WO2023224674A2 - Rapidly enhanced spin polarization injection in an optically pumped spin ratchet - Google Patents
Rapidly enhanced spin polarization injection in an optically pumped spin ratchet Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/62—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using double resonance
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
- G01R33/282—Means specially adapted for hyperpolarisation or for hyperpolarised contrast agents, e.g. for the generation of hyperpolarised gases using optical pumping cells, for storing hyperpolarised contrast agents or for the determination of the polarisation of a hyperpolarised contrast agent
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
- G01R33/32—Excitation or detection systems, e.g. using radio frequency signals
- G01R33/323—Detection of MR without the use of RF or microwaves, e.g. force-detected MR, thermally detected MR, MR detection via electrical conductivity, optically detected MR
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/24—Arrangements or instruments for measuring magnetic variables involving magnetic resonance for measuring direction or magnitude of magnetic fields or magnetic flux
- G01R33/26—Arrangements or instruments for measuring magnetic variables involving magnetic resonance for measuring direction or magnitude of magnetic fields or magnetic flux using optical pumping
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- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
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- G21K1/00—Arrangements for handling particles or ionising radiation, e.g. focusing or moderating
- G21K1/16—Arrangements for handling particles or ionising radiation, e.g. focusing or moderating using polarising devices, e.g. for obtaining a polarised beam
Definitions
- This disclosure relates to spin polarization into nuclear baths, more particularly to boosting the spin injection rate.
- DNP dynamic nuclear polarization
- critical to such applications is the rate at which polarization can be injected, measured, for instance, in terms of total angular momenta injected per unit time. For DNP applications, this rate ultimately determines the possible throughput of hyperpolarized spectroscopy and imaging.
- FIGs. 1A-E show a graphic representation of spin-ratchet polarization and data.
- FIGs. 2A-E show an embodiment of an apparatus and related data for high power optical polarization.
- FIGs. 3A-D show an embodiment and related data for thermal management for high power optical pumping.
- FIGs. 4A-B show data for enhancing rate of polarization transfer.
- FIGs. 5A-E show graphs related to speed limits for polarization transfer.
- FIGs. 6A-D show graphs related to spin injection via high-power optical pumping.
- the embodiments here involve rapid injection of spin polarization into a nuclear bath is a problem of broad interest, spanning dynamic nuclear polarization (DNP) to quantum information science.
- the embodiments here involve strategy to boost the spin injection rate by exploiting electrons that can be rapidly polarized via high-power optical pumping.
- the embodiments demonstrate this in a model system of nitrogen vacancy center electrons injecting polarization into a bath of 13 C nuclei in diamond.
- the embodiments also include an apparatus with thirty lasers to deliver of greater 20W of continuous, nearly isotropic, optical power to the sample with only a minimal temperature increase.
- the embodiments also elucidate speed limits of nuclear spin injection that are individually bottlenecked by rates of electron polarization, electron-nuclear polarization transfer, and spin diffusion.
- the embodiments demonstrate opportunities for rapid spin injection employing non-thermally generated electron polarization, and has relevance to a broad class of experimental systems, including in DNP, quantum sensing, and spin-based MASERs. While the example of diamond nuclei are used here, the nuclear bath may be any ensemble of nuclear spins of any material with nuclei.
- FIGs. 1A-E shows a graphic representation of spin-ratchet polarization and data.
- FIG. 1A shows an electron e and nuclei n in a schematic lattice. Hyperpolarization builds up through optical polarization of the electron (NV center), polarization transfer to directly coupled nuclei ( 13 C), and spin diffusion to block nuclei. Corresponding rate coefficients are depicted.
- FIG. IB show DNP protocol that comprises continuous application of laser and swept-MWs for period T. MW sweep rate is a>r over bandwidth B.
- FIG. 1C shows a graphical representation of a spin ratchet.
- FIG. IE shows a typical DNP profile ( ⁇ r) as a function of MW sweep rate ⁇ r. The plot is shown against for clarity. Solid line is a fit to model in Eq. (1). Dashed line denotes optimal rate
- a key aspect of the embodiments includes an innovation that delivers high optical power continuously to the electrons, allowing to approach the regime.
- the time- averaged optical power here (greater than 20 W) is substantially higher than previous experiments.
- optical e-polarization permits DNP at low fields where high MW powers are readily accessible.
- the embodiments demonstrate an approach to increase the polarization injection rate through a simultaneous " lockstep" increase in laser and MW power.
- the embodiments identify hyperpolarization speed-limits by delineating experimental regimes where the three rates above individually bottleneck polarization injection.
- the discussion shows high-power optical DNP can yield significant gains in injection polarization rate, boosted by as much as two orders of magnitude compared to conventional approaches.
- Rapid hyperpolarization obtained here opens avenues for quantum sensors, such as gyroscopes and spin sensors, constructed out of diamond 13 C nuclei.
- the approach here is also readily generalizable to other experimental systems, including optically pumped triplet systems for DNP and MASERs.
- the experiments employ a ⁇ 16 mm 3 single-cry stal sample with ⁇ 1 ppm NV concentration and natural abundance 13 C (FIG. 1 A).
- the inter-NV spacing is ⁇ 24 nm
- 13 C lattice density is ⁇ 0.92/nm 3 .
