GB2494169A - Nuclear magnetic resonance spectroscopy using an excitation RF spectrum with a spectral gap - Google Patents

Abstract

A method of measuring a sample using nuclear magnetic resonance (NMR) spectroscopy uses a continuous broadband RF excitation spectrum having a first portion and a second higher frequency portion with a spectral gap between the portions (figure 1d). This is the inverse of the usual saturation NMR spectroscopy (figure 1a). If the frequency of the spectral gap matches the resonance frequency of a nuclear spin transition in the sample under test, this results in enhanced detectability (figure 1f). The spectral position of the spectral gap may be scanned by incrementing or decrementing its central frequency. The method may be used to measure a strained solid semiconductor sample such as a strained self-assembled quantum dots. An optical radiation source may be used to optically pump the sample, and optical radiation re-emitted from the sample may be measured using an optical detector.

Description

Nuclear Magnetic Resonance (NMR) Spectroscopy Method and Apparatus Therefor [0001] This invention relates to a nuclear magnetic resonance (NMR) spectroscopy method and an apparatus therefore, and, in particular, to a high sensitivity, non-invasive NMR spectroscopy method and apparatus for measuring a sample.

BACKGROUND

[0002] Novel solid state technology for single-photon light sources and detectors, photovoltaics, quantum computation using few spin systems etc rely on nanoscale fabrication for semiconductor quantum wells, quantum dots, and nanowires. Fabrication methods often rely on using strained semiconductor layers and related self-assembly crystal growth mechanisms. Well developed electron and atomic force microscopy techniques successfully applied for structural studies of such nano-systems normally require destruction of the nano-structure or its incomplete fabrication. As a result, important information is lacking on the exact material composition, strain magnitude and distribution and shape of the electron wave-function and its penetration into the barrier in the actual working nano-structures. Thus, establishing a direct link between the electron transport and optical properties of the device and its structure remains challenging. One of the possible solutions is development of sensitive NMR techniques, which can be applied in single nano-structures. The task of understanding and control of nuclear spins on the nanoscale also arose from recent development of spin-qubits and entangled photon generation for quantum computation and communication technologies. So far, direct control of nuclear spins using NMR has been achieved in strain-free quantum dots made of lattice-matched GaAs/AIGaAs layers, where nuclear quadrupole effects are weak [1,2]. However, nuclear spin systems in widely used strained self-assembled quantum dots are still inaccessible using direct NMR methods due to significant broadening of the resonances caused by strong quadrupole effects [3].

[0003] Thus, it is an object of at least one embodiment of the present invention to provide improved NMR methods that, in particularly preferable embodiments, facilitate the understanding of the spectral and coherence properties of nuclear spins in strained semiconductor nano-structures.

BRIEF SUMMARY OF THE DISCLOSURE

[0004] The present invention is defined in the appended claims.

[0005] In accordance with a first aspect of the present invention there is provided a method of measuring a sample using nuclear magnetic resonance (NMR) spectroscopy, comprising the steps of: i) providing: a) a sample to be measured; b) a magnet for applying a magnetic field to the sample; c) a first excitation source for emitting electromagnetic (EM) radiation that has a spectral profile that has a first excitation portion and a second excitation portion, wherein the second excitation portion is higher in frequency than the first excitation portion and the second excitation portion is spectrally separated from the first excitation portion by a spectral gap; and d) measuling means for measuring a property dependent on a degree of nuclear spin polarisation of the sample; U) applying a magnetic field to the sample using the magnet; Di) illuminating the sample with the first excitation source to electromagnetically excite the nuclei of the sample; and iv) measuring the sample using the measuring means.

[0006] The above-defined method according to the present invention provides a non-invasive NMR measurement technique that is highly sensitive in comparison with known NMR methods

of the prior art.

[0007] In a particularly preferable embodiment, the method further comprises the step of providing at least one optical source for optically exciting the sample, wherein the measuring means comprise a detector for detecting re-emitted optical signal from the sample, and the step of measuring the sample comprises detecting re-emitted optical signal from the sample using the detector. In a particularly preferable embodiment, at least one optical source provides an optical pump for increasing the degree of nuclear polarization in the sample, and an optical probe for exciting the optical signal from the sample. The optical source may be a

laser, for example.

[0005] The first excitation portion and/or the second excitation portion may include a series of modes spectrally spaced from one another, wherein the spacing between the modes is less than the spectral gap. Furthermore, each of modes of the first excitation portion and/or the second excitation portion may be equally spaced from one another. Additionally or alternatively, the amplitude of each mode may be substantially equal to the amplitude of the other modes.

[0009] In one particular preferable embodiment, the first excitation portion and the second excitation portion include broadband emission of substantially constant and equal amplitude.

[0010] In any embodiment, the amplitude of the EM radiation in the spectral gap may be equal to or less than 1/10 of the amplitude of the EM radiation in the first and second excitation portions. Preferably, the amplitude of the EM radiation in the spectral gap may be equal to or less than 1/30 of the amplitude of the EM radiation in the first and second excitation portions.

In a particularly preferable embodiment, the amplitude of the EM radiation in the spectral gap is substantially zero. The spectral density of ri power in the spectral gap may be equal to or less than 1/100 of that in the first and second excitation portions. Preferably, the spectral density of rf power in the spectral gap is equal to or less than 1/1000 of that in the first and second excitation portions.

[0011] The first excitation source may be configured such that the spectral position of the spectral gap is movable, and wherein steps iii) and iv) are repeated for spectral profiles having a spectral gap having an incrementally increased or decreased spectral position.

[0012] The method may further comprise the steps of: v) providing a second excitation source tor emitting EM radiation that has a spectral profile identical to the spectral profile of the first excitation source except wherein no spectral gap is present; vi) illuminating the sample with the second excitation source to electromagnetically excite the nuclei of the sample; vU) measuring the sample using the measuring means; and vDi) calculating the difference in detected signals obtained in steps iv) and vU).

