Hybrid Quantum Systems with Collectively Coupled Spin States: Suppression of Decoherence through Spectral Hole Burning

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Hybrid Quantum Systems with Collectively Coupled Spin States: Suppression of Decoherence through Spectral Hole Burning

Dmitry O. Krimer, Benedikt Hartl, and Stefan Rotter

Phys. Rev. Lett. 115, 033601 – Published 14 July 2015

Abstract

Spin ensemble based hybrid quantum systems suffer from a significant degree of decoherence resulting from the inhomogeneous broadening of the spin transition frequencies in the ensemble. We demonstrate that this strongly restrictive drawback can be overcome simply by burning two narrow spectral holes in the spin spectral density at judiciously chosen frequencies. Using this procedure we find an increase of the coherence time by more than an order of magnitude as compared to the case without hole burning. Our findings pave the way for the practical use of these hybrid quantum systems for the processing of quantum information.

Received 14 January 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.033601

This article is available under the terms of the Creative Commons Attribution 3.0 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

Authors & Affiliations

Dmitry O. Krimer^*, Benedikt Hartl, and Stefan Rotter

Institute for Theoretical Physics, Vienna University of Technology (TU Wien), Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria, European Union

^*dmitry.krimer@gmail.com

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Vol. 115, Iss. 3 — 17 July 2015

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Images

Figure 1
Sketch of the studied hybrid quantum system: a synthetic diamond (black) containing a spin ensemble (red arrows) coupled to a transmission-line resonator (curved gray line) confining the electromagnetic field to a small volume.
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Figure 2
Comparison of the cavity coupled to the inhomogeneously broadened spin ensemble without and with hole burning in the spin density profile (left and right panels, respectively). (a),(d): The $q$ -Gaussian spin density distribution, $ρ (ω)$ , without and with hole burning at $ω_{h} = ω_{s} \pm Ω$ . Both holes are of equal width, $Δ_{h} / 2 π = 0.7 MHz$ , and have a Fermi-Dirac profile. (b),(e): Transmission $T (ω)$ without and with hole burning in $ρ (ω)$ (note different $y$ axes scale). (c),(f): The corresponding nonlinear Lamb shift $δ (ω)$ . Filled circles label resonance values $ω_{r}$ of the transmission $T (ω)$ occurring at the intersections between the Lamb shift $δ (ω)$ and the dashed line $(ω - ω_{c}) / Ω^{2}$ . At empty circles such intersections are nonresonant (see text).
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Figure 3
Transmission through the cavity $T (ω)$ versus probe frequency $ω$ for different locations of the holes, $ω_{h}$ , in the spin density profile, $ρ (ω)$ (the width of the holes is $Δ_{h} / 2 π = 0.7 MHz$ ). (a) Red (gray) curve: $| T (ω) |^{2}$ in lin-log scale versus $ω$ for $ω_{h} = ω_{s} \pm Ω$ . Black curve: Transmission in the absence of hole burning. (b) Yellow (light gray) areas mark the most pronounced peaks in $| T (ω) |^{2}$ in the presence of hole burning. Blue (gray) areas stand for the secondary polaritonic peaks which stem from the case without hole burning. Dashed arrows designate the distance $Ω_{R}$ between polaritonic peaks. The white vertical cut corresponds to the transmission shown in (a).
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Figure 4
(a),(b): Decay of the cavity occupation $N (t) = ⟨ 1, ↓ | a^{†} (t) a (t) | 1, ↓ ⟩$ from the initial state, for which a single photon with frequency $ω_{c}$ resides in the cavity and all spins are unexcited. The asymptotic decay $C e^{- Γ t}$ with and without hole burning (see red lines) is determined by the constants $Γ / 2 π = 3 MHz$ in (a) and a drastically reduced $Γ = 0.42 κ = 2 π 0.17 MHz$ in (b). (c),(d): Dynamics of $| A (t) |^{2}$ under the action of 11 successive rectangular microwave pulses of duration corresponding to the Rabi period, $τ = 2 π / Ω_{R} = 52 ns$ , phase switched by $π$ (every second pulse is shown as a vertical gray bar). Also here the asymptotic decay is much slower due to the presence of the holes. In all panels the holes in $ρ (ω)$ have a width $Δ_{h} / 2 π = 1.4 MHz$ and are burnt at $t = 0$ at $ω_{h} = ω_{s} \pm Ω$ .
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