Microwave optomechanics with a carbon nanotube ... and some news - PowerPoint PPT Presentation

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks Microwave optomechanics with a carbon nanotube ... and some news about MoS 2 too ... Andreas K. H¨ uttel University of Regensburg current affiliation: Aalto University, Espoo, Finland IWEPNM 2020, Kirchberg in Tirol, 13 March 2020

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks suspended carbon nanotubes: NEMS and quantum transport metal nanotube D. R. Schmid et al. , PRB 91 , 155439 (2015), K. J. G. G¨ otz et al. , PRL 120 , 246802 (2018), M. Marga´ nska et al. , PRL 122 , 086802 (2019)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks low-temperature transport: Coulomb blockade tunnel barriers between contacts and nanotube; low temperature k B T ≪ e 2 / C : quantum dot all following measurements at T base � 10mK (unless noted) source dot drain Coulomb blockade single electron tunneling � V g N el. � s � d V sd I � s � d � s � d V g gate d I schematic drawing V sd ≈ 0 (linear response regime) d V sd CB CB CB N-1 N N+1 el. el. el. SET SET SET 0 V g

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks clean transport spectrum, shell effects K. J. G. G¨ otz et al. , PRL 120 , 246802 (2018)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks driven transversal vibrations, “the old-fashioned way” • transport spectroscopy setup plus rf irradiation • mechanical resonance visible in time-averaged current 2 -17.8 dBm Q =140670 -64.5 dBm 88 I (pA) I (nA) 87 1 86 0 100 300 500 293.41 293.42 293.43 293.44 f (MHz) f (MHz) (different device) A. K. H¨ uttel et al. , Nano Lett. 9 , 2547 (2009)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks how about doing microwave optomechanics with a nanotube? x 10 µm 6 mm C. A. Regal et al. , Nature Physics 4 , 555 (2008)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks highly active field of research g mass zg M. Aspelmeyer et al., Rev. Mod. Phys. 86 , 1391 (2014)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks how about doing microwave optomechanics with a nanotube? x 10 µm 6 mm C. A. Regal et al. , Nature Physics 4 , 555 (2008)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks dispersive optomechanical coupling ↔ moving element modulates CPW resonator capacitance optical cavity with moving mirror vibrating microwave drive capacitor LC circuit ˆ � ˆ b + ˆ a † ˆ b † � H int = − ¯ hg 0 ˆ a � � ∂ω cav ω cav ∂ C cav � � = = g 0 x zpf x zpf � � ∂ x ∂ x 2 C cav � � x = 0 x = 0 M. Aspelmeyer et al., Rev. Mod. Phys. 86 , 1391 (2014)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks numbers for dispersive coupling? carbon nanotube graphene drum aluminum beam V. Singh et al. (2014) C. A. Regal et al. (2008) 10 − 20 kg 2 × 10 − 15 kg mass m resonance frequency f mech 503MHz 36MHz 2 . 3MHz 10 4 10 5 10 5 quality factor Q mech zero point fluct. x zpf 2pm 30 fm 40 fm 5 . 7GHz 5 . 9GHz cavity frequency f cav 5GHz cavity Q Q cav 437 25000 10000 6 . 75 × 10 4 (6 . 75 × 10 4 ) (6 . 75 × 10 4 ) cavity occupation n cav 2 . 6aF coupling capacitance C g 580aF ∂ C g / ∂ x capacitance sensitivity 1pF/m 170pF/m 2 . 9mHz 0 . 83Hz 0 . 15Hz zero-photon coupling g 0 2 × 10 − 10 3 × 10 − 6 3 × 10 − 7 g 0 Q cav / f cav dispersive coupling ∼ 10 − 7 Hz κ opt ( ∝ n cav ) 0 . 77Hz sideband cooling rate 12mHz A single-wall carbon nanotube is a great mechanical resonator, but is also annoyingly small. S. Blien et al. , Nature Comm. 11 , 1636 (2020); V. Singh et al. , Nat. Nano 9 , 820 (2014); C. A. Regal et al. , Nat. Phys. 4 , 555 (2008)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks we built it anyway (geometry is not everything!) 1 mm S. Blien et al. , Nature Comm. 11 , 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks nanotube deposition area • gate finger connected to cavity • isolation layer (cross-linked PMMA) 100 µm • long resistive meanders as RF block • four gold electrodes (source, drain, and two for cutting) • deep-etched areas to allow fork deposition S. Blien et al. , Nature Comm. 11 , 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks nanotube growth on commercial quartz tuning forks 4 8 m m . nanotube 100 µm 1 µm nominally 1nm Co sputter-deposited as catalyst; growth in high gas flow details: S. Blien et al. , PSSb 255 , 1800118 (2018) S. Blien et al. , PSSb 255 , 1800118 (2018)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks nanotube deposition fork CNT electrodes 1 µm 1 2 3 4 lower fork, detect contact electrically, burn outer segments with current, retract fork details: S. Blien et al. , PSSb 255 , 1800118 (2018) S. Blien et al. , PSSb 255 , 1800118 (2018)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks now this is cooled to 10mK microwave VNA source port 1 port 2 V +30 dB +30 dB -20 dB filter 300 K 4 K -10 dB HEMT + 30dB 1.8 K -10 dB filter 700 mK -20 dB 100 mK -3 dB 10 mK -10 dB

