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arXiv:2503.05014 · Physical Review A

Mitigation of birefringence in cavity-based quantum networks using frequency-encoded photons

Chengxi Zhang, Justin Phillips, Inder Monga, Erhan Sağlamyürek, Qiming Wu, Hartmut Häffner

Published Jun 4, 2025• 4 citations
arXivHTMLPDF

Abstract

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 ${}^{40}{\mathrm{Ca}}^{+}$ and the hyperfine splitting in the ground state of ${}^{225}{\mathrm{Ra}}^{+}$. 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.

DOI
10.1103/physreva.111.062608

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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.
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.
Cavity-based quantum node is a competitive platform for distributed quantum networks. Here, we characterize a high-finesse Fabry-Pérot optical resonator for coupling single or few atomic quantum registers. Our cavity consists of two mirrors with different reflectivities: One has minimal optical loss, and the other high transmission loss where more than 90% of the intracavity photons would be emitted. Cavity finesse, birefringent effects, and mechanical resonances are measured using the lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters, we drive the adjacent longitudinal or transverse modes with two lasers simultaneously, and measure those frequencies using a precision wavelength meter (WLM). A major novelty of this method is that the parameters’ uncertainties are solely determined by the resolution of the WLM, eliminating all of the temporal environment fluctuations. Our scheme makes it possible to quantify the atom-cavity coupling constant up to four significant figures, the most precise and accurate estimation so far, which would become a key ingredient for benchmarking a cavity-based quantum node. Furthermore, the distortion of polarized photonic qubits would be minimized owing to the small birefringent splitting, below 4.9% of the cavity linewidth. Our system should operate in the intermediate atom-cavity coupling regime that would allow us to implement various quantum network protocols.
The steady-state transmission spectrum of a cavity with two modes of orthogonal polarization strongly coupled to a single atom with multiple Zeeman states is computed. Effects due to cavity birefringence and atomic ac-Stark shifts are included. The transmission spectrum is compared to experimental results for a single Cesium atom trapped via an intracavity FORT in a Fabry-Perot cavity. The excellent agreement of the theory with the data is used to infer the distribution of the position of the trapped atom. The intensity correlation function of this system is also calculated, and found to be strongly antibunched and sub-Poissonian. This effect is explained in terms of photon blockade, based on the structure of the lowest energy eigenvalues. Experimental results confirm the strong nonlinearity at the single-photon level. We present theoretical predictions of the weak field spectra of microtoroid and photonic bandgap cavities strongly coupled to the D2 transition of single Cesium atoms. These calculations include all hyperfine and Zeeman states of the transition and model the cavity as a single-mode, linearly polarized resonator. Finally, we outline a technique for using multiple hyperfine and Zeeman levels of a single atom in a strongly coupled atom-cavity system to generate polarized single photons on demand in a well-defined temporal mode via adiabatic passage. The technique is insensitive to cavity birefringence and only weakly sensitive to atomic position. Variations of this technique for generating entanglement of photon polarization and atomic Zeeman state are also discussed.
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.
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.
For quantum computation the efficient preparation and connection of multiple qubits must be addressed. This includes linear optical quantum computation and quantum networks of stationary nodes interlinked by flying qubits. A quantum emitter coupled to a single mode of the electric field is a versatile tool, with the potential to provide the on-demand generation of single photons or a matter-light interface in a quantum network. This thesis presents the construction and characterisation of an \emph{a priori} deterministic single-photon source using single 87Rb atoms coupled to a high finesse optical cavity. These photons show a high degree of indistinguishability and long coherence times with a two-photon Hong-Ou-Mandel visibility of (70.8±4.6)% over the entire interaction time of 300ns long photons, further increasing to ≥97.8% by post-selecting only detection events within 23ns of each other. No degradation of performance is observed when interfering these pairs through a 4x4 multimode interferometer integrated onto a photonic chip with non-classical correlations measured between photon detections orders of magnitude further separated in time than the propagation time through the chip. The production scheme for polarised single photons is considered in detail. Cavity birefringence is found to alter the polarisation state of the emitted photons and a novel model to incorporate this effect is presented. Further deviations from a simple coupling model are observed in the modified hyperfine atomic structure in the intermediate strength magnetic fields required for polarised photon emission. The behaviour in this regime is modelled and shown to explain previously unresolved observations of the asymmetric production efficiencies of orthogonally polarised photons.