Abstract

Efficient, low noise conversion between different colors of light is a necessary tool for interfacing quantum optical technologies that have different operating wavelengths. Optomechanically mediated wavelength conversion and amplification is a potential method for realizing this technology, and it is demonstrated here in microdisks fabricated from single crystal diamond—a material that can host a wide range of quantum emitters. Frequency up-conversion is demonstrated with internal conversion efficiency of 45% using both narrow and broadband probe fields, and optomechanical frequency conversion with amplification is demonstrated in the optical regime for the first time to our knowledge.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

The interaction of light and vibration of matter is a rich area of physics dating to Brillouin and Raman’s studies of scattering phenomena [1,2]. With the advent of quantum mechanics, the concept of vibrational energy quanta, phonons [3], has spurred the study of photon–phonon scattering processes, leading to many technological breakthroughs in spectroscopy, medicine, and communications. Photon–phonon interactions are becoming increasing relevant for solid-state quantum technologies, which utilize phonons for transducing [4,5], storing [6,7], and transmitting information [8]. Cavity optomechanics aims to enhance coherent phonon–photon interactions through co-localization of mechanical and optical resonances coupled via radiation pressure or other optical forces [9]. These systems provide a platform that could have application in a quantum network or quantum internet [10], namely, as a phonon-mediated way of transducing quantum information from visible or microwave photons to telecommunication wavelength photons [1113]. Phonon-mediated wavelength conversion has been demonstrated in both the optical [1416] and microwave [11,17] regimes, and many current efforts are focused on optical-to-microwave transduction [1823].

Recently, nanofabrication advances have enabled initial investigations of wide electronic bandgap materials such as single crystal diamond (SCD) for cavity optomechanics [2426]. Diamond does not suffer from nonlinear absorption at the telecommunications wavelengths, which can limit achievable local field strength and corresponding optomechanical coupling rates in smaller bandgap materials such as silicon [27,28]. A bonus of working with diamond is that it also hosts highly coherent artificial atoms such as the nitrogen vacancy (NV) and silicon vacancy (SiV) color centers [29], which have been used in demonstrations of quantum memory [30,31], quantum entanglement [32,33], quantum teleportation [34], loophole-free Bell’s inequality violation [35], and the transfer of phase information from microwave to optical fields [36]. Diamond cavity optomechanics can in principle interface these color centers with light and other quantum systems in new ways [12,13]. One such application is conversion of color center emission to telecommunication wavelengths. A purely optomechanical approach allows high-efficiency wavelength conversion between any two wavelengths of a cavity’s mode spectrum [1416,37] for relatively low input power, negating the need for material-dependent nonlinear optical processes [3845]. Here we demonstrate optomechanical wavelength conversion in a diamond cavity for the first time to our knoweldge and show that this scheme can be operated in a regime where the converted signal is optomechanically amplified. We also probe the bandwidth and gain properties of this process using a novel broadband coherent spectroscopy technique.

Cavity optomechanical wavelength conversion coherently couples two optical cavity modes at frequencies ωo,1 and ωo,2 via their independent optomechanical coupling to a common cavity mechanical resonance at frequency ωm. In microdisk cavities, such as the diamond cavity studied here and illustrated in Fig. 1(a), the optomechanical coupling is created by the radiation pressure force exerted by optical whispering gallery modes on the microdisk. This interaction can coherently exchange energy between optical and mechanical domains when a strong control laser is input into the cavity at a frequency ωc red-detuned Δoc=ωoωc=ωm from the cavity mode by the mechanical resonance frequency. The resulting system can be represented by a photon–phonon beam splitter Hamiltonian [9], and it has been used to demonstrate optomechanically induced transparency (OMIT) and slow light [46,47] in a variety of devices, including in diamond microdisks [26].

2. OPTOMECHANICALLY MEDIATED WAVELENGTH CONVERSION

 figure: Fig. 1.

Fig. 1. (a) Illustration of the system under study. Two microdisk optical whispering gallery mode resonances at λ1 and λ2 are coupled to the microdisk’s mechanical radial breathing mode whose frequency is ωm. Schematics illustrating the cavity density of states, control and probe field detunings for the case of frequency up- and down-conversion with (b, c) no amplification and (d) frequency up-conversion with amplification.