- Tin ⁇ 5 min sets the overall polarization memory time for the system.
- the discussion refers to the optical and MW power in Watts as r/e and ⁇ r respectively. These are related to ⁇ Ke, ⁇ in FIG. 1A, but specify experimentally employed parameters.
- ⁇ the discussion denotes the effective incident power, including effects of geometry, occlusion, and laser performance. Similar, ⁇ r denotes MW power after accounting for all reflection losses.
- K e c e ⁇ e is approximately proportional to the optical power applied.
- the absolute e-polarization obtained depends on several factors, including interconversion between NV center charge states and is difficult to precisely quantify.
- the experiments employ pulsed spin-lock read-out that permits long 13 C precession lifetimes exceeding 100 s, with a decay constant T'2 > 20s. Signal is accumulated for the entire period and sampled every 1 nanosecond in windows between the pulses. As a result, the experiments obtained high measurement fidelity , with integrated SNR (signal to noise ratio) as high as
- Diagonalization leads to four Landau-Zener level anti-crossings (LZ-LACs), with energy gaps, (see FIG. 1D), such that ⁇ 2 ⁇ ⁇ 1 . Swept MWs cause a traversal through this LZ-LAC cascade. Its action can be evaluate under simplify ing approximations that capture the experiments: (i) LZ-LACs are assumed to be traversed sequentially, and, (ii) e-repolarization is assumed to occur at the start of every sw eep event. This entails negligible laser action at the LZ-LACs, and is valid when B>> ⁇ 1,2 , as in the experiments.
- Hyperpolarization buildup occurs because the energy gaps are conditioned on the nuclear state. Traversals through the LZ-LACs are differentially adiabatic or diabatic, leading to a population bias towards one nuclear state Indeed, population bifurcation at a LZ-LAC is set by its adiabaticity and captured by respective tunneling probabilities (FIG. 1C). Hyperpolarization occurs when sweep rates ⁇ r are such that (adiabatic) and (diabatic). The rate of polarization is then:
- the first term in square brackets is the rate of e-polarization and the last term captures the e ⁇ n polarization transfer efficiency per sweep.
- Mr can allow faster ratchet operation, but come at the cost of (i) reduced electron polarization and (ii) lower transfer efficiency per sweep because the differential adiabaticity in FIG. ID is compromised. Indeed, at high- ⁇ r, T1 ⁇ T2 ⁇ 1, and P ⁇ O. Therefore ⁇ opt sets an overall speed-limit for e ⁇ n polarization transfer, and defines the rate at which the ratchet (FIG. 1C) should be operated.
- connections to recent work concerned with speed-limits of quantum state transfer in qubit networks with long-range interactions include P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith. M. Foss-Feig, S. Michalakis, A. V.
- Eq. (1) suggests that the rate of polarization transfer, encoded in ⁇ opt , can be enhanced through a simultaneous increase in laser and MW power - higher-pe allows faster e-repolarization, and higher-pr permits faster sweeps while maintaining differential adiabaticity.
- Spin injection rates can potentially exceed that of conventional DNP because optically polarizable electrons can be polarized faster than and be carried out at low field. Achieving sufficient optical power to access this regime, however, is a technical challenge.
- the CW optical excitation here yields continuous e-repolarization, and is especially advantageous for DNP with electrons with broad ESR spectra. Furthermore, lower peak power injection here al-lows more efficient heat diffusion and higher average power before sample damage thresholds are reached.
- the apparatus shown in FIG. 2A, consists of a dome-shaped structure (“laser dome” ), shown in more detail in FIG. 2B, that houses 30 diode lasers.
- the structure comprises a 3D printed dome.
- the lasers have power of approximately ⁇ 0.8W each, delivered via multimode fibers, with a beam diameter ⁇ 4mm.
- FIGs. 2A and 2B show an embodiment of a system 10 for high power optical hyperpolarization.
- the laser dome in FIG. 2B inserts into the fixture of FIG. 2A.
- the system includes laser fibers 12 through which lasers, one embodiment uses laser diodes such as 14, transmit the laser light from the diodes to the sample undergoing hyperpolarization.
- Laser drivers such as 16 drive the lasers. That many lasers in a confined space will generate a lot of heat, so the system includes a cooling column 20 that has at least one air or gas inlet 18.
- the fixture is encased in a Plexiglas shell 22.
- FIG. 2B shows a view of the laser dome 24.
- the laser fibers insert into centrally aligned bores such as 26.
- the sample undergoing hyperpolarization 32 resides in an insertable structure, such as a test tube, 30.
- the insertable structure or holder inserts into the center space of the laser dome through the cooling tower 20.
- This view allows one to see one of the air inlets 18.
- the inset picture of FIG. 2C shows the laser dome with all bores having fibers.
- FIG. 2D shows a graphical depiction of the sample 32 being illuminated with multiple lasers through multiple fibers inside the laser dome 24.
- the microwave coil 48 provides the microwave energy while the sample undergoes optical polarization.
- the method of boosting spin injection rates into an ensemble of nuclear spins then involves applying a microwave field to a sample having nuclear spins, and continuously applying laser illumination from multiple lasers to the sample to effect transfer of polarization from electrons in the sample to the nuclear spins in the sample.
