On-Chip Microwave Quantum Hall Circulator

Circulators are nonreciprocal circuit elements that are integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their nonreciprocity arises from the interference of microwaves over the centimeter scale of the signal wavelength, in the presence of bulky magnetic media that breaks time-reversal symmetry. Here, we realize a completely passive on-chip microwave circulator with size $1/1000\mathrm{th}$ the wavelength by exploiting the chiral, “slow-light” response of a two-dimensional electron gas in the quantum Hall regime. For an integrated GaAs device with $330\mu \mathrm{m}$ diameter and about 1-GHz center frequency, a nonreciprocity of 25 dB is observed over a 50-MHz bandwidth. Furthermore, the nonreciprocity can be dynamically tuned by varying the voltage at the port, an aspect that may enable reconfigurable passive routing of microwave signals on chip.

Popular Summary

Isolating quantum systems from their noisy and hot environments is of crucial importance for quantum computation. A key challenge then is to make measurements of these fragile systems by ensuring the one-way flow of information. To date, this has been done using large, bulky devices the size of a human hand called circulators. These devices allow for routing of signals from one port to the next in only one direction. However, given the number of devices needed to construct useful quantum machines, the footprint of such components serves as a significant barrier to scaling up this technology. We demonstrate a microwave circulator just a few hundred micrometers in size that makes use of a directional, quantum phenomenon, called the quantum Hall effect, to achieve a high degree of signal isolation.

Our design is comprised of a disk-shaped plane of electrons that forms at the interface between two semiconductors, gallium arsenide and aluminum gallium arsenide. The device takes advantage of standing waves—known as edge magnetoplasmons—that guide input signals from one port to the next. In addition, we show that the frequency and direction of circulation can be changed by varying the applied electric or magnetic field at the edge of the device.

The ability to route microwave signals using edge magnetoplasmons opens up prospects for a range of compact, integrated, nonreciprocal devices that are useful for enhanced readout, control, and coupling of quantum systems.

Figure 1

Detecting microwave edge magnetoplasmons. (a) Experimental setup including photograph of a coplanar transmission-line device similar to that used to perform measurements coupled to a $350\text{−}\mu \mathrm{m}$ etched disc of 2DEG (black dashed circle) at a fridge temperature of $T=20\mathrm{mK}$. A vector network analyzer is used to excite EMP modes across a wide frequency range, and microwave absorption is measured as the ratio of the amplified output to input signal ($S_{21}$) from the CTL. (b) Illustration of the fundamental (top row) and first harmonic (bottom row) EMP modes as they evolve with time, where ${\omega }_0$ is the fundamental mode and $2{\omega }_0$ the first harmonic (adapted from Ref. [20]). Charge distributions and electric fields $\overrightarrow{E}$ are indicated schematically. An external magnetic field $B$ applied to the device points out of the page. (c) EMP spectrum of the quantum Hall disk showing absorbed microwave power as a function of frequency and magnetic field. A background obtained at high field has been subtracted from the data. The inset shows the position of absorption dips at integer quantum Hall filling factors. The black line is a fit that allows an average effective dielectric constant of ${\epsilon }^{*}\approx 8.7$ to be extracted, consistent with excitations of an edge state in GaAs (see Ref. [28]). (d) Transverse ($R_{xy}$) and longitudinal ($R_{xx}$) Hall resistance measurements taken at $T=20\mathrm{mK}$ on a Hall bar proximal to the microwave disk. The 2DEG is 270 nm below the surface with carrier density ${\mathrm{n}}_s=1.1\times {10}^{11}{\mathrm{cm}}^{-2}$ and mobility $\mu =5.2\times {10}^6{\mathrm{cm}}^2/\mathrm{Vs}$.