[0013] The sample may be a semiconductor material that may be a bulk semiconductor material or a quantum structure such as one or more quantum dots. In a specific example, in which the method of the present invention is particularly effective, the sample may be one or more strained self-assembled quantum dots. Depending on the type of sample and the type of detection, the method may be carried out at a variety of temperatures. In one example, the sample is cooled to a temperature below 80 K, which may be below 5 K, and possibly to about 4.2 K. [0014] In a particularly preferable embodiment, the first excitation source (and second excitation source, if present) is a radio frequency (ii) source.

[0015] In accordance with a second aspect of the present invention, there is provided an apparatus for measuring a sample using nuclear magnetic resonance (NMR) spectroscopy, comprising: a magnet for applying a magnetic field to the sample; a first excitation source arranged to emit electromagnetic (EM) radiation that has a spectral profile that has a first excitation portion and a second excitation portion, wherein the second excitation portion is higher in frequency than the first excitation portion and the second excitation portion is spectrally separated from the first excitation portion by a spectral gap; and measuring means arranged to measure a property dependent on a degree of nuclear spin polarisation of the sample [0016] The apparatus may further comprise at least one optical source for optically exciting the sample, and the measuring means may comprise a detector arranged to detect re-emitted optical signal from the sample. In a particularly preferable embodiment, the at least one optical source provides an optical pump for increasing the degree of nuclear polarization in the sample, and an optical probe for exciting the optical signal from the sample. The optical source may be a laser, for example.

[0017] Additionally or alternatively, the apparatus may further comprise a second excitation source arianged to emit EM radiation that has a spectral profile identical to the spectral profile of the first excitation source except wherein no spectral gap is present.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Embodiments of the invention are further described hereinafter with reference to the accompanying drawings, in which: Figure 1 shows a comparison of a known "saturation" NMR method (Figures 1(a)-(c)) and an "inverse" NMR method (Figure 1(d)-(f)) in accordance with an embodiment of the present invention, where Figures 1(a) and (d) show the RF excitation spectra for the two methods, Figures 1(b) and (e) show the nuclear spectrum of a nucleus with spin 1=5/2, and Figures 1(c) and (f) show the population probabilities of the nuclear spin levels; Figures 2(a) and (b) show typical photoluminescence spectra for lnGaAs/GaAs (Figure 2(a)) and lnF/GalnP (Figure 2(b)) quantum dots measured in magnetic field B7 = 5.3 and 6 1, respectively; Figure 2(c) shows (schematically) the spectrum of rf excitation; Figure 2(d) shows the timing diagram of the experimental cycle including optical pump and probe, and rf excitation; Figure 3 shows CDNMR spectra measured in selt-assembled QOs using the "inverse" method in accordance with an embodiment of the present invention, where Figures 3(a) and 3(b) show ODNMR spectra for lnP/GalnP dots measured with resolution Wgap 280 kHz in Figure 3(a) and 16 kHz in Figure 3(b), and applying "saturation" spectroscopy with single-frequency excitation for spin 112 °1P in Figure 3(a), and Figures 3(c)-(f) show ODNMR spectra for InGaAs/GaAs dots measured with resolution wgap =280 kHz in Figure 3(c), 8-24 kHz in Figure 3(d), and 800 kHz in Figures 3(e,f);

DETAILED DESCRIPTION

[0019] Figure 1 shows the basic principles of a nuclear magnetic resonance (NMR) spectroscopy method according to an embodiment of the present invention (Figures 1 (d)-(f)) and its comparison with known "saturation" NMR techniques applied in strain-free materials, using an example of spin I = 5/2 nuclei. In the external magnetic field B1 along 0 axis nuclear spin levels shift according to their spin projections I as i B111. The oscillating magnetic field B perpendicular to 01 couples only the adjacent spin levels with I differing by ±1. In the absence of strain, the energy spacings between all such levels are equal, i. e. all transitions occur at the same resonant frequency. If the nucleus is subject to an electric field gradient (EFG) along 0 axis (e.g. induced by elastic strain), in addition to the splitting induced by B1, the energies of spin levels will change by a value proportional to I2, and all dipole active transitions will have different frequencies, as depicted in Fig. 1(b).

[0020] Considering an ensemble of nuclei with spins I = 5/2 all subject to the same EFO. It is assumed that nuclei are polarized with higher population of I = 5/2 than I = -5/2 levels. The probabilities p1 to find nucleus with I spin will depend on I as sketched with solid lines in Fig. 1(c), and the total nuclear spin polarization degree (which is detected optically) is SN = p1. x k/I, so that SNI «= 1. Arrows in Fig. 1(c) indicate the maxima in the NMR spectrum in Fig. 1(b) corresponding to transitions between the adjacent pairs of nuclear spin levels.

[0021] In saturation NMR spectroscopy, radio-frequency (ri) excitation at a frequency v or, a distribution of frequencies with a width Wex. is applied (Fig. 1(a)). SN will only change in the case when v is in resonance with a transition between l' and l' + 1 levels, for example, -3/2 -* -1/2 in Figs. 1 (a-c).This occurs as the populations of these spin levels equalize under a long enough resonant rf excitation (dotted lines in Fig. 1(c)), which at the same time has no effect on populations of all other spin levels. As a result, the overall change in nuclear polarization ASfft is small, making the resonance difficult to detect.

[0022] A significant enhancement of the changes in SN can be achieved by using an alternative approach in accordance with the present invention (see Fig. 1(d)). In accordance with one embodiment of the present invention, a broad band excitation with a continuum spectrum containing a gap of a width Wgap is used. As the ri excitation spectrum in Fig. 1(d) is an inversion of that in Fig. 1(a), the term "inverse" spectroscopy is used hereinafter to describe the method of the present invention. The effect of such excitation on the populations of the nuclear spin levels is demonstrated in Fig.1 (f). If the gap is out of resonance with all transitions, all population probabilities p1 are equalized (solid lines) and nuclear spin polarization is completely erased (SN = 0). If, however, the gap is in resonance with I' transition (for example, -3/2 -* -1/2), i. e. one of the transitions is not excited, the equalization of populations occurs independently for two groups of levels with l «= Il' or l »= l' + 1 (dotted lines). Crucially, populations of l = ±1 states, which give the largest contribution to average nuclear polarization SN, are affected. It is possible to show (see Appendix) that for a wide range of conditions the enhancement of the changes in nuclear polarization AS$V is more than -100 for spin I = 9/2 (e.g. 1151n) compared to the saturation NMR method in Fig. 1(a), whereas the two methods are equivalent for spin 1/2 isotopes (e. g. 31F). In embodiments of the present invention, in order to obtain an NMR spectrum using the "inverse" method, the central frequency of the gap is scanned, whereas the width of the gap Wgap is used to control the balance between the spectral resolution and NMR signal amplitude.

