Laser switch for stroboscopic read-out of magnetic flux

Transcription

1 REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 75, NUMBER 6 JUNE 2004 Laser switch for stroboscopic read-out of magnetic flux Marco Ferrara a) Università di L Aquila, Monteluco di Roio, L Aquila, Italy Pasquale Carelli b) INFM and Università di L Aquila, L Aquila, Italy Fabio Chiarello, Maria Gabriella Castellano, and Guido Torrioli IFN, Istituto di Fotonica e Nanotecnologie, CNR, Roma, Italy Carlo Cosmelli Università La Sapienza, Roma, Italy Received 27 October 2003; accepted 30 March 2004; published online 24 May 2004 We have realized and tested a fast stroboscopic detector for magnetic flux measurements. The key element of our detector is a hysteretic dc superconducting quantum interference device SQUID. Stroboscopic read-out of the magnetic flux coupled with the SQUID is accomplished by biasing the SQUID with fast current pulses. The shorter these pulses, the more stroboscopic and less invasive the measurement we are performing. In order to reduce the duration of the current pulses, we take advantage of the superconducting-normal transition induced by laser light in thin superconducting films. The interaction of laser light with superconducting thin films has been investigated thoroughly in the past and many applications have been proposed which rely on the fast typical times with which superconductivity is broken and a resistive behavior arises. We have measured a threshold resolution of 6.9m 0 at 4.2 K, and this value corresponds to the thermodynamic limit of the SQUID. The detector has been accurately characterized: An improved and more sensitive version might prove useful for quantum mechanics and quantum computation experiments, for example, in detecting the state of flux qubits American Institute of Physics. DOI: / I. INTRODUCTION Superconducting quantum interference devices SQUIDs are a valuable benchmark for macroscopic quantum coherence experiments, 1,2 as well as attractive candidates for quantum computation QC solid state devices. A number of different implementations for solid state QC have been proposed which rely on the quantization of the charge or of the flux occurring in superconducting devices under particular conditions. Charge, flux, and hybrid charge-flux qubits have been demonstrated, and Rabi oscillations have been measured. 3 7 In the particular case of flux qubits based on macroscopic SQUIDs, the quantization of energy levels and other quantum mechanical properties have been verified, but Rabi oscillations have not been measured so far, although an experimental evidence has already been reported. 8 In this article, we present a stroboscopic read-out system for the magnetic flux. The flux could represent the state of a flux qubit. Our read-out system follows the general principle elsewhere proposed: 9 a hysteretic dc SQUID is used as a threshold detector of the magnetic flux coupled with it. The stroboscopic read-out is accomplished by biasing the SQUID with fast current pulses. The significance of our work is that we can generate these pulses directly on the chip by exploiting the fast superconducting-normal SN transition which a thin superconducting film experiences when it is illuminated a Electronic mail: mferrara@ing.univaq.it b Electronic mail: carelli@ing.univaq.it by a laser beam. This technique has some significant advantages over traditional implementations, which use current pulses generated at room temperature and sent to the SQUID through transmission lines: The intrinsic response of the SN transition is very fast and very fast light modulators are available, thus very short current pulses can be generated and real stroboscopic read-out can be accomplished. Furthermore, a great deal of optical fibers, suitable to guide the light to the chip, which is located in a cryogenic chamber, is commercially available. These fibers induce low distortion and dispersion on the light pulses traveling across them. Finally, as the current pulses are generated on the chip, the bias current can be heavily filtered from noise and interference. The arguments are organized as follows. Section II introduces the main features of SN transition and reports on the measurements we performed on a thin Nb film patterned as a small meander. This meander is a part of our detector. Section III analyzes the theory of stroboscopic detection through dc SQUIDs and its fundamental limits. This section discusses also our particular implementation and its advantages over conventional methods. Finally, Sec. IV reports on the experimental characterization of the detector and the drawbacks of the laser switching technique. II. LIGHT INDUCED SUPERCONDUCTING-NORMAL TRANSITION The investigation of the interaction of laser light with superconductivity in thin films started with an experiment by /2004/75(6)/2116/6/$ American Institute of Physics