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In multimode cavity optomechanical systems, coherent photon–phonon coupling is harnessed to convert probe photons input on resonance with a mode at ωo,1 to a mechanical excitation that is in turn converted to signal photons resonant with the second cavity mode ωo,2. This process requires inputting two control lasers, referred to as write and read fields, to the cavity. Typically, both control lasers are red-detuned by Δoc=ωm from their respective cavity modes as illustrated in Figs. 1(b) and 1(c). This setup, which has been used in previous optical domain wavelength conversion demonstrations [1416], can in principle be amplified by blue-detuning the read laser from the cavity (Δoc=ωm) as shown in Fig. 1(d). This enables low noise amplification of the converted photons, as recently demonstrated by Ockeloen-Korppi et al. in the microwave regime [48] and reported below for the first time in the optical domain. Such two-port amplification avoids optomechanical self-oscillation by balancing optomechanical amplification with damping for the blue- and red-detuned optical modes, respectively, and unlike traditional optomechanical amplification [4951] has a fundamentally unlimited gain-bandwidth product.

The diamond microdisks used here for wavelength conversion, an example of which is shown in the scanning electron micrograph image in Fig. 2(a), support whispering gallery modes with optical quality factor Qo sufficiently high for operation in the resolved sideband regime of cavity optomechanics. These devices were fabricated using an optimized reactive ion undercutting process described in Ref. [52] that results in a smooth diamond microdisk supported by a thin diamond pillar, and they have higher Qo than those previously used for single-mode diamond optomechanics studies [26].

 figure: Fig. 2.

Fig. 2. (a) Scanning electron micrograph of a diamond microdisk similar to the device under study here (5μm diameter). (b, c) Optical whispering gallery mode resonances used in the frequency conversion process. Intrinsic optical quality factors of the symmetric (Qsi) and anti-symmetric (Qai) doublet modes extracted from fit line shapes are indicated. (d) Photodetected power spectral density of the optomechanically transduced thermally driven microdisk RBM motion in ambient pressure and temperature. (Inset: COMSOL simulated mode profile). Measured at input power sufficiently low to not affect the mechanical resonance dynamics. Mechanical quality factor Qm5,800 is extracted from the fit line shape.

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All of the measurements presented below involve two sets of microdisk optical modes widely separated in wavelength and mutually coupled to the same mechanical radial breathing mode (RBM) of the microdisk, whose mechanical displacement profile is illustrated in Fig. 1(a). Their optomechanical properties were probed using coherent fiber taper optical mode spectroscopy as in previous work [24,26,52] using the apparatus described in more detail below. Fiber taper transmission spectra for the two modes are shown in Figs. 2(b) and 2(c), revealing resonances with frequencies ωo,1/2π=195THz (λ1=1535nm) and ωo,2/2π=191THz (λ2=1566nm) and unloaded Qoi1.4×105 and 2.1×105, respectively. The doublet nature of the resonances indicates that they are standing wave modes [53]; the red mode of each doublet was used for all of the measurements described below. The λ1 mode was found to be TM-like, while the λ2 mode was TE-like, which is reflected in the different splitting of each doublet, but is not an essential ingredient for the results presented here. These modes are used to optomechanically transduce the motion of the microdisk mechanical resonances, with a typical photodetected power spectral density of the thermomechanical motion of the microdisk’s RBM shown in Fig. 2(d), revealing a resonance frequency ωm/2π=2.27GHz and mechanical quality factor Qm=ωm/Γm5,800 in the ambient conditions used for all of the reported measurements. The device’s combination of high mechanical frequency and high Qo places it in the resolved sideband regime κ/ωm1, where κ=ωo/Qo is the total cavity photon decay rate.

The experimental setup used to coherently couple light at multiple wavelengths to the microdisk’s mechanical motion is shown in Fig. 3(a). Two independent tunable diode lasers (Newport TLB-6700) generate the control fields. An amplitude or phase electro-optic modulator (EOM, EOSpace) driven by a vector network analyzer (Keysight E5063A) at a swept frequency δωp generates the probe field by adding sidebands to the ωc,1 or ωc,2 control field, respectively. An RF switch selects which control laser will be modulated, determining whether to carry out frequency down- or up-conversion, respectively. The control field intensities are amplified via an erbium-doped fiber amplifier (EDFA, Pritel) before being coupled to the microdisk via the optical fiber taper. The transmitted signal is used for the optical mode spectroscopy described above, while the reflected signal is routed via an optical circulator through a tunable band-pass filter (TBF, Optoplex, 100 GHz) that separates the converted signal and the read control field from the write control and the input probe fields. The beat note from the converted signal field interfering with the read control field is then demodulated from the photodetector output by the vector network analyzer.

 figure: Fig. 3.