Example Experimental Methods (0023] In the foregoing, results are presented of NMR measurements in two different types of strained semiconductor nano-structures, in accordance with an embodiment of the present invention. In particular, the strained semiconductor nano-structures are lnP/GalnP and lnGaAs/GaAs self-assembled quantum dots (QDs). All measurements were performed at T = 4.2 K, in external magnetic field B1 normal to the sample surface. Under optical excitation with circularly polarized light, dynamic nuclear polarization is observed in QDs, a phenomenon occurring due to the hyperfine interaction of electrons and nuclear spins [4]. The resulting nuclear spin polarization on the dot is detected in photoluminescence (PL) of excitons in single ODs as shown in Fig. 2(a) for lnGaAs and in Fig. 2(b) for lnP dots placed in high magnetic field B7>5 T. Each spectrum consists of an exciton Zeeman doublet, the splitting of which, E1, strongly depends on the polarization of optical excitation used to pump nuclear spins.

Detection of E1 allows measurement of the electron Overhauser shift directly proportional to the degree of nuclear polarization.

(0024] A digital arbitrary waveform generator was used to generate the rf signal, which was fed after amplification to the mini-coil wound around the sample. In experiment, the model excitation with spectrum shown in Fig. 2(c) was approximated with the excitation of a finite spectral width wexc consisting of a large number of discrete modes with equal spacing wm (Fig. 2(c)). Optically detected NMR (ODNMR) measurements were carried out using the pump-probe method schematically shown in Fig. 2(d). The dot is first excited with a circularly polarized laser pulse of duration After that the ii excitation is applied in the dark for duration Th. Finally, a short (Tprnbe) laser pulse is applied to measure PL spectrum of the QD exciton. The ODNMR signal at a frequency v is obtained as the difference in E7 measured for excitation with the continuum spectrum with total width Wexe and excitation with a gap of width Wgap in the spectrum, positioned at the central frequency v. Further details of example experimental methods are described in the Appendix.

NMR spectra [0025] Fig. 3 shows a set of ODNMR spectra measured using "inverse" spectroscopy on single lnP (a,b) and lnGaAs (c-f) ODs at Bz 5.3 T for various values of Wgap. ODNMR spectra were measured for nuclear spins polarized (anti-)parallel to the external field by (a+)a-circularly polarized light. In Fig. 3(a), where Wgap=28O kHz is used in the nominally lnP dots grown in the GalnP barrier, contributions from quadrupolar nuclei 1151n, 69Ga and 7lGa are clearly detected. 11 5ln peak dominating the spectrum, consists of a sharp central line (corresponding to +1/2 --1/2 transition) with amplitude -40 peV at -49.7MHz, and two broad bands of satellite transitions (ST5) to lower and higher frequencies each stretching up to ±10 MHz. These sidebands are due to quadrupole split transitions between spin levels with lIzi > 1/2. As seen, the relative amplitudes of the side-bands reflect the initial alignment of the nuclear spins by circularly polarized excitation: the high (low) frequency band has a higher (lower) intensity for a-(a+) excitation. The ODNMR spectra for spin 1/2 31 P nuclei using the saturation method was also measured, and reveals a single line with a width of -8 kHz at vp =91605 khz.

[0026] The ODNMR spectra of a lnGaAs/GaAs QD measured using the "inverse" method under the same conditions (B 5.3 T, wgap=28O kHz) are shown in Fig.3(c). Here, central transitions have similar amplitudes for the four isotopes present in the dot, implying significant substitution of indium by gallium. Satellite transitions are observed only for spin 9/2 115ln and have similar widths to the case of lnP dots. In order to observe these transitions for spin 3/2 nuclei "inverse" NMR measurements were carried out, with a larger wgap=800 kHz as shown in Figs. 3(e) and (f) for 1Ga and 5As respectively. For 1Ga the spectral range where ST5 are observed is within ±2.5 MHz on both sides of the central line, whereas it is significantly broader for 75As due to its larger quadrupole moment 0 (also Sis for 5As partly overlap with STs for 115ln) A significant difference in the asymmetry of the spectra is noted: for 5As the low (high) frequency ST band is enhanced for a-(+) pumping while for indium and gallium isotopes this asymmetry is reversed. This is likely to reflect the opposite signs of the electric field gradients experienced by nuclei of As (anion) and Ga (cation) ions.

[0027] The structure of the central transitions (CTs) is measured using "inverse" NMR with smaller wgap824 kHz providing higher resolution. In Figs. 3(b, d) the smallest linewidth is observed for 1Ga: in lnGaAs QDs it is only -8 kHz, still likely to be limited by the resolution.