2 Rev. Sci. Instrum., Vol. 75, No. 6, June 2004 Laser switch for stroboscopic flux 2117 FIG. 1. A thin Nb film is patterned to form a small meander and is illuminated by laser light. The superconductor becomes resistive with a fast transition time. The figure shows the experimental setup used to illuminate the meander and measure its resistance. A picture of the real meander is shown in the inset. Testardi, 10 who found that superconductivity is destroyed by laser light in Pb films of thickness comparable to the optical penetration depth and less than the superconducting coherence length; this phenomenon is very fast and experimental observations cannot be explained by thermal effects only. Theoretical models have been proposed in which an effective chemical potential * is introduced to account for the excess of quasiparticles 11 or a modified heating model is elaborated 12 in which Rothwarf and Taylor equations 13 are combined with Debye phonon distribution to give an equivalent temperature T* for the irradiated sample. In both cases the properties of the superconductor are described by usual Bardeen Cooper Schieffer theory with the parameters mentioned above appropriately determined as a function of the power of the laser light, i.e., the excess of quasiparticles. Both the model by Owen and Scalapino 11 and the model by Parker 12 are in excellent agreement with experimental results on irradiated tunnel junctions and microwave reflectivity of illuminated thin films In the context of this article we are not interested in analyzing the details and microscopic explanation of such a transition. Rather, the main macroscopic and phenomenological features of light-induced superconductive-normal SN transition in Nb thin films are essential to the functionality of our device. These features, which have been extensively reported in literature, are 1 Fast transition times, due to the fast characteristic times of Cooper pairs and quasiparticles dynamics, which are in the range of 1 ns or below. 2 SN transition appears above a threshold, that is an appropriate value of the light intensity, which is usually a few tenths of W/ m 2 for Nb films of a few nanometers thickness. 3 Resistance value reaches a plateau above a certain light intensity; the plateau is about the resistance value at the transition temperature T c. The threshold intensity is influenced by the film thickness, as expected from a simple model which assumes that a certain minimal amount of energy has to be transferred to each elementary volume of the film and that the light undergoes some attenuation while traveling across it. In order to reduce the threshold power, and, thus, the operating power, the film must be thin. In our particular case, the sample consists of a 15 nm thick Nb film patterned to form a small meander. In order to reduce the effects of the noise of the laser light and increase the signal-to-noise ratio the film must always be switched between zero resistance and saturated resistance states. 4 The film, when switched into the normal state, has a noise temperature which is well above the temperature of the thermal bath. Actually, the film is strongly energized by the incoming photon flux. Some of these characteristics are ideal to build a fast current switch from a superconducting thin film. In our experimental setup Fig. 1 a 15 nm thick Nb film is patterned through electron beam direct writing to form a meander consisting of seven strips, each 1 m wide and 20 m long, connected in series. The meander fills a square with 20 m side. The contacts and the pads are much larger than the meander strips, in order to make their contribution to resistance negligible. We used a four terminal setup for resistance measurements. Three different bias currents have been used, namely, 5, 10, and 50 A, and the similarity of the experimental results obtained proves that the bias current is not a critical parameter within this range. A small cylindrical holder made of Plexiglas is glued on the top of the chip, 17 with a thin Mylar film under it, in order to protect the film. The holder s dimensions are about 2 mm diameter and 1.5 mm height; a small hole is drilled at its center and the hole s diameter is about 170 m, such that the optical fiber can be inserted in it. Particular care has been paid in the meanderholder alignment and in the symmetry of the holder design and of its bonding to the chip. In fact, these are key factors in guaranteeing that meander-fiber alignment will be preserved also at cryogenic temperatures. The precise alignment, together with the small meander dimensions, if compared with the core of the optical fiber m, assures that the meander will be completely irradiated. On its turn, the complete illumination of the meander is a prerequisite to reach a plateau value of the resistance and to be less sensitive to mechanical noise which causes the fiber to oscillate with respect to the meander. The laser is a solid state laser diode with 830 nm and maximum output power 150 mw 19 and calibration data at the output of the optical fiber have been taken after resistance measurements. Meander resistance versus laser power for three different values of the bias current is reported in Fig. 2. Many different applications of laser switching have already been demonstrated. Perturbations induced by laser light can be used to measure quasiparticles lifetime, 20 the correlation of flux states of superconducting circuits, 21 the absolute magnetic penetration depth in Nb thin films, 22 and to demonstrate the absolute magnetic flux quantization in superconducting circuits. 23 At a less fundamental level, laser switching has been used to chop the input of a SQUID amplifier for low frequency noise reduction 24,25 as well as in other electronic devices for specific applications.

