Abstract
The ability to engineer nonreciprocal interactions is an essential tool in modern communication technology as well as a powerful resource for building quantum networks. Aside from large reverse isolation, a nonreciprocal device suitable for applications must also have high efficiency (low insertion loss) and low output noise. Recent theoretical and experimental studies have shown that nonreciprocal behavior can be achieved in optomechanical systems, but performance in these last two attributes has been limited. Here we demonstrate an efficient, frequency-converting microwave isolator based on the optomechanical interactions between electromagnetic fields and a mechanically compliant vacuum gap capacitor. We achieve simultaneous reverse isolation of more than 20 dB and insertion loss less than 1.5 dB over a bandwidth of 5 kHz. We characterize the nonreciprocal noise performance of the device, observing that the residual thermal noise from the mechanical environments is routed solely to the input of the isolator. Our measurements show quantitative agreement with a general coupled-mode theory. Unlike conventional isolators and circulators, these compact nonreciprocal devices do not require a static magnetic field, and they allow for dynamic control of the direction of isolation. With these advantages, similar devices could enable programmable, high-efficiency connections between disparate nodes of quantum networks, even efficiently bridging the microwave and optical domains.
Highlights
Many branches of physics and engineering employ nonreciprocal devices to route signals along desired paths of measurement networks
Enabled much of the progress in classical and quantum signal processing, overcoming their limitations could lead to exciting new developments in both areas
Signal losses due to these conventional nonreciprocal devices have become the bottleneck for the overall efficiency of, for example, state-of-the-art microwave measurements [6,7,8]
Summary
We use the framework established in Ref. [17] with the notational conventions used in Ref. [20] to analyze a fourmode isolator. We put an explicit eiφ on β14 for the loop phase, so that the mode-coupling matrix becomes. At high cooperativity, maximizing this function yields C3 1⁄4 C4 ≡ C with corrections at order 1=C, simplifying the transmission difference to ΔT 1⁄4 η1η21⁄21 − ð2CÞ−1. With these conditions applied, the scattering matrix at high cooperativity and ηj 1⁄4 1 becomes ðA6Þ. To find the bandwidth of nonreciprocity, we calculate the transmission difference as a function of the detuning δω from the cavity centers with the approximation that the cavity widths are much larger than the mechanical widths. With the above optimizations for drive detunings, loop phase, and cooperativities, the result is ΔTðωÞ γÃ2. The above shows that in the high cooperativity limit, the bandwidth of nonreciprocity is independent of cooperativity and equal to ΓNR γ3γ4 γ3 þ γ4
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