For 69Ga the resonance is slightly broader. For 115ln, a linewidth of -40 kHz is found in both materials. 5As has a similar width of -40 kHz, but in addition has broad and less intense shoulders. Such width variations are proportional to Q/[l(2l -1)1 and reflect the change of the quadrupole moments, which forthe studied isotopes are: Q(9Ga) 0.17, Q('10a) 0.10, Q('5As) 0.31 barn (1 barn = 1028 m2) for 1=312 nuclei and Q(151n) 0.8 barn for 1=9/2 1151n. In the lnP sample, from comparison with the resonance frequency for 31P, vp =91605 kHz, unaffected by the strain, it is found that the CT for ln also occurs at a frequency similar to that expected for bulk lnP [5] v1 49633 kHz (a vertical line in Fig. 3(b)). It is observed in Figs. 3 (ac) that individual STs of 1151n are not resolved. This suggests a strong variation of the quadrupolar shifts over the volume of the dot resulting from the variation of elastic strain. In particular, it can be seen that ST bands have non-zero amplitudes at the CT frequency, implying that for some nuclei the quadrupole splitting is zero. This is most likely due to relaxation of elastic strain in some parts of the dot. The alternative explanation that it is a result of strong deviation between directions of the strain and growth (O axis) is rather unlikely since such angle deviations should be accompanied by significant shift and broadening of the CT transition not observed experimentally (Fig. 3(b)). On the other hand, the maximum values of strain can be readily estimated from the maximum frequency shifts observed for the Sis. For lnP/GalnP dots, U51n quadrupole split transitions are observed at frequencies as large as - ±10 MHz. Using the values of the gradient-elastic tensor SijkI measured in bulk lnF this allows to estimate the maximum biaxial strain 8b = -z -( +cJ2 as 5%. For the spin 3/2 1Ga, the largest shift of the STs from the CT in lnGaAs/GaAs QDs is within -2.5 MHz (Fig. 3(e)). This leads to the estimate of the maximum strain -6% (See Appendix).

(0028] The NMR data in Fig.3 can be used to estimate gallium and indium concentrations Pca and Pin. For this, it is taken into account that the detected Overhauser shift due to the i-th isotope is directly proportional to the product of its spin Ii and hyperfine constant A, and Al p, where p is the nuclear magnetic moment. Thus, the "inverse" NMR signal due to the i-th isotope AE, ci: p,p4S, where ASt is the change in the degree of polarization of the i-th isotope due to rf excitation. For lnGaAs dots in Fig. 3(c) similar NMR signals are observed for 71Ga and 1151n. Assuming similar LS for both isotopes, and taking into account 40% natural abundance of 1Ga and enhancement of the 115ln signal by a factor of P(1151n/P(710a) 2, the relative gallium and indium concentrations can be estimated: PGa P(llca)/°.4 (IJ(ll5in)/P(zlGa))P(ll5in)/O.4 SP(llsin), i.e. Pin 20% and PGa = 80% for lnGaAs dots. This agrees well with a short wavelength of QD PL of 910 nm in this sample. Similar estimates for lnP dots give Pin 65% and PGa 35%. This is in good agreement with a weak contrast with the Ga05ln05 P barrier these dots exhibit in TEM images, and may also be explained by penetration of the electron wave-function into the barrier. These estimates are in close agreement with results of more detailed measurements and rigorous analysis presented in the Appendix.

Further Description of Figures

(0029] Figure 1. shows a known "saturation" NMR spectroscopy method Figures 1(a)-(c) and an inverse" NMR spectroscopy method (d)-(f) in accordance with an embodiment of the present invention. Both methods are applied to quadrupolar nuclei in the examples shown in Figure 1. The case of an ensemble of spin 5/2 nuclei subject to the same electric field gradient is considered for clarity. Figures 1(a) and 1(d) show ri excitation spectra in the two spectroscopy methods. Spectra of dipole transitions between the nuclear spin levels are shown in Figures 1(b) and 1(e). Figures 1(c) and 1(f) show population probabilities of the nuclear spin levels. Arrows show the transitions in the nuclear spectra in Figures 1(b) and 1(e) corresponding to pairs of the spin states coupled by the ri field. Solid lines show the population probabilities for the case when the rf maximum in Figure 1(a) and the gap in Figure 1(d) are off resonance with all transitions. Dashed lines show the case when the maximum in Figure 1(a) and the gap in Figure 1(d) are in resonance with -3/2 <-* -1/2 transition.

(0030] Figures 2(a) and 2(b) show typical photoluminescence spectra for lnGaAs/GaAs (Figure 2(a)) and lnP/GalnP (Figure 2(b)) quantum dots measured in magnetic field B7 = 5.3 and 6 T, respectively. Squares (circles) show PL spectra measured for o-(+) excitation exhibiting differing Zeeman splittings E due to the nuclear spin polarization aligned (anti-) parallel to B. Figure 2(c) shows (schematically) the spectrum of ri excitation. The spectrum has a total width wex. up to 20 MHz and consists of many modes with a spacing w1,, which is varied in different measurements in the range 0.1÷4 kHz (Wm = 0.4 kHz is used for "inverse" spectroscopy). The spectrum also has a gap with a width wgap varied in the range 8-800 kHz.

Figure 2(d) shows the timing diagram of the experimental cycle including optical pump and probe, and if excitation. According to an embodiment of the present invention, Tpump = 4 7 5, = 4÷ 6 sand Tprobe = 3÷ 16 ms are used.

(0031] Figure 3 shows ODNMR spectra measured in self-assembled ODs using the "inverse" method in accordance with an embodiment of the present invention. Figures 3(a) and 3(b) show CDNMR spectra for lnP/GalnP dots measured with resolution wgap =280 kHz in Figure 3(a) and 16 kHz in Figure 3(b), and applying "saturation" spectroscopy with single-frequency excitation for spin 1/2 31 P in Figure 3(a). Figures 3(c)-(f) show ODNMR spectra for lnGaAs/GaAs dots measured with resolution w902 =280 kHz in Figure 3(c), 8-24 kHz in Figure 3(d), and 800 kHz in Figures 3(e,f). Vertical line in Figure 3(b) shows indium frequency corresponding to unstrained lnP calculated as v1,, = v1k!v± 49633 kHz using 31P frequency Vp 91605 kHz measured in a QD and frequencies vtMik measured for both isotopes in bulk lnP [5]. "Inverse" spectra for 0+ optical pumping were measured as a difference -E' exciton Zeeman splitting Ef" measured under rf-excitation with a gap in the spectrum and the splitting E°-measured without the gap. For o-pumping the same difference was used but taken with the opposite sign -( Ei"" -E'°°') in order to simplify comparison with the case of o+ pumping. For "saturation" spectroscopy on 0+ optical pumping was used and the calculated signal was E'°--E7, where E' (E°-) is the spectral splitting measured with (without) rf excitation.

