Radiation power and linewidth of a semifluxon-based Josephson oscillator
M. Paramonov, M. Yu. Fominsky, V. P. Koshelets, B. Neumeier, D. Koelle, R. Kleiner, E. Goldobin
aa r X i v : . [ c ond - m a t . s up r- c on ] N ov Radiation power and linewidth of a semifluxon-based Josephson oscillator
M. Paramonov, M. Yu. Fominsky, V. P. Koshelets, B. Neumeier, D. Koelle, R. Kleiner, and E. Goldobin a)1) Kotel’nikov Institute of Radioengineering and Electronics RAS, Mokhovaya 11, 125009 Moscow,Russia Physikalisches Institut and Center for Collective Quantum Phenomena in LISA + , Universit¨at T¨ubingen,Auf der Morgenstelle 14, D-72076 T¨ubingen, Germany (Dated: 4 June 2018 File: SemifluxonGen06.TEX ) We demonstrate a high-frequency generator operating at ∼
200 GHz based on flipping a semifluxon in aJosephson junction of moderate normalized length. The semifluxon spontaneously appears at the π discon-tinuity of the Josephson phase artificially created by means of two tiny current injectors. The radiation isdetected by an on-chip detector (tunnel junction). The estimated radiation power (at the detector) is ∼ ∼
100 nW consumed by the generator. The measured radiationlinewidth, as low as 1 . π Josephson junction, semifluxonJosephson oscillators based on the shuttling of flux-ons along a long Josephson junction (LJJ) in the zero-field step (ZFS) mode were investigated in the 1980s .Unfortunately such oscillators cannot deliver appreciablepower to the load because of contradictory requirements.On one hand, to maximize the power delivered from aLJJ to the output microwave line the coupling betweenthe output line and the LJJ should be strong (impedancematching). On the other hand, for such a good coupling,the fluxon will not reflect from the edge of the LJJ. It willannihilate (i.e. be lost), thus stopping the generation.Currently, Josephson oscillators are mainly used in theflux-flow regime optionally at the Fiske (geometrical)resonances. In this regime the power delivered to theload can reach ∼ µ W, an efficiency of dc to ac con-version ∼
10 %, and a free-running radiation linewidth ∼ . After introducing a π discontinu-ity of the Josephson phase, the LJJ reacts by creat-ing a semifluxon pinned at such a discontinuity.A semifluxon being biased over its depinning current (= (2 /π ) I c in an infinite LJJ, where I c = j c A is the“intrinsic” critical current, j c is the critical current den-sity, A is the area of the LJJ) flips continuously betweenthe semifluxon and antisemifluxon states . Upon eachflip, an integer (anti)fluxon is emitted and moves underthe action of the bias current towards the left (right)edge of the LJJ. Usually the bias current can accel- a) Current address: Center of Interdisciplinary Studies, Ostmark-strasse 8, 72135 Dettenhausen, Germany erate the (anti)fluxons up to the Swihart velocity anda semifluxon voltage step (half-integer ZFS) appears onthe current-voltage characteristic of the LJJ . Althoughsuch semi-integer ZFS were observed experimentally no measurements of the radiation power or the radiationlinewidth were carried out. If the LJJ is biased to thehalf-integer ZFS, the end of the LJJ can be well coupledto the output line so that the arriving (anti)fluxon caneven be absorbed and a considerable part of its energyis emitted into the output line. Still, the generation willnot stop like in the case of ZFS described above. It willcontinue as it originates from the center of the LJJ. Thus,such a generator based on a flipping semifluxon shouldprovide much better output power and dc-to-ac energyconversion efficiency.In this letter we report on the high-frequency studyof such a generator based on a flipping semifluxon. Wecouple it to a detector and investigate the power deliveredto the detector, dc-to-ac power conversion efficiency aswell as radiation linewidth of such a generator. Finally,we demonstrate that using a phase-locking feedback loopone can reduce the linewidth practically to zero, definedjust be the accuracy of our measurement equipment ( ∼ | AlO x | Nb JJ technology . Each device consists ofa generator JJ equipped by a pair of current injectors,see Fig. 1. Injectors are connected to the center of thetop superconducting electrode by microstrip lines thatare equipped with high-frequency filters to avoid escapeof the rf power along injector lines (filters are situatedoutside of the Fig. 1(a) frame). The samples have differ-ent generator JJ lengths L , width w , as well as differentinjectors widths ∆ x and gaps ∆ x between them. Thebottom electrode of the generator JJ is embedded intoa control line connected in-line (along the length of the1 IG. 1. (Color online) (a) Optical photograph of the wholedevice
Raith e-LiNE(colored manually).
