Method and device for very high sensitivity electron spin resonance spectroscopy

Abstract

A device for detecting and characterising electron spins in a sample includes an electromagnetic microresonator, having a resonant frequency cor in the microwave range and a quality factor Q and into which the sample is inserted; a device for creating a magnetic field B0 in the sample for bringing a spin transition frequency cos into resonance with the resonant frequency cor, such that cos=B0, where is a gyromagnetic factor of the spins; a spin detection device receiving signals from the electromagnetic microresonator associated with the sample and including at least one low-noise amplifier operating at a temperature of between 1 and 10 K and a series of amplifiers and a demodulator operating at ambient temperature.

Claims

1. A very-high-sensitivity spin-resonance spectroscopy device for detecting and characterizing electron spins in a given sample, comprising an electromagnetic microresonator having a resonant frequency r in the microwave domain and a quality factor Q and into which the sample is inserted, a device for creating a magnetic field B0 in the sample in order to bring into resonance with the resonant frequency r a transition frequency s of the spins, such that s=B0, where is a gyromagnetic ratio of the spins, and a spin-detecting device receiving signals from the electromagnetic microresonator that is associated with the sample and comprising at least one low-noise amplifier operating at a temperature between 1 and 10 K, and a series of amplifiers and a demodulator operating at room temperature, wherein the electromagnetic microresonator is made of superconductive metal and is produced on the nanoscale in that it comprises an active zone consisting of an essentially parallelepipedal constriction with a thickness comprised between 8 and 30 nm, a width comprised between 10 and 500 nm and a length comprised between 100 and 5000 nm.

2. The device as claimed in claim 1, wherein the microresonator is made of niobium, aluminum, NbN, NbTiN, or TiN.

3. The device as claimed in claim 1, further comprising a Josephson parametric amplifier that is placed upstream of said low-noise amplifier and that operates at temperatures T respecting Tr/.sub.B where is a reduced Planck's constant and .sub.B is Boltzmann's constant.

4. The device as claimed in claim 3, further comprising an additional Josephson parametric amplifier operating at temperatures Tr/.sub.B and placed such that an output of the additional Josephson parametric amplifier is connected to an input of said microresonator in order to produce a squeezed vacuum.

5. The device as claimed in claim 1, wherein the spin-detecting device is a continuous-wave device and comprises a device for injecting a microwave signal at the frequency r into the electromagnetic microresonator.

6. The device as claimed in claim 1, wherein the spin-detecting device is a pulsed-wave device and comprises a device for injecting sequences of brief pulses of microwave frequency equal to the frequency r into the electromagnetic microresonator in order to cause the spin to rotate by a well-defined Rabi angle.

7. A very-high-sensitivity spin-resonance spectroscopy method for detecting and characterizing electron spins in a given sample, comprising producing an electromagnetic microresonator having a resonant frequency r in the microwave domain and a quality factor Q and into which the sample is inserted; creating a magnetic field B0 in the sample in order to bring into resonance with the resonant frequency r a transition frequency s of the spins, such that s=B0, where is a gyromagnetic ratio of the spins; and receiving signals from the electromagnetic microresonator with which the sample is associated via at least one low-noise amplifier operating at a temperature between 1 and 10 K, and a series of amplifiers and a demodulator operating at room temperature, wherein in the step of producing the electromagnetic microresonator an electromagnetic microresonator made of superconductive metal is chosen, which microresonator is produced on the nanoscale in that it comprises an active zone consisting of an essentially parallelepipedal constriction the dimensions of which are: a thickness of 8 to 30 nm, a width of 10 to 500 nm, and a length comprised between 100 and 5000 nm.

8. The method as claimed in claim 7, wherein, in the receiving signals from the electromagnetic microresonator step, a Josephson parametric amplifier is furthermore placed upstream of said low-noise amplifier said Josephson parametric amplifier operating at temperatures T respecting Tr/.sub.B where is a reduced Planck' s constant and .sub.B is Boltzmann' s constant.

9. The method as claimed in claim 8, wherein, in the step of producing an electromagnetic microresonator, an additional Josephson parametric amplifier operating at temperatures T respecting Tr/.sub.B is placed such that an output of the additional Josephson amplifier is connected to an input of said microresonator in order to produce a squeezed vacuum.

10. The method as claimed in claim 8, wherein the measurement frequencies are comprised between 5 and 10 GHz and the temperature T is comprised between 10 and 200 mK.

11. The method as claimed in claim 8, wherein the measurement frequencies are comprised between 20 and 40 GHz and the temperature T is comprised between 1 and 3 K.

12. The device of claim 4, wherein the squeezed vacuum is a quantum state of the electromagnetic field in which noise in one of two quadratures is decreased with respect to vacuum quantum noise.

