DE19840071A1 - Shapiro step SQUID - Google Patents

Abstract

The invention relates to a dc-SQUID comprising two Josephson junctions, whereby means for operating the SQUID are provided in the area inside the first Shapiro step. In this manner, a SQUID is obtained which is much more sensitive in comparison to conventional SQUID's.

Description

The invention relates to a Shapiro step SQUID for measuring egg magnetic field or a magnetic flux.

As the prior art, superconducting quantum interference is De tectors (SQUIDs) known, their mode of action on the non-li proximity of Josephson contacts (JK) is based. It is about extremely sensitive detectors for magnetic fields or for magnetic flux. Because of their compared to other sensors superior sensitivity when measuring magnetic fields or magnetic flux at low frequencies (up to a few kHz), SQUIDs are used in many applications. The the The most promising applications are in the areas Biomagnetism (measurement of brain and heart activity), destroy maintenance-free material testing (e.g. detection of corrosion or Cracks in aircraft fuselages or magnetic inclusions in Turbine wheels), and geology (e.g. search for minerals).

The scientific work of many research groups targeted the improvement in SQUID sensitivity and led to the Development of different types of SQUIDs. The most famous Types include rf-SQUIDs, dc-SQUIDs (with two Josephson- Contacts), double (D) rf SQUIDs and relaxation oscillation SQUIDs. After the discovery of high temperature superconductivity (HTS) in 1986 sensitive HTS SQUIDs were also developed celt. The advantages of HTS-SQUIDs over low-temperature SQUIDs due to the use at considerably higher operating temperatures opened new perspectives for the use of SQUIDs in practical applications.  

The well-known HTSL dc-SQUIDs with two Josephson contacts show a limited sensitivity at the temperature T = 77K, im Range around, for example, three to four orders of magnitude from the Quantum boundary removed.

It is therefore an object of the invention a dc-SQUID with two Jo provide sephson contacts with increased sensitivity.

The task is solved by a dc-SQUID with two Josephson Contacts according to the entirety of the features according to claim 1. Find further expedient or advantageous embodiments itself in the on claim 1 indirectly or directly related subclaims.

The dc-SQUID according to the invention with two Josephson contacts has Means for applying a microwave current for operation in the Be get up within a single Shapiro level. They are Sha piro levels known as such. However, it was surprisingly ge found such Shapiro stages advantageous for operating a DC Use SQUIDs. In this way, the sensitivity of the dc-SQUID significantly increased. For example, in this Wei se for sensitivity in flow or field measurements Factor 10 to 100 can be increased. While the well-known HTSL SQUIDs at 77K still about three orders of magnitude from the quan are removed, you can with the fiction dc-SQUID at the same temperature, for example up to get one or two orders of magnitude to this limit.

According to claim 2, an embodiment of the Invention according to dc-SQUIDs means for applying a microwave current for Operating within the first Shapiro stage, which is particularly pronounced and therefore sensitive particularly favored by the SQUID.  

According to claim 3, the dc-SQUID advantageously has an Am plitude of the microwave current or a microwave power, at which the selected Shapiro level is maximal.

According to claim 4, a dc-SQUID with a microwave frequency ν in the range from 2 to 5 ν _{c is} proposed to optimize the operating mode.

The invention is further based on figures and Ausfüh tion examples explained in more detail. It shows:

Fig. 1: I-V characteristics of a Shapiro be on the first-stage exaggerated SQUIDs according to the invention for three different Flußstärken: nΦ _{ο, ^1/2} (2n + 1) and _{ο Φ ^1/4} (2n + 1) Φ _ο

Fig. 2: Comparison of the transfer function for a SEN according to the invention Type of Shapiro-stage SQUID and a common dc SQUID as a function of the normalized SQUID inductance;

Fig. 3: Comparison of the energy resolution according to the invention for a SEN type Shapiro-stage SQUID and a common dc SQUID as a function of the normalized SQUID inductance;

Embodiment

In Fig. 1, the IV characteristics are one operated on the first Sha piro-stage SQUIDs according to the invention for three ver different Flußstärken: _ο nΦ, _^1/2 (2n + 1) _ο Φ and _^1/4 (2n + 1) Φ _ο shown. The current I is standardized to 2 (ν / ν _c ) I _c and the voltage to νΦ _ο .

In FIG. 2, the comparison of the transfer function for an inventive type of Shapiro-stage SQUID and a Get used union dc SQUID as a function of the normalized SQUID inductance is shown. The transfer function is normalized to πI _c R / Φ ₀ .

In Fig. 3 the comparison of the energy resolution of an inventive type of Shapiro-stage SQUID and a Get used union dc SQUID as a function of the normalized SQUID inductance is shown. These data are shown for the temperature T = 77K.

It was recognized in the context of the invention, a known ten SQUID more sensitive component for the measurement of small to provide the most magnetic fields or magnetic flux. in the This SQUID according to the invention is also called "shapiro Stage SQUID "or" Shapiro SQUID ".