JJ) to produce a magnetic field. Each edge of the gener-ator JJ is coupled to the high frequency coupling circuit.On one (dead) end it contains only an impedance trans-former. On the other (active) end used for detectionand linewidth measurements it contains two impedancetransformers and a dc break. The coupling circuit is cal-culated to transmit the emitted radiation in a certainfrequency range (typical bandwidth ∼
100 GHz at a fre-quency range of 200–500 GHz). The active coupling cir-cuit was finally connected to an on-chip detector/mixerequipped with a special tuning circuit. A tuning circuitconsists of an inductance (a piece of a microstrip) andradial stubs. It is used to tune out the detector junctioncapacitance to provide a real impedance at the frequencyof the generator. The detector is a small ∼ µ m tunnelJJ, which was connected to an external reference rf source(local oscillator) by means of a microstrip line. This mi-crostrip is used (a) to dc bias the detector junction, (b)to supply an external reference (local oscillator) signaland (c) to send the IF signal from the detector/mixerto the external spectrum analyzer. The parameters ofthe samples discussed in this paper are summarized inTab. I. The particular fabrication run discussed heredelivered j c ≈ . / cm , which gives the Josephsonlength λ J ≈ µ m. For all the samples discussed herethe voltage of the semifluxon step (the same as the volt-age of the first Fiske step) V FS1 ≈ µ V.First, we have calibrated the injectors by measuringthe dependence of the critical current of the generator JJvs. injector current, i.e. , I c ( I inj ). As predicted , it lookslike an almost periodic function with parabolic maximaand cusp-like minima as shown in Fig. 2. The “period” name L ( µ m) w ( µ m) ∆ w ( µ m) ∆ x ( µ m) ≈ . µ m smaller than in the file,widths of the injector lines come ∼ . µ m larger than in thefile). -15 -10 -5 0 5 10 150.00.10.20.30.40.5 I c ( H ) c r i t i c a l c u rr en t I c o f t he gene r a t o r injector I inj or control line I CL current (mA) I c ( I inj ) FIG. 2. The dependence I c ( I inj ) (black) of the generator JJused for injector calibration and determination of I ± π inj . Thedependence I c ( I CL ) (gray) looks similar to a Fraunhofer pat-tern demonstrating good uniformity of the generator JJ. Bothdependences are obtained for the sample corresponds to a phase discontinuity κ ∝ I inj changed by2 π . This allows to calibrate injectors, i.e. , to determinethe proportionality coefficient between I inj and κ . In thecase shown in Fig. 2, the π discontinuity needed to createa semifluxon is reached for I inj = I ± π inj ≈ . I c ( I inj ) at the ± st maximais related to the finite size of injectors .Second, we have measured the I – V characteristic(IVC) of the generator JJ at I inj = I π inj and comparedit with the IVC measured at I inj = 0, which looks likethe usual IVC of a tunnel JJ, see Fig. 3. At I π inj a π discontinuity of the phase is produced. This results inthe creation of a(n) (anti)semifluxon pinned at it. Ac-tually, the localized flux is smaller than Φ / λ J instead of ∞ (Φ ≈ . × − Wb is a magnetic flux quantum).In this case the critical current of the JJ is, in fact, adepinning current of the (anti)semifluxon and is muchlower than I c at I inj = 0, see Fig. 3. Upon exceeding thecritical current the generator JJ jumps to the semifluxonstep aka half-integer zero-field step (HiZFS) . It isthe dynamics at this step that is the main subject of ourstudy.Third, we choose a working point of the generator JJsomewhere at the semifluxon step and measure the IVC2 .0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.00.20.40.60.81.01.2 gene r a t o r b i a s c u rr en t I ( A ) generator voltage (mV)semifluxon step FIG. 3. (Color online) IVCs of generator JJ with I inj = 0(black) and I inj = I π inj (pink/gray) from sample S I S de t e c t o r / m i x e r c u rr en t I d e t ( A ) SIS detector/mixer voltage V det (mV)pumping(detection) FIG. 4. (Color online) Autonomous (black) and pumped(pink/gray) IVC of the detector JJ from sample of the detector JJ. An example of such an IVC of apumped detector is presented in Fig. 4 in comparisonwith the unpumped detector, i.e. , when the generator JJis at I = V = 0. One can observe that in the vicinityof the gap voltage V g ≈ . V det < V g ) or decreases(for V det > V g ). By fitting the IVC of the pumped de-tector using a Tien-Gordon model we can estimate theac power P acdet delivered to the detector. In the typicalcase P acdet ∼ P dcgen consumed by thegenerator at the working point situated at the semifluxonstep is V × I ∼ µ V × µ A ∼
80 nW. These figureslet us conclude that the generator makes a rather effi-cient conversion of dc power to ac power. At this pointquasi-dc measurements were complete.Forth, to measure the emitted radiation linewidth thedevice (chip) was mounted in a specially designed highfrequency cryostat described in detail elsewhere . Thegenerator JJ was biased to the semifluxon step exactlyas described above. The detector JJ was not dc biased(for N even, see below) or somewhat biased (for odd N ) . An external reference rf source (local oscillator) Rhode&Schwarz SMP03 sends a microwave power ata frequency ∼ N -th harmonic ( N ∼ HP E4440A .Fig. 5 shows several radiation spectra taken at closely sit-uated bias points at the semifluxon step. We were ableto continuously tune the central frequency of the radia-tion peak by changing the bias current of the generatorJJ. The power P acdet (height of the peak) and the radia-tion linewidth are weak functions of the generator biascurrent. Among all samples the values of linewidth ∆ f between 1 . I inj from I π inj the ra-diation frequency and the linewidth do not change sub-stantially until I inj changes so much that the semifluxonstep disappears (or the bias point jumps from it). Thisis in contrast to the generators working in the flow-flowmode. Their frequency depends on applied magnetic field H ∝ I CL and the linewidth is, therefore, sensitive to I CL noise .Finally, a proven technique to reduce the radia-tion linewidth is to use a feedback phase-locking loop(PLL) . To be effective the bandwidth of the PLL cir-cuitry should exceed the linewidth of the free-runninggenerator. The PLL’s feedback signal was added to thebias current I of the generator. After this the linewidth,measured relative to the reference oscillator, collapses al-most to zero having the spectral ratio of 95% (the ratio ofthe power in the main narrow peak to the total emittedpower). The remaining linewidth is defined just by theaccuracy of our instrumentation ( ∼ L/λ J ∼
2. Thegenerator delivers an output power of ∼ ∼
10 % of dc input power to ac output power includingthe losses on the way from the generator to the on-chipdetector and the power lost in higher harmonics. Thetypical measured linewidth of a free-running semifluxongenerator is ∼ I inj from I π inj , i.e. , to the3
00 350 400 450 500-40-30-20-100 po w e r s pe c t r a a t I F ( d B ) intermediate frequency (MHz) FIG. 5. (Color online) Emission spectra measured at inter-mediate frequency at different bias points of the generatorJJ (sample N = 16 harmonic of the local oscillatorfrequency f = 12 .