13. The method of claim 9, wherein the squeezed vacuum is a quantum state of the electromagnetic field in which noise in one of two quadratures is decreased with respect to vacuum quantum noise.

14. The device as claimed in claim 2, further comprising a Josephson parametric amplifier that is placed upstream of said low-noise amplifier and that operates at temperatures T respecting Tr/.sub.B where is a reduced Planck's constant and .sub.B is Boltzmann' s constant.

15. The device as claimed in claim 2, wherein the spin-detecting device is a continuous-wave device and comprises a device for injecting a microwave signal at the frequency r into the electromagnetic microresonator.

16. The device as claimed in claim 3, wherein the spin-detecting device is a continuous-wave device and comprises a device for injecting a microwave signal at the frequency r into the electromagnetic microresonator.

17. The device as claimed in claim 2, wherein the spin-detecting device is a pulsed-wave device and comprises a device for injecting sequences of brief pulses of microwave frequency equal to the frequency r into the electromagnetic microresonator in order to cause the spin to rotate by a well-defined Rabi angle.

18. The device as claimed in claim 3, wherein the spin-detecting device is a pulsed-wave device and comprises a device for injecting sequences of brief pulses of microwave frequency equal to the frequency or r into the electromagnetic microresonator in order to cause the spin to rotate by a well-defined Rabi angle.

19. The method as claimed in claim 9, wherein the measurement frequencies are comprised between 5 and 10 GHz and the temperature T is comprised between 10 and 200 mK.

20. The method as claimed in claim 9, wherein the measurement frequencies are comprised between 20 and 40 GHz and the temperature T is comprised between 1 and 3 K.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of the invention will become apparent from the following description of particular embodiments, which are given by way of nonlimiting example with reference to the appended drawings, in which:

(2) FIG. 1 is a schematic showing the basic structure of an ESR spectrometer,

(3) FIG. 2 is a schematic perspective view showing an example of a coplanar-microresonator-based ESR spectrometer,

(4) FIG. 3 is a schematic perspective view of a nanoresonator for ESR spectroscopy according to one aspect of the invention,

(5) FIG. 3A is an enlarged view of one portion of the nanoresonator of FIG. 3 showing a constriction receiving a nanoscale sample,

(6) FIG. 4 is a schematic of a Josephson-parametric-amplifier-based ESR spectrometer according to a second aspect of the invention, and

(7) FIG. 5 is a schematic of one particular embodiment that is an improvement on the ESR spectrometer of FIG. 4 with regard to producing a non-noisy echo.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS OF THE INVENTION

(8) According to a first aspect of the invention, which is shown in FIG. 3, a nanoscale microresonator 202 is employed in an ESR spectrometer.

(9) It is a question, within the inductive portion of a microresonator (for example the microresonator 202 of coplanar geometry shown in FIG. 3), of introducing a small zone 220 in which the dimensions of the resonator become much smaller, typically between 10 and 500 nm (see FIGS. 3 and 3A). Such a constriction 220 may be produced using standard e-beam lithography techniques. Thus, an active zone typically of (100 nm).sup.3 size is obtained within which the spins present will be coupled with a coupling constant that may reach from 1 to 10 kHz, about two orders of magnitude higher than has been achieved up to now.

(10) FIG. 3 shows a substrate 225 on which plate-shaped metal layers 221 and 222 have been placed, these corresponding to the capacitive portion of the resonator of the ESR spectrometer of FIG. 1, which also allows the coupling to the measuring waveguides (not shown). The exact geometry of this capacitive portion may be adapted with respect to that indicated in the schematic, for example an interdigitated capacitor is usable. The metal layers 221 and 222 are aligned in a direction 203 corresponding to the direction of the applied magnetic field B0. The metal layers 221 and 222 are connected together by narrower conductive tracks 223, 224 that are aligned with each other in the direction 203 and joined by an even narrower portion forming the constriction 220 on which a sample 201 to be analyzed is placed (see FIGS. 3 and 3A).

(11) The parallelepipedal-shaped constriction 220 may for example have a cross section of 20 nm20 nm and a length of 200 nm.

(12) More generally, the essentially parallelepipedal constriction 220 has a thickness from 8 to 30 nm, a width from 10 to 500 nm, and a length comprised between 100 and 5000 nm.

(13) More particularly, the dimensions of the constriction 220 and those of the sample 201 are adapted to be mutually compatible.

(14) In particular, this type of nanoresonator 202 is very suitable for measuring samples 201 of 100 nm typical size, such as biological samples, with which the amount of available material is very small.