Fig. 3. (a) Experimental setup used for wavelength conversion and amplification. Phase and amplitude EOMs driven by the vector network analyzer (VNA) are used to generate the probe fields from the control fields where an RF switch controls which laser to modulate. A 50%/50% waveguide coupler combines the input fields, which are coupled to the microdisk via a dimpled tapered fiber. A tunable band-pass filter (TBF) is used to filter the output of the cavity, and the photodetected signal is analyzed by the VNA. (b) The beat note between converted photons and control field of the same color measured on the VNA for frequency up-conversion with and without amplification. OMIT spectra for the λ2 and λ1 optical modes are shown as insets, where the cooperativity is extracted from the depth of the OMIT feature. (c) Predicted added noise to amplified signal based on Eq. (3) and system parameters, with operating regime circled.

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To demonstrate wavelength conversion, the lasers were first set up in the standard up-conversion configuration illustrated in Fig. 1(c): both read and write control fields were red-detuned from their respective cavity modes by Δoc,1=Δoc,2=ωm, and the write control field was weakly modulated at δωp to generate the probe sideband (wavelength λ2). The resulting measured beat note SC(δωp) between the up-converted field at λ1 and the read control field is shown in Fig. 3(b). Efficient conversion is observed when δωp=ωm, i.e., when the probe field is on resonance with the cavity mode, and it is observed over a bandwidth defined by the optomechanically broadened mechanical linewidth.

Calibrating SC and writing it as a wavelength conversion efficiency requires careful characterization of the detectors and electronics used in the experiment. Instead, following previous reports [14,16], we infer an external conversion efficiency ηext=η1η2ηint between λ2 and λ1 from the optomechanical properties of our device. Here η1=13% and η2=21% are the experimentally measured waveguide–cavity coupling efficiencies at wavelengths λ1 and λ2, respectively, extracted by determining the coupling rate κe between the microdisk standing wave modes and the forward propagating fiber mode from fits to the doublet resonances, taking into account the standing wave modes’ equal coupling to the backwards propagating fiber mode. The internal conversion efficiency ηint=4C1C2/(1+C1+C2)2 is determined solely by the optomechanical cooperativity Cj of each mode λj [14]. Here Cj=4Njg0,j2/κjΓm was measured from the modes’ OMIT dips, shown in the insets to Fig. 3(b), where Nj and g0,j are the respective control field intracavity photon number and the vacuum optomechanical coupling rate of mode j. These single-color OMIT measurements record the beat note between control field j in the red-detuned configuration (Δωoc,j=ωm) and its modulator generated sideband at ωc,j+δωp. Note that while both control lasers were kept on during this measurement, only one OMIT process was carried out at a time by placing the other laser off resonance. By fitting the OMIT spectra in Fig. 3(b) to the model described in Supplement 1, we extract C13.94 and C21.02 for N13.1×106 and N22.2×105, respectively, corresponding to ηint45%. Here Nj and Δoc,j were used as the only fitting parameters, where all other required parameters were measured independently. Measurements of g0 were performed using the phase tone calibration method [54], giving g0/2π15kHz and 27 kHz for the λ1 and λ2 modes, respectively, as described in Supplement 1. Note that the Fano shape of the λ1 OMIT dip is related to a non-zero phase imparted by the amplitude modulator, and the demodulation process of the vector network analyzer (VNA) as described in detail in Supplement 1 (See also Visualization 1 and Visualization 2). These measured values for Cj are consistent with the estimated fiber taper input power for each control field of Pin16mW and 3.8mW.

Increasing ηint could be achieved by operating in the Cj1 regime and by matching C1=C2. For the diamond cavities studied here, in practice Nj can be increased above 106 until becoming limited by thermal instabilities within the cavity. For example, C>3.9 is demonstrated for measurements presented in Supplement 1. In this experiment we were unable to balance C1 and C2 while maintaining Cj>1, as the input laser used to drive the λ2 mode was less efficiently amplified in the EDFA. Combined with greater loss in the system at λ2, this resulted in N2<N1. The use of a second EDFA with a gain maximum near λ2 would allow independent control of N for each mode. Assuming each mode could reach C2, ηint64% would be achievable. Finally, the relatively small ηext=1.23% demonstrated here could be improved by operating in the over-coupled regime, which requires either higher Qo or improved coupling via, for example, an external on-chip waveguide. Unfortunately, the ωo,2 mode was outside the range of the TBF, prohibiting measurement of down-conversion for this device. However, down-conversion was measured using a different device with lower conversion efficiency as described in Supplement 1.