- FIG. 2E show ray -trace simulations that help discern the best positions of laser fibers in both side and top views. Density' of overlapping ray traces here serve as a proxy for relative intensity of irradiation onto the sample. The central portion of the sample sees excitation from multiple sources which, to an extent, compensates for attenuation through it, although quantifying the exact penetration depth through the sample is experimentally challenging.
- the apparatus may include an in-situ heat exchanger that efficiently ejects heat while keeping the sample free from motion.
- FIG. 3A shows one embodiment of such a heat exchanger.
- the sample is held in a test tube 30 surrounded by a quantify of water.
- Thermal energy injected into the sample rapidly dissipates into the water, which serv es as a heat sink.
- the water is kept at a stable temperature by flowing cool nitrogen gas, which may have a temperature of -20° C at inlet 18, across the test tube.
- the gas is delivered from slits built into the neck region of the laser dome, show n by vertical dow n arrows such as 44 and short horizontal arrows in FIG. 3A.
- Nitrogen flow rate is calibrated so the w ater temperature is ⁇ 9° C when lasers are off.
- Heat exchange exploits the excellent thermal conductivity of the sample, especially of diamond (2200 W/mK), and the large heat capacity of water for efficient thermal dissipation, show as the twisting upward arrow 46 in FIG. 3A.
- the benefit of this relayed strategy is that the cold gas does not contact the sample directly, and the sample volume can be enclosed, an advantage for sample shuttling to high field.
- FIGs. 3B-C elucidates measured temperature buildup in the sample and surrounding fluid under 120 secs continuous irradiation at different optical powers. After 120 s, the lasers are turned off, and the temperature dissipation is again monitored. Even at sustained 24 W optical power, corresponding to an intensity of ⁇ 0.19 kW/cm 2 , the (asymptotic) steady-state temperature is remarkably less than 30° C.
- FIG. 3D plots the steady-state temperatures for different powers. From the buildup rate, the embodiments estimate that approximately 50W power can be applied before system limits (related to water boiling) are reached.
- FIG. 5A-B show obtained maximal polarizations against for the MW power regimes (colorbar) considered, plotted on a linear (FIG. 5A) and logarithmic (FIG. 5B) scale. Signal here is measured at ⁇ opt .
- Solid lines are guides to the eye.
- points in FIG. 5C display the extracted optimal rates coopt ( ⁇ e ) for different MW powers. Solid lines are linear fits.
- FIG. 5E plots the slope of these lines, ⁇ d ⁇ opt ( ⁇ e)/d ⁇ e , while FIG.
- a combined view of data in FIG. 4-FIG. 5 allows the ability to correlate ⁇ opt to the absolute spin injection rates into the 13 C nuclei.
- FIG. 4B(iii) considers a further 10-fold increase in MW power (regime III).
- a rightward shift in ⁇ opt is clearly evident with increasing optical power, and spin-ratchet operation is rapid, evidenced by the increased slope in FIG. 5C(III).
- Higher ⁇ r allows faster sweeps due to weaker adiabaticity constraints, and ⁇ e can be simultaneously boosted to increase the rate of source e-polarization, yielding a lockstep Ke-Kr increase in hyperpolarization rate.
- the concomitant signal increase is evident in FIG. 5A-B.
- the resulting maximal rates ⁇ opt ⁇ 0.65 kHz approach, and potentially exceed, the thermal rate expected in this sample.
- FIG. 5B-C demonstrates that while e-polarization rates increase with ⁇ e , nuclear spin injection is ultimately limited by spin diffusion. As such, spin injection can be considered optimally rapid in this regime.
- FIG. 6C considers the small-time regime (T ⁇ 0.6s).
- Polarization buildup is approximately linear in this regime; color-bar shows different optical powers employed. Corresponds slopes (FIG. 6D) permit quantification of absolute polarization injection rates (%/s) by comparing against the thermal polarization at 7T ( ⁇ 10-5).
- FIG. 6D demonstrates that spin injection rate scales approximately linearly with optical power, arising from the increased rate of source e- polarization K e at the NV center sites. Indeed, the sustained high-power optical delivery possible via FIG. 2, yields an approximately 167-fold increase in polarization injection with respect to using a single weak laser.
- the experiments measure a linearized bulk injection rate of ⁇ 0.06%/s averaged over the sample.
- Kaptein Level anti-crossings are a key factor for understanding para-hydrogen-induced hyperpolarization in sabre experiments, ChemPhysChem 14, 3327 (2013). . The elucidation of spin injection speed limits is relevant for quantum information transfer and memories. [0047] Second, the strategy for high-power optical illumination and thermal management developed here is extensible to other systems, including organic triplet molecular systems, and UV generated non-persistent radicals. These applications could be applied to e-spin MASERs, and quantum sensors with e-spin ensembles, where reaching higher optical powers is the primary factor limiting magnetometer sensitivity.
- the rapidly injected spin polarization here projects onto applications that exploit hyperpolarized 13 C spins as quantum sensors, leveraging their long lifetimes in the laboratory and rotating frames. This includes magnetometers, gyroscopes, sensors for dark-matter searches, and as RF imaging agents.