(15) The resonator 202 must imperatively be fabricated from superconductive metal (for example niobium or NbN or NbTiN below 5 K, aluminum below 200 mK, or indeed TiN below 2 K) so that its quality factor Q is high enough for an effective detection (Q preferably being chosen between 10.sup.3 and 10.sup.5).

(16) The other elements of the ESR spectrometer may be such as those described above.

(17) In particular, the electromagnetic microresonator 202 having a resonant frequency r in the microwave domain and a quality factor Q and into which the sample 201 is inserted and a device for creating a magnetic field B0 in the sample 201 in order to bring into resonance with the resonant frequency r a transition frequency s of the spins, such that s=B0, where is a gyromagnetic ratio of the spins, the ESR spectrometer according to the invention comprises a spin-detecting device receiving signals from the electromagnetic microresonator 202 and from the sample 201.

(18) The spin-detecting device comprises at least one low-noise amplifier 303 operating at a temperature comprised between 1 and 10 K, and a series of amplifiers 304 and a demodulator 305 operating at room temperature, as shown in FIG. 4.

(19) A second aspect of the invention, which also contributes to increasing detection sensitivity, and that is therefore advantageously implemented with the nanoresonator 202 described above with reference to FIG. 3 in order to increase the sensitivity of the latter, but that may also be implemented independently of the nanoresonator 202 described above, i.e. could be implemented with a conventional microresonator or resonator without a constriction and capable of receiving a sample of arbitrary size, will now be described with reference to FIG. 4.

(20) According to this other aspect of the invention, a Josephson parametric amplifier is used. Josephson parametric amplifiers are a type of microwave amplifier recently developed for quantum computer applications and the major advantage of which is to have the best possible noise performance since they reach the limit of what is achievable in quantum physics, i.e.: n= 0.5 to 1.

(21) Josephson parametric amplifiers (JPAs) are based on superconductor circuits containing Josephson junctions. They typically operate at temperatures T such that Tr/.sub.B where is the reduced Planck's constant and .sub.B is Boltzmann's constant (the value of which is .sub.B=1.38 J/K=1.3810.sup.23 m.sup.2kgs.sup.2K.sup.1).

(22) This corresponds to temperatures from 10 to 200 mK for frequencies from 5 to 10 GHz, and to temperatures from 1 to 3 K for frequencies from 20 to 40 GHz. They have been used in various experiments, but not for high-sensitivity magnetic-resonance measurements.

(23) The reader may in particular refer to the article by M. A. Castellanos-Beltran, K. W. Lehnert, Appl. Phys. Lett. 91, 083509 (2007) and to the article by N. Bergeal et al., Nature 465, 64 (2010).

(24) According to the invention, it has been found that, for high-sensitivity magnetic-resonance measurements, it is advantageous to use a JPA in the degenerate regime, in which regime amplification of just one quadrature with no addition of noise by the amplifier is achieved by setting up the amplifier so that only the quadrature in which the spin echo is emitted is amplified. In this regime, the only noise limiting the measurement sensitivity is the vacuum quantum noise, this corresponding to n=0.5.

(25) If reference is made to FIG. 4, it may be seen that, using an assembly 301 comprising a resonator and a sample, which may advantageously consist of a resonator 202 and a sample 201 such as described above with reference to FIGS. 3 and 3A to obtain a maximum sensitivity, but that could also be produced in the conventional way without the constriction 220 of the resonator 202, the signals induced in the resonator subjected to a magnetic field BO as indicated above are applied to a Josephson parametric amplifier 302 (JPA amplifier) placed, just like the assembly 301, in an environment the temperature of which is that adapted to the amplifier 302 as indicated above.

(26) The output of the JPA amplifier 302 is connected to the input of a low-noise amplifier 303, itself placed in an environment at a temperature between 1 and 10 K. The output of the low-noise amplifier 303 is connected to the input of a series of amplifiers 304, which series is associated with a demodulator 305 implementing a local oscillator. All of the series of amplifiers 304 and the demodulator 305 are at room temperature, for example about 300 K.

(27) FIG. 5 illustrates an improvement to the embodiment of FIG. 4.

(28) In the embodiment in FIG. 5, a device generating a squeezed vacuum is used in order to further increase, by a factor of possibly of as much as one order of magnitude, the sensitivity of the spectrometer. Squeezed vacuum is a quantum state of the electromagnetic field in which the noise on one of the two quadratures is decreased by a factor S with respect to the vacuum quantum noise, i.e. the number of noise photons added becomes n= 0.5/S. In practice, it is possible to achieve S= 10 to 100. The squeezed quadrature is chosen so that it corresponds to that on which the spin echo is emitted. The sensitivity of the spectrometer is then further increased by a factor S, i.e. potentially by an order of magnitude more.

