Quantum simulation of weak-field light-matter interactions

Open Access

Quantum simulation of weak-field light-matter interactions

Steve M. Young, Hartmut Häffner, and Mohan Sarovar

Phys. Rev. Research 5, 013027 – Published 20 January 2023

Abstract

Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials and for modeling next-generation nonlinear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.

Received 7 February 2022
Revised 20 September 2022
Accepted 5 December 2022

DOI:https://doi.org/10.1103/PhysRevResearch.5.013027

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum algorithms Quantum simulation

Quantum Information, Science & Technology

Authors & Affiliations

Steve M. Young^1,*, Hartmut Häffner², and Mohan Sarovar ^3,†

¹Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
²Department of Physics, University of California, Berkeley, California 94720, USA
³Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA

^*[email protected]
^†[email protected]

Article Text

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Issue

Vol. 5, Iss. 1 — January - March 2023

Subject Areas

Quantum Physics

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Images

Figure 1
We develop a quantum simulation approach that enable platforms with controllable bosonic degrees of freedom, such as the trapped ion system shown on the right, to simulate the dynamics of matter, such as the chromophoric complex on the left, in response to illumination by extremely weak light fields. Such dynamics is relevant for understanding the behavior of photodetectors, photovoltaics, biochemical systems such as photosynthetic light harvesting complexes, and for modeling new weak-field spectroscopy experiments.
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Figure 2
(a) Example pulse/measurement schedules (top) and a sketch of their inclusion in the response reconstruction (bottom). The pulse profiles $γ (t)$ (red) are chosen with spacing $t_{int}$ and measurements are performed at $t_{m}$ after the second pulse, allowing for the generation of samples of $G i_{M}$ according to Eq. (18). For an arbitrary wavepacket profile $ɛ (t)$ , the response at a time $t$ is simulated by multiplying $G_{i_{M}} (t_{m}, t_{int})$ by $ɛ (t - t_{m} - t_{int}) ɛ (t - t_{m})$ and summing over relevant $t_{m}, t_{int}$ [Eq. (16)]. (b) A depiction of a system interacting with a field characterized by a continuum with a single-photon wavepacket (red oscillatory lineshape), traversing the system. At early times the matter system (black circle), represented here as a two-level system with a decay mode (red lines), interacts only with the vacuum and remains in the ground state. At some point during the traversal of the wavepacket the matter system may absorb the photon and enter the excited state, leaving the field in the vacuum state. Later, the matter system may emit a photon back into the field, decaying to the ground state; afterwards the photon is not present at the matter system and may not be reabsorbed. (c) A system comprising a single mode for the field (red circle) whose coupling can be rapidly adjusted with time and a highly incoherent bath (dashed line circle) coherently coupled (gray double arrow) to the matter system (black circle). Initially the boson mode is in the first excited state and uncoupled to the matter system. At some time the interaction (red double arrow) is rapidly turned on and off, allowing for possible transfer of the excitation. At some point later this population will be transferred to the bath and almost immediately decay, mimicking a spontaneous emission event. Shown is the response for a single coupling pulse; as discussed in the text, in general multiple pulses are necessary to capture the impact of interference between excited matter states created by interaction with an external field at different times.
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Figure 3
Schematic for the example illustrated in Sec. 5. (a) The physical scenario being simulated. Two chromophores represented by black circles are excited by a weak-field wavepacket. Each chromophore has a ground state, corresponding to a lowest unoccupied molecular orbital (LUMO), and an excited state, corresponding to the highest occupied molecular orbital (HOMO); these are drawn in red and cyan to indicate optical coupling and are shown with wavy arrows to indicate the optically mediated decay process. (b) Schematic of trapped ion simulator capable of simulating the physical setup in panel (a). The internal states of each chromophore are encoded into states of distinct ions (indicated by the dashed circles). The excited states no longer have internal decay processes, but are instead coherently coupled to an auxiliary ion that is damped. In addition, each of ions encoding chromophore states is coupled to a vibrational mode representing the field (red circle). The monitored state of the red chromophore, encoded in the top ion, is the shown attached to an output channel that represents measurement.
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Figure 4
(a) The population of the excited state of 1 in response to two $δ$ pulses spaced $t_{int} = 250$ apart (gray) along with the independent contributions from each pulse (dashed line) and $G_{1} (t, 250)$ (blue), the latter of which captures the interference between coherent excitations due to the pulses. (b) shows the impact of $n_{γ}$ and $χ^{2}$ on the simulated value of $G_{1} (50, 250)$ in the limit of $δ$ pulses ( $t_{γ} = 1$ ). The dashed line marks the exact value. $χ^{2} = 5$ for the $n_{γ}$ sweep, and $n_{γ} = 0.25$ for the $χ^{2}$ sweep.
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Figure 5
(a) A plot of $G_{1} (200, t)$ for different $t_{γ}$ . (b) The population of excited state 1 in response to a single photon with a Gaussian-shaped temporal profile. The top panel shows the exact response $P^{M} (t)$ with the simulated time of measurement marked by a vertical dashed line. The gray shaded area shows the profile shape of the intensity of the photon pulse. The contour plot in the bottom panel shows the relationship between the error (computed population less the exact value indicated in the top panel) in the simulated population at $t = 200$ for different values of $t_{γ}$ and sampling intervals $Δ t$ of $t_{m}$ and $t_{int}$ , for $n_{γ} = 1$ and $χ^{2} = 5$ .
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Figure 6
(a) Schematic of the Example 2. This model has one optically active element, e.g., a quantum dot, that couples to a chain of optically inactive (dark) elements, which could be other quantum dots. We are interested in the transfer of a photoexcitation down the chain to a state ( $f$ ) in the final dark element. Note that the two-headed arrows indicate coherent coupling between elements and the single-headed arrow indicate incoherent transfer. Making this transfer difficult to model is that one of the intermediate dark elements (2) is coupled to classical fluctuators (shaded circles), which induce non-Markovian stochastic dynamics in the remainder of the system. (b) The trapped ion simulation is setup similarly to the small system. Again, we model the internal states of each of the quantum dots with internal states of ions (shown in dashed circles). The coherent coupling between quantum dots and fluctuators are implemented through Hamiltonian engineering (see main text). Ion 3 encodes both states in quantum dot 3 and also the $f$ state. The incoherent coupling to state $f$ is implemented through optical pumping via an intermediate state (similar to ion readout). (c) The measured population of the end state for different $n_{γ}$ as a function of $t_{γ} = 2 Δ t_{int}$ . (d) The $G_{f} (\infty, t)$ that describes the response of the system to input pulses of varying width. In both cases, $ω_{0} = ω_{1} = 1.0, ω_{2} = 0.8, ω_{3} = 0.9, ω_{f} = 0.5, ω_{α} = ω_{β} = 0.1, J_{12} = 0.096, J_{23} = 0.1, J_{2 α} = J_{2 β} = 0.02, l = 0.01, Γ_{f}^{2} = 0.4, Γ_{α}^{2} = 0.25, Γ_{β}^{2} = 0.5, n_{γ} = 1$ , and $χ^{2} = 5$ .
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