As with all known SQUID types, the radio is based Principle of the Shapiro level SQUID on the non-linearity of the Josephson contacts. However, the occurrence was recognized to use such a Shapiro level to operate the SQUID. There at should with appropriate means, the operation of such a Sha piro level SQUID in the area of only one Shapiro level respectively. The choice of the first Shapi is very advantageous ro stage for operating the SQUID according to the invention.

It is known that the current-voltage characteristic of a Josephson contact operated with a direct current I when a microwave current I is applied has _mw stages of constant voltage, so-called Shapiro stages. This also applies to two identical contacts connected in parallel, including the dc-SQUID. The two Josephson contacts can advantageously be identical and arranged symmetrically in the SQUID ring with an inductor L.

These Shapiro steps are based on the ac Josephson effect and occur at voltages V that are given by V _n = nνΦ ₀ . Here n is an integer and indicates the stage number, ν is the frequency of the irradiated microwave and Φ ₀ is the flux quantum. The shape, in particular the sharpness, of the Shapiro stages is modulated by the low-frequency, applied flux Φ _x to be measured and by the microwave power.

It was recognized within the scope of the invention to operate the SQUID in the Shapiro stage SQUID according to the invention with a direct current (dc current) I on the first (n = 1) Shapiro stage (bias level in FIG. 1). However, it is also conceivable to operate the SQUID according to the invention on one of the next Shapiro stages. The microwave frequency ν should be above the so-called characteristic frequency of the Josephson contacts, typically in the order of a few gigahertz (GHz) to over 100 GHz, for example in the range from 1 to 150 GHz, although other values are also conceivable. The microwave power or the amplitude of the microwave current I _mw should be selected so that the respective Shapiro stage intended for operation, preferably the first (n = 1) Shapiro stage, becomes maximum. Since the structure of the Shapiro stage depends on a variation of the low-frequency, applied flow to be measured, it is possible to define different transfer functions for this SQUID type. Thermal noise generated in the Josephson contacts also influences the structure of the Shapiro steps. The influence of thermal noise on the operation of a Shapiro stage SQUID is explained in more detail below.

It is well known that thermal noise has a decisive influence on the value of the voltage transfer function of a SQUID. The larger the value for L / L _F , the more the transfer function decreases. Here L is the SQUID inductance, L _F = (Φ ₀ / 2π) ² / k _B T is the so-called thermal limit inductance, k _B is the Boltzmann constant and T is the absolute temperature. At T = 77 Kelvin, L _F = 100pH. However, a higher SQUID inductance enables better flux coupling into the SQUID, which is crucial for the measurement of magnetic fields.

For these reasons, an optimization with respect to L is required. For an ordinary dc-SQUID, this problem has been analyzed in detail, and it has been found that, for the operation of an optimal system, the dc-SQUID inductance should preferably not be above 1 L _F to 1.5 L _F .

In the following this problem is within the scope of the invention Shapiro step SQUID according to the invention explained.

The analysis was based on a rigorous and powerful method, the so-called Fokker-Plank approach. This approach is appropriate when thermal fluctuations are important. On this basis, the time-averaged voltage V was calculated taking into account the influence of thermal fluctuations. The voltage transfer function is obtained by forming the derivative ∂V / ∂Φ _{x of} the voltage V after the applied flux Φ _x to be measured. The comparison with an optimal known dc-SQUID, the values of which are shown as a broken line in FIG. 2, shows that an optimal Shapiro step SQUID (solid line in FIG. 2) has a better voltage transfer function ( on average about ten times higher). This applies to inductors in a range of values of practical interest, i.e. 0.5L _F <L <3L _F , or 50 pH <L <300 pH.

It is well known that the energy resolution ε represents the essential figure of merit of a SQUID. If only thermal noise is taken into account, then ε for an ordinary dc-SQUID is approximately as follows:

R is the normal resistance of the two identical Jo sephson contacts, R _{dyn is} the dynamic resistance of the SQUID and the size in parentheses: (V _Φ ) _voltage = ∂V / ∂Φ _x , is the voltage transfer function of the dc-SQUID. The calculations give a good approximation of R _dyn = R / 2.

In addition, it was found that in the frequency range in the low-frequency 1 / f noise does not dominate, as in the known dc-SQUID, the most important source for noise from thermal noise is also given for a Shapiro-SQUID. Therefore, equation (1) could be applied to both types of 2-JK SQUIDs in a good approximation. By inserting the calculated values for the voltage transfer function of the two 2-JK SQUID types from FIG. 2 in equation (1), the energy resolution is obtained as a function of the standardized SQUID inductance.

In this context, it can be seen from FIG. 3 that the energy resolution of an optimal Shapiro stage SQUID (solid line in FIG. 3) for all inductances relevant in practice, the energy resolution of an optimal dc-SQUID (broken line in the Fig. 3) exceeds when the temperature is 77K. The result clearly shows two relevant examples from the figure. At L = L _F = 100 pH, the energy resolution of a Shapiro step SQUID is about five times better. With L = 2L _F = 200 pH the value is even ten times better than that of a dc-QUID, with the same values for the parameters R, L, and I _c (I _c is the critical current of the two identical Josephson contacts).

