Bidirectional conversion between microwave and light via ferromagnetic magnons

Coherent conversion of microwave and optical photons in the single quantum level can significantly expand our ability to process signals in various fields. Efficient up-conversion of a feeble signal in the microwave domain to the optical domain will lead to quantum-noise-limited microwave amplifiers. Coherent exchange between optical photons and microwave photons will also be a stepping stone to realize long-distance quantum communication. Here we demonstrate bidirectional and coherent conversion between microwave and light using collective spin excitations in a ferromagnet. The converter consists of two harmonic oscillator modes, a microwave cavity mode and a magnetostatic mode called the Kittel mode, where microwave photons and magnons in the respective modes are strongly coupled and hybridized. An itinerant microwave field and a traveling optical field can be coupled through the hybrid system, where the microwave field is coupled to the hybrid system through the cavity mode, while the optical field addresses the hybrid system through the Kittel mode via Faraday and inverse Faraday effects. The conversion efficiency is theoretically analyzed and experimentally evaluated. The possible schemes for improving the efficiency are also discussed.

Figure 1

Architecture of the proposed microwave-light converter. The converter consists of two strongly coupled harmonic oscillator modes: a microwave cavity mode $\widehat{a}$, whose energy is specified by $\hslash {\omega }_c$, and a magnetostatic mode called Kittel mode $\widehat{c}$, whose energy is specified by $\hslash {\omega }_m$, and these are strongly coupled at a rate $g$. An input (output) itinerant microwave field mode ${\widehat{a}}_i$ (${\widehat{a}}_o$) is coupled to the converter through the microwave cavity mode at a rate ${\kappa }_c$, whereas an input (output) traveling optical field mode ${\widehat{b}}_i$ (${\widehat{b}}_o$) is coupled to the converter through the Kittel mode at a rate $\zeta$. $\gamma$ and $\kappa$ are the rates of the intrinsic energy dissipation for the Kittel mode and the internal energy loss for the cavity, respectively.

Figure 2

Experimental setup for converting microwave to light. A spherical crystal (0.75 mm in diameter) made of yttrium iron garnet (YIG) is placed in a microwave cavity to form a strongly coupled hybrid system between the Kittel mode and the microwave cavity mode. A static magnetic field is applied to the YIG sample with permanent magnets. The field can be varied with a coil through a magnetic circuit made of pure iron. A vector network analyzer is used to characterize the hybrid system by measuring the microwave reflection coefficient from the system. To convert microwave to light, a 1550-nm cw carrier laser is impinged on the YIG sample. Under the microwave drive, the polarization of the carrier laser oscillates at the frequency of the induced magnetization oscillation producing the optical sideband field. The beat signal between the carrier and the sideband field is measured using a polarizer and a fast photodetector, is amplified with two low-noise microwave amplifiers, and fed into the vector network analyzer.

Figure 3

(a) Power reflection coefficient $|S_{11}{|}^2$ as a function of the microwave drive frequency (drive power: 0 dBm) and the coil current. (b) Spectrum of $|S_{11}|, \arg \left(S_{11}\right)$, and their polar plot, at a coil current $I=400$ mA indicated by the dashed line in (a). Blue dots show the experimental data and red curves show the fitting results based on Eq. (A5). The two pronounced dips in the reflection coefficient $S_{11}\left(\omega \right)$ in (b) are the signature of the hybridization between the Kittel mode and the cavity mode. (c) $|S_{\mathrm{LM}}{|}^2$ as a function of the microwave drive frequency and the coil current (carrier laser power: 450 $\mu \mathrm{W}$). The data are simultaneously taken with $|S_{11}{|}^2$ in (a). (d) Spectrum of $|S_{\mathrm{LM}}|, \arg \left(S_{\mathrm{LM}}\right)$, and their polar plot, at $I=400$ mA indicated by the dashed line in (c). Blue dots show the experimental data and red curves show the fitting results based on Eq. (13). Two tiny normal-mode splittings indicated by the arrows in (a) are caused by other magnetostatic modes. The dotted lines in (a) and (b) indicate the coil current $I=564$ mA, where the maximum conversion is realized (see Sec. 3c).

