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Physical Review A

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

Published Jun 28, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.95.067802

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

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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.

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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.
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 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.
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.
Introduction So far, we have discussed closed systems involving a single quantized mode of the field interacting with atoms, as for example in the Jaynes–Cummings model in Chapter 4. As we saw in this model, the transition dynamics are coherent and reversible: the atom and field mode exchange excitation to and fro without loss of energy. As we add more modes for the atom to interact with, the coherent dynamics become more complicated as the relevant atom–field states come in and out of phase and beat together to determine the total state occupation probabilities. As time goes on, these beats get out of phase, leading to an apparent decay of the initial state occupation probability. But at later times, the beating eigenfrequencies get back in phase in a manner rather reminiscent of the Jaynes–Cummings revival discussed earlier in this book, and this leads to a partial recurrence or revival of the initial state probability. The time scale for this partial revival depends on the number of participating electromagnetic field modes and as these increase to the level appropriate for an open system in free space the recurrence disappears off to the remote future, and the exponential decay law appropriate for decay is recovered as an excellent approximation. We have already discussed the origin of spontaneous emission and the Einstein A coefficient using perturbation theory in Chapter 4.