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Effects of cavity birefringence on remote entanglement generation

Ezra Kassa, W. F. Hughes, Shaobo Gao, Joseph F. Goodwin

Published Aug 26, 2020• 0 citations
OpenAlex

Abstract

The generation of entanglement between distant atom via single photons is the basis for networked quantum computing, a promising route to large-scale trapped ion and atom processors. Locating the emitter within an optical cavity provides an efficient matter-light interface, but mirror-induced birefringence within the cavity introduces time-dependence to the produced photons' polarisation. We show that such polarisation oscillation effects can lead to severe loss of fidelity in the context of interference-based remote entanglement schemes. While total elimination of birefringence-inducing mirror ellipticity is preferable, we propose two remedies for systems where this cannot be achieved: one which restores high entanglement fidelities in the presence of polarisation oscillation via local qubit corrections, and one which suppresses polarisation oscillations for experiments with linearly polarised atomic emission projection by employing highly elliptical mirrors. We conclude that even modest cavity birefringence can be detrimental to remote entanglement performance and should be carefully considered when designing such experiments.

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The generation of entanglement between distant atom via single photons is the basis for networked quantum computing, a promising route to large-scale trapped ion and atom processors. Locating the emitter within an optical cavity provides an efficient matter-light interface, but mirror-induced birefringence within the cavity introduces time-dependence to the produced photons' polarisation. We show that such polarisation oscillation effects can lead to severe loss of fidelity in the context of interference-based remote entanglement schemes. While total elimination of birefringence-inducing mirror ellipticity is preferable, we propose two remedies for systems where this cannot be achieved: one which restores high entanglement fidelities in the presence of polarisation oscillation via local qubit corrections, and one which suppresses polarisation oscillations for experiments with linearly polarised atomic emission projection by employing highly elliptical mirrors. We conclude that even modest cavity birefringence can be detrimental to remote entanglement performance and should be carefully considered when designing such experiments.
Abstract The generation of entanglement between distant atoms via single photons is the basis for networked quantum computing, a promising route to large-scale trapped-ion and trapped-atom processors. Locating the emitter within an optical cavity provides an efficient matter-light interface, but mirror-induced birefringence within the cavity introduces time-dependence to the polarisation of the photons produced. We show that such ‘polarisation oscillation’ effects can lead to severe loss of fidelity in the context of two-photon, polarisation encoded measurement-based remote entanglement schemes. It is always preferable to suppress these errors at source by minimising mirror ellipticity, but we propose two remedies for systems where this cannot be achieved. We conclude that even modest cavity birefringence can be detrimental to remote entanglement performance, to an extent that may limit the suitability of polarisation-encoded schemes for large-scale quantum networks.
Entanglement has been recognised as a puzzling yet central element of quantum physics. While photons serve as flying qubits to distribute entanglement, the entanglement of stationary qubits at remote sites is a key resource for envisioned applications like distributed quantum computing. In our experiment we create remote entanglement between a single atom located inside a high-finesse optical cavity and a Bose-Einstein condensate (BEC). To this end we generate a single photon in the atom-cavity system, entangling the photon polarisation with the atomic Zeeman state. The photon is transported to a different laboratory in an optical fiber, where it is stored in a BEC employing electromagnetically induced transparency (EIT). This converts the atom-photon entanglement into remote matter-matter entanglement. Subsequently we map the matter-matter entanglement onto photon-photon entanglement. The experimental setup is sketched in Fig. 1.
We present the effects of resonator birefringence on the cavity-enhanced interfacing of quantum states of light and matter, including the first observation of single photons with a time-dependent polarization state that evolves within their coherence time. A theoretical model is introduced and experimentally verified by the modified polarization of temporally long single photons emitted from a ^{87}Rb atom coupled to a high-finesse optical cavity by a vacuum-stimulated Raman adiabatic passage process. Further theoretical investigation shows how a change in cavity birefringence can both impact the atom-cavity coupling and engender starkly different polarization behavior in the emitted photons. With polarization a key resource for encoding quantum states of light and modern micron-scale cavities particularly prone to birefringence, the consideration of these effects is vital to the faithful realization of efficient and coherent emitter-photon interfaces for distributed quantum networking and communications.
We numerically investigate the generation and dynamics of tripartite entanglement among qubits (quantum emitters or atoms) in multimode cavity quantum electrodynamics (cQED). Our cQED architecture features three initially unentangled excited two-level quantum emitters confined within a triangle-shaped multimode optical cavity, which later become entangled due to a Jaynes-Cummings-like interaction. Using the tripartite negativity measure of entanglement and fidelity with respect to the genuine tripartite entangled state (Greenberger-Horne-Zeilinger state, to be precise), we analyze the impact of the number of cavity modes, qubit locations, and losses (spontaneous emission from qubits and photon leakage from the cavity mirrors) on the generated entanglement. Our key results include the presence of two kinds of retardation effects: one resulting from the time it takes for photons to propagate from one qubit to another, and the other to complete one round trip in the cavity. We observed these retardation effects only in multimode cavities, with the exciting possibility of controlling the collapse and revival patterns of tripartite entanglement by altering the qubit locations in the cavity. Furthermore, the impact of losses on the generated entanglement and the dependence of maximum entanglement on the total number of modes yield results that surpass those reported for single and two excitations. With recent advances in circuit quantum electrodynamics, these findings hold promise for the development of entanglement-based quantum networking protocols and quantum memories.
Atom-cavity systems offer unique advantages for building large-scale distributed quantum computers by providing strong atom-photon coupling while allowing for high-fidelity local operations of atomic qubits. However, in prevalent schemes where the photonic state is encoded in polarization, cavity birefringence introduces an energy splitting of the cavity eigenmodes and alters the polarization states, thus limiting the fidelity of remote entanglement generation. To address this challenge, we propose a scheme that encodes the photonic qubit in the frequency degree of freedom. The scheme relies on resonant coupling of multiple transverse cavity modes to different atomic transitions that are well separated in frequency. We numerically investigate the temporal properties of the photonic wave packet, two-photon interference visibility, and atom-atom entanglement fidelity under various cavity polarization-mode splittings and find that our scheme is less affected by cavity birefringence. Finally, we propose practical implementations in two trapped ion systems, using the fine-structure splitting in the metastable D state of 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ and the hyperfine splitting in the ground state of 225Ra+{}^{225}{\mathrm{Ra}}^{+}225Ra+. Our study presents an alternative approach for cavity-based quantum networks that is less sensitive to birefringent effects and is applicable to a variety of atomic and solid-state emitter-cavity interfaces.
We describe a series of experiments showing how a single trapped ion, which interacts with its own resonance fluorescence via a distant mirror, exhibits cavity-QED effects such as modified spontaneous emission, level shifts, and even mechanical forces. The same interaction is used to establish feedback on the ion's quantum motion, providing additional cooling and phase stabilisation of its vibration in the trap. Based on these methods and results we present an experiment dedicated at creating entanglement between two distant ions by projective measurements.