Ultrafast Linear Kinetic Inductive Photoresponse of YBa2Cu3O7-δ Meander-Line Structures by Photoimpedance Measurements
Haig A. Atikian, Behnood G. Ghamsari, Steven M. Anlage, A. Hamed Majedi
aa r X i v : . [ phy s i c s . i n s - d e t ] F e b Ultrafast Linear Kinetic Inductive Photoresponse of YBa Cu O − δ Meander-Line Structures by Photoimpedance Measurements
Haig A. Atikian, a) Behnood G. Ghamsari, Steven M. Anlage, and A. Hamed Majedi Electrical and Computer Engineering Department and the Institute for Quantum Computing, University of Waterloo,Waterloo, ON, N2L 3G1, Canada Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD,20742-4111, USA (Dated: 1 March 2018)
We report the experimental demonstration of the linear kinetic-inductive photoresponse of thin-filmYBa Cu O − δ (YBCO) meander-line structures, where the photoresponse amplitude, full-width-half-maximum (FWHM), and rise-time are bilinear in the incident optical power and bias current. This bilinearbehavior reveals a trade-off between obtaining high responsivity and high speed photodetection. We alsoreport a rise-time as short as 29ps in our photoimpedance measurements.The interaction of light with superconducting samplesis long known to perturb superconductivity , whichcan be used as a probing mechanism for optoelectronicapplications . In general, photons of energy greaterthan the Cooper pair binding energy (2∆) can initiatea chain of pair-breaking events resulting in a deviationof the quasiparticle and pair densities from their equi-librium values. Typically, these distributions dependon temperature, optical power and wavelength, thermalboundary conditions, and material properties such aselectron-electron and electron-phonon interactions times,electron density, coherence length, penetration depth,and geometry . While determining the spatial andtemporal distribution of quasiparticles and pairs undera time-varying optical illumination is a profound prob-lem in non-equilibrium superconductivity, many of theimportant concepts of such an interaction for device ap-plications can be captured by means of a much simplerand more phenomenological approach, namely the ki-netic inductance model . Within the kinetic inductancemodel the presence of the superconductive condensate,at a macroscopic level, can be adequately modeled by anadditional inductive channel for charge transport. Theoptically initiated pair breaking mechanism, within thisframework, should be interpreted as the spatial and tem-poral variations of the kinetic inductance and the normalresistance of the superconducting specimen.Many researchers have experimentally studied the ki-netic inductive photoresponse of superconducting thinfilms through photoimpedance measurements . Inphotoimpedance measurements, light induced changes inthe microwave impedance of the superconducting struc-ture are measured by an external high-frequency circuit.In its simplest form, the specimen is externally biasedwith a dc current and connected to a fast oscilloscope inseries with a high bandwidth amplifier; absorption of op-tical photons then changes the impedance of the sampleand produces a transient voltage response. A number a) Author to whom correspondence should be addressed. Electronicaddress: [email protected] of previous works have reported photoimpedance mea-surements on different superconductors mainly conclud-ing that: 1) the resistive photoresponse dominates attemperatures well below the critical temperature (T c ),whereas the kinetic inductive response becomes the mainmechanism of photoresponse close to T c ; 2) In the kineticinductive regime the photoresponse could be very fast,with a rise time as low as 50ps, and is mainly limited bythe time constants of the peripheral measuring appara-tus; 3) the dependence of the photoresponse amplitudevaries nonlinearly with the incident optical power.The nonlinearity of the kinetic inductive photore-sponse intrinsically arises from the nonlinear dependenceof the kinetic inductance of a superconducting sample onthe Cooper pair density. Therefore, even though changesin the Cooper pair density, under certain conditions, mayvary linearly with the incident optical power, the resul-tant variation of the kinetic inductance is generally non-linear. This point can be readily observed for a thin-filmsample : L k = m ∗ ℓn ∗ ( q ∗ ) A , (1)where L k is the kinetic inductance, ℓ and A are the lengthand the cross section area of the sample, m ∗ and q ∗ re-spectively are the mass and charge of a Cooper pair, and n ∗ is the density of Cooper pairs. Accordingly, the ki-netic inductive photoresponse approximately reads V ph = ddt ( L k I ) , (2)where I is the bias current. Nevertheless, we have the-oretically shown elsewhere that if the optical powerand the bias current are far from their critical values,and the temperature is not too close to T c the kineticinductive response can be linearized giving a frequency-dependent voltage responsivity R v ( ω ) ≡ V ph ( ω ) P o ( ω ) = (cid:18) η Q τ Q I Aℓn ∗ (cid:19) (cid:18) jωL k R n jωL k + R n (cid:19) , (3)where P o and ω are the incident optical power and mod-ulation frequency, η Q is the pair breaking efficiency, τ Q (a) −20 −10 0 10 20−1.5−1−0.500.511.5 V ( m V ) I (mA) (b)
