecular system, interacting with the thermal states of a cavity with a single mode or with a few discrete modes [D. Avisar and A. D. Wilson-Gordon, Phys. Rev. A 93, 033843 (2016)]. The authors speculate that these results may be relevant to excitation with natural incoherent radiation, such as sunlight, which has a continuous spectrum. We claim that this is incorrect, as are their comments about prior work on natural incoherent radiation that does properly deal with a continuous spectrum. Specifically, while their results obtained for the Jaynes-Cummings systems may be of interest for excitation by thermal states of cavities with a few modes, the discrete nature of their field modes produces dynamics that are fundamentally different from those induced by natural sunlight. Hence, we show here that the criticisms leveled in their paper regarding prior treatments that dealt with the continuous spectrum of natural incoherent radiation, as well as their speculation that excitation with continuous-mode thermal radiation can induce long-lived molecular coherences, are incorrect.
We recently presented an extended Jaynes-Cummings model for the interaction of a realistic molecular system of two Born-Oppenheimer potential energy surfaces and a quantized electromagnetic field [Avisar and Wilson-Gordon, Phys. Rev. A 93, 033843 (2016)]. We studied the interaction of this molecular model, and also a prototype VVV-type system, with single-mode and multimode thermal states of the field, characterized by low and high average photon number n‾\overline{n}n. Among our results, we showed that the three-mode thermal state of the field induces excited-state material coherence and that a thermal state of high n‾\overline{n}n can induce ``coherentlike'' collapse and revival patterns. The preceding Comment by Dodin and Brumer [Phys. Rev. A 95, 067801 (2017)] criticizes our work for allegedly drawing conclusions regarding sunlight-induced dynamics from our results, and for unjustified citation of previous work. However, we think the Comment fails to represent the contents of our paper, and we therefore reply to it. We show it is based on misinterpretation of our paper.
We examine the interaction of thermal light with matter with emphasis on two aspects that have not been considered before. By employing a fully quantized Jaynes-Cummings--type interaction model on a VVV-type three-level system, we show that multimode thermal light induces coherence in the excited material states. This is in contrast to previous studies that suggest thermal light cannot induce coherence in material systems. We also show that the ratio between the field detuning and the interaction constant has a significant influence on the characteristic time-dependent dynamics. In particular, for some ratio regimes, the thermal light induces dynamics with a ``coherentlike'' collapse and revivals pattern rather than the familiar pattern. We then extend the Jaynes-Cummings model to a two-state Born-Oppenheimer potential energy surface molecular system where the internal vibrational degrees of freedom are fully taken into account. The matter-field bipartite system is represented, and propagated, in the full electronic bond-coordinate Fock product space. We show that single-mode thermal light induces extensive excited-state vibrational coherence in the molecule that, when observed in coordinate space, exhibits wave-packet-like dynamics. The molecular Jaynes-Cummings model we propose is useful for cavity molecular dynamics simulations.
Under natural conditions, excitation of biological molecules, which display nonunitary open system dynamics, occurs via incoherent processes such as temperature changes or irradiation by sunlight or moonlight. The dynamics of such processes is explored analytically in a non-Markovian generic model. Specifically, a system S in equilibrium with a thermal bath TB is subjected to an external incoherent perturbation BB (such as sunlight) or another thermal bath TB${}^{\ensuremath{'}}$, which induces time evolution in (S+TB\text{S}+\text{TB}S+TB). Particular focus is on (i) the extent to which the resultant dynamics is coherent, and (ii) the role of ``stationary coherences'' established in the (S+TB\text{S}+\text{TB}S+TB) equilibration in response to the second incoherent perturbation. Results for systems with parameters analogous to those in light-harvesting molecules in photosynthesis show that the resultant dynamical behavior is incoherent beyond a very short response to the turn on of the perturbation.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of a radiation field prepared in a Glauber-Lachs state is investigated to study the development of seemingly chaotic oscillations of the atomic inversion from a regular collapse-and-revival phenomenon, as the field statistics is changed from the coherent state to the thermal state. The effect of thermal photons on the coherent light is shown to be striking: Both the photon distribution as well as the atomic inversion are highly sensitive to even a very small addition of thermal photons to an initially coherent radiation field. We also compare the collapse and revival occurring in the micromaser case with the Glauber-Lachs version of the Jaynes-Cummings model.
We have in this thesis looked at two very different problems related to quantum optics. In Part I we have studied the Jaynes-Cummings model with cavity damping and a thermal background. To give an introduction to the field we started Chapter 2 by repeating how one in general derives the master equations for a system coupled to a reservoir. We then repeat the Jaynes-Cummings model and show extensions of the Jaynes-Cummings model where cavity-damping and a thermal background are taken into account. We proceed, in Chapter 3, by finding an analytical solution to the Jaynes-Cummings model with cavity damping in a thermal background when there is no detuning in the system, i.e. we have resonance between the energy of the photons in the cavity and the energy difference in the excited and ground state of the atom. We derive analytical expressions for P+(t), the probability of finding the atom in an excited state after some transition time t given that the atom was prepared in an excited state, and P++(t), the probability of finding the atom in an excited state after some transition time t when a previous atom was measured to be in the excited state. Both atoms where initially prepared in the excited state. We also, in Section 3.7 make use of the Poisson summation formula to rewrite the analytical solution P+(t) in terms of a Fourier series, from which we can predict the location of the revivals in the system. In Section 3.8 we derive stationary results, i.e. when the transition time t→∞, for the probabilities P+(t) and P++(t) and the mean number of photons ‹ n(t) › in the cavity. From our analytical results one is, for instance, led to believe that the probability P+(t) approaches 0 as the transitiontime increases, when it in reality approaches the value nb/(1 + 2nb). The results of our study of the extended Jaynes-Cummings model is presented in the article “Macroscopic Interference Effects in Resonant Cavities” and is published in Physica Scripta [5]. The article is reprinted as Article 1 at the end of this thesis. In Chapter 4 we present the result of a numerical solution of the Jaynes-Cummings model with cavity damping in a thermal background. Here we consider both the resonant case and also the case where detuning is present in the system. When we compare our numerical simulation with our analytical solutions we find that the correlation between the two are close to 1, at least when experimental values of Walther et al. [22] and Brune et al. [15, 16] are used. We also present some figures that show how the revival times and probabilities previously discussed is affected by detuning. In Section 4.2 we find an analytical formula for the revival time where detuning is embedded. In Chapter 4 we also, shortly, discuss how the detuning changes the effective number of photons in the cavity and what criteria should be present in order to separate the revival times.In Part II we study some aspects of quantum mechanical phase. We start, in Section 5.1, by repeating the definition and some results of the Susskind-Glogower phase operator. We then turn our attention to the Pegg-Barnett phase operator [26, 27, 28] in Section 5.4. We describe how to evaluate expectation-values and variances of the Pegg-Barnett phase. In Section 5.5 we establish an upper and lower bound on the phase based on the Pegg-Barnett phase description.In Section 5.9 we repeat some details of a new formalism of the phase which we have conveniently called the NFM-formalism after its inventors Noh, Foug`eres and Mandel [29, 30, 31]. We then describe how to find expectation-values using the Pegg-Barnett phase operator definition applied to the NFM-experiment described in Section 5.9. Our work on the quantum mechanical phase operator is presented in the paper “On the Quantum Phase Operator for Coherent States” and is published in Physica Scripta [6]. This paper is reprinted as Article II at the end of this thesis.