- the embodiments here have demonstrated the ability to rapidly inject spin polarization into a lattice of nuclear spins via optical polarized electrons under simultaneously applied high-power optical and MW irradiation. In the process, the embodiments elucidated speed-limits that bottleneck bulk polarization transfer in various regimes, and showed an approximately 167-fold gain in spin-injection rate via high power excitation. These techniques inform on interesting new opportunities afforded by non- thermally polarized electrons for DNP and quantum sensing.
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Abstract
An apparatus for spin polarization into a collection of nuclear spins has a housing, an array of lasers arranged around a periphery of the housing, a holder configured to hold a sample of material at the center of the housing in a position that can be illuminated by the lasers, and an energy source to power the lasers to optically hyperpolarize electrons in the sample to transfer polarization from the electrons to nuclear spins in the sample. A method of boosting spin injection rates into an ensemble of nuclear spins includes applying a microwave field to a sample having nuclear spins, and continuously applying laser illumination from multiple lasers to the sample to effect transfer of polarization from electrons in the sample to the nuclear spins in the sample.
Description
RAPIDLY ENHANCED SPIN POLARIZATION INJECTION IN AN OPTICALLY PUMPED SPIN RATCHET
RELATED APPLICATION
[0001] This application claims priority to and the benefit of US Provisional Application No. 63/287,626 filed December 9, 2021, which is incorporated herein by reference in its entirety.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT
[0002] This invention was made with Government support under grant number N 00014-20- 1-2806 awarded by the Office of Naval Research. The Government has certain rights in this invention.
TECHNICAL FIELD
[0003] This disclosure relates to spin polarization into nuclear baths, more particularly to boosting the spin injection rate.
BACKGROUND
[0004] The injection of polarization into a bath of spins is a task of central importance in a variety of contexts. Not only is it the basis for dynamic nuclear polarization (DNP), but is also important for the initialization of spin-based quantum information processors, quantum sensors, and in emerging applications in spintronics. Critical to such applications is the rate at which polarization can be injected, measured, for instance, in terms of total angular momenta injected per unit time. For DNP applications, this rate ultimately determines the possible throughput of hyperpolarized spectroscopy and imaging.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] FIGs. 1A-E show a graphic representation of spin-ratchet polarization and data.
[0006] FIGs. 2A-E show an embodiment of an apparatus and related data for high power optical polarization.
[0007] FIGs. 3A-D show an embodiment and related data for thermal management for high power optical pumping.
[0008] FIGs. 4A-B show data for enhancing rate of polarization transfer.
[0009] FIGs. 5A-E show graphs related to speed limits for polarization transfer.
[0010] FIGs. 6A-D show graphs related to spin injection via high-power optical pumping.
DETAILED DESCRIPTION OF THE EMBODIMENTS
[0011] The embodiments here involve rapid injection of spin polarization into a nuclear bath is a problem of broad interest, spanning dynamic nuclear polarization (DNP) to quantum information science. The embodiments here involve strategy to boost the spin injection rate by exploiting electrons that can be rapidly polarized via high-power optical pumping. The embodiments demonstrate this in a model system of nitrogen vacancy center electrons injecting polarization into a bath of 13C nuclei in diamond. The embodiments also include an apparatus with thirty lasers to deliver of greater 20W of continuous, nearly isotropic, optical power to the sample with only a minimal temperature increase. This constitutes a substantially higher power than in previous experiments, and through a spin-ratchet polarization transfer mechanism, yields boosts in spin injection rates by close to two orders of magnitude. The polarization of the electrons in the sample can then be transferred to the nuclear spins in the sample.
[0012] The embodiments also elucidate speed limits of nuclear spin injection that are individually bottlenecked by rates of electron polarization, electron-nuclear polarization transfer, and spin diffusion. The embodiments demonstrate opportunities for rapid spin injection employing non-thermally generated electron polarization, and has relevance to a
broad class of experimental systems, including in DNP, quantum sensing, and spin-based MASERs. While the example of diamond nuclei are used here, the nuclear bath may be any ensemble of nuclear spins of any material with nuclei.
[0013] The embodiments demonstrate the potential for enhanced rates of spin injection employing non-thermally generated electron polarization. FIGs. 1A-E shows a graphic representation of spin-ratchet polarization and data. FIG. 1A shows an electron e and nuclei n in a schematic lattice. Hyperpolarization builds up through optical polarization of the electron (NV center), polarization transfer to directly coupled nuclei (13C), and spin diffusion to block nuclei. Corresponding rate coefficients
are depicted. FIG. IB show DNP protocol that comprises continuous application of laser and swept-MWs for period T. MW sweep rate is a>r over bandwidth B. FIG. 1C shows a graphical representation of a spin ratchet. MW sweeps drive optically generated e-polarization to nuclei akin to cranks of a ratchet. (D) Shows energy versus frequency for the DNP mechanism. Polarization transfer occurs via MW driven traversals of cascaded Landau-Zener anti-crossings. Show n is the case for a single e-n system (NV-13C). Energy gaps ε1,2 are conditioned on the nuclear state. FIG. IE shows a typical DNP profile (ωr) as a function of MW sweep rate ωr. The plot is shown against for clarity. Solid line is a fit to model in Eq. (1). Dashed line denotes
optimal rate Here B =24 MHz, = 3.815 GHz and T=20 s.