3. OPTOMECHANICALLY AMPLIFIED WAVELENGTH CONVERSION

These devices are also promising for quantum-limited amplification of the wavelength-converted signal field as previously demonstrated in the microwave domain [48]. As described above and shown in Fig. 1(d), signal amplification is achieved by placing the λ1 read control laser blue-detuned from the cavity Δoc,1=ωm, while keeping the λ2 write control laser red-detuned as before (Δoc,2=ωm). This results in what can be thought of as a two-step process involving a beam splitter interaction between the λ2 mode and the mechanical mode and parametric amplification between the mechanical mode and the λ1 mode [48]. The converted amplified signal is detected in the same fashion as above, where the beat note SCA produced by the amplified converted light and the read control field is shown in Fig. 3(b). The frequency and linewidth of the amplified (SCA) and unamplified (SC) spectra are governed by the optomechanical damping (Γopt) and optical spring effect (δωm) induced on the mechanical resonance dynamics by each control laser. As both control lasers are red-detuned for SC, its effective mechanical linewidth is broader, and the center frequency is red-shifted compared to its intrinsic value shown in Fig. 2(d). In contrast, as described above, for SCA, the λ1 laser is blue-detuned, while λ2 is red-detuned. As the photon-assisted optomechanical coupling rates Gj=g0,jNj are such that G1>G2 (G1=2π×26.4MHz, G2=2π×12.5MHz), this initially resulted in the microdisk being in the self-oscillation regime (Γm+Γopt<0). To obtain the amplified spectra in Fig. 3(b), Δoc,1 was adjusted such that the device was no longer in the self-oscillation regime, although a narrowed linewidth and blue-shift of the center frequency is still observed due to the imbalance of G1 and G2. Balancing G1 and G2 was a technical limitation in our experiment, which could be remedied by using a second EDFA to independently tune G1 and G2, enabling operation in the large-gain-bandwidth product regime. Ideally, in the low-noise amplification scheme described in Ref. [48], the system should be operated in the G2G1 regime to avoid instabilities associated with optomechanical self-oscillation.

To characterize the noise properties of the SCA spectrum, we follow the analysis in Ref. [48], starting with expected frequency-converted gain, given by

Ax=2(κeκ4G1G2/κΓm4G¯2/κ),
where the optical cavity dissipation constants have been taken to be equal and G¯2=G12G22. The adjusted G1 value was determined from the linewidth of SCA where G2 was held constant, giving G12π×14.1MHz. For the operating conditions here, and taking κ=κ2, Eq. (1) gives Ax1.2. For these operating conditions, the amplifier is not in a low-noise regime, as the added noise to SCA is dominated by the contribution from the mechanical bath, whose equivalent added noise on resonance is given by Sadd,m/|Ax|2 where
Sadd,m=ΓmκeG12|Γmκ/4G¯2|2(nth+12),
and nthkBT/ωm is the thermal occupation of the RBM. For this experiment, this results in 6.52×103 added quanta to the SCA spectra. To predict future performance of this system within the context of low-noise single-photon wavelength conversion, we calculate the added noise to the amplified optical signal in the ideal high gain (G2G1) and large Γopt regime, given by
Sadd=Γmκ4G22κκe(nth+12)+κiκe+12.
Here κi=κ2κe is the intrinsic cavity photon decay rate, where the optical decay rates have been taken to be similar for each cavity. The predicted added noise as a function of N2 is shown in Fig. 3(c) for the parameters of the device under study and for various temperatures. We predict that the minimum added noise of 2 quanta, limited by the coupling efficiency achieved here, can be approached for N21×106 at 10 mK and N21×108 at 4 K for this device, provided that operation in the (G2G1) regime is enabled by overcoming technical limitations in our experiment. Furthermore, amplification at the SQL of 1/2 quanta could be possible by improving the coupling to the device such that κeκi.

4. BROADBAND PROBE MEASUREMENT

To further characterize the converted amplified signal, we used a broadband (compared to κ) RF noise source to drive the phase modulator generating the OMIT probe field, similar to the approach described in Ref. [55]. Here an arbitrary waveform generator (AWG, Tektronix 70002A) outputting a pseudo-Gaussian white noise signal with a sampling rate and length of 25 GS/s and 2 GS, respectively, drove the RF input of the phase EOM (20 GHz bandwidth) to create a broadband optical probe field from the write field control laser. When the control laser is tuned to Δωoc,2=ωm, observation of both OMIT and wavelength conversion on a real-time spectrum analyzer (Tektronix RSA5106B) is possible. Figure 4(a) shows the measured probe field’s power spectral density, revealing the cavity response for frequency components of the probe that do not coherently drive the mechanics, which in these measurements is the broad peak in the demodulator signal with a linewidth of κ/2π=1.4GHz and an OMIT dip at δωp=ωm, i.e., where the OMIT condition is satisfied. This demonstrates a straightforward method for measuring OMIT and the cavity response simultaneously in frequency space.

 figure: Fig. 4.

