Nonreciprocal Frequency Domain Beam Splitter

Nils T. Otterstrom, Shai Gertler, Eric A. Kittlaus, Michael Gehl, Andrew L. Starbuck, Christina M. Dallo, Andrew T. Pomerene, Douglas C. Trotter, Peter T. Rakich, Paul S. Davids, and Anthony L. Lentine

Phys. Rev. Lett. 127, 253603 – Published 15 December 2021

Abstract

The canonical beam splitter—a fundamental building block of quantum optical systems—is a reciprocal element. It operates on forward- and backward-propagating modes in the same way, regardless of direction. The concept of nonreciprocal quantum photonic operations, by contrast, could be used to transform quantum states in a momentum- and direction-selective fashion. Here we demonstrate the basis for such a nonreciprocal transformation in the frequency domain through intermodal Bragg scattering four-wave mixing (BSFWM). Since the total number of idler and signal photons is conserved, the process can preserve coherence of quantum optical states, functioning as a nonreciprocal frequency beam splitter. We explore the origin of this nonreciprocity and find that the phase-matching requirements of intermodal BSFWM produce an enormous asymmetry ( $76 \times$ ) in the conversion bandwidths for forward and backward configurations, yielding $\sim 25 dB$ of nonreciprocal contrast over several hundred GHz. We also outline how the demonstrated efficiencies ( $\sim 10^{- 4}$ ) may be scaled to near-unity values with readily accessible powers and pumping configurations for applications in integrated quantum photonics.

Received 24 June 2021
Accepted 26 October 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.253603

Physics Subject Headings (PhySH)

Nonlinear optics Photonics

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Nils T. Otterstrom ^1,*, Shai Gertler ², Eric A. Kittlaus ³, Michael Gehl¹, Andrew L. Starbuck¹, Christina M. Dallo¹, Andrew T. Pomerene¹, Douglas C. Trotter¹, Peter T. Rakich², Paul S. Davids¹, and Anthony L. Lentine¹

¹Photonic and Phononic Microsystems, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
²Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
³Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA

^*ntotter@sandia.gov

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Vol. 127, Iss. 25 — 17 December 2021

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Figure 1
(a) Basic operation of a nonreciprocal frequency beam splitter. (ai) In the forward direction, a signal wave is split into both signal and idler modes. (aii) In the backward direction, by contrast, the signal is transmitted without splitting into the idler mode. (b) Energy conservation for BSFWM. (c) Implementation of nonreciprocal frequency conversion (i.e., frequency beam splitting) through intermodal BSFWM. The schematic diagrams the operation scheme for frequency conversion in the forward direction. Pump fields (of frequencies $ω_{p}^{(1)}$ and $ω_{p}^{(2)}$ , respectively) are coupled into the symmetric mode of the multimode waveguide (inset) using an integrated mode multiplexer. A signal wave, of frequency $ω_{s}$ , is injected into the antisymmetric mode. As the fields traverse the nonlinear active region of the device, signal light ( $ω_{s}$ ) is converted to the idler frequency ( $ω_{i}$ ) through intermodal BSFWM. Inset: the waveguide cross-sectional geometry. (di) Phase-matching for intermodal BSFWM in the forward direction. The sum of wave vectors from the signal and pump 2 fields must equal the corresponding sum for the idler and pump 1 fields within the phase-matching uncertainty $Δ k_{f}$ . (dii) Backward intermodal BSFWM precluded by phase matching. If $ω_{p}^{(2)}$ is outside the narrow phase-matching bandwidth, there is a nonreciprocal phase mismatch given by $Δ k_{b}$ , and light in the counterpropagating signal wave does not experience frequency conversion to the idler frequency ( $ω_{i}$ ).
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Figure 2
Experimental apparatus for nonlinear laser spectroscopy. Laser light from the pumps ( $ω_{p}^{(1)}$ and $ω_{p}^{(2)}$ ) is coupled together and amplified using an EDFA. The total power is controlled with a VOA. Light at the signal frequency is created from pump 1 using an IM driven at $Ω = 10 GHz$ (such that $ω_{s} = ω_{p}^{(1)} - Ω$ ). The signal wave is then routed into the antisymmetric mode of the multimode waveguide in either the forward or backward directions. A strong optical local oscillator for heterodyne spectroscopy is created from the pump 2 wave using an acousto-optic modulator (AOM), which blueshifts light by $Δ / 2 π = 44 MHz$ . Combining this reference with the light exiting the antisymmetric mode yields a microwave signal at $Ω + Δ$ that corresponds to the generated idler wave. (b) Frequency conversion efficiency as a function of pump 2 wavelength ( $λ_{p}^{(2)} = 2 π c / ω_{p}^{(2)}$ ) and combined maximum pump powers (normalized). (c) Peak efficiency vs total pump power, demonstrating good agreement with the theoretical trend. Inset: the normalized idler heterodyne spectrum (averaged, near RBW-limited), demonstrating that the BSFWM process preserves the signal-idler phase coherence. The estimated on-chip signal power in these measurements is of order $5 μ W$ . (d) Nonreciprocal frequency conversion measurements. (di) signal to idler conversion efficiency as a function of pump 2 wavelength ( $λ_{p}^{(2)} = 2 π c / ω_{p}^{(2)}$ ) in the forward (red) and backward directions (dark blue), demonstrating $> 25 dB$ of nonreciprocal contrast. (dii) Backward frequency conversion over a $76 \times$ smaller range, revealing the much tighter phase-matching constraints for backward intermodal BSFWM. Over this range, by contrast, the forward conversion efficiency (red) is flat due to its much larger phase-matching bandwidth. As such, there exist nm-wide+ spectral regions over which $\sim 25 dB$ of nonreciprocal contrast is possible. The semitransparent data points are due to carrier-enhanced BSFWM effects (see Supplemental Material of Ref. [55]) that occur only at small frequency separations of $| ω_{p}^{(1)} - ω_{p}^{(2)} | < 2 π / τ_{c}$ ( $\sim 1 GHz$ ), where the free carrier lifetime $τ_{c} \approx 1 ns$ .
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