3 2118 Rev. Sci. Instrum., Vol. 75, No. 6, June 2004 Ferrara et al. Stroboscopic measurements are made by reading the physical quantity of interest for a very short time. Thus, a stroboscopic measurement is a sampling procedure of a certain physical quantity. An interesting feature is that the detector is off most of the time, which may prove useful in many experiments of quantum mechanics. Furthermore, in many cases we are more interested in determining whether the physical quantity of interest, in our case the magnetic flux, is above or below a certain threshold than to measure it exactly. These two motivations led us to the realization of a threshold flux detector and the implementation of a stroboscopic read-out procedure for it. The main element of our detector is a dc SQUID magnetometer used as a threshold detector. A dc SQUID is a superconducting ring interrupted by two identical Josephson junctions. A useful quantity is the reduced inductance parameter L I c L/ 0, where I c is the critical current of the SQUID, L is the inductance of the SQUID ring, and 0 is the flux quantum h/2e. When L is much smaller than one, the current-voltage characteristic becomes that of a Josephson junction, but with a tunable critical current 28,29 Eq. 1. Figure 3 shows the characteristic of the SQUID used in our detector, which was designed and realized at the IFN labs in Rome. The critical current I c, the gap voltage V g, and the retrapping current I t are indicated. When the SQUID bias current is swept above I c and then back to zero, the hysteretic cycle in Fig. 3 is drawn. The critical current depends on the flux coupled with the SQUID FIG. 2. Meander resistance vs laser power. The similarity of the experimental results obtained with three different bias currents proves that the bias current is not a critical parameter within our range of operation. III. LASER SWITCH FOR STROBOSCOPIC READ-OUT OF THE MAGNETIC FLUX FIG. 3. Current-voltage characteristic of the dc SQUID used in the detector. I c 2I cjj cos SQUID. 1 0 Here, I cjj is the critical current of a single Josephson junction and SQUID is the flux coupled with the SQUID. A dc SQUID is ideal for stroboscopic read-out of magnetic flux. When a current pulse biases the SQUID, the voltage across it jumps at the gap value V g according to the magnetic flux in the SQUID loop; in particular, assuming that I max is the amplitude of the current pulse, V out remains zero, if I max I c, or jumps at the gap, if I max I c. As far as the noise is considered, which is due to the internal dissipation of Josephson junctions and the noise on external biases and signals, thermal phase activation can induce spurious voltage jumps even for I max I c, and the flux resolution of the detector is consequently reduced. This leads to a probability of activation which is exponentially distributed, that is the probability density function associated with the event of an activation within t and t dt is given by p t exp t, 2 where is the activation rate and contains information about the current flowing though the SQUID, the critical current I c, the total noise and the microscopic damping parameter, which also determines the phase activation speed. If a stroboscopic current pulse is applied which can be approximated by a step function of amplitude I max and duration T, we can simply write P activation p t dt 1 exp T, 3 0 where I N, SQUID,I max 4 and I N is the total equivalent noise current through the SQUID. The typical shape of probability curves versus SQUID resembles an S. The flux interval between the points at 10% and 90% of the probability curves is an indication of the goodness and resolution of our flux threshold detector. In order to maximize this resolution, we have to 1 Reduce all external noise sources; 2 Reduce ripples and distortions on the read-out current pulses; 3 Possibly work with the external bias flux in a region where probability curves become narrower. In fact, probability curves width depends also on the working range of SQUID. In this respect, laser switching may provide some significant advantages over traditional stroboscopic read-out techniques, which use current pulses generated at room temperature and sent to probe the SQUID: 1 The light pulses have no significant ripples and can be transmitted to the meander through an optical fiber, without significant distortion, losses, or electromagnetic coupling;

4 Rev. Sci. Instrum., Vol. 75, No. 6, June 2004 Laser switch for stroboscopic flux The residual noise on the laser light, mainly due to mechanical noise and mode mixing, is not influent if the laser power is sufficient to saturate the meander resistance; 3 The current pulses are generated on the chip and do not have to be transmitted through a waveguide. Furthermore, the current read-out pulses generated by laser switching can be made very short, because of the time duration of the light pulses below 1 ns with state of the art Mach Zender modulators, and the mechanism by which superconductivity is broken, which is very fast characteristic times below 1 ns. This feature may permit real stroboscopic measurements and prove useful for experiments of quantum mechanics. The influence of the time duration of the read-out pulses on the resolution of the detector deserves some consideration. When the read-out pulses become very short, that is comparable with 1/ 10 ps to 1 ns, where is the damping parameter in the equation which describes the phase dynamics of a Josephson junction, the statistics of activation changes significantly and the exponential distribution cannot be adopted. When T 1/ and the exponential distribution is correct, an optimum range of values for T can be found in order to maximize the resolution of the detector. The values 10 and 90 corresponding to the activation probabilities 10% and 90% are given by / T, / T, where and The corresponding fluxes 10 and 90 can be calculated using the Kramers formula, 27 which was derived in the case of thermal escape from a deep well, but works fairly well to study the thermal