[0032] To summarise, in a specific embodiment of the present invention there is provided an optically detected nuclear magnetic resonance (ODNMR) method that is highly sensitive and non-invasive. When the method is applied to nano-structured semiconductors, it provides a direct link between electronic and structural properties. The present invention is particularly suited to measuring strained semiconductor materials where prior art methods have failed due to significant broadening of NMR spectra. In a specific embodiment of the present invention, the ODNMR technique may be used for high resolution spectroscopy of 105 nuclear spins in single strained quantum dots, enabling detection of features with widths of 10 kHz in ODNMR spectra of half-integer quadrupole nuclei having the total widths of 10-20 MHz. Furthermore, non-Lorenzian lineshapes for individual transitions and enhanced nuclear spin coherence with T2 2.5 nis is found in the presence of strain. The developed NMR methods of the present invention can be readily applied for non-invasive investigations of a wide range of materials beyond single nano-structures or, indeed, semiconductors. Additionally, the present invention is not limited to optical detection methods but may be used in conjunction with any measuring means for measuring a property dependent on a degree of nuclear spin polarisation of the sample. For example the measuring means may measure the nuclear spin polarisation (i.e. nuclear or magnetisation) of the sample. In some embodiments the measuring means may measure polarization of light, magnetisation of the sample or current in a pickup coil.

[0033] The sample may be any material, and may be a solid state sample. In particular, the sample may be a semiconductor material, such as a bulk semiconductor material or a quantum structure (e.g. one or more quantum dots, such as one or more strained self-assembled quantum dots).

[0034] Preferably the amplitude of the EM radiation in the spectral gap is zero or essentially zero. However, in some embodiments the amplitude of the EM radiation in the spectral gap is non-zero, and less than the amplitude of the RF radiation outside the spectral gap. According to some embodiments the amplitude of the EM radiation in the spectral gap is equal to or less than 1/10, and preferably 1/30 or less. In some embodiments, the spectral density of rf power in the gap is equal to or less than 1/100 that outside the gap. Preferably the spectral density of ri power in the gap is equal to or less than 1/1 000 that outside the gap.

[0035] In the above embodiment of the invention, the rf excitation had discrete modes with equal spacing wm. However, in other embodiments the spacing of the modes may vary, provided that the spacing of the modes is smaller than the width of the spectral gap. In some embodiments the spectrum does not have discrete modes.

[0036] In an embodiment of the invention, the excitation spectrum may be produced by generating a white if spectrum and filtering the spectrum to produce the gap. An avalanche diode may be used to produce the if white noise, and this can be filtered electronically to produce the gap.

[0037] Figures 1(d) and 2(c) illustrate a preferred embodiment in which the if excitation has a constant amplitude outside the gap (i.e. at frequencies above and below the gap). Analysis of the data is simplified by having a constant amplitude outside the gap. In other embodiments, the amplitude outside the gap may vary.

[0038] Where the amplitude in the gap in non-zero and the amplitude of the rf excitation outside the gap varies, it is preferable that the amplitude in the vicinity of the gap (i.e. in a frequency range immediately above and below the gap) is larger than the amplitude in the gap such that the amplitude of the EM radiation in the spectral gap may be equal to or less than 1/10, and preferably 1/30 or less. In some embodiments, the spectral density of if power in the gap is equal to or less than 1/100 that outside the gap. Preferably the spectral density of if power in the gap is equal to or less than 1/1000 that outside the gap.

[0039] Throughout the description and claims of this specification, the words comprise" and "contain" and variations of them mean "including but not limited to", and they are not intended to (and do not) exclude other moieties, additives, components, integers or steps. Throughout the description and claims of this specification, the singular encompasses the plural unless the context otherwise requires. In particular, where the indefinite article is used, the specification is to be understood as contemplating plurality as well as singularity, unless the context requires otherwise.

[0040] Features, integers, characteristics, compounds, chemical moieties or groups described in conjunction with a particular aspect, embodiment or example of the invention are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.

[0041] The reader's attention is directed to all papers and documents which are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference.

REFERENCES

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[2] M. N. Makhonin, E. A. Chekhovich, P. Senellart, A. Lemaitre, M. S. Skolnick, and A. I. Tartakovskii Phys. Rev. B 82, 161309 (2010).

[3] P. Maletinsky, M. Kroner, A. Imamoglu, Nature Physics 5, 407 (2009).

[4] D. Gammon, A. L. Efros, T. A. Kennedy, M. Rosen, D. S. Katzer, D. Park, S. W. Brown, V. L. Korenev, and I. A. Merkulov, Phys. Rev. Lett. 86, 5176 (2001).

15] T. lijima, K. Hashi, A. Goto, T. Shimizu, and S. Ohki, Journal of the Physical Society of Japan 73, 1045 (2004).

Appendnc Details of experimental techniques. We use InP/CaInP self-assembled quantum dots grown by metal-organic vapor-phase epitaxy (MOVPE) and InGaAs/GaAs quantum dots grown by molecular beam epitaxy. Both samples are not intentionally doped and have no electric gates. The dots in InGaAs sample are embedded in low-Q microresonator which enhances collection efficiency of their light emission.

The experiments are performed with the sample placed in an exchange-gas cryostat at T = 4.2 K, and using an external magnetic field B2 normal to the sample surface. In order to detect nuclear polarization on thc dot we use high resolution micro-photoluminescenee (PL) spectroscopy of single QJ)s. The QD PL is excited by a laser resonant with the wetting layer states (Ecrc.1.88 cV for ml' dots and E_.l.46 eli for InGaAs dots) and analyzed with a double 1 m spectrometer coupled to a CCD. Manipulation and probing of nuclear spin polarization relies on the hyperfine interaction of electrons and nuclear spins 1], and requires polarization-resolved excitation and detection of light as described in the main text.

The waveform for the radio-frequency excitation is produced by a digital arbitrary waveform generator.

