Nonreciprocal Transport Based on Cavity Floquet Modes in Optomechanics

Laure Mercier de Lépinay, Caspar F. Ockeloen-Korppi, Daniel Malz, and Mika A. Sillanpää

Phys. Rev. Lett. 125, 023603 – Published 10 July 2020

Abstract

Directional transport is obtained in various multimode systems by driving multiple, nonreciprocally interfering interactions between individual bosonic modes. However, systems sustaining the required number of modes become physically complex. In our microwave-optomechanical experiment, we show how to configure nonreciprocal transport between frequency components of a single superconducting cavity coupled to two drumhead oscillators. The frequency components are promoted to Floquet modes and generate the missing dimension to realize an isolator and a directional amplifier. A second cavity left free by this arrangement is used to cool the mechanical oscillators and bring the transduction noise close to the quantum limit. We furthermore uncover a new type of instability specific to nonreciprocal coupling. Our approach is generic and can greatly simplify quantum signal processing and the design of topological lattices from low-dimensional systems.

Received 19 December 2019
Accepted 15 June 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.023603

Physics Subject Headings (PhySH)

Hybrid quantum systems Optomechanics Quantum fluctuations & noise Quantum measurements Quantum optics Synthetic gauge fields Topological effects in photonic systems

Atomic, Molecular & Optical

Authors & Affiliations

Laure Mercier de Lépinay ^1,*, Caspar F. Ockeloen-Korppi ¹, Daniel Malz ², and Mika A. Sillanpää¹

¹QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
²Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany

^*Corresponding author. laure.mercierdelepinay@aalto.fi

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Vol. 125, Iss. 2 — 10 July 2020

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Images

Figure 1
Principle of Floquet nonreciprocal devices. (a) Scheme of a four-mode nonreciprocal transducer. (b) Simplified system exhibiting nonreciprocal transport between off-resonant components of a single cavity field. An auxiliary cavity mode can be used to sideband cool mechanical modes. (c) Scheme of the double mechanically mediated coupling between Floquet modes represented in the generated synthetic dimensions. Mechanical susceptibilities filtering restrict the coupling picture to the central plaquette. (d) Drive frequencies used to build an optomechanical directional amplifier. The auxiliary cavity pumping scheme is not represented (see Supplemental Material [58]). (e) Similar driving scheme to build an isolator. (f) Optical micrograph of the pair of micromechanical drum oscillators.
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Figure 2
Microwave isolator. (a) Scattering parameters $S_{12}$ (solid red line) and $S_{21}$ (light green solid line) for $φ = 55 °$ and fits (darker dashed lines). The dashed gray line marks the optimal working frequency. (Inset) Reflection $S_{11}$ on isolated port 1 and fit (darker dashed line). (b) Same as (a) for $φ = - 55 °$ . (Inset) Reflection $S_{22}$ on isolated port and fit (darker dashed line). (c) Schematic of the paths taken by noise from mechanical oscillator 1 to port 1. (d) Same as (c) for noise from mechanical oscillator 1 to port 2. (e) For $φ = + 55 °$ , noise at port 1 (solid red) corresponding to backward-propagating noise for the isolator with this phase and at port 2 (solid light green) corresponding to forward-propagating noise.
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Figure 3
Directional amplification. (a) Scattering parameters $S_{12}$ (solid red line) and $S_{21}$ (solid blue line) for $φ = + 48 °$ and fits with expressions from the text (darker dashed lines). (Inset) Reflection $S_{11}$ (solid line) on isolated port and fit (darker dashed line). (b) Same as (a) for the opposite phase $φ = - 48 °$ . (Inset) Reflection $S_{22}$ on isolated port (solid line) and fit (darker dashed line).
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Figure 4
Noise and phase-dependent instability. (a) Backward-propagating noise for optimal phase $φ = + 48 °$ , corresponding to noise at port 1 (solid red) and theory superimposed (darker dashed line). (b) Added noise for optimal phase $φ = + 48 °$ (solid blue) and theory (darker dashed line). (c) Noise at port 1 as a function of frequency and pump phase. Gray dashed area: unstable region. White horizontal dashed lines: optimal phases $φ = \pm 48 °$ . (d) Same as (c) but at port 2. Dashed vertical white line: frequency of optimal directionality. (e) Calculated real parts of the optical eigensusceptibilities at zero frequency (solid and dashed gray lines, right-side scale). The lower real part is negative for $| φ | > 55 °$ , causing the instability. Noise at optimal frequency [cut of (d) along dashed vertical line] at port 2 (blue dots, left-side scale) diverges at the onset of the instability, as does noise at port 1 (red dots, left-side scale) although noise paths destructive interference at $φ = + 48 °$ limits the maximum measured noise.
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