Polarization Oscillations in Birefringent Emitter-Cavity Systems

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Polarization Oscillations in Birefringent Emitter-Cavity Systems

Thomas D. Barrett, Oliver Barter, Dustin Stuart, Ben Yuen, and Axel Kuhn

Phys. Rev. Lett. 122, 083602 – Published 1 March 2019

Abstract

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.

Received 29 November 2018
Corrected 9 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.083602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Polarization of light Single photon sources Stimulated Raman adiabatic passage

Polarization

Jaynes-Cummings model

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Corrections

9 May 2019

Correction: The previously published Figure 4 contained an error in the units and has been replaced.

Authors & Affiliations

Thomas D. Barrett, Oliver Barter, Dustin Stuart, Ben Yuen, and Axel Kuhn^*

University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom

^*axel.kuhn@physics.ox.ac.uk

Article Text

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Issue

Vol. 122, Iss. 8 — 1 March 2019

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Images

Figure 1
Decomposition of cavity and $Λ$ system into coupled and uncoupled polarization bases. The upper plots show how the linear polarization eigenmodes of a birefringent cavity can equivalently be considered as degenerate circularly polarized modes with an effective coupling between them. The lower plots equivalently illustrate a simple $Λ$ -system coupling of circularly polarized transitions within an atom in both bases. The state notation is $| x^{S}, n_{i}, n_{j} ⟩$ , with $x^{S}$ denoting an atomic state $x$ of spin $S$ , and $n_{z}$ the photon number in the cavity supporting mode $| Z ⟩$ .
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Figure 2
Experimental summary. (a) Experimental setup for the production, routing, and detection of polarized single photons. The relevant couplings for each cavity-assisted Raman transition are distinguished by color. (b) The transmission of laser light through the cavity for direct characterization of cavity birefringence. The cavity length is scanned over resonance with an incident laser which has sidebands at $\pm 100 MHz$ as a frequency reference. The double-peaked Lorentzian (an adequate line shape approximation for high-finesse cavities [62]) fit (solid blue) is comprised of the individual transmissions of the nondegenerate polarization eigenmodes (dashed orange). (c) Fractional routing of emitted photons as a function of the quarter-wave plate angle. The dashed and solid theory traces include and exclude the effects of cavity birefringence, respectively. The error bars in both plots are found from the $\pm \sqrt{N}$ uncertainty on $N$ events exhibiting Poissonian counting statistics.
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Figure 3
Time-dependent polarization of the emitted photons. Measured data (solid traces, filled) overlaid with theoretical predictions (dashed traces) of the photon wave packets measured in various polarization bases using a quarter-wave plate at angle $ϕ$ and a PBS. The blue and red wave packets correspond to detections in the different outputs of the PBS and so correspond to different polarizations. The measured data are presented as density histograms with bin widths of 8 ns.
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Figure 4
Polarization dynamics of emitted photons simulated for increasing splitting of the linearly polarized cavity eigenmodes, $| H ⟩$ and $| V ⟩$ . Photon emission is driven by a $1 μ s$ pump pulse with a $\sin^{4}$ intensity profile and a peak Rabi frequency $Ω / 2 π = 7 MHz$ and $Ω / 2 π = 2 MHz$ for $Δ_{P} / 2 π = {0, 4} MHz$ and $Δ_{P} / 2 π = 20 MHz$ , respectively. The cavity resonances are tuned such that either (a) the polarization eigenmodes are oppositely detuned from Raman resonance, or (b) a single polarization eigenmode is on Raman resonance. The photon wave packet is plotted in both a linear and a circular polarization basis, with the overall efficiency of the emission process, $η$ , inset.
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