Optomechanical Coupling between a Multilayer Graphene Mechanical Resonator and a Superconducting Microwave Cavity

Left to Right: (top row) V. Singh, S. J. Bosman, B. H. Schneider, (bottom row) Y. M. Blanter, A. Castellanos-Gomez, G. A. Steele.

Authors: 
V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, 
G. A. Steele

Affiliation:
Kavli Institute of NanoScience, Delft University of Technology, The Netherlands.

Introduction:

Mechanical resonators made from two dimensional exfoliated crystals offer very low mass, low stress, and high quality factor due to their crystalline structure [1]. These properties make them very attractive for application in mass sensing, force sensing, and exploring the quantum regime of motion by providing large quantum zero-point fluctuations over a small bandwidth. The most studied exfoliated crystal so far is graphene, where a considerable progress has been made in exploring its properties for mass sensing, study of nonlinear mechanics, and voltage tunable oscillators [2-9]. These properties also make graphene attractive for exploring the quantum regime of motion.

Past 2Physics articles by Andres Castellanos-Gomez and Gary A. Steele:

July 20, 2014: "Few-layer Black Phosphorus Phototransistors for Fast and Broadband Photodetection" by Michele Buscema, Dirk J. Groenendijk, Sofya I. Blanter, Gary A. Steele, Herre S.J. van der Zant, Andres Castellanos-Gomez.

A possible route towards exploring the quantum regime of graphene motion is cavity optomechanics [10]. It has shown exquisite position sensitivity, enabled the preparation and detection of mechanical systems in the quantum ground state with conventional top-down superconducting mechanical resonators [11-18]. Therefore, a natural candidate for implementing cavity optomechanics with graphene resonator is to couple it to a high Q superconducting microwave cavity. However, coupling graphene resonators with superconducting cavities in such a way that both retain their excellent properties (such as their high quality factors) is technologically challenging. Using a deterministic dry transfer technique [19], we combine a multilayer graphene resonator to a high quality factor microwave cavity [20]. Although multilayer graphene has a higher mass than a mono-layer, it could be advantageous for coupling to a superconducting cavity because of its lower electrical resistance.

Results:

Device

To fabricate the superconducting cavities in coplanar waveguide geometry, we use an alloy of molybdenum and rhenium with superconducting transition temperature of 8.1 K. Using the dry transfer technique, we place a few layer thick graphene mechanical resonator near the coupler forming coupling capacitor for the cavity. Figure 1(a) shows a false color scanning electron microscope image of a device with a 10 nm thick multilayer graphene resonator coupled to a superconducting cavity. Figure 1(b) shows an equivalent schematic diagram with graphene resonator acting as a capacitor (C_g ) between the superconducting cavity (formed by L_sc and C_sc ) and the external microwave source. By cooling these cavities to very low temperatures (14 mK), we measured internal quality factor as high as 107,000.

FIG. 1: Coupling of a multilayer graphene mechanical resonator to a superconducting cavity. (a) A tilted angle scanning electron micrograph (false color) near the coupler showing 4 μm diameter multilayer (10 nm thick) graphene resonator (cyan) suspended 150 nm above the gate. (b) Schematic lumped element representation of the device with the equivalent lumped parameters as C_sc ≈ 415 fF and L_sc ≈ 1.75 nH.

Mechanical motion readout sensitivity

To the first order, the superconducting microwave cavity can be thought simply as motional transducer for the graphene resonator. To readout the motion of the graphene resonator, we inject a microwave near the cavity frequency given by

                                       
The motion of graphene resonator modulates the cavity frequency and hence its displacement gets imprinted on the phase of the reflected microwave signal from the cavity. By measuring the phase of the reflected signal (technically known as the homodyne detection), one can directly read the mechanical motion of the resonator [11]. The large quality factor of our cavity and its ability to sustain superconductivity with large number of the microwave photons enable us to measure the thermo-mechanical motion of the graphene resonator down to temperatures of 96 mK and a displacement sensitivity as low as 17 fm/√Hz.

Optomechanical coupling

In addition to detecting the motion of the graphene drum, we can also exert a force on the mechanical drum by using the radiation pressure of microwave photons trapped in the superconducting cavity. This force comes from the fact that light carries momentum: shining light from a flashlight at a piece of paper would in principle apply a force to it, pushing it away from the light source. The radiation pressure force that light exerts, however, is usually far too small to detect. Due to the tiny mass of the graphene sheet and the ability to detect small displacement, we could see the graphene sheet shaking in response to a "beat" set by the microwave light sent into the cavity.

