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arXiv:2103.02689 · Physical Review A

Boosting energy-time entanglement using coherent time-delayed feedback

Kisa Barkemeyer, Marcel Hohn, Stephan Reitzenstein, Alexander Carmele

Published Jun 28, 2021• 7 citations
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Abstract

The visibility of the two-photon interference in the Franson interferometer serves as a measure of the energy-time entanglement of the photons. We propose to control the visibility of the interference in the second-order coherence function by implementing a coherent time-delayed feedback mechanism. Simulating the non-Markovian dynamics within the matrix product state framework, we find that the visibility for two photons emitted from a three-level system (3LS) in ladder configuration can be enhanced significantly for a wide range of parameters by decelerating the decay of the upper level of the 3LS.

DOI
10.1103/physreva.103.062423

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The visibility of the two-photon interference in the Franson interferometer serves as a measure of the energy-time entanglement of the photons. We propose to control the visibility of the interference in the second-order coherence function by implementing a coherent time-delayed feedback mechanism. Simulating the non-Markovian dynamics within the matrix product state framework, we find that the visibility for two photons emitted from a three-level system (3LS) in ladder configuration can be enhanced significantly for a wide range of parameters by decelerating the decay of the upper level of the 3LS.
We numerically show that time-delayed coherent feedback controls the statistical output characteristics of driven quantum emitters. Quantum feedback allows us to enhance or suppress a wide range of classical and nonclassical features of the emitted quantum light. As an exemplary quantum system, we use a pumped cavity containing two emitters. By applying phase-selective feedback, we demonstrate that photon antibunching and bunching can be increased for a given set of parameters in orders of magnitude due to intrinsically and externally controllable quantum interferences. Our modeling is based on a fully non-Markovian quantum simulation of a structured photon continuum. We show that an approximative method in the Schr\"odinger picture allows a very good estimate for quantum feedback induced features for low pump rates.
Quantum entanglement first attracted attention as the heart of the Einstein-Podolsky-Rosen (EPR) paradox and one of the most counterintuitive phenomena in the view of classical physics [1]. Hong-Ou-Mandel (HOM) [2] and Franson interferences [3] are regarded as important evidence of the non-classical nature of photon sources. Since a two-photon interference experiment with time-energy entangled photons was proposed by J. D. Franson [2], the fourth-order interferences beyond the one-photon coherence length have attracted considerable attention as important and interesting quantum phenomena in quantum optics. Surprisingly, Franson interference has been not experimentally demonstrated by use of two-photon pairs emitted from a cascade-type atomic system with continuous wave (CW) pumping, as originally proposed by Franson.
We investigate the coherence and steady-state properties of the Jaynes-Cummings model subjected to time-delayed coherent feedback in the regime of multiple excitations. The introduced feedback qualitatively modifies the dynamical response and steady-state quantum properties of the system by enforcing a non-Markovian evolution. This leads to recovered collapses and revivals as well as non-equilibrium steady states when the two-level system (TLS) is directly driven by a laser. The latter are characterized by narrowed spectral linewidth and diverging correlation functions that are robust against the time delay and feedback phase choices. These effects are also demonstrated in experimentally accessible quantities such as the power spectrum and the second-order correlation function g(2)(τ)g^{(2)}(τ)g(2)(τ) in standard and widely available photon-detection setups.
We experimentally demonstrate Franson interference of a time–energy entangled photon pair generated via collective two-photon coherence in the 5S1/2−5P3/2−5D5/2 transition of warm Rb87 atoms. The two unbalanced Michelson interferometers used in our setup are spatially separated in order to understand entanglement as a nonlocal property of the photon pairs from the warm atomic ensemble. We observe a Franson interference fringe with a high visibility of 99.1±1.3% with continuous-wave-mode photon pairs from the cascade-type atomic ensemble. To the best of our knowledge, this work is the first demonstration of the nonlocal two-photon interference experiment in separated photon channels by use of two-photon pairs emitted from a cascade-type atomic system as originally proposed by Franson [Phys. Rev. Lett.62, 2205 (1989)PRLTAO0031-900710.1103/PhysRevLett.62.2205].
In classical optics, interference occurs between two optical fields when they are indistinguishable from one another. The same holds true in quantum optics, where a particular experiment, the Franson interferometer, involves the interference of a photon pair with a time-delayed version of itself. The canonical version of this interferometer requires that the time delay be much shorter than the coherence length of the pump used to generate the photon pair, so as to guarantee indistinguishability. However, when this time delay is comparable to the coherence length, conventional wisdom suggests that interference visibility degrades significantly. In this work, though, we show that the interference visibility can be restored through judicious temporal post-selection. Utilizing correlated photon pairs generated by a pump whose pulsewidth (460 ps) is shorter than the interferometer’s time delay (500 ps), we are able to observe a fringe visibility of 97.4±4.3%. We believe this new method can be used for the encoding of high-dimensional quantum information in the temporal domain.
Quantum information science relies on the feature of distant quantum entities (mostly "qubits") to form non-local states. A main challenge consists of generating such non-local entangled states between qubits. We exploit the fact that for coupled qubits, the eigenstates of the coupled system are usually highly entangled, and of different excitation energies. This allows to address the different entangled eigenstates by frequency-dependent control schemes. In our proposal, we present such a control mechanism, and demonstrate how it can be used to create entanglement from a fully separable initial state. The mechanism of our choice is time-delayed quantum-coherent feedback. If a qubit occupation decays via the emission of a photon, one can store this photon for a delay time τ and couple the radiation back into the qubit afterwards. Through the choice of τ, one can set the phase of the feedback, which will then lead to either an increased or decreased qubit decay. Since this phase depends on sin(ωτ), this effect strongly depends on the qubit frequency ω. In particular, it can be used to separate different entangled states in a quantum network by enhancing the decay of all entangled eigenstates except one. We discuss this protocol on the example of two coupled qubits, and analyze in detail its effectiveness depending on the feedback delay time τ.