Demonstration of Efficient Nonreciprocity in a Microwave Optomechanical Circuit^*

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. 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.

Popular Summary

Electrical and optical signals usually travel forwards as easily as they travel backwards, a property known as reciprocity. Modern communication devices and quantum networks, however, often require isolators, which allow signals to flow only in one direction. Traditionally, magnetic materials have provided the crucial ingredient for violating reciprocity, but these devices are both lossy and bulky. An attractive alternative is to use a material whose properties can be modulated in time. In optomechanical systems, the coupling between light and motion can be modulated, leading to several recent proposals and proof-of-principle demonstrations of nonreciprocity. Ideally, these same ideas and devices could be extended to route even fragile quantum signals between nodes of a quantum network. To this end, we engineer nonreciprocity in a microwave optomechanical circuit with efficiency and noise performance approaching the stringent requirements of quantum applications.

Our isolator is based on optomechanical interactions between electromagnetic fields and a mechanical resonator. We are able to attenuate reverse signals by more than a hundredfold while maintaining high forward transmission of greater than 70%. We also fully characterize the noise performance and find that residual thermal noise of less than 10 photons is routed solely to the input of the isolator. The strong agreement between our data and coupled-mode theory demonstrates the precise control with which we can direct microwave signals.

Looking forward, similar nonreciprocal optomechanical systems could be used to route photons and phonons (packets of vibrational motion) over a wide range of frequencies, for example, to build a directional bridge between microwave and optical devices.

Figure 1

Concept and experimental realization. (a) Mode-coupling diagrams for the optomechanical isolator. Optomechanical interactions (double-sided arrows) between two cavity modes (${\widehat{a}}_1$ and ${\widehat{a}}_2$) and two mechanical modes (${\widehat{b}}_1$ and ${\widehat{b}}_2$) induce directional scattering between the two cavities when the parametric loop phase is equal to its optimal values $\pm {\varphi }_{\mathrm{opt}}$. (b) Microscope images of the device. A microfabricated vacuum-gap capacitor (inset) resonates with spiral inductors to produce two electromagnetic cavities. (c) Schematic of the optomechanical circuit. Input signals from microwave generators couple inductively to the device and reflect back through the amplification chain to be measured by a network or spectrum analyzer. (d) Frequency space diagram. Mode susceptibilities are plotted versus frequency. Two mechanical modes and two cavity modes are characterized by their resonant frequencies (${\mathrm{\Omega }}_k$ and ${\omega }_j$) and their linewidths (${\mathrm{\Gamma }}_k$ and ${\kappa }_j$), and the cavities are further characterized by their coupling efficiencies ${\eta }_j$.

Figure 2

Reciprocal mechanically mediated frequency conversion. (a) Mode-connection diagrams. Double-sided arrows indicate driven optomechanical interactions. (b) Frequency-space diagrams. A red-detuned drive applied at each cavity induces frequency conversion through one mechanical mode. Dashed lines indicate frequencies of microwave drives. (c) Measured magnitude of reciprocal transmission from cavity 2 to cavity 1 as a function of the probe detuning from cavity center for a particular drive power. Frequency conversion through the first mechanical mode is shown in red on the left and through the second mechanical mode in orange on the right. Solid lines are fits to Lorentzian line shapes. (d) Maximum transmission as a function of total input drive power for the first (red) and second (orange) mechanical modes. Solid lines are fits to a model described in Ref. [26]. The arrow indicates the drive power used in (c).

Figure 3

Optomechanical isolation. (a) Frequency space diagram. Four drives (dashed lines) induce frequency conversion between the two cavities through both mechanical modes simultaneously. (b) Measured magnitude of transmitted signal received at cavity 1 (left) and cavity 2 (right) for two choices of loop phase. At $\varphi =+0.21\pi$ (solid blue) signals are transmitted from cavity 2 to cavity 1 and attenuated in the reverse direction. The behavior reverses at $\varphi =-0.21\pi$ (dashed green line). Solid lines are fits to the expanded coupled-mode theory model described in the text. (c) Transmission (color scale) as a function of detuning and loop phase. Lines show the source of data shown in (b). (d) Result of the least-squares fit of the two-dimensional data in (c).

Figure 4

Noise performance of the optomechanical isolator. (a) Graphical representation of signal flow. The mode-connection diagram (left) induces signal flow diagrams (right) at the optimal loop phases $\pm {\varphi }_{\mathrm{opt}}$. Arrow widths are proportional to their corresponding scattering matrix element [Eq. (1)]. (b) Measured output noise at cavities 1 (left) and 2 (right) near loop phases $+0.21\pi$ (solid blue line) and $-0.21\pi$ (dashed green line). We subtract constant noise offsets of 31.5 and 22.8 photons due to the measurement chain at the two cavity frequencies. (c) Output noise data (color scale) as a function of detuning from the cavity frequencies and loop phase. Lines indicate the cuts shown in (a). (d) Fit of the data in (c) to a coupled-mode theory with the mechanical environment occupation numbers as free parameters.

Figure 5

Ten-mode graph diagram. Like-colored double-sided arrows indicate optomechanical coupling driven by the same microwave drive. Modes 1–4 are the four modes in the simplified four-mode model. Modes 5–10 are duplicates evaluated off resonance.

Figure 6

Full scattering matrix including transmission and reflection. Measured scattering parameters are shown on the top row and the results of a least-squares fit to our expanded coupled-mode theory are shown on the bottom row.