Observation and characterization of cavity Rydberg polaritons

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Observation and characterization of cavity Rydberg polaritons

Jia Ningyuan, Alexandros Georgakopoulos, Albert Ryou, Nathan Schine, Ariel Sommer, and Jonathan Simon

Phys. Rev. A 93, 041802(R) – Published 13 April 2016

Abstract

We experimentally demonstrate the emergence of a robust quasiparticle, the cavity Rydberg polariton, when an optical cavity photon hybridizes with a collective Rydberg excitation of a laser-cooled atomic ensemble. Free-space Rydberg polaritons have recently drawn intense interest as tools for quantum information processing and few-body quantum science. Here, we explore the properties of their cavity counterparts in the single-particle sector, observing an enhanced lifetime and slowed dynamics characteristic of cavity dark polaritons. We measure the range of cavity frequencies over which the polaritons persist, corresponding to the spectral width available for polariton quantum dynamics, and the speed limit for quantum information processing. Further, we observe a cavity-induced suppression of inhomogeneous broadening channels and demonstrate the formation of Rydberg polaritons in a multimode cavity. In conjunction with recent demonstrations of Rydberg-induced cavity nonlinearities, our results point the way towards using cavity Rydberg polaritons as a platform for creating high-fidelity photonic quantum materials and, more broadly, indicate that cavity dark polaritons offer enhanced stability and control uniquely suited to optical quantum information processing applications beyond the Rydberg paradigm.

Received 5 November 2015

DOI:https://doi.org/10.1103/PhysRevA.93.041802

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Effects of atomic coherence on light propagation Polaritons

Rydberg atoms & molecules

Atomic, Molecular & Optical

Authors & Affiliations

Jia Ningyuan, Alexandros Georgakopoulos, Albert Ryou, Nathan Schine, Ariel Sommer, and Jonathan Simon

Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA

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Issue

Vol. 93, Iss. 4 — April 2016

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Figure 1
Cavity Rydberg EIT. (a) Schematic of the experimental setup, showing the ${}^{87}{Rb}$ atomic sample in the waist of a running-wave cavity after being transported by a moving optical lattice. The cavity mirrors are high finesse at the probe wavelength (780 nm), and antireflection (AR) coated for the control laser (480 nm) that counterpropagates through the sample. (b) Level diagram showing that the cavity mode couples the atomic ground state to an excited state, with collective vacuum Rabi frequency $G$ and detuning $δ_{c}$ , while the control laser couples the excited state to a Rydberg level, with Rabi frequency $Ω$ and detuning $δ_{R}$ . (c) Transmission spectrum as a fraction of the peak empty-cavity transmission showing peaks due to the cavity Rydberg dark polariton state $|D〉$ and two bright polariton states $|B \pm〉$ . Here, $G = 13$ MHz, $Ω = 7$ MHz, $δ_{c} = δ_{R} = 0$ . (d) Decomposition of the dark polariton into cavity photon and Rydberg components, set by the couplings $G$ and $Ω$ that define the dark-state rotation angle $θ$ .
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Figure 2
Spectroscopy of cavity Rydberg polaritons. (a) Cavity transmission spectra as a function of cavity detuning $δ_{c}$ for several values of the control laser power. From left to right, $θ (deg) = 43$ , 62, and 72; $Ω = 13.1 (1)$ , 6.9(1), and 4.9(1) MHz; $G = 12.3 (2)$ , 13.0(1), and 14.7(1) MHz. Here, $| δ_{R} | < 1$ MHz. Insets in (a) and (b): Spectra along the vertical line at $δ_{c} = 0$ . Color scale for (a) and (b): Cavity transmission as a fraction of the empty-cavity peak transmission. (b) Transmission spectrum at nonzero control laser detuning $δ_{R} = 9.8 (4)$ MHz. Here, $Ω = 8.2 (6)$ MHz, $G = 16.8 (3)$ MHz. (c) Energy and lifetime vs dark-state rotation angle. Red circles (left): Dark-polariton slope $d δ_{D} / d δ_{c}$ . Blue squares (right): Dark-polariton inverse lifetime $γ_{D}$ . Solid lines: Theoretical predictions, using $Ω$ obtained from the calibrated control laser power and $G$ obtained from fitting to the transmission spectrum. (d) and (e) show the effect of detuning the cavity from EIT resonance using the data in (a). Correspondence to (a): left, diamonds (red); middle, squares (green); right, circles (blue). (d) $γ_{D}$ vs cavity detuning from EIT resonance. Solid lines: Second-order prediction (1), using $γ_{R}$ and $G$ obtained from the transmission spectrum at $δ_{R} - δ_{c} = 0$ . (e) Height $T_{D}$ of the dark-polariton peak vs cavity detuning. Solid lines: Theoretical prediction using (2) plus higher-order corrections [40] that are only significant for the lower (blue) curve.
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Figure 3
Collective suppression of decoherence. (a) Inhomogeneous broadening couples the dark polariton to a bath of states orthogonal to the cavity mode. The splitting from the control laser detunes these states from the dark state, suppressing the lossy channel. (b) Effective decay rate $γ_{R}$ of the collective Rydberg state for varying principle quantum number $n$ vs the polarizability of the Rydberg state. Here, $n = 40$ , 48, 52, 56, 58, 60, and 62. $Ω (MHz) = 7.8 (5), G (MHz) = 12 (2)$ , average and standard deviation (std. dev.) over the data sets. Solid line: Quadratic fit.
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Figure 4
Rydberg polaritons in two cavity modes. The ${TEM}_{02}$ and ${TEM}_{10}$ modes are tuned to $\pm 10$ MHz from EIT resonance. (a) Transmission spectrum for $Ω / G = 0.39$ , with $G = 27$ MHz. The dark-polariton resonances (dashed lines) are separated by $Δ δ_{D} = 2.3$ MHz. Curve: Fit to theoretical model for two orthogonal collective states. (b) Adjusting the control laser power varies the photonic component of the dark-polariton states, tuning $Δ δ_{D}$ . Dashed curve: First-order prediction. Solid curve: Numerical solution.
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