activation of the phase in Josephson junctions and dc SQUIDs K b 2 exp U kt. Here, U is the potential barrier height, is the damping parameter, and b is the frequency of the small oscillations in the well. K( ) depends on the value of the damping parameter. In the case of small barrier height, that is I b I c, one can approximate b J 2 1/4 1 1/4, 5 6 FIG. 4. Activation rate as a function of I b /I c, where I b is the bias current of the SQUID and I c is the critical current of the SQUID. The parameter of the curves is the bias current I b. From the uppermost curve I b 8; 7.5; 7; 6.5; 6; 5.5; 5; 4.5 A. where 90 / T is much smaller than the value of Eq. 5 at the inflection point, one can determine 10 and 90 as a function of the read-out pulse duration and 10 and 90, from Eq. 1. The behavior of the flux resolution with the duration of the read-out pulses depends strongly on the equivalent temperature and the working point, that is the current I b. In general, resolution increases when the bias current is smaller this is easily understood, as we move to a region of Eq. 1 where the slope I c / SQUID is higher but, in this condition, the smaller T, the higher. The complete schematic of our stroboscopic flux detector is illustrated in Fig. 5. A stray resistance R stray is shown. On the branch in parallel with the meander a resistance R 0 andadc SQUID are mounted. When no light impinges on the meander, it is superconducting and all the bias current flows across it. When a light pulse impinges on the meander, this changes its state into resistive, the SQUID is biased by a current pulse, and, according to the magnetic flux in the SQUID loop, V out switches or does not. The bias current I b is constant and the current read-out pulses are generated on the U E J /2, 7 where I b /I c, E J 0 I c /2, and J 2 I c /C 0. In order to have an idea of the problem, we can assume some reasonable values, such as C 0.5 pf, I cjj 5 A, K( ) 1. The activation rate is plotted in Fig. 4 as a function of I b /I c, for different values of the bias current I b. Only the first portion of the curve represented by Eq. 5 is physically meaningful: Here, the model of thermal activation from a well is a good approximation. A discriminating point is the inflection point. By solving the equations 10 T b T b 90 2 exp U 10 kt, 8 exp U 90 kt, 9 FIG. 5. Schematic of the laser switch detector. When a light pulse impinges on the meander, this becomes resistive and the current is deviated through the SQUID. Current pulses are used to accomplish stroboscopic readouts of the magnetic flux coupled with the SQUID.

5 2120 Rev. Sci. Instrum., Vol. 75, No. 6, June 2004 Ferrara et al. FIG. 6. The experimental setup used to characterize our stroboscopic detector. chip and are modulated by light pulses. An acusto-optic modulator has been used, whose characteristic rise and fall times are in the range of a few tens of ns. 26 This particular device makes use of the acoustic waves excited on the surface of a piezoceramic to modulate the index of refraction of the surrounding medium usually air and induce a first-order diffracted beam which can be focused and collected by an optical fiber. The first-order beam can be switched on and off with the rise and fall times of the acoustic waves on the piezoceramic, and these times are usually quite fast. The maximum laser diode output power is 150 mw at 830 nm wavelength, 19 the optical fiber is a large numerical aperture multimode fiber with a core diameter of about 100 m. 18 For the switch proper functioning, the meander off resistance and the stray resistance have to be much smaller than the fixed resistance R 0, while the meander on resistance has to be much bigger than R 0. We chose R 0 100, as R stray 1, and R meander 2k while on. IV. DETECTOR CHARACTERIZATION FIG. 7. Probability of activation as a function of the flux coupled with the SQUID, when I b 4.5 A and T 2 s a ; 6 s b ; 13 s c ; and 19 s d. The complete experimental setup for the characterization of the stroboscopic detector is illustrated in Fig. 6. The bias current I b is set through a low noise current generator and the flux SQUID is controlled via computer through a test coil: The flux can be swept using different slopes and shapes. The fast voltage signals across the SQUID are collected through 50 cryogenic coaxial cables, sent to a fast differential amplifier and then recorded and visualized on a fast digital oscilloscope. We are interested in measuring the probability of activation, as a function of the flux coupled with the SQUID, and estimating the flux resolution of our detector. In order to do this, we set a value for the flux SQUTD and pulse the laser light at a repetition rate of 10 khz. Each laser pulse has a duration of 20 s. Then we sample the voltage across the SQUID after a certain delay T from the rising edge of the laser pulse. For each value of the flux we measure the voltage across the SQUID i.e., if the SQUID has been activated or not many times such that we can reconstruct the activation probability as a function of SQUID. We repeat this procedure for different values of the time delay T. Figure 7 shows experimental probability curves, measured with I b 4.5 A. This current is much smaller than the maximum critical current of our SQUID 2I cjj 8.8 A, thus we expect that the threshold resolution decreases when T increases: experimental results confirm this expectation, as Fig. 8 shows. The flux SQUID has been calculated from the external flux control current I flux by the formula SQUID MI flux offset, where M and offset can be determined from the periodic trend of multiple probability curves. These are obtained by sweeping the flux coupled with the SQUID by more than a flux quantum 0 and measuring the activation probability for each point. The best threshold resolution of our detector is 6.9m 0 at the temperature of 4.2 K and has been measured with T 19 s. This result is aligned with FIG. 8. Flux resolution as a function of the duration of the read-out pulses T. The dashed line is a guide for the eye.