By sending two microwave signals, a probe signal ω_p (near the cavity resonance frequency ω_c ) and another signal at ω_d (detuned by mechanical frequency ω_m , such that ω_d = ω_c +ω_m ), one can apply a a radiation pressure force on the mechanical resonator. This radiation pressure force beats at the mechanical resonance frequency, leading to coherent driven motion of the mechanical resonator, as shown schematically by process 1 in Figure 2(a). In presence of the significant optomechanical coupling, this coherent drive of the mechanical resonator down-converts the detuned drive photons exactly at the probe frequency (pink arrow) shown by process 2 in Figure 2(a). These two signals at probe frequency interfere with each other leading to a transmission window, appearing as a sharp peak in the cavity response, shown in Figure 2(b). This phenomena is known as "optomechanically induced transparency" (OMIT) and is a signature of the optomechanical coupling between the graphene mechanical resonator and the superconducting cavity [21-23]. As this effect rely on the coherent driven motion of the graphene mechanical resonator, the width of the transparency window is set by the mechanical resonator's linewidth as shown in the inset of Figure 2(b). Using the radiation pressure force driving, we measure the quality factor of the graphene resonator as high as 220,000.

FIG. 2: Optomechanically induced transparency (OMIT). (a) Schematic illustrate OMIT features in terms of the interference of the probe field (black arrow) with the microwave photons that are cyclically down- and then up- converted by the optomechanical interaction (pink arrow). (b) Measurement of the cavity reflection |S₁₁| in presence of sideband detuned drive tone. A detuned drive at ω_c+ω_m results in a window of optomechanically induced reflection (OMIR) in the cavity response. Inset: Zoom of the OMIR window. (c) Measurement of the cavity reflection |S₁₁| with a stronger detuned drive. At the center of the cavity response, the reflection coefficient exceeds 1, corresponding to mechanical microwave amplification of 17 dB by the graphene resonator.

By increasing the drive signal amplitude further, one can increase the strength of the optomechanical coupling. Using this, we make an amplifier in which microwave signals are amplified by the mechanical motion of the graphene resonator [16]. With a stronger detuned drive, we observed a microwave gain of 17 dB (equivalent to a photon gain of 50) as shown in Figure 2(c), before the nonlinear effects from the mechanical resonators come into play. Similarly, a different "beat" of the microwave photons (having ω_d = ω_c - ω_m ) allows one to store microwave photons into the mechanical motion of the resonator [24]. To this end we show a storage time up to 10 millisecond, which is equivalent to delay from a few hundreds of kilometer long coaxial cable.

The phenomena of OMIT also allow one to directly extract a quantity called "cooperativity" C without any fi t parameters. The quantity C is an important fi gure of merit in characterizing the optomechanical systems. For example, in sideband resolved limit (when mechanical frequency exceeds the cavity linewidth), the criteria for quantum-coherent regime can be simply written as C + 1 > n_th , where n_th is the average number of thermal phonon in the mechanical resonator. In our experiment, we have been able to achieve C = 8 close to the expected number of thermal phonon in the mechanical resonator at 14 mK, bringing this system close to the quantum coherent regime.

Summary and outlook:

In our work, we demonstrated the potential of exfoliated graphene crystal applied to form an optomechanical device, which so far have been realized using top-down technology. This opens up a new dimension to explore exfoliated two-dimensional crystals in optomechanical systems, and harnessing their unique properties such as extremely low mass and high quality factors. For future devices, two-dimensional superconducting exfoliated flakes could be of great interest for such applications. Superconducting cavity in our work is a very good detector for mechanical displacement with a bandwidth three orders of magnitude larger than the mechanical line-width. This would provide a new tool to study nonlinear restoring forces, nonlinear damping, and mode coupling in mechanical resonators from twodimensional crystals. The characterization of our device shows that in future by making little larger area mechanical resonators, devices operating in quantum regime can be easily realized, which can possibly be used as a memory element in a quantum computer. As many of the 2D crystals can be grown by chemical processes in large areas, they also hold the promise of scalability.

