Controlled-Phase Gate Using Dynamically Coupled Cavities and Optical Nonlinearities

Mikkel Heuck, Kurt Jacobs, and Dirk R. Englund

Phys. Rev. Lett. 124, 160501 – Published 20 April 2020

Abstract

We show that relatively simple integrated photonic circuits have the potential to realize a high fidelity deterministic controlled-phase gate between photonic qubits using bulk optical nonlinearities. The gate is enabled by converting travelling continuous-mode photons into stationary cavity modes using strong classical control fields that dynamically change the effective cavity-waveguide coupling rate. This architecture succeeds because it reduces the wave packet distortions that otherwise accompany the action of optical nonlinearities [J. Shapiro, Phys. Rev. A 73, 062305 (2006); J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)]. We show that high-fidelity gates can be achieved with self-phase modulation in $χ^{(3)}$ materials as well as second-harmonic generation in $χ^{(2)}$ materials. The gate fidelity asymptotically approaches unity with increasing storage time for an incident photon wave packet with fixed duration. We also show that dynamically coupled cavities enable a trade-off between errors due to loss and wave packet distortion. Our proposed architecture represents a new approach to practical implementation of quantum gates that is room-temperature compatible and only relies on components that have been individually demonstrated.

Received 30 September 2019
Accepted 13 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.160501

Physics Subject Headings (PhySH)

Integrated optics Optical quantum information processing Quantum gates Second order nonlinear optical processes Third order nonlinear optical processes

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalNonlinear Dynamics

Authors & Affiliations

Mikkel Heuck ^1,2,*, Kurt Jacobs^3,4,5, and Dirk R. Englund²

¹DTU Fotonik, Technical University of Denmark, Building 343, 2800 Kongens Lyngby, Denmark
²Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
³U.S. Army Research Laboratory, Computational and Information Sciences Directorate, Adelphi, Maryland 20783, USA
⁴Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125, USA
⁵Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803, USA

^*mheuck@mit.edu

Photon-photon interactions in dynamically coupled cavities

Mikkel Heuck, Kurt Jacobs, and Dirk R. Englund

Phys. Rev. A 101, 042322 (2020)

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 124, Iss. 16 — 24 April 2020

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Absorption, storage, and emission process with schematic illustrations of cavity implementations in $χ^{(2)}$ (left) and $χ^{(3)}$ (right) materials. Two sets of photonic crystal mirrors oriented perpendicularly ( $χ^{(2)}$ ) or inline ( $χ^{(3)}$ ) have band gaps in different frequency ranges as illustrated by the black lines in the bottom panel. One-sided cavities required for complete absorption are achieved by a slight frequency offset between the band gaps of the right (solid black) and left (dashed black) mirror. The decoupled mode (blue) is within the band gap of both mirrors while the coupled mode (purple) lies at the band edge of the left mirror. Only the decoupled cavity modes must have small volumes for efficient photon-photon interaction. The control modes are confined by weak mirrors ( $ω_{1}$ and $ω_{2}$ ) located at the exterior of the small cavity modes.
Reuse & Permissions
Figure 2
(a) Absorption of a Gaussian wave packet including the solution of $Λ^{(k)}$ for both $χ^{(2)}$ and $χ^{(3)}$ materials. (b) Fourier transformations of $Λ^{(k)} (t)$ from (a). The shaded areas plot Lorentzian resonances of mode $a$ with linewidths $γ / Ω_{G} = 6$ for a $χ^{(2)}$ material (blue) and $γ / Ω_{G} = 30$ for a $χ^{(3)}$ material (red).
Reuse & Permissions
Figure 3
Error in one-photon state fidelity, $1 - F_{1}$ , as a function of the linewidth of mode $a$ for different loss rates (solid lines). Gray corresponds to $γ_{L} / Ω_{G} = 0$ while it increases from $10^{- 7}$ (blue) to $10^{- 2}$ (red) in steps of 10 dB. Dashed lines plot the corresponding error in the conditional one-photon state fidelity, $1 - {\bar{F}}_{1}$ .
Reuse & Permissions
Figure 4
(a) Plot of $1 - F_{11}$ for a $χ^{(3)}$ material as a function of storage time, $T$ , for different loss rates. Gray corresponds to $γ_{L} / Ω_{G} = 0$ and it increases from $4 \times 10^{- 7}$ (blue) to $10^{- 3}$ (red). Dashed lines with the same color plot the corresponding values of the error in conditional fidelity, $1 - {\bar{F}}_{11}$ . (b) Plot of $1 - F_{11}$ as a function of the intrinsic quality factor, $Q_{L}$ , corresponding to the vertical cross sections in (a). The legend shows the limiting values of the conditional fidelity, $1 - {\bar{F}}_{11}$ . Parameters: $γ / Ω_{G} = 30$ , $χ^{(3)} = 1.8 \times 10^{- 19} m^{2} / V^{2}$ [22], $λ = 1550 nm$ , $\bar{n} = 3.4$ , $V_{m}^{(3)} = 10^{- 3} (λ / \bar{n})^{3}$ .
Reuse & Permissions
Figure 5
(a) Plot of $1 - F_{11}$ for second-order nonlinearity as a function of storage time. Gray corresponds to $γ_{L} / Ω_{G} = 0$ and it increases from $10^{- 5}$ (blue) to $2 \times 10^{- 3}$ (red). Dashed lines with the same color plot the corresponding values of the error in conditional fidelity, $1 - {\bar{F}}_{11}$ . (b) Plot of the minimum error as a function of $χ_{k} / γ_{L}$ corresponding to the circles in Fig. 4 ( $k = 3$ , red) and Fig. 5 ( $k = 2$ , blue). Dashed lines plot the corresponding values of the conditional fidelity. The slope of all curves are $- 1$ , demonstrating the relationship $1 - F_{11} = C^{(k)} γ_{L} / χ_{k}$ , where $C^{(2)} = 5.5$ and $C^{(3)} = 18.7$ . Note that (a) and (b) share the $y$ axis.
Reuse & Permissions

Physical Review Letters