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Parametric and non-linear behaviour of a YBa2Cu3O7−δ RF squid at 77K
Physica C 153-155 (1988) 1407-1408 North-Holland, Amsterdam
PARAMETRIC AND NON-LINEAR BEHAVIOUR OF A YBa2Cu307_$
RF SQUID AT 77K
Gordon B. DONALDSON, Hilan ODEHNAL*, Colin H. PEGRI~4, John R. BUCKLEY Department of Physics and Applied Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, UK
We describe SQUID behaviour and the excitation of harmonics of the drive frequency (up to the 15th) in bulk pieces of YBa2Cu307_ ~. We have studied these effects under the influence of strong RF fields, (I-21HHz), microwave fields (9 and 90GHz), static magnetic fields (up to 40mT), between 77K and the critical temperature of the material. We give a tentative explanation of the observed effects in terms of both the highly non-linear and parametric behaviour of unbiased Josephson inductances and of non-hysteretic SQUID loops.
I. EXPERIMENTAL OBSERVATIONS
We report several new effects in bulk YBa2Cu307_$ samples of differing densities. The key feature of the experimental configuration, described in (1), is an RF drive coil which is separate from the coil of the resonant tank circuit, driven by a current Irf at a frequency frf, generally in the range 1 to 21MHz, but exceptionally up to 60HHz. The tank circuit is always tuned to a frequency fres, about 20HHz. This permits us to observe harmonic responses when frf = fres/n, with n = 2,3 ..... A tuned amplifier and detector measure the amplitude VT of the tank circuit RF voltage. Usually our samples were held at 77K in the Earth's magnetic field, and we studied the effects of varying: (a) the RF drive, using a supply with output power up to 2W (b) the static external magnetic field B X (0.1mT - to 40mT), and (c) microwave radiation, either at 9GHz, or at 80-110GHz ( t h e s a m p l e s w e r e positioned in front of simple horn antennae fed from 20mW and 30mW sources). I n some cases we also varied the temperature T from 77K up to the critical temperature T C. We divide the observed effects loosely into two classes - SQUID and parametric. The distinction is artificial, since the SQUID itself can be viewed as a parametric upconverter. I.i. SQUID effects We have proposed (I) that the grains in the material are interconnected by Josephson junctions in networks of loops, and it is this internal topology that gives rise to SQUID behaviour. The response (that is, the periodic variation of V T as the DC field is varied) is not fully 'triangular', as normally obtained with a conventional RF SQUID. The
signal-to-noise ratio (SNR) of the response is best with the tank circuit slightly detuned either side of the drive frequency, and its phase reverses on passing through resonance. The magnitude of the response also increases steadily as the RF drive level is increased over a wide range. All of these observations indicate clearly that the SQUID is operating in the non-hysteretic mode (2,3). In some very low-density samples, the SNR of the response is enhanced by up to 4 times for B X = 0. I to ImT. The SQUID response
can be decreased or suppressed by microwaves at 9GHz, but at 90Hz there is no effect, possibly due to capacitive shunting of the junctions in the sample, or due to the shorter skin depth at the higher frequency. The SNR of the SQUID response increases several times when frf = fres/n, with n = 2 , 3 , . . . . 15, compared w i t h t h e r e s p o n s e with drive at fres. The RF d r i v e voltage u n d e r t h e s e c o n d i t i o n s was t y p i c a l l y 20 t o 100 times greater than that used for direct drive at fres" 1.2. Parametric effects With harmonic drive (frf = fres/n, n : 2,3,...15), we could greatly enhance the mean value of VT, either by applying a large static field, or by varying T. In all cases VT still had a small periodic dependence on BX, that is, the sample still acted as a SQUID. We f o u n d t h a t : (a) VT grew i n a m p l i t u d e a s I r f was i n c r e a s e d f o r odd an__dde v e n h a r m o n i c d r i v e . (b) I n c r e a s i n g BX up t o 40mT c a u s e d t h e odd h a r m o n i c s t o b e e n h a n c e d i n a m p l i t u d e , i n some cases by up to 60 times. The even harmonics were not enhanced, but were slightly depressed.
* On leave from the Institute of Physics, Czechoslovak Academy of Sciences, HEZ,250 68,Czechoslovakia
0921-4534/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics PublishingDivision)
1408
G.B. Donaldson et al. / Parametric and non-linear behaviour
( c ) On i n c r e a s i n g T, t h e a m p l i t u d e o f t h e odd h a r m o n i c s ( w i t h I r f h e l d c o n s t a n t ) f i r s t decreased, before being greatly e n h a n c e d as T ~ TCFor T > TC, all these effects vanished. 2.