Fig. 4. Measurement of OMIT and wavelength conversion via the RSA. (a) Broadband and narrowband (inset) spectrum showing the cavity response and the OMIT feature at ωm/2π when a phase EOM is driven with a broadband RF noise source for the device shown in Supplement 1. (b, c) Wavelength conversion for the same device in Fig. 3 (b) without and (c) with amplification as measured on the RSA, with the noisy broadband probe (B.P.) field. The thermal motion of the RBM is also shown, which was measured at low power with a single laser to avoid optomechanical back action. Here the noise floor is set by the photodetector whose noise equivalent power NEP=33pW/Hz.

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Wavelength conversion of the λ2 broadband probe generated by the RF noise source, in both the unamplified and amplified configurations, measured in reflection, is shown in Figs. 4(b) and 4(c), respectively. The plots in Figs. 4(b) and 4(c) show the detected power spectral density of the converted signal at λ1 (blue trace) compared for reference with the corresponding measurement when the λ2 probe is off (orange trace) so that the detected spectrum is derived entirely from the optomechanically modified motion of the microdisk due to the λ1 and λ2control fields. As above, when both control lasers are red-detuned in Fig. 4(b), the effective mechanical linewidth is broader and the center frequency is red-shifted compared to its intrinsic value (purple trace), which was measured at low power with a single optical mode to avoid optomechanical back action. In the amplified conversion case shown in Fig. 4(c), the linewidth is slightly narrowed and shifted to higher frequency due to the fact that G1>G2. In principle, this technique could be utilized in balancing Gj by adjusting Nj such that the linewidth of the observed spectra with the broadband probe off is equal to the intrinsic linewidth observed in the absence of the strong control fields. Here the ratio of the amplified to unamplified peak height is 2.4× larger than what was observed for the coherently driven case in Fig. 3(b). While the control field input power of each mode was held constant between these measurements, Δoc,1 and Δoc,2 were manually set for each case, which could account for this discrepancy.

The converted signal power in both amplified and unamplified cases can be computed directly from the area under the spectrum. When the probe is off, we see the added noise from the thermally driven signal level that would have to be overcome by increasing Cj to allow operation at the single-photon level. We estimate the gain utilizing measurement of the cavity transmission profile of the λ2 mode on the RSA via the broadband probe and the data in Fig. 4(c), as outlined in Supplement 1. Using this method, we estimate a gain of Ax,exp3.2, which, combined with the total linewidth, results in Γtot=Γm+Γopt=2π×5.8kHz giving a gain-bandwidth product GBW19kHz. Possible explanations for the mismatch of Ax and Ax,exp include the approximation of similar κ and κe for each optical mode in calculating Ax, uncertainty in the measured optical output power from the cavity, and variation in Δoc,1 and Δoc,2 as mentioned above. With the data available, a measurement of the added noise to the converted signal was not possible; however, the thermal component is expected to dominate as discussed above. To compare the amplified versus unamplified wavelength conversion, we have defined the signal ratio as the difference in integrated power with the broadband probe field on and off to isolate the converted signal from the thermal component, which is then divided by the off-resonant noise floor. We find that the amplified conversion signal is 1.62× larger than without amplification for the same input broadband probe. With calibration of the probe spectrum, this broadband probe technique could also be used to determine the conversion efficiency, similar to what has been suggested by Liu et al. in Ref. [16] where a coherent drive and RSA were used to characterize the converted signal.

5. SUMMARY

In summary, we have demonstrated a diamond cavity optomechanical system capable of phonon-mediated wavelength conversion with an internal conversion efficiency of 45%. While we were limited by an imbalance of G1 and G2, and κe<κ in this experiment, operation in the stable, high-gain regime G2G1 should be possible by utilizing a second EDFA to allow separate control of G1 and G2, and improving waveguide–cavity coupling would enable Ax1. To the best of our knowledge, this is also the first demonstration of optomechanical amplification, albeit not operating in the low-noise regime, of the converted light in the optical domain. In this configuration, this system has promise for reaching a minimum added noise of 2 quanta during the amplification process by operating at larger photon number and with G2G1. This device can in principle operate at the SQL where a minimum of half an energy quanta of noise is added to the signal by improving the waveguide–cavity coupling efficiency, and it has immediate practical use in increasing signal-to-noise ratio when measuring quantum optomechanical effects [56]. In addition, use of a broadband noisy optical probe field was introduced for both OMIT and wavelength conversion. Finally, as previous studies in these structures [24] have demonstrated the existence of high-Qo optical modes at 738nm and 637nm, near the zero phonon lines of SiV and NV color centers, respectively, these devices have potential as a converter of diamond color center emission to telecommunications wavelengths for application in quantum networks.

Funding

National Research Council Canada (NRC); Alberta Innovates; Natural Sciences and Engineering Research Council of Canada (NSERC); Canada Foundation for Innovation (CFI).