"Inverse" spectroscopy with continious ri excitation spectrum shown in Fig.1(d) requires a completely aperiodic signal, which can not be produced by the digital device. For that reason we approximate the spectrum shown in Fig. 1(d) with spectrum consisting of a large number of discrete modes with equal spacing in as shown in Fig.2(c). Also real rf signal must have a finite power, and thus it has to be limited in spectral domain to a width w. The signal waveform is synthesized to have no spectral components within the gap of a width Wear, however due to imperfection of the rf circuit (harmonics and spurious noise) the amplitude of the rf field within the gap is not zero. In our experiments spectral density of the rf power inside the gap is.i1000 times smaller then power spectral density of the modes. Typical mean square ariiplitude of the in-plane rI oscillating magnetic field used in "inverse" spectroscopy experiments is 0.15 mT while the phases of the modes are chosen so that the peak value is B7 9.3 mT.

The duration of the rf pulse for inverse spectroscopy Tr; = 5.5 s is chosen to be long enough to produce steady-state population probability distribution of the nuclear spin states shown in Fig. 1 (f). On the other hand for spectroscopy on phosphorus in order to avoid broadening we use T=SO ms which is shorter than the time required to completely erase nuclear polarization, and thus gives non-saturated spectrum. Both InP and InCaAs dots used in this work exhibit long nuclear spin decay times [2] T >100 sso that natural decrease of nuclear polarization during rf excitation and rf pulse is negligible.

Nuclear spin spectrum in the presence of strain. Below we briefly summarize the effect of external fields on the nuclear spin spectrum. In magnetic field B along Oz axis and in the presence of elastic strain, the Hannltonian for a nuclear spin I can be written as [3: -hvLI -I-Hq, (1) where 11L = 7B/(27i-) is Larmor frequency and HQ describes interaction of the nuclear quadrupole moment with the electric field gradient (EPa), described by a second rank traeeless tensor of the elec-trostatic potential second derivatives 3⁄4j. In the frame Ox'y'z' with the axes along the principal axes of V: HQ = huQ(3J --ij(I -I,))/6, (2) 3cQV, V.c, . where Uq = 21(21-flh and rj = ,, describe strength and deviation of the EFO from the axial symmetry, respectively [3].

In the case of high magnetic field (UL 2 VQ) studied here the quadrupole interaction can be treated as perturbation. The main first order effect arises due to the V,. component of the EFG: for the uniaxial EFG with main axis along external magnetic field the frequency of the I <-J -f-I transition reads as VL + (I +1/2)vq, i.e. 21 NMR lines are observed equally spaced by VQ. In the ease of non-axial symmetry of the EFG (ij $ 0) or deviation of the EFG principle axis Qz' from the magnetic field direction Oz, further changes in the transition frequencies are observed. However, the shift of the central transition -1/2.-1/2 appears only in the second order and can be written as: 2 V2 = __q(J(J + 1)-3/4)G(o, , #) (3) 9 1"L where angle 0 describes orientation of the EFO principle axes, G(0 = O,tj = 0, ) = 0 and -1 < G(O, r, i5) c 1/2 for all possible values ci O,q, (complete expression for G(O, i, ) can be found in Ref.

4]). Thus for 11L > VQ the shift of the CT is much smaller than for STs, resulting in narrow central peak in NMR spectrum.

Calculation of the NMR signal for "inverse" spcctroscopy. here we will refer to the figures in the main text for illustration of our discussion. Let us first consider "saturation" spectroscopy when the spectrum of rf excitation has a single frequency component only. If the rf frequency V equals to the frequency of the transition between I and + 1 states (-3/2 ++ -1/2 in Figs. l(a-c), thc populations of these spin levels are equalized (the dotted lines in Fig. 1(e)). The populations of all other spin levels are not affected, and the total change of nuclear spin polarization 8N due to rf excitation is determined only by the contributions of I and I -I-1 states. Taking the difference between the initial polarization [(J + 1)pp÷i + 1p"l/I and the polarization after saturation of the transition (1 + 1) + I] x (pI+1 + we find the amplitude of the detected NMR signal as: -(pI+i -pj)/(2I). (4) By contrast in the "inverse" spectroscoy method [Figs.1(d)-(f) all spin states contribute to the NMR signal. For simplicity we consider the ease of a narrow gap, i. e. when the frequency of only one nuclear transition coincides with the gap. Calculations for a general ease are bulky but straightforward. First we note, that if the gap is not in resonance with any transitions then all nuclear polarization will be erased yielding the final polarization SN = 0. II the gap is in resonance with I 4-* I + 1 transition 1-3/2 i-> -1/2 in Figs.1 (d-f)1, i. e. this transition is not excited, then the equalization of populations takes place separately for two groups of spin levels: for states with 4 < I and for states J > I + 1 (dotted lines in Fig. 1 (f)). This is because transfer of population induced by the rf field is allowed only between spin levels with 4 differing by +1. For each group, the population probabilities of the spin levels after the rf pulse will be the average of the their initial populations pj. Thus non-zero polarization astnv will be retained: 1 Pa (5) a I k=II1 The initial polarization of the nuclear spins created via the hyperfine interaction with the optically pumped spin-polarized electrons can be expressed in terms of the electron spin temperature T, assum-ing that the nuclear spin populations pi, follows the Bolzman distribution. In large magnetic fields when vI >> VQ, energies of the nuclear spin levels are approximately proportional to L and the initial populations can be described as [I)yakonov+Perel, JETPI973H = Z exp(Iji), (Eez Erz\ 6 kBT kBT,)' () where Z is the normalization factor, ks -Bolzman constant, E0 -the electron Zeeman splitting. /3 describes dynamic nuclear polarization occurring as a result of deviation of the electron spin temperature 2', from the bath temperature T due to optical orientation of the electrons.