[0014] The discussion focuses on the central spin system as in FIG. 1 A, reflective of the scenario encountered in DNP, employing optically polarizable Nitrogen Vacancy (NV) center electrons (labeled e) in diamond and considering polarization transfer to lattice 13C nuclei (n). Considering FIG. 1 A, the bulk nuclear polarization proceeds through a relayed process and the rate of spin injection is determined as an interplay between three rates: (i) the rate at
which the electron polarization is generated. Ke. (ii) the rate of e-n polarization transfer, Kr , and (iii) 13C spin diffusion,
that serves to transmit polarization over long distances in the lattice. In thermal DNP settings,
is system specific, cannot be controlled, and is limited at low temperatures. Likewise Kr is constrained by the available microwave (MW) power at high magnetic fields. In contrast, in optical DNP, Ke is set by laser intensity, and can potentially allow access to the regime wherein source polarization can be rapidly
generated. In turn, rapidly transmitting this polarization to the nuclei via high power MWs portends the ability to significantly enhance the hyperpolarization rate.
[0015] A key aspect of the embodiments includes an innovation that delivers high optical power continuously to the electrons, allowing to approach the regime. The time-
averaged optical power here (greater than 20 W) is substantially higher than previous experiments. Simultaneously, optical e-polarization permits DNP at low fields where high MW powers are readily accessible. Combining both factors, the embodiments demonstrate an approach to increase the polarization injection rate through a simultaneous " lockstep" increase in laser and MW power. The embodiments identify hyperpolarization speed-limits by delineating experimental regimes where the three rates above individually bottleneck polarization injection. Ultimately, the discussion shows high-power optical DNP can yield significant gains in injection polarization rate, boosted by as much as two orders of magnitude compared to conventional approaches. Rapid hyperpolarization obtained here opens avenues for quantum sensors, such as gyroscopes and spin sensors, constructed out of diamond 13C nuclei. The approach here is also readily generalizable to other experimental systems, including optically pumped triplet systems for DNP and MASERs.
[ 0016] The experiments employ a ≈16 mm3 single-cry stal sample with ~1 ppm NV concentration and natural abundance 13C (FIG. 1 A). The inter-NV spacing is ~24 nm, and 13C lattice density is ~0.92/nm3. Tin ≈5 min sets the overall polarization memory time for the system.
[0017] In what follows, the discussion refers to the optical and MW power in Watts as r/e andηr respectively. These are related to {Ke, } in FIG. 1A, but specify experimentally employed parameters. For η the discussion denotes the effective incident power, including effects of geometry, occlusion, and laser performance. Similar, ηr denotes MW power after accounting for all reflection losses.
[0018] NV centers are optically polarized to the ms=Q state, yielding an e-polarization, Pe (t)=1-exp(-tke) (FIG. 1B), assuming a monoexponential rate constant Ke. In reality, Ke=ceη e is approximately proportional to the optical power applied. The absolute e-polarization obtained depends on several factors, including interconversion between NV center charge states and is difficult to precisely quantify.
[0019] Optically generated polarization obviates the need for high magnetic fields for DNP. Lower fields come with significant advantages, such as the availability of high MW powers at low frequencies. DNP is excited at Bo=36 mT through a mechanism involving CW optical and swept MW irradiation (FIG. IB) for period T. Examples of techniques that may be used to hyperpolarize the nuclei are discussed in US Patent Publications 202102216, and 20210364583. Each sweep event injects polarization into e-proximal nuclei, akin to a “ratchet” shown in FIG. 1C. Bulk polarization is interrogated via RF induction at 7T. The experiments employ pulsed spin-lock read-out that permits long 13C precession lifetimes exceeding 100 s, with a decay constant T'2 > 20s. Signal is accumulated for the entire period
and sampled every 1 nanosecond in windows between the pulses. As a result, the experiments obtained high measurement fidelity , with integrated SNR (signal to noise ratio) as high as
108 per shot. This high sensitivity plays an important role in unraveling factors that affect polarization injection rates.
[0020] To elucidate the hyperpolarization mechanism, consider that the MW sweeps have an instantaneous frequency,
(FIG. 1B), where B is the sweep bandwidth around fo, the electronic spectral center, and ωr is the sweep rate. plays a key role in determining the ultimate rate of hyperpolarization buildup in the nuclei as shown in FIG. IE). Every sweep event transfers a finite amount of polarization, and the total number of sweeps, Tωr, is curtailed by the nuclear T 1n. Ideal ratchet operation involves maximizing ωr while maintaining high polarization transfer efficiency per sweep. Optimal operation occurs when the sweep rate ωr =ω opt, and can be derived by elucidating how the polarization buildup rate (ωr) depends on the interplay of rates in FIG. 1 A.
[0021] Consider that the e-n Hamiltonian for N nuclei (FIG. 1 A) in the rotating frame at field B0 has the form:
where S(I) refers to electron (nuclear) operators and ye,n are the respective magnetogyric rations. The first two terms denote the NV zero-field splitting (A = 2.87 GHz) and Zeeman field. Ωe is the e-Rabi frequency ( Ωe = crηr) proportional to the MW power applied. The process assumes an NV axis aligned with B0 (along
). The last term in described nuclear field in either electronic manifold - P0 and P1 are projection operators in the ms = 0 and ms = 1 manifolds, and then nuclear resonance frequency here in are respectively:
wher is the hyperfine coupling.