 

See Supplement 1 for supporting content.

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29. I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641 (2016). [CrossRef]  

30. M. Pfender, N. Aslam, P. Simon, D. Antonov, G. Thiering, S. Burk, F. Fávaro de Oliveira, A. Denisenko, H. Fedder, J. Meijer, J. A. Garrido, A. Gali, T. Teraji, J. Isoya, M. W. Doherty, A. Alkauskas, A. Gallo, A. Grüneis, P. Neumann, and J. Wrachtrup, “Protecting a diamond quantum memory by charge state control,” Nano Lett. 17, 5931–5937 (2017). [CrossRef]  

31. D. D. Sukachev, A. Sipahigil, C. T. Nguyen, M. K. Bhaskar, R. E. Evans, F. Jelezko, and M. D. Lukin, “Silicon-vacancy spin qubit in diamond: a quantum memory exceeding 10 ms with single-shot state readout,” Phys. Rev. Lett. 119, 223602 (2017). [CrossRef]  

32. E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, M. V. G. D. L. Childress, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010). [CrossRef]  

33. H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, “Heralded entanglement between solid-state qubits separated by three meters,” Nature 497, 86–90 (2013). [CrossRef]  

34. W. Pfaff, B. J. Hensen, H. Bernien, S. B. van Dam, M. S. Blok, T. H. Taminiau, M. J. Tiggelman, R. N. Schouten, M. Markham, D. J. Twitchen, and R. Hanson, “Unconditional quantum teleportation between distant solid-state quantum bits,” Science 345, 532–535(2014). [CrossRef]  

35. B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015). [CrossRef]  

36. I. Lekavicius, D. A. Golter, T. Oo, and H. Wang, “Transfer of phase information between microwave and optical fields via an electron spin,” Phys. Rev. Lett. 119, 063601 (2017). [CrossRef]  

37. A. H. Safavi-Naeini and O. Painter, “Proposal for an optomechanical traveling wave phonon-photon translator,” New J. Phys. 13, 013017 (2011). [CrossRef]  

38. A. Dréau, A. Tchebotareva, A. E. Mahdaoui, C. Bonato, and R. Hanson, “Quantum frequency conversion of single photons from a nitrogen-vacancy center in diamond to telecommunication wavelengths,” Phys. Rev. Appl. 9, 064031 (2018). [CrossRef]  

39. P. Farrera, N. Maring, B. Albrecht, G. Heinze, and H. de Riedmatten, “Nonclassical correlations between a C-band telecom photon and a stored spin-wave,” Optica 3, 1019–1024 (2016). [CrossRef]  

40. N. Maring, P. Farrera, K. Kutluer, M. Mazzera, G. Heinze, and H. de Riedmatten, “Photonic quantum state transfer between a cold atomic gas and a crystal,” Nature 551, 485–488 (2017). [CrossRef]  

41. M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4, 786–791 (2010). [CrossRef]  

42. J. S. Pelc, L. Yu, K. D. Greve, P. L. McMahon, C. M. Natarajan, V. Esfandyarpour, S. Maier, C. Schneider, M. Kamp, S. Höfling, R. H. Hadfield, A. Forchel, Y. Yamamoto, and M. M. Fejer, “Downconversion quantum interface for a single quantum dot spin and 1550-nm single-photon channel,” Opt. Express 20, 27510–27519 (2012). [CrossRef]  

43. K. De Greve, L. Yu, P. L. McMahon, J. S. Pelc, C. M. Natarajan, N. Y. Kim, E. Abe, S. Maier, C. Schneider, M. Kamp, S. Höfling, R. H. Hadfield, A. Forchel, M. M. Fejer, and Y. Yamamoto, “Quantum-dot spin-photon entanglement via frequency downconversion to telecom wavelength,” Nature 491, 421–425 (2012). [CrossRef]  

44. A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894–899 (2010). [CrossRef]  

45. Q. Li, M. Davanço, and K. Srinivasan, “Efficient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics,” Nat. Photonics 10, 406–414 (2016). [CrossRef]  

46. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010). [CrossRef]  

47. A. H. Safavi-Naeini, T. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011). [CrossRef]  

48. C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, T. T. Heikkilä, F. Massel, and M. A. Sillanpää, “Low-noise amplification and frequency conversion with a multiport microwave optomechanical device,” Phys. Rev. X 6, 041024 (2016). [CrossRef]  

49. F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature 480, 351–354 (2011). [CrossRef]  

50. T. G. McRae and W. P. Bowen, “Near threshold all-optical backaction amplifier,” Appl. Phys. Lett. 100, 201101 (2012). [CrossRef]  