Using the Bolzman population distribution of Eq. 6 we can calculate the sums in Eqs.4 and 5 and obtain the following expressions for the signal amplitudes for both saturation" and "inverse" NMR: -[() -Cfl] sinh(/3/2) N -21 sinh(21 + 1)fi/2]' (I -1) + (1 + 2 + l)e(21rn -(21 + N = 2I[e(2I*1) -1] . ( ) It is useful to consider several practical cases. For example, the amplitude of the CT signal is obtained from Eqs. 7 by substituting J = 1/2. For a givcn I, the CT NMIt signal ASN becomes a function of /3. For example, for I = 9/2 spin (indium) it can be easily derived that for any /3, "inverse" spectroscopy yields the signal enhancement of at least S) B/zXS.?tuJ > 125. Since CT signal gives narrow line in NMR spectrum it is much easicr to detect even for large quadrupole effects. Thus thu use of inverse NMR greatly enhances sensitivity for detection of even small amounts of quadrupole isotopes, in particular with large 1. For the smallest half-integer quadrupole nuclear spin 1-3/2, "inverse" NMR for the CT rnv,B sat B. still leads to a signal cnhancement of aSN /8N > 8. For thc S I transitions the sensitivity of "inverse" NMR reduces with increasing 1. However, even for the most split-off transitions -I ++ -1+1 and I -1 <-*1, the enhancement is > 9 for I = 9/2 and > 3 for I = 3/2.

Estimation of the chemical composition of the dots. This section presents an experimental method and numerical analysis enabling estimation of Ga and In intermixing within the volume of thc electron wavefunction in a QD. We use a long rf pulse leading to selective (and complete) depolarization of the i-th isotope, and thus enabling a selective measurement of the corresponding change in the exciton spectral splitting zXEz,. call be expressed via the nuclear polarization degrec Spj of the i-th isotope as: = pA1Sjy, (8) where p is the relative concentration of that isotope and A, is its hyperfinc constant. For InP, where the contribution of 1151n dominates, the hyerfine constant has been measured experimentally[5]: 47 teV. Using this value, and neglecting variation of electron density between gallium and indium sites, we can estimate the hyperfine constant for 60Ga as[3] AeGa = Aui3Jfl) 3/2 51 jieV, and similarly for T1Ga as AIiGa 65 peV. We also take into account that the two gallium isotopes have the natural abundances 0.6 and ar:ca 0.4. By introducing the total gallium concentration PCa we can write P69Ga = (Ga)PGa, P'Ga = 5('ua)PGa Since "5b and 69Ga have close NMR frequencies, we can only measure their combined Overhauser shift LXEgsoc, + The Overhauser shift for

U

710a, Ez,nGa, is measured separately. Finally, nuclear spin polarization for each isotope SN, i can be calculated using the Bolzman distribution Eq. 6 and thus expressed in terms of /3 for a given spin I. Using Eq. 8 we can write the following system of equations for PGa, pj,. and /3: Ez,G9ca + Ez,ll5J = ;P1_A(llSJfl)SN,(flSJTh) + U(69Ga)PGaA(69Ga)SN,(69Ga), Ez.71Ga = °r' Ca) PCaA (TlCa)SN,(7bCa). PGa pj 1. (9) For InP/GdnP QDs we measured the following values of the hyperfine shifts: A1.fzn5jn + àEz,GQCa jicV and Eii0 8 j.zeV. Solving Eq. 9 we find PGa 35%, p 65% implying signifi-cant penetration of electron wavefunetion into GaIn? barrier and/or diffusion of gallium into the dot.

We also find /3 0.8 corresponding to the average electron spin polarization of (sH 0.2. For In-GaAs quantum dots we assumc the same values of hyperfine constants A. Using the measured shifts + AEzrica 56 bLeV and AEZI1Ga c 18 peV, we find /3 0.8 and, as expected, a much lower concentration of indium Pin 20%. For both types of quantum dots we find very similar degrees of optically pumped nuclear spin polarization: 8N in) 0.8 and 8N('Ca) 0.6.

Estimation of strain in a QD. For uniaxial = c) strain Ch = i -(en -i-c)/2 along the direction of the applied magnetic field, the frequency shift of the 1/2÷43/2 transition from the CT reads as = J(2J1)' where Q is the quadrupole moment, Ii is the Plank constant, Sj is a component of the elastic-gradient tensor. For t1Ga in InGaAs dots the maximum t'q -.2.5 MHz can be estimated from the width of thc sidebands in the NMR spectrum in Fig.3(e). Using the value 2.7 x 1022 V/m2 measured for gallium in bulk GaAs[6] we estimate csi 6%.

In InP dots we use NMR, on 1151n satellite transitions to estimate strain. According to Eq. 7, the amplitude of the "inverse" NMR signal from the satellite transition 1 -1 decreases with increasing spill I, leading to insufficient signal for large J and unreliable estimation of the maxi'nun' quadrupole shift. This is overcome in an additional experiment, where long broadband rf pulse (without the gap) centered at the frequency of the indium CT transition is used to erase polarization of indium. The total width of the excitation spectrum w is varied. We find that the magnitude of the erased nuclear polarization initially increases with iv, and saturates at a constant level at 20 MHz. This allows to estimate the maximum shift of the 7/2 9/2 transition frequency as 10 Mlix, which, on the other hand, is also equal to 4vq. Using then 811 5.9 x 1022 V/m2 for indium in InP we estimate 5%.

Elastic strain also affects CT frequency. For example using VQ 2.5 MHz derived for 151n we estimate that the shift according to Eq. 3 can be as large -0.65 MHz at ML 49.7 MHz. On the other hand in experiment we observe shifts only on the order of iSO kllz (Fig.3(b)). This suggests that the deviation between the strain axis and external field (charneterized by 0) as well as non-axial symmetry of EFC (characterized by 7) are small, while the most likely reason for inhomogeneolls distribution of ST shifts is due to variation of 747 within the dot volume rather than 0 and i. We also note that for ToAs nuclei large FF0 can result not only from elastic strain but also from electric fields created by random substitution of gallium atoms by indium. This may explain further broadening of 75As CT transition.

[1] A. I. Tartakovskii, T. Wright, A. Russell, V. I. Falko, A. B. Vankov, 3. Skiba-Szymanska, I. Drouzas, R. S. Kolodka, M. S. Skolnick, P. W. Fry. A. Tahraoui, H.-Y. Lit, M. Ilopkinson, Phys. Rev. Lett. 98, 026806 (2007).

[21 E. A. Chekhovich, MN. Makhorrin, J. Skiba..Szymanska, A. H. Krysa, V. D. Kulakovskii, M. S. Skolnicic. A. I. Tartakovskii, Phys. Rev. B 81, 245308 (2010).