[0022] Spin ratchet polarization transfer is simplest to illustrate for a single e-n system.
Diagonalization leads to four Landau-Zener level anti-crossings (LZ-LACs), with energy gaps, (see FIG. 1D), such that ε2 < ε1. Swept MWs cause a traversal
through this LZ-LAC cascade. Its action can be evaluate under simplify ing approximations that capture the experiments: (i) LZ-LACs are assumed to be traversed sequentially, and, (ii) e-repolarization is assumed to occur at the start of every sw eep event. This entails negligible laser action at the LZ-LACs, and is valid when B>> ε1,2, as in the experiments.
[0023] Hyperpolarization buildup occurs because the energy gaps are conditioned on the nuclear state. Traversals through the LZ-LACs are differentially adiabatic or diabatic, leading to a population bias towards one nuclear state Indeed, population bifurcation at a
LZ-LAC is set by its adiabaticity and captured by respective tunneling probabilities (FIG. 1C). Hyperpolarization occurs when sweep rates ωr are such
that (adiabatic) and (diabatic). The rate of polarization is then:
The first term in square brackets is the rate of e-polarization and the last term captures the e→ n polarization transfer efficiency per sweep.
1 E show a typical measured DNP profile (ωr), from where ωopt is easily identifiable. The solid line here is a fit to Eq. (1 ).
[0025] It is intuitive to see why an optimal rate ωopt should exist. More rapid sweeps (high-
Mr) can allow faster ratchet operation, but come at the cost of (i) reduced electron polarization and (ii) lower transfer efficiency per sweep because the differential adiabaticity in FIG. ID is compromised. Indeed, at high-ωr, T1≈T2≈1, and P→O. Therefore ωopt sets an overall speed-limit for e^n polarization transfer, and defines the rate at which the ratchet (FIG. 1C) should be operated. One should note connections to recent work concerned with speed-limits of quantum state transfer in qubit networks with long-range interactions. These include P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith. M. Foss-Feig, S. Michalakis, A. V. Gorshkov, and C. Monroe, Non-local propagation of correlations in quantum systems with long-range interactions, Nature 511, 198 (2014), M. C. Tran, A. Y. Guo, C. L. Baldwin, A. Ehrenberg, A. V. Gorshkov, and A. Lucas, Lieb-robinson light cone for power-law interactions , Physical review letters 127, 160401 (2021), J. M. Epstein and K. B. Whaley, Quantum speed limits for quantum-information-processing tasks, Physical Review A 95, 042314 (2017), and K. Funo, N. Shiraishi, and K. Saito, Speed limit for open quantum systems, New Journal of Physics 21, 013006 (2019).
[0026] Experiments primarily probed bulk nuclei, entailing a non-negligible role from spin diffusion. However, the physics of direct e→ n polarization transfer is essentially unchanged from Eq. (1).
[0027] Importantly, Eq. (1) suggests that the rate of polarization transfer, encoded in ωopt , can be enhanced through a simultaneous increase in laser and MW power - higher-pe allows faster e-repolarization, and higher-pr permits faster sweeps while maintaining differential adiabaticity.
[0028] Spin injection rates can potentially exceed that of conventional DNP because optically polarizable electrons can be polarized faster than and be carried out at low field.
Achieving sufficient optical power to access this regime, however, is a technical challenge. Previous experiments with NV centers, both for DNP and quantum sensing, were predominantly in the r/e < 3 W regime and limited by sample heating. This work develops a novel laser delivery system that enables continuous sample irradiation at ηe >20W.
[0029] This constitutes the highest time-averaged power employed for DNP. There have been several reports of DNP with pulsed lasers such as K. Tateishi, M. Negoro, S. Nishida, A.
Kagawa, Y. Morita, and M. Kitagawa. Room temperature hyperpolarization of nuclear spins in bulk. Proceedings of the National Academy of Sciences 111, 7527 (2014), T. R. Eichhorn, Y. Takado, N. Salameh, A. Capozzi. T. Cheng, J.-N. Hyacinthe, M. Mishkovsky, C. Roussel, and A. Comment. Hyper polarization without persistent radicals for in vivo real-time metabolic imaging, Proceedings of the National Academy of Sciences 110, 18064 (2013). [0030] While possessing significantly higher peak power, they entail very long dead times (>> T1e), where electrons are not being polarized. In contrast, the CW optical excitation here yields continuous e-repolarization, and is especially advantageous for DNP with electrons with broad ESR spectra. Furthermore, lower peak power injection here al-lows more efficient heat diffusion and higher average power before sample damage thresholds are reached.
[0031] The apparatus, shown in FIG. 2A, consists of a dome-shaped structure (“laser dome" ), shown in more detail in FIG. 2B, that houses 30 diode lasers. In one embodiment, the structure comprises a 3D printed dome. In one embodiment the lasers have power of approximately ≈ 0.8W each, delivered via multimode fibers, with a beam diameter ≈ 4mm. The apparatus exploits relaxed requirements on optical mode quality necessary for e- polarization.