DISCUSSION
The e x p l a n a t i o n o f t h e b a s i c SQUID r e s p o n s e in terms o f the non-hysteretic mode of operation is well-documented (2,3) and will not be discussed in detail here, though we note in this mode, the SQUID behaviour should depend crucially on HF drive level, detuning and the static magnetic field, just as we observe. Our observation that a ImT field enhanced the SQUID response can also be explained in terms of the detailed interaction of a non-hysteretic SQUID and its tank circuit (2,3), given that the medium has a non-linear susceptibility (4). Also, a SQUID will always act as a harmonic generator, owing to its intrinsic nonlinearity, so our observation that we can drive our sample at fres/n (for n even or odd) is to be expected. Equally predicted is the behaviour in a microwave field: the critical currents of the junctions are suppressed and SQUID action c e a s e s . Of much greater interest is the observation of an improved SNR of the SQUID response with harmonic drive. Here we turn to a parametric description of the SQUID for a possible explanation. We believe two mechanisms contribute to the amplification. Firstly, under strong HF drive, the SQUID acts as a simple parametric amplifier. But in addition the sample acts an a SUPARAMP (Superconducting Unbiased Parametric Amplifier), which has been discussed recently (5,6). The 'pump' frequency is frf, and the upper and lower sidebands of n(frf) are the 'signal' and 'idler.' This dual-amplification mechanism is discussed in detail in (5,6). We believe the observations listed in 1.2 are due to two competing processes within the material. These can be distinguished by the order of the harmonics they produce, and by their field and tamperature dependences. The first is due to the fundamental Josephson non-linear (or parametric) inductance of junctions in the material. An RF current induced in non-superconducting loops containing one or more junctions (which have zero DC bias) causes an RF voltage to appear across the Josephson inductance. We have Fourier analysed the expression for this voltage, and find that it contains only odd harmonics (see also Ref 2, p95). Their magnitude depends strongly on the ratio a : Irf/Ic(BX,T), where I c is the critical current. When a~l,there is a very strong enhancement of these odd Fourier components, which are detected by the tank circuit. We believe that with our normal level of RF drive
a
PARAMETRIC AND NON-LINEAR BEHAVIOUR OF A YBa2Cu307_$
RF SQUID AT 77K
Gordon B. DONALDSON, Hilan ODEHNAL*, Colin H. PEGRI~4, John R. BUCKLEY Department of Physics and Applied Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, UK
We describe SQUID behaviour and the excitation of harmonics of the drive frequency (up to the 15th) in bulk pieces of YBa2Cu307_ ~. We have studied these effects under the influence of strong RF fields, (I-21HHz), microwave fields (9 and 90GHz), static magnetic fields (up to 40mT), between 77K and the critical temperature of the material. We give a tentative explanation of the observed effects in terms of both the highly non-linear and parametric behaviour of unbiased Josephson inductances and of non-hysteretic SQUID loops.
I. EXPERIMENTAL OBSERVATIONS
We report several new effects in bulk YBa2Cu307_$ samples of differing densities. The key feature of the experimental configuration, described in (1), is an RF drive coil which is separate from the coil of the resonant tank circuit, driven by a current Irf at a frequency frf, generally in the range 1 to 21MHz, but exceptionally up to 60HHz. The tank circuit is always tuned to a frequency fres, about 20HHz. This permits us to observe harmonic responses when frf = fres/n, with n = 2,3 ..... A tuned amplifier and detector measure the amplitude VT of the tank circuit RF voltage. Usually our samples were held at 77K in the Earth's magnetic field, and we studied the effects of varying: (a) the RF drive, using a supply with output power up to 2W (b) the static external magnetic field B X (0.1mT - to 40mT), and (c) microwave radiation, either at 9GHz, or at 80-110GHz ( t h e s a m p l e s w e r e positioned in front of simple horn antennae fed from 20mW and 30mW sources). I n some cases we also varied the temperature T from 77K up to the critical temperature T C. We divide the observed effects loosely into two classes - SQUID and parametric. The distinction is artificial, since the SQUID itself can be viewed as a parametric upconverter. I.i. SQUID effects We have proposed (I) that the grains in the material are interconnected by Josephson junctions in networks of loops, and it is this internal topology that gives rise to SQUID behaviour. The response (that is, the periodic variation of V T as the DC field is varied) is not fully 'triangular', as normally obtained with a conventional RF SQUID. The
