Efficient general waveform catching by a cavity at an absorbing exceptional point

Letter

Efficient general waveform catching by a cavity at an absorbing exceptional point

Asaf Farhi, Wei Dai, Seunghwi Kim, Andrea Alù, and Douglas Stone

Phys. Rev. A 109, L041502 – Published 17 April 2024

Abstract

We study a system tuned to an absorbing exceptional point and explore its use to efficiently receive and store an incoming wave with an envelope different from the absorbing-eigenmode envelope. Specifically, while absorbing states of lossless resonators have an exponentially increasing envelope, we focus on capturing naturally emitted waves with an exponentially decreasing envelope. We find that, when tuning a cavity to an $n th$ -order absorbing exceptional point (EP), $n + 1$ temporal orders of any incoming waveform can be perfectly captured, leading to significantly less scattering and increasing the overall absorption efficiency for general waveforms. We present an approach to tune a cavity to an EP and demonstrate less scattering by an order of magnitude for a decaying incoming waveform. Our results may be used for efficient passive state transfer and detection of spontaneous emission.

Received 14 October 2023
Accepted 27 March 2024

DOI:https://doi.org/10.1103/PhysRevA.109.L041502

Physics Subject Headings (PhySH)

Optical transient phenomena Scattering theory Spontaneous emission

Atomic systems Molecules Non-Hermitian systems Quantum cavities Trapped ions

Atomic, Molecular & OpticalQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Asaf Farhi¹, Wei Dai¹, Seunghwi Kim ², Andrea Alù^2,3, and Douglas Stone^1,4

¹Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
²Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, USA
³Physics Program, Graduate Center, City University of New York, New York, New York 10016, USA
⁴Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA

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Issue

Vol. 109, Iss. 4 — April 2024

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Images

Figure 1
(a) Naturally emitted waveform from a cavity decays (increases) exponentially in time (space, presented above). Such a waveform is emitted in spontaneous emission by an atom or molecule. (b) A waveform that increases (decays) exponentially in time (space) is perfectly captured by a cavity. Right: The complex excitation frequency (blue circle) and absorbing eigenfrequency (red cross) match. (c) Passive state transfer with standard cavities. Since the naturally emitted and perfectly captured waves do not match, 40% of the incident field is scattered. (d) Passive state transfer with a cavity system tuned to a virtual absorbing exceptional point where two absorbing eigenfrequencies coalesce. Since the EP cavity captures another order in time of the incoming waveform, there is very small scattering.
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Figure 2
A schematic of the setup: A flux-controlled coupler and two transmission lines (microwave analog of the optical cavities) loaded by a transmon, tuned to an absorbing virtual exceptional point. The coupler is composed of two capacitors each of capacitance $2 C$ and a superconducting quantum interference device (SQUID), which can be modeled by an inductance $L = L_{J} / cos (Φ / ϕ_{0})$ .
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Figure 3
(a) $| r |$ as a function of $Re (ω)$ and $Im (ω)$ close to the EP in surface and contour (inset) plots. The scaling is quadratic in two dimensions (2D) as expected since at the EP $| r | \propto {(ω - ω_{n})}^{2}$ and the derivative with respect to a complex variable is equal to the derivatives from all directions, which verifies the calculation of the virtual CPA EP. (b) Coalescence of the eigenfrequencies that satisfy the equation $r = 0$ at the EP when varying $l_{1} / l_{2}$ , where the diamond denotes the EP.
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Figure 4
The incoming and scattered fields as functions of time for the inputs (a) $e^{i ω t + Γ t}$ and (b) $t e^{i ω t + Γ t}$ . (c) Fractional scattered energy for both incoming fields as functions of time. Note that for the EP parameters, the roundtrip is less than an oscillation period, resulting in rapid equilibration.
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Figure 5
(a) The incoming and scattered fields as functions of time for the inputs $e^{i ω t - Γ t}$ , which show that the naturally emitted wave $e^{i ω t - Γ t}$ is well captured by the CPA EP cavity. (b) Fractional scattered energy as a function of time. Importantly, the efficiency for this passive quantum state transfer is $> 93 %$ . Note that there are only two or three roundtrips of the incoming wave, and therefore no significant scattering is expected for the input $e^{i ω t - Γ t}$ during the second half since there is a delay between the input and output and the linear approximation holds in the first half.
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