51. H. Li, Y. Chen, J. Noh, S. Tadesse, and M. Li, “Multichannel cavity optomechanics for all-optical amplification of radio frequency signals,” Nat. Commun. 3, 1091 (2012). [CrossRef]  

52. M. Mitchell, D. P. Lake, and P. E. Barclay, “Realizing Q> 300 000 in diamond microdisks for optomechanics via etch optimization,” APL Photon. 4, 016101 (2019). [CrossRef]  

53. M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef]  

54. M. Gorodetksy, A. Schliesser, G. Anetsberger, S. Deleglise, and T. Kippenberg, “Determination of the vacuum optomechanical coupling rate using frequency noise calibration,” Opt. Express 18, 23236–23246 (2010). [CrossRef]  

55. Y. Zou, Y. Jiang, Y. Mei, X. Guo, and S. Du, “Quantum heat engine using electromagnetically induced transparency,” Phys. Rev. Lett. 119, 050602 (2017). [CrossRef]  

56. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982). [CrossRef]  

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    [Crossref]
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    [Crossref]
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    [Crossref]
  54. M. Gorodetksy, A. Schliesser, G. Anetsberger, S. Deleglise, and T. Kippenberg, “Determination of the vacuum optomechanical coupling rate using frequency noise calibration,” Opt. Express 18, 23236–23246 (2010).
    [Crossref]
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    [Crossref]

2019 (1)

M. Mitchell, D. P. Lake, and P. E. Barclay, “Realizing Q> 300 000 in diamond microdisks for optomechanics via etch optimization,” APL Photon. 4, 016101 (2019).
[Crossref]

2018 (5)

A. Dréau, A. Tchebotareva, A. E. Mahdaoui, C. Bonato, and R. Hanson, “Quantum frequency conversion of single photons from a nitrogen-vacancy center in diamond to telecommunication wavelengths,” Phys. Rev. Appl. 9, 064031 (2018).
[Crossref]

R. N. Patel, Z. Wang, W. Jiang, C. J. Sarabalis, J. T. Hill, and A. H. Safavi-Naeini, “Single-mode phononic wire,” Phys. Rev. Lett. 121, 040501 (2018).
[Crossref]

A. P. Higginbotham, P. S. Burns, M. D. Urmey, R. W. Peterson, N. S. Kampel, B. M. Brubaker, G. Smith, K. W. Lehnert, and C. A. Regal, “Harnessing electro-optic correlations in an efficient mechanical converter,” Nat. Phys. 14, 1038–1042 (2018).
[Crossref]

L. Fan, C.-L. Zou, R. Cheng, X. Guo, X. Han, Z. Gong, S. Wang, and H. X. Tang, “Superconducting cavity electro-optics: a platform for coherent photon conversion between superconducting and photonic circuits,” Sci. Adv. 4, eaar4994 (2018).
[Crossref]

D. P. Lake, M. Mitchell, Y. Kamaliddin, and P. E. Barclay, “Optomechanically induced transparency and cooling in thermally stable diamond microcavities,” ACS Photon. 5, 782–787 (2018).
[Crossref]

2017 (8)

A. P. Reed, K. H. Mayer, J. D. Teufel, L. D. Burkhart, W. Pfaff, M. Reagor, L. Sletten, X. Ma, R. J. Schoelkopf, E. Knill, and K. W. Lehnert, “Faithful conversion of propagating quantum information to mechanical motion,” Nat. Phys. 13, 1163–1167 (2017).
[Crossref]

M. Pfender, N. Aslam, P. Simon, D. Antonov, G. Thiering, S. Burk, F. Fávaro de Oliveira, A. Denisenko, H. Fedder, J. Meijer, J. A. Garrido, A. Gali, T. Teraji, J. Isoya, M. W. Doherty, A. Alkauskas, A. Gallo, A. Grüneis, P. Neumann, and J. Wrachtrup, “Protecting a diamond quantum memory by charge state control,” Nano Lett. 17, 5931–5937 (2017).
[Crossref]

D. D. Sukachev, A. Sipahigil, C. T. Nguyen, M. K. Bhaskar, R. E. Evans, F. Jelezko, and M. D. Lukin, “Silicon-vacancy spin qubit in diamond: a quantum memory exceeding 10  ms with single-shot state readout,” Phys. Rev. Lett. 119, 223602 (2017).
[Crossref]

I. Lekavicius, D. A. Golter, T. Oo, and H. Wang, “Transfer of phase information between microwave and optical fields via an electron spin,” Phys. Rev. Lett. 119, 063601 (2017).
[Crossref]