[0032] FIGs. 2A and 2B show an embodiment of a system 10 for high power optical hyperpolarization. The laser dome in FIG. 2B inserts into the fixture of FIG. 2A. The system includes laser fibers 12 through which lasers, one embodiment uses laser diodes such as 14, transmit the laser light from the diodes to the sample undergoing hyperpolarization. Laser drivers such as 16 drive the lasers. That many lasers in a confined space will generate a lot of heat, so the system includes a cooling column 20 that has at least one air or gas inlet 18. The fixture is encased in a Plexiglas shell 22.
[0033] FIG. 2B shows a view of the laser dome 24. The laser fibers insert into centrally aligned bores such as 26. The sample undergoing hyperpolarization 32 resides in an insertable structure, such as a test tube, 30. The insertable structure or holder inserts into the center space of the laser dome through the cooling tower 20. This view allows one to see one of the air inlets 18. The inset picture of FIG. 2C shows the laser dome with all bores having fibers. FIG. 2D shows a graphical depiction of the sample 32 being illuminated with multiple lasers through multiple fibers inside the laser dome 24. The microwave coil 48 provides the microwave energy while the sample undergoes optical polarization.
[0034] The method of boosting spin injection rates into an ensemble of nuclear spins then involves applying a microwave field to a sample having nuclear spins, and continuously applying laser illumination from multiple lasers to the sample to effect transfer of polarization from electrons in the sample to the nuclear spins in the sample.
[0035] This allows arrays of low-cost diode lasers to generate a high total optical power. The fibers are pressure fit into grooves that geometrically align towards the dome center. The almost isotropic excitation pattern uniformly illuminates each of the sample facets and the exact beam arrangement is staggered for minimal overlap with the MW excitation coil, as
shown in FIG. 2D. It also allows a significantly larger sample volume to be irradiated compared to previous approaches, since an approximate 4π solid-angle is illuminated.
[0036] FIG. 2E show ray -trace simulations that help discern the best positions of laser fibers in both side and top views. Density' of overlapping ray traces here serve as a proxy for relative intensity of irradiation onto the sample. The central portion of the sample sees excitation from multiple sources which, to an extent, compensates for attenuation through it, although quantifying the exact penetration depth through the sample is experimentally challenging.
[0037] Large optical powers require the ability to mitigate sample heating. The apparatus may include an in-situ heat exchanger that efficiently ejects heat while keeping the sample free from motion. FIG. 3A shows one embodiment of such a heat exchanger. The sample is held in a test tube 30 surrounded by a quantify of water. Thermal energy injected into the sample rapidly dissipates into the water, which serv es as a heat sink. The water is kept at a stable temperature by flowing cool nitrogen gas, which may have a temperature of -20° C at inlet 18, across the test tube. The gas is delivered from slits built into the neck region of the laser dome, show n by vertical dow n arrows such as 44 and short horizontal arrows in FIG. 3A. Nitrogen flow rate is calibrated so the w ater temperature is ≈ 9° C when lasers are off. Heat exchange exploits the excellent thermal conductivity of the sample, especially of diamond (2200 W/mK), and the large heat capacity of water for efficient thermal dissipation, show as the twisting upward arrow 46 in FIG. 3A. The benefit of this relayed strategy is that the cold gas does not contact the sample directly, and the sample volume can be enclosed, an advantage for sample shuttling to high field.
[0038] Heat exchanger performance is found to be highly effective. FIGs. 3B-C elucidates measured temperature buildup in the sample and surrounding fluid under 120 secs continuous
irradiation at different optical powers. After 120 s, the lasers are turned off, and the temperature dissipation is again monitored. Even at sustained 24 W optical power, corresponding to an intensity of ≈0.19 kW/cm2, the (asymptotic) steady-state temperature is remarkably less than 30° C. FIG. 3D plots the steady-state temperatures for different powers. From the buildup rate, the embodiments estimate that approximately 50W power can be applied before system limits (related to water boiling) are reached.
[0039] The discussion can now demonstrate that high power optical delivery via the apparatus in FIG. 2, allied with simultaneous high MW power, can yield significant enhancements to the optimal ratchet rates ωopt, and thereby increase the rate of nuclear spin injection. In parallel, the experiments quantity' the speed-limits for bulk polarization buildup as an interplay of the rates in FIG. 1A. As such this is complementary to recent work studying flow of polarization in conventional DNP. Consider first data in FIG. 4A. The experiments measure sweep rate dependent DNP profiles (uir) with T = 20s similar to FIG. IE, but at several regimes of optical ηe and MW ip power. In particular, one can consider four regimes of MW power ip =0. 1-53 W, and for each, measure (ωr) profiles for different effective optical powers ηe =0.4 W (1 weak laser) - 20.8 W (26 lasers). This is estimated here by measuring the effect of each laser individually on the 13C hyperpolarization signals. Upper and lower axes in FIG. 4A denote
and ω1/2 respectively. Solid lines are fit to Eq. (1). Optimal sweep rates ωopt (dashed lines) are determined from maxima of the fitted curves. To improve clarity, lower panels (FIG. 4B) focus on normalized profiles at ηe =0.4 W and 20.8 W. Increasing optical power ηe leads to a rightward shift in ωopt (arrows), and the magnitude of the shift apparently increases at higher MW powers.
[0040] The discussion also briefly introduces FIG. 5 that will aid the discussion that follows.
