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The Journal of Chemical Physics

Theory of entangled two-photon emission/absorption [E2P-EA] between molecules

Tse-Min Chiang, George Chappell Schatz

Published Aug 15, 2023• 1 citation
Publisher

Abstract

This paper presents a comprehensive study of the theory of entangled two-photon emission/absorption (E2P-EA) between a many-level cascade donor and a many-level acceptor (which could be quantum dots or molecules) using second-order perturbation theory and where the donor-acceptor pair is in a homogeneous but dispersive medium. To understand the mechanism of E2P-EA, we analyze how dipole orientation, radiative lifetime, energy detuning between intermediate states, separation distance, and entanglement time impact the E2P-EA rate. Our study shows that there are quantum interference effects in the E2P-EA rate expression that lead to oscillations in the rate as a function of entanglement time. Furthermore, we find that the E2P-EA rate for a representative system consisting of two quantum dots can be comparable to one-photon emission/absorption (OP-EA) when donor and acceptor are within a few nm. However, the E2P-EA rate falls off much more quickly with separation distance than does OP-EA.

DOI
10.1063/5.0156501

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Publisher’s Note: “Theory of entangled two-photon emission/absorption [E2P-EA] between molecules” [J. Chem. Phys. 159, 074103 (2023)]

Tse-Min Chiang, George Chappell Schatz

This is a correction to: Theory of entangled two-photon emission/absorption [E2P-EA] between molecules

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This paper presents a comprehensive study of the theory of entangled two-photon emission/absorption (E2P-EA) between a many-level cascade donor and a many-level acceptor (which could be quantum dots or molecules) using second-order perturbation theory and where the donor-acceptor pair is in a homogeneous but dispersive medium. To understand the mechanism of E2P-EA, we analyze how dipole orientation, radiative lifetime, energy detuning between intermediate states, separation distance, and entanglement time impact the E2P-EA rate. Our study shows that there are quantum interference effects in the E2P-EA rate expression that lead to oscillations in the rate as a function of entanglement time. Furthermore, we find that the E2P-EA rate for a representative system consisting of two quantum dots can be comparable to one-photon emission/absorption (OP-EA) when donor and acceptor are within a few nm. However, the E2P-EA rate falls off much more quickly with separation distance than does OP-EA.
Inspired by the unique nonclassical character of two-photon interactions induced by entangled photons, we develop a new comprehensive Förster-type formulation for entangled-two-photon resonance energy transfer (E2P-RET) mediated by inhomogeneous, dispersive, and absorptive media with any space-dependent and frequency-dependent dielectric function and with any size of donor/acceptor. In our theoretical framework, two uncoupled particles are jointly excited by the temporally entangled field associated with two virtual photons that are produced by three-level radiative cascade decay in a donor particle. The temporal entanglement leads to frequency anticorrelation in the virtual photon’s field, and vanishing of one of the time-ordered excitation pathways. The underlying mechanism leads to more than 3 orders of magnitude enhancement in the E2P-RET rate compared with the uncorrelated photon case. With the power of our new formulation, we propose a way to characterize E2P-RET through an effective rate coefficient K E2P, introduced here. This coefficient shows how energy transfer can be enhanced or suppressed depending on rate parameters in the radiative cascade, and by varying the donor–acceptor frequency differences.
A well controlled, triggered source of entangled photons is desirable for many applications in quantum information processing. The two-photon cascade from a biexciton state, two electrons and holes, confined in a quantum dot can be such a source of polarisation-entangled photons provided the two decay paths from the biexciton carry no “which-path” information. In recent years many techniques have been employed to make the two optical decay paths from the biexciton state indistinguishable. A number of these techniques will be discussed and entangled-photon emission from a single quantum dot with a high fidelity in the expected Bell-state from the cascade will be demonstrated. This source of entangled photons allows optical interferometry beyond the limits imposed by the photon wavelength. Interference fringes of the entangled biphoton state reveals a periodicity half of that obtained with the single photon, and much less than that of the pump laser. High fringe visibility indicates that biphoton interference is less sensitive to decoherence than interference of two sequential single photons. The effect of the exciton fine-structure splitting on our entangled photon source will be shown. Surprisingly the entanglement is found to persist despite relatively large separations between the intermediate energy levels of up to 4µeV. Measurements demonstrate that entanglement of the photon pair is robust to the dephasing of the intermediate exciton state responsible for the first order coherence time of either single photon. We distinguish between the first-order coherence time, and a parameter defined as the cross-coherence time, this is illustrated in the figure.
Emitters based on semiconductor quantum dots are promising sources for both single photons and pairs of polarization-entangled photons. Typically, single photons are generated through a photon emission event bringing the electronic system from a single-exciton state back to the ground state. In the case of entangled photons two photons are generated through a cascaded emission from the biexciton to either one of the single-exciton states and then back to the ground state. Alternatively, emission of two photons can also be achieved through a higher-order two-photon process bringing the quantum dot directly from the biexciton state (through a virtual intermediate state) back to the ground state. Here we discuss in particular how this two-photon process can lead to certain conceptual advantages in both the generation of polarization-entangled photon pairs and generation of single photons.
Second-order interference effects in the spontaneous emission by two identical two-level atoms, separated a distance apart and both initially excited, are considered. On the basis of the analysis in our previous paper published in 2004, within fourth-order perturbation, detailed analysis of the second-order quantum interference in the emitted field is made. The interference arises both from single-photon states and two-photon states owing to interferences between different decaying sequences. By detailed analysis we have found some cancellations between single-photon and two-photon interference terms, and an interpretation of this is given. The contributions from the single- and the two-photon states as well as the total interference are analysed numerically for various interatomic distances and times. The contribution from a two-photon state is mostly larger than that from a single-photon state except when the atomic electric dipole is large, in which case the two contributions can be comparable. It is shown that the emission patterns from the two interacting atoms provide more information on atom–atom correlations than the decay time evolution of the atomic states population does. The number of interference fringes and the distance between them depend on the interatomic distance in a similar fashion to Young's interference fringes.
We consider the general scenario of an excited level $|i\ensuremath{\rangle}$ of a quantum system that can decay via two channels: (i) via a single-quantum jump to an intermediate, resonant level $|\overline{m}\ensuremath{\rangle}$, followed by a second single-quantum jump to a final level $|f\ensuremath{\rangle}$, and (ii) via a two-quantum transition to a final level $|f\ensuremath{\rangle}$. Cascade processes $|i\ensuremath{\rangle}\ensuremath{\rightarrow}|\overline{m}\ensuremath{\rangle}\ensuremath{\rightarrow}|f\ensuremath{\rangle}$ and two-quantum transitions $|i\ensuremath{\rangle}\ensuremath{\rightarrow}|m\ensuremath{\rangle}\ensuremath{\rightarrow}|f\ensuremath{\rangle}$ compete (in the latter case, $|m\ensuremath{\rangle}$ can be both a nonresonant as well as a resonant level). General expressions are derived within second-order time-dependent perturbation theory, and the cascade contribution is identified. When the one-quantum decay rates of the virtual states are included into the complex resonance energies that enter the propagator denominator, it is found that the second-order decay rate contains the one-quantum decay rate of the initial state as a lower-order term. For atomic transitions, this implies that the differential-in-energy two-photon transition rate with complex resonance energies in the propagator denominators can be used to good accuracy even in the vicinity of resonance poles.