signal-to-noise ratio (SNR) of the response is best with the tank circuit slightly detuned either side of the drive frequency, and its phase reverses on passing through resonance. The magnitude of the response also increases steadily as the RF drive level is increased over a wide range. All of these observations indicate clearly that the SQUID is operating in the non-hysteretic mode (2,3). In some very low-density samples, the SNR of the response is enhanced by up to 4 times for B X = 0. I to ImT. The SQUID response
can be decreased or suppressed by microwaves at 9GHz, but at 90Hz there is no effect, possibly due to capacitive shunting of the junctions in the sample, or due to the shorter skin depth at the higher frequency. The SNR of the SQUID response increases several times when frf = fres/n, with n = 2 , 3 , . . . . 15, compared w i t h t h e r e s p o n s e with drive at fres. The RF d r i v e voltage u n d e r t h e s e c o n d i t i o n s was t y p i c a l l y 20 t o 100 times greater than that used for direct drive at fres" 1.2. Parametric effects With harmonic drive (frf = fres/n, n : 2,3,...15), we could greatly enhance the mean value of VT, either by applying a large static field, or by varying T. In all cases VT still had a small periodic dependence on BX, that is, the sample still acted as a SQUID. We f o u n d t h a t : (a) VT grew i n a m p l i t u d e a s I r f was i n c r e a s e d f o r odd an__dde v e n h a r m o n i c d r i v e . (b) I n c r e a s i n g BX up t o 40mT c a u s e d t h e odd h a r m o n i c s t o b e e n h a n c e d i n a m p l i t u d e , i n some cases by up to 60 times. The even harmonics were not enhanced, but were slightly depressed.
* On leave from the Institute of Physics, Czechoslovak Academy of Sciences, HEZ,250 68,Czechoslovakia
0921-4534/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics PublishingDivision)
1408
G.B. Donaldson et al. / Parametric and non-linear behaviour
( c ) On i n c r e a s i n g T, t h e a m p l i t u d e o f t h e odd h a r m o n i c s ( w i t h I r f h e l d c o n s t a n t ) f i r s t decreased, before being greatly e n h a n c e d as T ~ TCFor T > TC, all these effects vanished. 2.
DISCUSSION
The e x p l a n a t i o n o f t h e b a s i c SQUID r e s p o n s e in terms o f the non-hysteretic mode of operation is well-documented (2,3) and will not be discussed in detail here, though we note in this mode, the SQUID behaviour should depend crucially on HF drive level, detuning and the static magnetic field, just as we observe. Our observation that a ImT field enhanced the SQUID response can also be explained in terms of the detailed interaction of a non-hysteretic SQUID and its tank circuit (2,3), given that the medium has a non-linear susceptibility (4). Also, a SQUID will always act as a harmonic generator, owing to its intrinsic nonlinearity, so our observation that we can drive our sample at fres/n (for n even or odd) is to be expected. Equally predicted is the behaviour in a microwave field: the critical currents of the junctions are suppressed and SQUID action c e a s e s . Of much greater interest is the observation of an improved SNR of the SQUID response with harmonic drive. Here we turn to a parametric description of the SQUID for a possible explanation. We believe two mechanisms contribute to the amplification. Firstly, under strong HF drive, the SQUID acts as a simple parametric amplifier. But in addition the sample acts an a SUPARAMP (Superconducting Unbiased Parametric Amplifier), which has been discussed recently (5,6). The 'pump' frequency is frf, and the upper and lower sidebands of n(frf) are the 'signal' and 'idler.' This dual-amplification mechanism is discussed in detail in (5,6). We believe the observations listed in 1.2 are due to two competing processes within the material. These can be distinguished by the order of the harmonics they produce, and by their field and tamperature dependences. The first is due to the fundamental Josephson non-linear (or parametric) inductance of junctions in the material. An RF current induced in non-superconducting loops containing one or more junctions (which have zero DC bias) causes an RF voltage to appear across the Josephson inductance. We have Fourier analysed the expression for this voltage, and find that it contains only odd harmonics (see also Ref 2, p95). Their magnitude depends strongly on the ratio a : Irf/Ic(BX,T), where I c is the critical current. When a~l,there is a very strong enhancement of these odd Fourier components, which are detected by the tank circuit. We believe that with our normal level of RF drive
a