FIG. 1: (a) Image of the 5 µm meander-line (b)Measured current-voltage characteristics of the 5 µm meander-line at 77K.is the Cooper pairs recombination life time, and R n and L k are the equilibrium normal resistance and kinetic in-ductance of the sample in the absence of illumination.This regime of operation is particularly useful for opto-electronic device applications such as photodetectors andoptically tunable microwave-photonic devices such as de-lay lines, resonators, and filters where linear tunability ishighly desirable .To serve as a detecting element, we have used a 100nm-thick YBCO thin film (THEVA, Ismaning, Germany)meander line structure with 5- µ m line widths and slots,covering an area of 176 µ m × µ m. The meander linestructure is placed at the midpoint of the center strip of a50GHz-bandwidth 50Ω superconducting coplanar waveg-uide (CPW) transmission line. Figure 1 shows the imageof the meander line and the current-voltage characteris-tics at 77K. The critical current is found to be 13mA,and the bias current is selected to be below this value.The meander line is externally dc biased through highbandwidth bias-tees. One end of the CPW is terminatedwith a 50Ω load to suppress any reflected signals. Theother end is connected to a high-bandwidth microwaveamplifier with a gain of 28dB, followed by a fast oscil-loscope where the response to a train of 1550nm wave-length, 45ps-wide Gaussian optical pulses is measured.A block diagram of the measurement setup is shown inFigure 2. More details in regards to the photoimpedanceexperimental setup can be found in .Figure 3 illustrates typical photoresponse waveformsfor different bias currents at an incident optical powerof 1.6mW. The inset of Figure 3 illustrates an operat-ing point where we have measured rise times as shortas 29ps. Figure 4a shows that the photoresponse ampli-tudes of the detector, for fixed bias currents, varies lin-early with the incident optical power. Moreover, Figure4b demonstrates that the responsivity of the device has alinear dependence on the bias current. These two obser-vations confirm our previous theoretical prediction of thelinear kinetic inductive response represented by equation(3). This linear response sustains as long as the pertur-bation in both kinetic inductance and normal resistanceis small. This also implies that the fractional change inboth the Cooper pair density and quasiparticles is small.These values, in general, depend on temperature, bias Bias Tee Bias Tee 1550nm Pulsed Laser Laser Pulse 50
Load Microwave Amplifier High-Speed Oscilloscope Current Source
FIG. 2: Block diagram of the photoimpedancemeasurement setup of the meander line structure. P ho t o r e s pon s e ( m V ) I =15.5mAI =14.5mAI =13.5mAI =12.5mAI =11.5mAI =10.5mAI = 9.5mAI = 8.5mAI = 7.5mA0 200 400 600 800 10000246810 time (ps) P ho t o r e s pon s e ( m V ) FIG. 3: Photoresponse waveforms for the 5 µm meander-line under 1.6mW of incident optical powerwith a varying bias at 77K and 28dB amplification.(Inset) Photoresponse waveform under 1.2mW ofincident optical power and 7.5mA bias current with a29ps risetime. P ho t o r e s pon s e A m p li t ude ( m V ) I = 7.5mAI = 8.5mAI = 9.5mAI =10.5mAI =11.5mA (a) R e s pon s i v i t y ( m V / W ) (b) FIG. 4: (a) Photoresponse amplitude versus incidentoptical power with a varying bias current for. (b)Responsivity versus bias current. F W H M ( n s ) I = 7.5mAI = 8.5mAI = 9.5mAI =10.5mAI =11.5mA (a) d F W H M / d P o ( p s / m W ) (b) FIG. 5: (a) FWHM of the photoresponse waveformversus incident optical power with varying bias currents.(b) The slope of the changes in FWHM with opticalpower as a function of bias current. R i s e T i m e ( p s ) I = 7.5mAI = 8.5mAI = 9.5mAI =10.5mAI =11.5mA (a) d τ r / d P o ( p s / m W ) (b) FIG. 6: (a) Rise-time versus incident optical power withvarying bias currents (b) The slope of the changes inrise-time with optical power as a function of biascurrent.current, and average incident optical power. The linearregime of operation for this device, at a given temper-ature, is clearly illustrated by the range of current andoptical power values in Figure 4.The FWHM of the photoresponse is a measure of thephotoinduced disturbance in the detector, which accord-ing to (2) equals to ( δL k I ). The perturbation in thekinetic inductance, δL k , in the linear kinetic inductiveregime, linearly varies with optical power and is indepen-dent of the bias current . Thus, the ( δL k I ) product,and consequently the FWHM, should be bilinear in theoptical power and bias current which is clearly shownby Figure 5. This point readily reveals the trade offbetween obtaining high responsivity and short photore-sponse waveforms in linear kinetic inductive detectors,because the former requires a higher bias current whereasthe latter demands a small bias current.In addition to amplitude and FWHM, the rise time of the photoresponse waveform is also bilinear in opticalpower and bias current, as illustrated by Figure 6. Interms of an electrical circuit model, the detector actslike an RL circuit with time varying R and L , and aconstant total current I . In this scenario, the risetime depends on the ( δL k I ), which was shown to bebilinear in current and optical power. 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