283 GHz. The radiation linewidths ∆ f of2 . ± . I in the range 338–345 µ A. value of the phase discontinuity. We have also demon-strated the possibility to phase lock the oscillator withthe reference generator frequency, which collapses thelinewidth theoretically to zero having the spectral ratioof 95%. Thus, this type of Josephson oscillator is com-parable with those based on flux-flow and even has someadvantages, such as smaller size and insensitivity to I inj ( i.e. , I CL in the case of flux-flow).This work was supported by the RFBR and the Min-istry of Education and Science of the Russian Federation(agreement 8641). REFERENCES B. Dueholm, O. A. Levring, J. Mygind, N. F. Pedersen,O. H. Soerensen, and M. Cirillo, Phys. Rev. Lett. ,1299 (1981). E. Joergensen, V. P. Koshelets, R. Monaco, J. Mygind,M. R. Samuelsen, and M. Salerno, Phys. Rev. Lett. , 1093 (1982). M. P. Soerensen, R. D. Parmentier, P. L. Christiansen,O. Skovgaard, B. Dueholm, E. Joergensen, V. P.Koshelets, O. A. Levring, R. Monaco, J. Mygind, N. F.Pedersen, and M. R. Samuelsen, Phys. Rev. B , 2640(1984). T. Nagatsuma, K. Enpuku, F. Irie, and K. Yoshida, J.Appl. Phys. , 3302 (1983). T. Nagatsuma, K. Enpuku, K. Yoshida, and F. Irie, J.Appl. Phys. , 3284 (1984). T. Nagatsuma, K. Enpuku, K. Sueoka, K. Yoshida,and F. Irie, J. Appl. Phys. , 441 (1985). V. P. Koshelets and S. V. Shitov, Supercond. Sci. Tech. , R53 (2000). V. Koshelets, A. Ermakov, L. Filippenko, A. Khud-chenko, O. Kiselev, A. Sobolev, M. Torgashin,P. Yagoubov, R. Hoogeveen, and W. Wild, IEEETrans. Appl. Supercond. , 336 (2007). A. V. Ustinov, Appl. Phys. Lett. , 3153 (2002). E. Goldobin, A. Sterck, T. Gaber, D. Koelle, andR. Kleiner, Phys. Rev. Lett. , 057005 (2004). J. H. Xu, J. H. Miller, and C. S. Ting, Phys. Rev. B , 11958 (1995). E. Goldobin, D. Koelle, and R. Kleiner, Phys. Rev. B , 100508(R) (2002). H. Hilgenkamp, Ariando, H.-J. H. Smilde, D. H. A.Blank, G. Rijnders, H. Rogalla, J. R. Kirtley, andC. C. Tsuei, Nature (London) , 50 (2003). H. Susanto, S. A. van Gils, T. P. P. Visser, Ariando,H.-J. H. Smilde, and H. Hilgenkamp, Phys. Rev. B ,104501 (2003). E. Goldobin, D. Koelle, and R. Kleiner, Phys. Rev. B , 224515 (2003), cond-mat/0209214. In some non-Lorenz invariant systems the Swihart ve-locity can be exceeded and one observes a Cherenkovradiation tail behind the fluxon . N. Stefanakis, Phys. Rev. B , 214524 (2002),nlin.ps/0205031. J. Pfeiffer, M. Kemmler, D. Koelle, R. Kleiner,E. Goldobin, M. Weides, A. K. Feofanov, J. Lisenfeld,and A. V. Ustinov, Phys. Rev. B , 214506 (2008),0801.3229. V. Koshelets, S. Kovtonyuk, I. L. Serpuchenko, L. Fil-ippenko, and A. Shchukin, IEEE Trans. Magn. ,3141 (1991). P. Dmitriev, I. Lapitskaya, L. Filippenko, A. Er-makov, S. Shitov, G. Prokopenko, S. Kovtonyuk, andV. Koshelets, IEEE Trans. Appl. Supercond. , 107(2003). T. Gaber, E. Goldobin, A. Sterck, R. Kleiner,D. Koelle, M. Siegel, and M. Neuhaus, Phys. Rev.B , 054522 (2005), cond-mat/0408214. P. K. Tien and J. P. Gordon, Phys. Rev. , 647(1963). V. P. Koshelets, S. V. Shitov, L. V. Filippenko, V. L.Vaks, J. Mygind, A. M. Baryshev, W. Luinge, andN. Whyborn, Rev. Sci. Instr. , 289 (2000). K. Kalashnikov, A. Khudchenko, A. Baryshev, andV. P. Koshelets, J. Comm. Tech. Electron. , 699707(2011), original Russian Text is published in “Ra-diotekhnika i Elektronika”, 2011, Vol. 56, No. 6, pp.751759. V. P. Koshelets, P. N. Dmitriev, A. B. Ermakov, A. S.Sobolev, A. M. Baryshev, P. R. Wesselius, and J. My-gind, Supercond. Sci. Tech. , 1040 (2001). E. Goldobin, A. Wallraff, and A. V. Ustinov, J. LowTemp. Phys.119