Tensor network simulation of multi-environmental open quantum dynamics via machine learning and entanglement renormalisation

Schröder, Florian A. Y. N.; Turban, David H. P.; Musser, Andrew J.; Hine, Nicholas D. M.; Chin, Alex W.

doi:10.1038/s41467-019-09039-7

Cited by 99 publications

(124 citation statements)

References 67 publications

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“…It can be seen that ω v is very close to the frequency of the dominant vibrational mode in J v (ω). We have additionally checked the validity of the single-mode approximation by comparing the model calculations above with time-dependent variational matrix product states (TDVMPS) calculations [10,47] in which the full phononic spectral density, describing all vibrational modes of the molecule and surroundings, is taken into account. The tensor network approach to quantum dynamics relies on the assumption that the ground-state and low-energy excitations live in a corner of the Hilbert space where entanglement is mainly local (entanglement area law).…”

Section: Methodsmentioning

confidence: 99%

Polaritonic molecular clock for all-optical ultrafast imaging of wavepacket dynamics without probe pulses

et al. 2020

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Conventional approaches to probing ultrafast molecular dynamics rely on the use of synchronized laser pulses with a well-defined time delay. Typically, a pump pulse excites a wavepacket in the molecule. A subsequent probe pulse can then dissociates or ionizes the molecule, and measurement of the molecular fragments provides information about where the wavepacket was for each time delay. In this work, we propose to exploit the ultrafast nuclear-position-dependent emission obtained due to large light-matter coupling in plasmonic nanocavities to image wavepacket dynamics using only a single pump pulse. We show that the time-resolved emission from the cavity provides information about when the wavepacket passes a given region in nuclear configuration space. This approach can image both cavity-modified dynamics on polaritonic (hybrid light-matter) potentials in the strong light-matter coupling regime as well as bare-molecule dynamics in the intermediate coupling regime of large Purcell enhancements, and provides a new route towards ultrafast molecular spectroscopy with plasmonic nanocavities. :1907.12607v1 [cond-mat.mes-hall] arXiv

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Section: Methodsmentioning

confidence: 99%

Polaritonic molecular clock for all-optical ultrafast imaging of wavepacket dynamics without probe pulses

et al. 2020

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“…In particular, if the coupling between the system and the bath is weak, one can apply the Markov approximation (which assumes that the bath has "no memory"), such that the EM environment simply introduces a frequency-dependent decay rate (corresponding exactly to the Purcell effect). When this approximation is not applicable, more advanced numerical approaches such as tensor network calculations 47,48 or hierarchical equations of motion 49 can be employed, possibly after a chain transformation of the associated Hamiltonian 50 . Such approaches have been used to study static properties and dynamics in organic polaritons 51,52 .…”

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confidence: 99%

Cumulant expansion for the treatment of light–matter interactions in arbitrary material structures

Mónica

Silva

Feist

2020

The Journal of Chemical Physics

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Strong coupling of quantum emitters with confined electromagnetic modes of nanophotonic structures may be used to change optical, chemical and transport properties of materials, with significant theoretical effort invested towards a better understanding of this phenomenon. However, a full theoretical description of both matter and light is an extremely challenging task. Typical theoretical approaches simplify the description of the photonic environment by describing it as a single or few modes. While this approximation is accurate in some cases, it breaks down strongly in complex environments, such as within plasmonic nanocavities, and the electromagnetic environment must be fully taken into account. This requires the quantum description of a continuum of bosonic modes, a problem that is computationally hard. We here investigate a compromise where the quantum character of light is taken into account at modest computational cost. To do so, we focus on a quantum emitter that interacts with an arbitrary photonic spectral density and employ the cumulant or cluster expansion method to the Heisenberg equations of motion up to first, second and third order. We benchmark the method by comparing with exact solutions for specific situations and show that it can accurately represent dynamics for many parameter ranges.Light-matter interaction is of paramount importance for unraveling the laws of nature and its deep understanding allows us to control and manipulate physical and chemical systems. In particular, one can modify the properties of a quantum emitter simply by changing its electromagnetic environment, for example by enclosing it within an optical cavity. This may give rise to a change of the decay rate for spontaneous emission in the weak coupling regime, the so-called Purcell effect 1 , or to the appearance of hybrid light-matter states, socalled polaritons, in the strong-coupling regime 2-5 . Over the last decades, it has been shown that strong light-matter coupling can be achieved using a large variety of physical implementations as the "cavity" that provides the electromagnetic field confinement. These include Fabry-Perot cavities consisting of two mirrors 5 , propagating surface plasmon polaritons 6 , plasmonic hole 7 and nanoparticle arrays 8 , isolated plasmonic nanoparticles 9 and nanoparticle-on-mirror geometries 10,11 , as well as hybrid cavities combining plasmonic and dielectric materials [12][13][14] . In many of these systems, the electromagnetic field modes are not well-described by isolated lossy cavity modes, and a correct treatment demands theoretical approaches that are able to deal with the complexity of the electromagnetic field modes and their spectrum.In principle, to treat the problem of light-matter interaction, one can rely on the most general theory that describes light and matter on equal footing, i.e., quantum electrodynamics (QED) 15 . However, treating all light and matter degrees of freedom in the systems described above in a quantum mechanical way is an intractable problem and approx...

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“…Furthermore, DMRG-based algorithms for time evolution 35,36,38,109,110 can straightforwardly be applied to TTNS. 39,111 It will be very interesting to see how they compare to the MCTDH-based algorithms. Also, we believe that the diagrammatic notation used in the DMRG community and in this work will highlight new facets of established MCTDH methodology.…”

Section: Discussionmentioning

confidence: 99%

Computing vibrational eigenstates with tree tensor network states (TTNS)

Larsson

2019

The Journal of Chemical Physics

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We present how to compute vibrational eigenstates with tree tensor network states (TTNS), the underlying ansatz behind the multilayer multi-configuration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on the density matrix renormalization group (DMRG). We apply this to compute the vibrational spectrum of acetonitrile (CH 3 CN) to high accuracy and compare TTNS with matrix product states (MPS), the ansatz behind the DMRG. The presented optimization scheme converges much faster than ML-MCTDH-based optimization. For this particular system, we found no major advantage of the more general TTNS over MPS. We highlight that for both TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of required parameters. We furthermore propose a procedure to find good trees.

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Tensor network simulation of multi-environmental open quantum dynamics via machine learning and entanglement renormalisation

Cited by 99 publications

References 67 publications

Polaritonic molecular clock for all-optical ultrafast imaging of wavepacket dynamics without probe pulses

Polaritonic molecular clock for all-optical ultrafast imaging of wavepacket dynamics without probe pulses

Cumulant expansion for the treatment of light–matter interactions in arbitrary material structures

Computing vibrational eigenstates with tree tensor network states (TTNS)

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