Figure 4

(a) Experimental setup for converting light to microwave. The hybrid system consisting of the Kittel mode and the microwave cavity mode is used for the conversion. Two phase-coherent laser fields generated from a monochromatic cw laser are simultaneously impinged on the YIG sample to induce the inverse Faraday effect. The created magnons predominantly decay to the microwave cavity, and the coupled-out microwave signal from the cavity is amplified and fed into a spectrum analyzer. (b) Scheme to generate two phase-coherent laser fields. A monochromatic cw laser field with the wavelength of 1550 nm (the angular frequency of ${\mathrm{\Omega }}_c$) is split into two paths. The field in one of the paths is phase modulated with modulation angular frequency of ${\omega }_E$ by an EOM and filtered out the carrier and all other sideband photons except for the one of the first-order sidebands (the angular frequency of $\mathrm{\Omega }={\mathrm{\Omega }}_c+{\omega }_E$) with a Fabry-Pérot filter cavity. The filtered field is then combined at a polarizing beam splitter with the field in the other path with the angular frequency of ${\mathrm{\Omega }}_0$, which is also frequency shifted by ${\omega }_A/2\pi =80$ MHz from ${\mathrm{\Omega }}_c$ with an AOM. A piezoelectric actuator is used to compensate the fluctuation of the optical path-length difference between two fields for stabilizing the relative phase between the two fields. The two resultant fields are separated by ${\omega }_a={\mathrm{\Omega }}_0-\mathrm{\Omega }$ in angular frequency as shown in (c). Both of the fields are coupled to a polarization-maintaining (PM) fiber before the sample so as to match their spatial modes. The power is about 15 mW for each field before entering the sample.

Figure 5

(a) Measured noise power spectrum at a coil current $I=564$ mA, indicated by the dotted lines in Figs. 3 and 3. The peak of the noise power corresponds to the lower branch of the normal modes. The inset shows the zoom-in of the peak region in (a) under illumination of the two laser fields inducing the inverse Faraday effect. The sharp peak above the broad noise level indicates the presence of the coherent magnetization oscillations. (b) Calibrated photon conversion efficiency $|S_{\mathrm{ML}}^{+}{|}^2$ as a function of the frequency difference between the two laser fields ${\omega }_a={\mathrm{\Omega }}_0-\mathrm{\Omega }$. The blue points are experimentally determined efficiencies, while the red curve is drawn based on Eq. (11). (c) $\arg \left(S_{\mathrm{ML}}^{+}\right)$ of the generated microwave output as a function of time, where the upper and the lower points represent the data with the relative phase shift by $\pi$.

Figure 6

Energy-level diagram relevant to the Faraday and the inverse Faraday effects with YIG. The states describing the electronic ground and excited states are specified by $|g\rangle$ and $|e\rangle$ and the magnon Fock states are denoted as $|n\rangle$. Here depicted is the configuration in which the inverse Faraday effect with the parametric-amplification-type Hamiltonian (A13) is induced by two phase-coherent fields with a detuning from the $|g\rangle \leftrightarrow |e\rangle$ transition being $\mathrm{\Delta }$. One of the two fields (blue arrows) having the angular frequency ${\mathrm{\Omega }}_0$ and being $z$ polarized ($\pi$ polarized) and the other field (red arrows) having the angular frequency $\mathrm{\Omega }$ ($\mathrm{\Omega }<{\mathrm{\Omega }}_0$) and being $y$ polarized coherently create and annihilate magnons (brown arrows). ${\widehat{b}}_z, {\widehat{b}}_i$, and $\widehat{c}$ denote the annihilation operators for the $z$-polarized field, the $y$-polarized field, and the magnon, respectively.

Figure 7

Shot-noise-based calibration scheme. (a) Schematic of the experimental setup. A loop coil generates an oscillating magnetic field perpendicular to the saturated magnetization. The light before entering the sample has the polarization plane inclined by $+{45}^{\circ }$ from the $z$ axis. After a polarization beam splitter (PBS), a high-speed photodetector converts the $z$-polarized photon flux as an instantaneous voltage signal. The resultant voltage signal is fed into a spectrum analyzer to give $S_{VV}\left(\omega \right)$ in Eq. (B8). (b) Power reflection coefficient $|S_{11}{\left(\omega \right)|}^2$ measured through the coupling coil. The blue dots are the measured value, while the red line shows a fitting curve based on Eq. (B1). (c) Observed power spectrum $S_{VV}\left(\omega \right)\mathrm{\Delta }\omega$ corresponding to Eq. (B9). Here the resolution bandwidth $\mathrm{\Delta }\omega /2\pi$ of the spectrum analyzer is set to 100 Hz. The inset shows the power spectral densities (PSD) of the total noise (blue triangles) and the noise after subtracting the electrical contribution (green squares) as a function of the incident laser power. The latter grows linearly with the laser power as indicated by the red line. In the main panel the laser power is $-0.5$ dBm and the electrical noise has been subtracted.

Figure 8

(a) Experimental setup for calibrating the transfer function $T_a\left(\omega \right)$ from the cavity port to the spectrum analyzer. A known calibration tone from a microwave generator is input to the microwave cavity via an additional port (antenna pin). (b) Pictorial representation of the calibration scheme. $P_i$ is the power of the itinerant microwave from a microwave generator, which is $a$ priori known. The input and output powers of the cavity, $P_i$ and $P_0$, are related by Eq. (C1). Here, ${\kappa }_1$ (${\kappa }_c$) is the coupling rate between the input (output) field and the cavity and $\kappa$ is the intrinsic energy dissipation rate of the cavity. $P_m$ is the power at the spectrum analyzer, which is generated after going through the gains of amplifiers and the losses and the interferences due to the intervened coaxial cables collectively denoted as $T_a$.