Y. Chu, P. Kharel, W. H. Renninger, L. D. Burkhart, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, “Quantum acoustics with superconducting qubits,” Science 358, 199–202 (2017).
[Crossref]

C. Simon, “Towards a global quantum network,” Nat. Photonics 11, 678–680 (2017).
[Crossref]

N. Maring, P. Farrera, K. Kutluer, M. Mazzera, G. Heinze, and H. de Riedmatten, “Photonic quantum state transfer between a cold atomic gas and a crystal,” Nature 551, 485–488 (2017).
[Crossref]

Y. Zou, Y. Jiang, Y. Mei, X. Guo, and S. Du, “Quantum heat engine using electromagnetically induced transparency,” Phys. Rev. Lett. 119, 050602 (2017).
[Crossref]

2016 (8)

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2015 (2)

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2014 (4)

W. Pfaff, B. J. Hensen, H. Bernien, S. B. van Dam, M. S. Blok, T. H. Taminiau, M. J. Tiggelman, R. N. Schouten, M. Markham, D. J. Twitchen, and R. Hanson, “Unconditional quantum teleportation between distant solid-state quantum bits,” Science 345, 532–535(2014).
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2013 (4)

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
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2011 (5)

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2010 (5)

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, M. V. G. D. L. Childress, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010).
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2008 (1)

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2005 (2)

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I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641 (2016).
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Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
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Alegre, T. M.

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M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
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Supplementary Material (3)

NameDescription
» Supplement 1       Supplemental document
» Visualization 1       Phasor visualization in a frame rotating with the carrier field (yellow arrow) and sidebands (blue lines) as a function of phase parameter f. Here f is changing as a function of time, illustrated by the purple arc.
» Visualization 2       Phasor visualization in the non-rotating frame where the yellow circle illustrates the phasor trajectory of the carrier field, tracing out the corresponding yellow sinusoid to the right. Sidebands are illustrated by the circles.

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Figures (4)

Fig. 1.
Fig. 1. (a) Illustration of the system under study. Two microdisk optical whispering gallery mode resonances at λ1 and λ2 are coupled to the microdisk’s mechanical radial breathing mode whose frequency is ωm. Schematics illustrating the cavity density of states, control and probe field detunings for the case of frequency up- and down-conversion with (b, c) no amplification and (d) frequency up-conversion with amplification.
Fig. 2.
Fig. 2. (a) Scanning electron micrograph of a diamond microdisk similar to the device under study here (5μm diameter). (b, c) Optical whispering gallery mode resonances used in the frequency conversion process. Intrinsic optical quality factors of the symmetric (Qsi) and anti-symmetric (Qai) doublet modes extracted from fit line shapes are indicated. (d) Photodetected power spectral density of the optomechanically transduced thermally driven microdisk RBM motion in ambient pressure and temperature. (Inset: COMSOL simulated mode profile). Measured at input power sufficiently low to not affect the mechanical resonance dynamics. Mechanical quality factor Qm5,800 is extracted from the fit line shape.
Fig. 3.
Fig. 3. (a) Experimental setup used for wavelength conversion and amplification. Phase and amplitude EOMs driven by the vector network analyzer (VNA) are used to generate the probe fields from the control fields where an RF switch controls which laser to modulate. A 50%/50% waveguide coupler combines the input fields, which are coupled to the microdisk via a dimpled tapered fiber. A tunable band-pass filter (TBF) is used to filter the output of the cavity, and the photodetected signal is analyzed by the VNA. (b) The beat note between converted photons and control field of the same color measured on the VNA for frequency up-conversion with and without amplification. OMIT spectra for the λ2 and λ1 optical modes are shown as insets, where the cooperativity is extracted from the depth of the OMIT feature. (c) Predicted added noise to amplified signal based on Eq. (3) and system parameters, with operating regime circled.
Fig. 4.
Fig. 4. Measurement of OMIT and wavelength conversion via the RSA. (a) Broadband and narrowband (inset) spectrum showing the cavity response and the OMIT feature at ωm/2π when a phase EOM is driven with a broadband RF noise source for the device shown in Supplement 1. (b, c) Wavelength conversion for the same device in Fig. 3 (b) without and (c) with amplification as measured on the RSA, with the noisy broadband probe (B.P.) field. The thermal motion of the RBM is also shown, which was measured at low power with a single laser to avoid optomechanical back action. Here the noise floor is set by the photodetector whose noise equivalent power NEP=33pW/Hz.

Equations (3)

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Ax=2(κeκ4G1G2/κΓm4G¯2/κ),
Sadd,m=ΓmκeG12|Γmκ/4G¯2|2(nth+12),
Sadd=Γmκ4G22κκe(nth+12)+κiκe+12.

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