(29) The squeezed vacuum is generated by an additional degenerate-mode JPA amplifier 306 placed such that its output is connected to the input of the assembly 301 comprising the resonator and the sample in the spectrometer (see FIG. 5). This improvement is useful in the case where the echo signal is then amplified by a JPA amplifier 302 at the quantum limit, as indicated above with reference to FIG. 4. The non-noisy echo output from the JPA amplifier 302 at the quantum limit is then amplified by the amplifiers 303 and 304 and demodulated by the demodulator 305 as illustrated in FIG. 4 and these elements have not been shown again in FIG. 5.

(30) By combining the three embodiments of FIGS. 3 to 5, N.sub.min=0.5 is achieved (for g=25 kHz, T=10 mK, S=100, Q=10.sup.5). This means that it becomes possible to perform EPR-spectroscopy measurements on any electron spin at the scale of a single spin.

(31) The invention thus aims to very significantly increase the sensitivity of an electron-paramagnetic-resonance (EPR) (a.k.a. electron-spin-resonance (ESR)) detection chain that allows the magnetic moment of electron spins of a sample of material to be tested to be measured.

(32) Sensitivity amounts to a quantification of the number of detected electron spins, and is measured either in spins/Hz (10.sup.9 spins/Hz at 300 K for commercially available devices) or in number of electron spins detected in a single echo (typically 10.sup.13 spins at 300 K with commercially available devices). It will be noted that experimental apparatuses measure this sensitivity in number of spins per echo, these two quantities being related by the repetition rate, which itself is set by the energy relaxation time T.sub.1 of the spins, which may depend on the type of spin in question. The best sensitivity that has been achieved in the laboratory is N1echo510.sup.7 spins at 1 or 2 K.

(33) In practice, this is achieved via superconductive planar resonators, in which a waveguide confines a planar resonator so as to form a resonator of very high quality coefficient (Q10.sup.4). The output of the planar resonator is conventionally applied directly to a low-noise amplifier cooled to a temperature comprised between 1 and 10 K, such as the amplifier 303 of FIG. 4. The invention, in the embodiment of FIG. 4, consists in introducing, between on the one hand the assembly 301 formed by the resonator and the sample and on the other hand the amplifier 303, a device issued from quantum physics, namely the JPA amplifier 302, which is an amplifier at the quantum limit. This amplifier at the quantum limit has an extremely low noise level, and improves the signal-to-noise ratio by about 10.The invention encompasses any possible type of superconductive resonator and therefore, a priori, superconductive resonators of any shape, although a preferred embodiment is that described with reference to FIGS. 3 and 3A.

(34) In the embodiment of FIG. 5, on the side opposite the output of the planar resonator, a second amplifier at the quantum limit (JPA amplifier 306 of FIG. 5) is added, the operation of which is slightly different but that again in the end also leads to a decrease in noise by generating a squeezed vacuum state at its output.

(35) Lastly, the quality coefficient of the cavity is also a key point.

(36) The core of the invention consists of a planar superconductive microwave resonator intended to measure a set of spins coupled to the oscillating magnetic field of the resonator. The resonator may be fabricated from a material allowing magnetic fields of up to 1 Tesla to be applied while preserving a high quality factor (between 10.sup.4 and 10.sup.5).

(37) In summary, in order to increase the sensitivity of this spectrometer (i.e. the minimum number of spins detectable in one second), the following measures are recommended according to the invention:

(38) The use of a microwave amplifier 302 at the quantum limit to amplify the spin-echo signal. This increases by a factor of 10 to 50 the signal-to-noise ratio, and therefore the sensitivity of the spectrometer, i.e. the minimum number of detectable spins. At a temperature of 10 mK (temperature reached in commercially available dilution cryostats), the achieved sensitivity is estimated to be 10.sup.3 spins in a single echo, this representing an improvement of four orders of magnitude with respect to the best published performance.

(39) In this case, sensitivity is further improved by illuminating the spectrometer with a squeezed vacuum, generated by a parametric amplifier 306 located before the input of the spectrometer. The squeezed vacuum decreases the noise on one of the quadratures of the microwave signal. By choosing the phase of this squeezed vacuum so that it coincides with the phase of the spin echo, the signal-to-noise ratio will be further increased by a factor that may be as high as 10.

(40) Lastly, to even more greatly increase sensitivity, for samples 201 of very small size (of about 100 nm or 200 nm or less), it is possible to introduce a constriction 220 within the resonator 202, as close as possible to the sample 201. It is thus possible to achieve a sensitivity corresponding to the detection of a single spin in less than one second of acquisition time.