Methods and systems are described for spectral decomposition of composite solid-state spin environments through quantum control of electronic spin impurities. Δ sequence of spin-control modulation pulses are applied to the electronic spin impurities in the solid-state spin systems. The spectral content of the spin bath that surrounds the electronic spin impurities within the solid-state spin system is extracted, by measuring the coherent evolution and associated decoherence of the spin impurities as a function of number of the applied modulation pulses, and the time-spacing between the pulses. Using these methods, fundamental properties of the spin environment such as the correlation times and the coupling strengths for both electronic and nuclear spins in the spin bath, can be determined.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method comprising: applying a sequence of spin-control modulation pulses to electronic spin impurities in a solid-state spin system; and extracting a spectral content of a spin bath that surrounds the electronic spin impurities within the solid-state spin system, by measuring the coherent evolution and associated decoherence of the spin impurities as a function of number of the applied modulation pulses, and the time-spacing between the pulses. 2. The method of claim 1, wherein the act of measuring the coherent evolution and associated decoherence of the spin impurities comprises: defining a time-dependent coherence function C(t)=eχ(t) to represent the coherence of spin impurities within the solid-state spin system, where χ(t) is a decoherence functional that describes the decoherence of the spin impurities as a function of time; and measuring the time-dependent coherence function C(t)=e−χ(t) so as to extract a spectral component S(ω0) of the composite solid-state spin system at the frequency ω0. 3. The method of claim 2, wherein the modulation pulse sequence has a modulation waveform described in a frequency domain by a filter function Ft(ω) that is mathematically related to the decoherence functional by: χ  ( t ) = 1 π  ∫ 0 ∞   ω   S  ( ω )  F t  ( ω ) ω 2 , where S(ω) is a spectral function describing coupling of the spin impurities to a spin bath environment of the composite solid-state spin system. 4. The method of claim 1, wherein the act of extracting the spectral content at a desired frequency ω0 comprises subjecting the spin impurities to a spectral δ-function modulation, with an ideal filter function Ft(ω) with a Dirac delta function localized at ω=ω0, so that the spectral content of the spin bath at the desired frequency ω0 is given by S(ω0)=πln(C(t))/t and the ideal filter function Ft(ω) is mathematically represented by: Ft(ω)/(ωLt)=δ(ω−ω0) 5. The method of claim 4, further comprising repeating, for a number of different frequencies ω=ωi, i=1 . . . n, the acts of subjecting the spin impurities to spectral S-function modulations with the Dirac delta function localized at each frequency co, so as to extract the spectral content S(ω) at all of the different frequencies ω=ωi, i=1 . . . n to obtain a broad range of spectral decomposition for the spin bath. 6. The method of claim 3, further comprising: approximating the delta function in the filter function TWO at a frequency slightly different from am, then extracting a spectral component S(ω0) of the composite solid-state spin system at the slightly different frequency. 7. The method of claim 6, wherein the modulation pulse sequence is an n-pulse CPMG sequence; and wherein a mathematical formula for the filter function for the n-pulse CPMG sequence is: F n CPMG  ( ω   t ) = 8  sin 2  ( ω   t 2 )  sin 4  ( ω   t 4  n ) cos 2  ( ω   t 2  n ) . 8. The method of claim 7, wherein the modulation pulse sequence is an n-pulse XY sequence. 9. The method of claim 1, wherein the solid state system is a diamond crystal, the spin impurities are NV centers in the diamond crystal. 10. The method of claim 9, wherein the spin bath environment in the diamond crystal is dominated by fluctuating N(nitrogen atom) electronic spin impurities so as to cause decoherence of the NV centers through magnetic dipolar interactions. 11. The method of claim 10, wherein the N spins of the spin bath are randomly oriented, and wherein the act of extracting the spectral content of the spin bath comprises extracting a Lorentzian spectrum of the N spin bath's coupling to the NV centers, given by: S  ( ω ) = Δ 2  τ C π  1 1 + ( ω   τ C ) 2 , where Δ is the average coupling strength of the N bath to the NV spin impurities, and where τc is the correlation time of the N bath spins with each other. 12. The method of claim 11, further comprising the act of determining the values of A and Tc from the extracted spectrum S(ω). 13. A system comprising: a microwave pulse generator configured to generate a sequence of spin-control modulation pulses and to apply the pulses to a sample containing electronic spin impurities in a solid-state spin system; and a processing system configured to measure the coherent evolution and associated decoherence of the electronic spin impurities as a function of the number of the applied pulses and the time-spacing between the pulses, so as to extract a spectral content of a spin bath that surrounds the electronic spin impurities within the solid-state spin system. 14. The system of claim 13, wherein the electronic spin impurities comprise NV (nitrogen-vacancy) centers, and wherein the solid-state spin system comprises a diamond crystal. 15. The system of claim 13, wherein the spin-bath environment comprises 13C nuclear spin impurities and N electronic spin impurities within the diamond crystal. 16. The system of claim 13, further comprising an optical system, including an optical source configured to generate excitation optical pulses that initialize and read out the spin states of the spin impurities, when applied to the sample. 17. The system of claim 16, wherein the optical source is a laser tunable to a frequency of about 532 nm. 18. The system of claim 16, wherein the processing system comprises a computer-controlled digital delay generator coupled to the optical source and the microwave source and configured to control the timing of the microwave pulses and the optical pulses. 19. The system of claim 16, further comprising a detector configured to detect output radiation from the NV centers after the microwave pulses and the optical pulses have been applied thereto. 20. The system of claim 16, wherein the optical system further comprises an acousto-optic modulator configured to time the optical pulses so as to prepare and read out the NV spin states. 21. The system of claim 19, wherein the optical system further includes at least one of: a dichroic filter configured to separate fluorescent radiation generated by the NV centers in response the excitation optical pulses; and an objective configured to collect the fluorescent radiation generated by the NV centers in response to the excitation optical pulses and directed the collected fluorescence to the detector. 22. The system of claim 13, wherein the solid state system is a diamond crystal, the spin impurities are NV centers in the diamond crystal, and the spin bath environment in the diamond crystal is dominated by fluctuating N(nitrogen atom) electronic spin impurities, so that the spectrum of the N spin bath's coupling to the NV centers is a Lorentzian spectrum given by: S  ( ω ) = Δ 2  τ C π  1 1 + ( ωτ C ) 2 . where Δ is the average coupling strength of the N bath to the NV spin impurities, and where τc is the correlation time of the N bath spins with each other. 23. The system of claim 22, wherein the processing system is further configured to determine the values of Δ and τc from the extracted spectrum S(ω). 24. The system of claim 13, wherein the electronic spin impurities comprise phosphorus donors, and wherein the solid-state spin system comprises silicon. 25. The system of claim 13, wherein the modulation pulse sequence comprises at least one of: an n-pulse CPMG sequence; and an n-pulse XY sequence.