References:
[1] Andres Castellanos-Gomez, Vibhor Singh, Herre S.J. van der Zant, Gary A. Steele, "Mechanics of freely-suspended ultrathin layered materials". arXiv:1409.1173 [cond-mat] (2014).
[2] J. Scott Bunch, Arend M. van der Zande, Scott S. Verbridge, Ian W. Frank, David M. Tanenbaum, Jeevak M. Parpia, Harold G. Craighead, Paul L. McEuen, "Electromechanical resonators from graphene sheets". Science, 315, 490-493 (2007). Abstract.
[3] Changyao Chen, Sami Rosenblatt, Kirill I. Bolotin, William Kalb, Philip Kim, Ioannis Kymissis, Horst L. Stormer, Tony F. Heinz, James Hone, "Performance of monolayer graphene nanomechanical resonators with electrical readout". Nature Nanotechnology, 4, 861-867 (2009). Abstract.
[4] Vibhor Singh, Shamashis Sengupta, Hari S Solanki, Rohan Dhall, Adrien Allain, Sajal Dhara, Prita Pant, Mandar M Deshmukh, "Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nanoelectromechanical systems resonators". Nanotechnology, 21, 165204 (2010). Abstract.
[5] Robert A. Barton, B. Ilic, Arend M. van der Zande, William S. Whitney, Paul L. McEuen, Jeevak M. Parpia, Harold G. Craighead, "High, size-dependent quality factor in an array of graphene mechanical resonators". Nano Letters, 11, 1232{1236 (2011). Abstract.
[6] A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, A. Bachtold, "Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene". Nature Nanotechnology, 6, 339-342 (2011). Abstract.
[7] Xuefeng Song, Mika Oksanen, Mika A. Sillanpää, H. G. Craighead, J. M. Parpia, Pertti J. Hakonen, "Stamp transferred suspended graphene mechanical resonators for radio frequency electrical readout". Nano Letters, 12, 198-202 (2012). Abstract.
[8] Robert A. Barton, Isaac R. Storch, Vivekananda P. Adiga, Reyu Sakakibara, Benjamin R. Cipriany, B. Ilic, Si Ping Wang, Peijie Ong, Paul L. McEuen, Jeevak M. Parpia, Harold G. Craighead, "Photothermal self-oscillation and laser cooling of graphene optomechanical systems". Nano Letters, 12, 4681-4686 (2012). Abstract.
[9] Changyao Chen, Sunwoo Lee, Vikram V. Deshpande, Gwan-Hyoung Lee, Michael Lekas, Kenneth Shepard, James Hone, "Graphene mechanical oscillators with tunable frequency". Nature Nanotechnology 8, 923{927 (2013). Abstract.
[10] Markus Aspelmeyer, Tobias J. Kippenberg, Florian Marquardt, "Cavity optomechanics". arXiv:1303.0733 [cond-mat.mes-hall] (2013).
[11] C. A. Regal, J. D. Teufel, K. W. Lehnert, "Measuring nanomechanical motion with a mi- crowave cavity interferometer". Nature Physics, 4, 555-560 (2008). Abstract.
[12] J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, K. W. Lehnert, "Nanomechanical motion measured with an imprecision below that at the standard quantum limit". Nature Nanotechnology 4, 820-823 (2009). Abstract.
[13] T. Rocheleau, T. Ndukum, C. Macklin, J. B. Hertzberg, A. A. Clerk, K. C. Schwab, "Preparation and detection of a mechanical resonator near the ground state of motion". Nature, 463, 72-75 (2010). Abstract.
[14] J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, R. W. Simmonds, "Circuit cavity electromechanics in the strong-coupling regime". Nature, 471, 204-208 (2011). Abstract.
[15] J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, R. W. Simmonds, "Sideband cooling of micromechanical motion to the quantum ground state". Nature, 475, 359-363 (2011). Abstract.
[16] F. Massel, T.T. Heikkilä, J.-M. Pirkkalainen, S.U. Cho, H. Saloniemi, P.J. Hakonen, M.A. Sillanpää, "Microwave ampli fication with nanomechanical resonators". Nature, 480, 351-354 (2011). Abstract.
[17] Fredrik Hocke, Xiaoqing Zhou, Albert Schliesser, Tobias J Kippenberg, Hans Huebl, Rudolf Gross, "Electromechanically induced absorption in a circuit nano-electromechanical system". New Journal of Physics, 14, 123037 (2012). Abstract.
[18] T. A. Palomaki, J. D. Teufel, R. W. Simmonds, K. W. Lehnert, "Entangling mechanical motion with microwave fields". Science, 342, 710-713 (2013). Abstract.
[19] Andres Castellanos-Gomez, Michele Buscema, Rianda Molenaar, Vibhor Singh, Laurens Janssen, Herre S J van der Zant, Gary A Steele, "Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping". 2D Materials, 1, 011002 (2014). Abstract.
[20] V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, G. A. Steele, "Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity". Nature Nanotechnology 9, 820–824 (2014). Abstract.
[21] G. S. Agarwal, Sumei Huang, "Electromagnetically induced transparency in mechanical eff ects of light". Physical Review A, 81, 041803 (2010). Abstract.
[22] Stefan Weis, Rémi Rivière, Samuel Deléglise, Emanuel Gavartin, Olivier Arcizet, Albert Schliesser, Tobias J. Kippenberg, "Optomechanically induced transparency". Science, 330, 1520-1523 (2010). Abstract.
[23] A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, O. Painter, "Electromagnetically induced transparency and slow light with optomechanics". Nature, 472, 69-73 (2011). Abstract.
[24] X. Zhou, F. Hocke, A. Schliesser, A. Marx, H. Huebl, R. Gross, T. J. Kippenberg, "Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics". Nature Physics, 9, 179-184 (2013). Abstract.