A special set of optimal parameter values for an inventor Shapiro step SQUID according to the invention is given below.

The parameters for a Shapiro step SQUID operated at T = 77 Kelvin are:

• - Microwave frequency ν = (2-5) ν _c , the characteristic frequency of the two identical Josephson contacts being given by 2πν _c = ω _c = 2πI _c R / Φ ₀ ;
• - SQUID inductance L = (0.5-3) L _F = (50-300) pH;
• - noise parameter Γ = 0.2, where Γ = 2πk _B T / I _c Φ ₀ ; this results in a value for the critical current I _c = 15 µA;

There is no limit to the value of the normal resistance R the Josephson contacts; therefore R should have typical values d. H. about several ohms or a multiple of 0.1 ohms.

A typical example is:

L = L _F = 100 pH, R = 1Ω, and I _c = 15 µA; in this case the values are Γ = 0.2 and ν _c = 10 GHz; the microwave frequency is in the range ν = (20-50) GHz.

With L = 100 pH and a typical value for the normal resistance R = 5Ω, the HTS-Shapiro step SQUID according to the invention has a calculated energy resolution of 2 × 10 ^-32 J / Hz at 77K, and with L = 200pH, ε = 6 × 10 ^-32 J / Hz. For comparison, a HTS-dc-SQUID operated at 77K with the same parameters for the two identical Josephson contacts, R and I _c , results in a calculated energy resolution of only 1 × 10 ^-31 J / Hz with L = 100 pH, and ε = 6 × 10 ^-31 J / Hz with L = 200pH.

The following are two possible modes of operation for one invented Shapiro stages SQUID explained in accordance with.

DC output voltage operating mode of a Sha according to the invention piro levels SQUIDs

The measured output signal is in this first operating mode of the Shapiro stage SQUIDs the dc output voltage. The dc Output voltage is determined by the input signal to be measured, the river, changed. In this case the readout Electronics for the output signal identical to that which is used for a dc-SQUID.

In this operating mode, the voltage transfer function for a Shapiro stage SQUID can be defined in the usual way: (VΦ) _voltage = ∂V / ∂Φ _x . The essential peculiarity for this case lies in the fact that a slight change in the direct current I in the vicinity of a Shapiro stage (see FIG. 1) leads to a sign change in the voltage transfer function, the transfer function being only moderate maxima Function of the direct current I passes.

AC output voltage operating mode of a Shapiro stage SQUID

In this second operating mode, a low-frequency current I _ac (with frequencies from a few 100 Hz to a few 10 kHz - depending on the SQUID application) is superimposed on the microwave current I _mw and the dc current I with a small amplitude. This results in an AC voltage V _ac as an output signal in this operating mode. The amplitude of V _ac is modulated by the flow to be measured. A standard lock-in technique is required to detect changes in the amplitude of V _ac .

There should be two conditions for this second mode of operation be filled.

First of all, the frequency Vtluß of the measured magnetic flux Φ _{x should be} significantly lower (approximately by a factor of ten or more) than the frequency ν _{ac of} the applied alternating current I _ac . For example, for measuring a magnetic flux at a frequency ν _ac = 100 Hz, the alternating current I _{ac can have} a frequency of at least approximately 1 kHz. The designation "niederfre quent" should therefore be interpreted to mean that this condition is fulfilled.

Furthermore, the amplitude of the low-frequency alternating current I _ac should not be greater than the critical current I _c . With a typical value for the critical current of I _c = 15 µA, the amplitude of I _ac should therefore be less than or equal to 15 µA.

In this operating mode, the dynamic conductivity is defined - (G _dyn = 1 / R _dyn ) - transfer function of a Shapi ro level SQUID according to the invention using the following expression:

(VΦ) _conductance = ∂G _dyn / ∂Φ _x = ∂ (∂I _ac / ∂V _ac ) / ∂Φ _x = ∂ (1 / R _dyn ) / ∂Φ _x .

The essential peculiarity for this case lies in the fact that a slight change in the dc current I in the vicinity of a Shapiro stage (see FIG. 1) leads to a sharp maximum in the dynamic conductivity transfer function.

The calculations in the context of the invention have shown that it this transfer function is more advantageous to use than the span tion transfer function of a Shapiro step SQUIDs. The reason for this is of a very general nature and  has been used in many other well-known areas to date where sensitive measurements were required. In in fact it is more advantageous to have a sharp maximum of transfer function (here the dynamic conductivity transfer function) a sensor (here the Shapiro step SQUID), as their monotonous change or just a moderate maximum.

Claims (4)

1. dc-SQUID with two Josephson contacts, characterized by means for applying a microwave current for operation in the area within a single Shapiro stage. 2. dc-SQUID with two Josephson contacts according to claim 1, ge characterized by means for applying a microwel current for operation in the area within the first Shapiro Step. 3. dc-SQUID with two Josephson contacts according to one of the previous ones existing claims, characterized by an amplitude of the microwave current or a microwave power at which the selected Shapiro level is maximal. 4. dc-SQUID with two Josephson contacts according to one of the preceding claims, characterized by a microwave frequency ν in the range from greater than 1 to 5 ν _c .