6 Rev. Sci. Instrum., Vol. 75, No. 6, June 2004 Laser switch for stroboscopic flux 2121 the best results obtained by conventional stroboscopic readout techniques 30 and corresponds to the thermodynamic limit of the SQUID. Further work is due in order to fully exploit the advantages of laser switching for stroboscopic read-out. An important improvement is the use of fast modulators and electronics to test the SQUID with very short current pulses 100 hs. Coming to the drawbacks, there are three main disadvantages with our experimental results. The first is the difficulty in mounting and aligning the optical fiber, especially when the objects to be illuminated are very small. In addition, the fiber holder is quite large and space-consuming if compared with the characteristic features of integrated circuits. Second, a significant amount of laser power has to be carried to the film, with power densities in the range of a few tenths of W/ m 2 for Nb films of a few nanometers thickness. In order to reduce the total power sent to the cryogenic chamber and make laser switching technology compatible with dilution refrigerators, the light must be focused on very small features, thus the use of very small lenses is necessary and an even more stringent problem of mechanical alignment arises. However, some of these problems might be overcome by the use of micromachining techniques to build fiber holders integrated on the chip. Finally, particular care must be paid in reducing the effects of the noise of the meander, when it is made resistive by laser irradiation. In general, the condition (T meander /T SQUID ) (R SQUID /R meander ) 1 must be met, where T meander is the equivalent temperature of the irradiated meander, T SQUID is the temperature of the SQUID resistance, R meander and R SQUID are the corresponding resistances. This can be accomplished by making the value of R meander at T c very big, that is by patterning very thin strips: we found that our value R meander 2k is sufficient to suppress the effects of the noise of the meander resistance. V. DISCUSSION We fabricated and tested a threshold detector for the magnetic flux and reached a threshold resolution of 6.9m 0 at 4.2 K. The detector is based on a dc SQUID, which is read by stroboscopic current pulses. The technique used to feed the SQUID with fast current pulses is based on the superconducting-normal transition which occurs in superconducting thin films, when they are illuminated by laser light. This technique allows us to generate fast current pulses directly on the chip and may take advantage of the fast optical technologies already available on the market in order to perform real stroboscopic measurements, which may prove useful for quantum mechanics and quantum computation experiments, for example in detecting the state of flux qubits. Further improvements of our detector are necessary, in terms of flux resolution and read-out speed, in order to exploit the advantages which laser switching presents over conventional fast stroboscopic read-out techniques: low distortion, no electromagnetic coupling, very fast switching i.e., real stroboscopic measurements, and very low thermal conductivity of silica fibers. ACKNOWLEDGMENTS The authors kindly acknowledge Daniela Simeone, Elia Palange, and Eugenio Del Re for their useful advice and precious help. We also acknowledge Cristian Antonelli for helpful discussions on the theoretical model for flux resolution. This work has been partially funded by MIUR Cofin 2001, Dispositivi metallici a singolo elettrone. 1 A. J. Legget and A. Garg, Phys. Rev. Lett. 54, P. Carelli, M. G. Castellano, F. Chiarello, C. Cosmelli, R. Leoni, and G. Torrioli, IEEE Appl. Sup. 11, Y. A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura, D. V. Averin, and J. S. Tsai, Nature London 423, I. Chiorescu, Y. 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