[3] A. Abragain, The primcp1es of Nuclear Magnetism (Oxford University Press, London, 1961).

[4] p. p. Man, Encyclopedia of Nuclear Magnetic Resonance (Wiley, 1996).

[5 B. Gotschy, G. Denninger, H. Obloh, W. Wilkening, and J. Schnieder, Solid State Comunications 71, 29 (1989).

[6] R. K. Sundfors, Phys. Rev. B 10, 4244 (1974).

Claims (24)

1. <claim-text>CLAIMS1. A method of measuring a sample using nuclear magnetic resonance (NMR) spectroscopy, comprising the steps of: i) providing: a) a sample to be measured; b) a magnet for applying a magnetic field to the sample; c) a first excitation source for emitting electromagnetic (EM) radiation that has a spectral profile that has a first excitation portion and a second excitation portion, wherein the second excitation portion is higher in frequency than the first excitation portion and the second excitation portion is spectrally separated from the first excitation portion by a spectral gap; and d) measuring means for measuring a property dependent on a degree of nuclear spin polarisation of the sample; H) applying a magnetic field to the sample using the magnet; Hi) illuminating the sample with the first excitation source to electromagnetically excite the nuclei of the sample; and iv) measuring the sample using the measuring means.</claim-text> <claim-text>
2. 2. A method according to claim 1, further comprising the steps of providing at least one optical source for optically exciting the sample, wherein the measuring means comprise a detector for detecting re-emitted optical signal from the sample, and the step of measuring the sample comprises detecting re-emitted optical signal from the sample using the detector.</claim-text> <claim-text>
3. 3. A method according to claim 2, wherein the at least one optical source provides an optical pump for increasing the degree of nuclear polarization in the sample, and an optical probe for exciting the optical signal from the sample.</claim-text> <claim-text>
4. 4. A method according to any preceding claim, wherein the first excitation podion and/or the second excitation portion includes a series of modes spectrally spaced from one another, wherein the spacing between the modes is less than the spectral gap.</claim-text> <claim-text>
5. 5. A method according to claim 4, wherein each of modes of the first excitation portion and/or the second excitation portion are equally spaced from one another.</claim-text> <claim-text>
6. 6. A method according to claim 4 or 5, wherein the amplitude of each mode is substantially equal to the amplitude of the other modes.</claim-text> <claim-text>
7. 7. A method according to claim 1, 2 or 3, wherein the first excitation portion and the second excitation portion include broadband emission of substantially constant and equal amplitude.</claim-text> <claim-text>
8. 8. A method according to any preceding claim, wherein: the amplitude of the EM radiation in the spectral gap is equal to or less than 1/10 of the amplitude of the EM radiation in the first and second excitation portions, or the amplitude of the EM radiation in the spectral gap is equal to or less than 1/30 of the amplitude of the EM radiation in the first and second excitation portions, or the spectral density of ri power in the spectral gap is equal to or less than 1/100 of that in the first and second excitation portions, or the spectral density of ii power in the spectral gap is equal to or less than 1/1 000 of that in the first and second excitation portions.</claim-text> <claim-text>
9. 9. A method according to any preceding claim, wherein the amplitude of the EM radiation in the spectral gap is substantially zero.</claim-text> <claim-text>
10. 10. A method according to any preceding claim, wherein the first excitation source is configured such that the spectral position of the spectral gap is movable, and wherein steps iii) and iv) are repeated for spectral profiles having a spectral gap having an incrementally increased or decreased spectral position.</claim-text> <claim-text>
11. 11. A method according to any preceding claim, further comprising the steps of: v) providing a second excitation source for emitting EM radiation that has a spectral profile identical to the spectral profile of the first excitation source except wherein no spectral gap is present; vi) illuminating the sample with the second excitation source to electromagnetically excite the nuclei of the sample; vii) measuring the sample using the measuring means; and viii) calculating the difference in detected signals obtained in steps iv) and vii).</claim-text> <claim-text>
12. 12. A method according to any preceding claim, wherein the sample is a semiconductor material.</claim-text> <claim-text>
13. 13. A method according to claim 12, wherein the sample is a bulk semiconductor material.</claim-text> <claim-text>
14. 14. A method according to claim 13, wherein the sample is one or more quantum dots
15. 15. A method according to claim 14, wherein the one or more quantum dots are strained self-assembled quantum dots.
16. 16. A method according to any preceding claim, wherein the sample is cooled to a temperature below 80 K.
17. 17. A method according to claim 14, wherein the sample is cooled to a temperature below K, and preferably to about 4.2 K.
18. 18. A method according to any preceding claim wherein the first excitation source comprises a radio frequency (rf) source.
19. 19. A method of measuring a sample using nuclear magnetic resonance (NMR) spectroscopy substantially as hereinbefore described with reference to the accompanying drawings.
20. 20. An apparatus for measuring a sample using nuclear magnetic resonance (NMR) spectroscopy, comprising: a magnet for applying a magnetic field to the sample; a first excitation source arranged to emit electromagnetic (EM) radiation that has a spectral profile that has a first excitation portion and a second excitation portion, wherein the second excitation portion is higher in frequency than the first excitation portion and the second excitation portion is spectrally separated from the first excitation portion by a spectral gap; and measuring means arranged to measure a property dependent on a degree of nuclear spin polarisation of the sample
21. 21. An apparatus according to claim 20, further comprising at least one optical source for optically exciting the sample, wherein the measuring means comprises a detector arranged to detect re-emifted EM radiation from the sample.
22. 22. An apparatus according to claim 21, wherein the at least one optical source provides an optical pump for increasing the degree of nuclear polarization in the sample, and an optical probe for exciting the optical signal from the sample.
23. 23. An apparatus according to any of claims 20 to 22, further comprising a second excitation source arranged to emit EM radiation that has a spectral profile identical to the spectral profile of the first excitation source except wherein no spectral gap is present.
24. 24. An apparatus for measuring a sample using nuclear magnetic resonance spectroscopy substantially as hereinbefore described with reference to the accompanying drawings.</claim-text>