Figure 2

Experimental setup for determining the response of the on-chip circulator. (a) Photograph of circulator device showing the three coplanar transmission lines connected to copper wire-wound chip inductors for impedance matching. (b) Close-up of false-colored photo of the circulator showing a $330\text{−}\mu \mathrm{m}$ diameter 2DEG disc with a $20\text{−}\mu \mathrm{m}$ gap to the metal defining the three signal ports. (c) Circuit schematic of the experimental setup indicating port-to-edge capacitive coupling $C_{\mathrm{edge}}$ and direct parasitic coupling between ports $C_p$. Resonant ($L{C}_{\text{stray}}$) matching circuits are indicated with blue boxes. The input of port 2 passes through a directional coupler, with the reflected signal coupled to the output line (denoted $2^{\prime }$) and amplified at 4 K. (d) Full six-way transmission response of the circulator at zero magnetic field, with $S$-parameter measurements indicating complete reciprocity and a frequency response that arises from the matching networks. For each port, the measured response of the amplifiers, couplers, and cold attenuators in the circuit has been subtracted.

Figure 3

Nonreciprocal response of the quantum Hall circulator. (a,b) Port transmission $S_{13}$ and $S_{31}$ with frequency and magnetic field. All measurements have been normalized to the gain-corrected background at $B=0$ [shown in Fig. 2], which defines the 0 dB point on the color scale. (c) Microwave response $S_{13}–S_{31}$ showing strong frequency and $B$-dependent nonreciprocity. (d,e) Full combination of transmission $S$ parameters, taken at $B$ fields indicated by the symbols in (c). (f) Cuts through the color scale data in (c), demonstrating forward and reverse circulation. (g) Isolation, $\mathrm{\Delta }S=S_{2^{\prime }1}\text{−}{S}_{2^{\prime }3}$, measured at positive and negative magnetic fields. Note that the positions of features are symmetric about the $B=0$ axis, but with opposite sign $\mathrm{\Delta }S$.

Figure 4

Comparison of data and model. (a,b) Proposed interferometric mechanism underlying the operation of the quantum Hall circulator, with a slow plasmonic path, via $C_{\mathrm{edge}}$, and a direct capacitive path, via $C_p$. A nonreciprocal response between ports is produced for frequencies where the two paths are out of phase by $\varphi =\pi$ in the forward direction and $\varphi =2\pi$ in the reverse direction. (c,d) Comparison of a simple model that captures this physics (bottom graphs), with experimental data (top graphs), at two different magnetic fields indicated by the symbols [with respect to Fig. 3]. The model is described in detail in the Appendix, with parameters set to values $Z_0=50\mathrm{\Omega }$, $C_p=315\mathrm{fF}$, $C_{\mathrm{edge}}=127\mathrm{fF}$, $R_{xy}=5000\mathrm{\Omega }$, with $R=80\mathrm{\Omega }$ in the center of an EMP resonance (star symbol) and $R=350\mathrm{\Omega }$ off resonance (square symbol). Note that the impedance-matching network transforms $R_{xy}=25\mathrm{k}\mathrm{\Omega }$ towards a few $\mathrm{k}\mathrm{\Omega }$, consistent with the value used in the model.

Figure 5

(a) Schematic of the gate-tunable device, with ports overlapping the edge of the disk and a grounded contact on the mesa. Bias tees enable the application of both rf and dc voltages. A large nonreciprocity $\mathrm{\Delta }S=S_{13}\text{−}{S}_{23}$ is observed as a function of magnetic field, as shown in (b) for the case $V_{g2}=-85\mathrm{mV}$. At fixed negative magnetic field values, varying $V_{g2}$ is found to affect the path from ports 3 to 1, and this produces a significant modulation in the frequency response of the circulator [shown in (c) and (d)]. This response is mirrored with a change of sign $\mathrm{\Delta }S$ at positive magnetic field values, where the direction of EMP propagation is reversed and $V_{g1}$ is varied (see Ref. [28]). The red arrow in (c) indicates a discontinuous jump in frequency as a gate voltage is first applied, while vertical lines show the positions of 1D cuts presented in (d). Horizontal striations in (c) are the result of small standing waves associated with an impedance mismatch between the amplifier and the device.