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AVS Quantum Science

Two-qubit-entanglement in matter created by entangled-photon pairs: A perturbative analysis

Upendra Harbola, Luca Candelori, John R. Klein, Vladimir Chernyak, Shaul Mukamel

Published Sep 1, 2024• 2 citations
Publisher

Abstract

We study entanglement created between two isolated qubits by interaction with entangled-photon pairs obtained by parametric down-conversion of a laser pump field. The induced entanglement is quantified using the mixed state Concurrence proposed by Wootters et al. [Phys. Rev. Lett. 78, 5022 (1997)]. A universal value of qubit-entanglement, which is independent on the photon-pair wavefunction is identified to leading order in the qubit–field interaction and the pump field amplitude. The qubit entanglement decreases at higher laser pump intensities due to interference between the entangled photon pairs, which creates excitations in the qubit system. Maximal Concurrence is produced by only generating coherences between the ground and the highest excited qubit states.

DOI
10.1116/5.0209565

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We study entanglement created between two isolated qubits by interaction with entangled-photon pairs obtained by parametric down-conversion of a laser pump field. The induced entanglement is quantified using the mixed state Concurrence proposed by Wootters et al. [Phys. Rev. Lett. 78, 5022 (1997)]. A universal value of qubit-entanglement, which is independent on the photon-pair wavefunction is identified to leading order in the qubit–field interaction and the pump field amplitude. The qubit entanglement decreases at higher laser pump intensities due to interference between the entangled photon pairs, which creates excitations in the qubit system. Maximal Concurrence is produced by only generating coherences between the ground and the highest excited qubit states.
We show that a high degree of steady-state entanglement between two spatially separated and initially uncoupled qubits can be achieved via interaction with a quantized squeezed field in a cavity. The cavity field induces two-photon coherence, which is crucial in creating entanglement between the qubits. Optimum entanglement is obtained when the less dissipative qubit is incoherently pumped while the other dissipates the excitation. Given the current state-of-the-art in cavity quantum electrodynamics and squeezed light sources, our scheme presents an effective way for light-to-matter entanglement transfer.
Phase singularities are topological defects around which the phase winds by an integer multiple of 2π2π2π. In entangled multiphoton states, they can emerge nonlocally in the joint wavefunction rather than in the field of either subsystem alone. Here we show that the quantum Gouy phase generates nonlocal phase singularities (NPSs) in the two-dimensional longitudinal propagation space of entangled photon pairs. We consider photon pairs produced via spontaneous parametric down-conversion pumped by a Laguerre--Gaussian beam, with the signal and idler photons propagating independently over different longitudinal distances. The accumulated radial-mode-dependent Gouy phases induce destructive interference among biphoton spatial-mode components, producing isolated intensity nulls with quantized phase winding. For a pump with radial mode number ppp, the NPS topological charges have magnitude ppp, whereas their propagation positions and charge signs are governed by the Rayleigh ranges of the pump and phase-matching functions. We further identify the radial-mode structure required for their formation, showing that separable biphoton states cannot support isolated longitudinal NPSs. Our results extend nonlocal singular optics from transverse spatial correlations to longitudinal propagation dynamics and establish propagation distance as a coordinate space for topological structures in entangled photon pairs.
In this paper, we primarily investigate the generation of quantum entanglement triggered by a single photon between two qubits or multiple qubits and analyze the impact of decoherence of the light field. In the model of single-photon interaction with two qubits, we first study the effect of the initial excited-state weight of the qubits on the entanglement triggered by a single photon. We find that the greater the initial excited-state weight, the smaller the maximum quantum entanglement triggered by the single photon between the two qubits. Specifically, when both qubits are in the excited state, a single photon cannot trigger quantum entanglement between the two qubits. We then examine the impact of the initial coherence of the two qubits on the entanglement triggered by a single photon, and find that a single photon can trigger the maximum quantum entanglement between two qubits when both qubits initially have maximum coherence. In the model of single-photon interaction with multiple qubits, in the limit of a large number of qubits, we find that when the initial excited-state weight of each qubit is larger than the ground-state weight, or when all qubits are initially in the ground state, a single photon cannot trigger quantum entanglement between any two qubits in the multiqubit system. Interestingly, we find that a single photon can trigger quantum entanglement between any two qubits from at least 2000 qubits. Moreover, in this limit, the maximum quantum entanglement between any two qubits in the multiqubit system triggered by a single photon changes with the initial-state parameters and almost no longer depends on the number of qubits. Finally, we discuss the effect of decoherence of the light field, and we find that a higher decoherence strength of the light field weakens the generation of quantum entanglement between qubits in both the single-photon interaction with two qubits and the single-photon interaction with multiple qubits models. However, interestingly, the initial coherence of the qubits can resist the impact of decoherence, especially when the two nonidentical qubits, both having maximum coherence, can maintain the maximum quantum entanglement between the two qubits at 0.5 even as the decoherence strength of the light field increases.
We study the spatial coherence properties of the entangled two-photon field produced by parametric down-conversion (PDC) when the pump field is, spatially, a partially coherent beam. By explicitly treating the case of a pump beam of the Gaussian Schell-model type, we show that in PDC the spatial coherence properties of the pump field get entirely transferred to the spatial coherence properties of the down-converted two-photon field. As one important consequence of this study, we find that, for two-qubit states based on the position correlations of the two-photon field, the maximum achievable entanglement, as quantified by concurrence, is bounded by the degree of spatial coherence of the pump field. These results could be important by providing a means of controlling the entanglement of down-converted photons by tailoring the degree of coherence of the pump field.
We experimentally measure the lower and upper bounds of concurrence for a set of two-qubit mixed quantum states using photonic systems. The measured concurrence bounds are in agreement with the results evaluated from the density matrices reconstructed through quantum state tomography. In our experiment, we propose and demonstrate a simple method to provide two faithful copies of a two-photon mixed state required for parity measurements: Two photon pairs generated by two neighboring pump laser pulses through optical parametric down conversion processes represent two identical copies. This method can be conveniently generalized for entanglement estimation of multi-photon mixed states.