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks optomechanically induced (in)transparency (I) f mech drive probe drive VNA 1 2 cavity reson. f f mech f f drive probe • strong drive at f drive = f cav − f mech (red sideband) 1 mm • probe transmission with weak signal f probe near V V f cav gate bias I dc • when f probe − f drive = f mech : interaction with mechanics − → signal loss S. Blien et al. , Nature Comm. 11 , 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks optomechanically induced (in)transparency (II) dB -30.6 • clear OMIT feature for -31,0 f probe − f drive = f mech -30.65 • in transparency due to specific cavity / -31,5 detection arrangement f drive = 5.23989 GHz -30.7 5.7424 5.7426 -32,0 • would not be visible with dB g 0 ∼ 10mHz -31 -31,0 (even at high drive power) -31,5 -31.05 • obviously something was f drive = 5.23809 GHz missing in the theory 5.7406 5.7408 -32,0 f probe (GHz) 5.740 5.742 S. Blien et al. , Nature Comm. 11 , 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks optomechanically induced (in)transparency (III) – now with gate! ω /2 π p • we trace the OMIT signal over a (GHz) sharp CB oscillation -30.8 5.74245 • “dip” position |S 21 | 2 ↔ f mech ( V g ) (dB) • depth, width of “dip” ↔ 5.74240 -31 optomechanical coupling g -1.191 -1.189 -1.187 V (V) g g /2 π • fit each trace, extract g ( V g ) 100 (kHz) • large on flanks of SET peak 20 75 g ≃ 20kHz g 0 = g / √ n cav ≃ 95Hz 50 10 g 0 /2 π (Hz) • in Coulomb blockade & at de- 0 0 -1.191 -1.189 -1.187 V (V) generacy point zero / no signal g S. Blien et al. , Nature Comm. 11 , 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks another type of capacitance • Capacitance “seen” by the coplanar resonator: C CNT = e ∂ � Q g � ∂ � N � = ··· = e C g + const. ∂ V g ∂ V g C Σ • The nanotube moves − → C g changes by δ C g − → the Coulomb oscillations shift in V g • We define an effective gate voltage modulation equivalent to the motion: C g δ V eff = V g δ C g g • This results in = ··· = e ∂ 2 � N � ∂ V eff ∂ C g ∂ C CNT = ∂ C CNT V g g ∂ x ∂ V eff ∂ x ∂ V 2 ∂ x C Σ g g amplification factor! S. Blien et al. , Nature Comm. 11 , 1636 (2020); similar concepts in articles of E. Laird, M. Sillanp¨ a¨ a, T. Duty

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks Coulomb blockade enhancement of coupling V g (V) -1.19 -1.188 -1.186 1 charge <N> � N � ( V g ) : tunneling through 0 Lorenz-broadened level, width Γ C 1 q-capacitance d CNT ∝ (aF) dI/dV dV g 5 = e ∂ 2 � N � (a.u.) ∂ C CNT ∂ C g V g 0 0 ∂ V 2 ∂ x C Σ ∂ x g 30 d coupling ∝ dV g 100 g 0 = ω cav ∂ C CNT � 80 20 � x zpf g/2 π � 0 /2 π ∂ x g 2 C cav (kHz) � x = 0 (Hz) 10 insert device values ... 20 0 0 V g (V) -1.19 -1.188 -1.186 S. Blien et al. , Nature Comm. 11 , 1636 (2020)

introduction preparation measurement explanation TMDC nanotubes conclusions & thanks Coulomb blockade enhancement of coupling V g (V) -1.19 -1.188 -1.186 1 <N> � N � ( V g ) : tunneling through 0 Lorenz-broadened level, width Γ C 1 d CNT ∝ (aF) dI/dV dV g 5 = e ∂ 2 � N � (a.u.) ∂ C CNT ∂ C g V g 0 0 ∂ V 2 ∂ x C Σ ∂ x g 30 d x 5.77 ∝ dV g 100 g 0 = ω cav ∂ C CNT � 80 20 � x zpf g/2 π � 0 /2 π ∂ x g 2 C cav (kHz) � x = 0 (Hz) 10 insert device values ... 20 0 0 V g (V) -1.19 -1.188 -1.186 S. Blien et al. , Nature Comm. 11 , 1636 (2020)