It extracts complementary information of polarization and ωopt from FIG. 4. FIG. 5A-B show obtained maximal polarizations against for the MW power regimes (colorbar) considered, plotted on a linear (FIG. 5A) and logarithmic (FIG. 5B) scale. Signal here is measured at ωopt. Solid lines are guides to the eye. In a complementary manner, points in FIG. 5C display the extracted optimal rates coopt (ηe ) for different MW powers. Solid lines are linear fits. FIG. 5E, in turn, plots the slope of these lines, ~dωopt (η e)/dηe , while FIG. 5F plots the polarization for different MW powers at ηe = 20.8W (vertical slice of data in FIG. 5 A). A combined view of data in FIG. 4-FIG. 5 allows the ability to correlate ωopt to the absolute spin injection rates into the 13C nuclei.
[0041] The discussion can now systematically consider factors setting ωopt from left-o-right in FIG. 4, starting from the low-MW power region I (ηr = 0. 1 W). This regime relates to the situation in high-field DNP where MW power is low due to technological constraints. In FIG. 4A(i), one can observe the DNP profiles clustered at ωr = 50-120 Hz. Increasing optical power only weakly increases the optimal sweep rate ωopt (see FIG. 4B(i) and FIG. 5C). This indicates a Kr induced speed limit set by adiabaticity constraints. In the ratchet picture in FIG. ID, the energy gaps are small and sweep rates ωr required to satisfy adiabaticity are slow. Increasing optical power therefore yields no significant increase in 13C polarization levels (see FIG. 4A(i)). One can observe in fact, a slight decrease in signal at high ηe (see also FIG. 5B), associated with the rightward shift in ωopt in FIG. 4B(i). This signal drop is beyond the scope of Eq. (1) and challenging to model. This may arise because the electrons are repolarized multiple times during each MW sweep event, including at the LZ-LACs, making
polarization transfer less efficient. Simultaneously, one can observe oscillations in the (ω ) profiles in the high ηe -ηr regime.
[0042] Now upon increasing MW power seven-fold (FIG. 4A(ii)) to regime II with ηr =0.7W. there is a larger increase in ωopt (ηe ) with optical power. This rightward shift in FIG. 4A(ii) manifests as an increased slope in FIG. 5C(II). Intuitively, higher yields larger energy gaps in FIG. ID and affords faster sweep rates. When the optical powers are low. electron polarization is not produced rapidly enough at the NV source. Increasing ηe therefore relieves this Ke bottleneck. From FIG. 5E, ωopt in regime II increases 2-fold with respect to regime I, and there is a simultaneous ~10x increase in polarization (FIG. 5B). However, clustering of (ωr) profiles in FIG. 4A(ii), and slow growth in FIG. 5C(II), still suggests that Kr limits the rate of polarization transfer.
[0043] FIG. 4B(iii) considers a further 10-fold increase in MW power (regime III). Here a rightward shift in ωopt is clearly evident with increasing optical power, and spin-ratchet operation is rapid, evidenced by the increased slope in FIG. 5C(III). Higher η r allows faster sweeps due to weaker adiabaticity constraints, and η e can be simultaneously boosted to increase the rate of source e-polarization, yielding a lockstep Ke-Kr increase in hyperpolarization rate. The concomitant signal increase is evident in FIG. 5A-B. One should also note that the resulting maximal rates ωopt ≈ 0.65 kHz approach, and potentially exceed, the thermal rate
expected in this sample.
[0044] One might expect that a further increase in MW power will continue to yield such gains. This is shown in simulations in FIG. 5D that model direct e→n polarization transfer without spin diffusion. Interestingly, however, one can experimentally observe that a subsequent increase in MW power to ηr =53W (regime IV) provides no significant increase
in ωopt (see FIG. 4A-B(iv)). This is also reflected in FIG. 5C, where ωopt (ηe ) manifests as a series of overlapping lines beyond ηr =7W. This plateauing of rates is also evident in FIG. 5E. Correspondingly, the relative signal increase in FIG. 5A-B begins to slow down (see FIG. 5F). Overall this points to the presence of a third speed limit, which may be ascribed to be due to spin diffusion Kd. Here polarization is rapidly transferred from the NV center to proximal 13C nuclei, but is limited in its ability to reach the bulk nuclei. Indeed, FIG. 5B-C demonstrates that while e-polarization rates increase with ηe , nuclear spin injection is ultimately limited by spin diffusion. As such, spin injection can be considered optimally rapid in this regime.
[0045] Finally, FIG. 4 and FIG. 5 measure quantitative polarization injection rates into the 13C nuclei focusing on regime IV (ηr =53 W). FIG. 6A shows two representative polarization buildup curves at ty=0.4 W and 20.8 W (one weak laser and 26 lasers respectively). Steeper polarization growth in the latter is evident. FIG. 6B shows the corresponding 13C NMR spectra at T=90 s, with a linewidth ≈ 16 mHz. An approximately 13 -fold increase in signal is found by employing 26 lasers compared to a single weak one. To focus on e-proximal polarization injection separately from strong effects from spin diffusion, FIG. 6C considers the small-time regime (T < 0.6s). Polarization buildup is approximately linear in this regime; color-bar shows different optical powers employed. Corresponds slopes (FIG. 6D) permit quantification of absolute polarization injection rates (%/s) by comparing against the thermal polarization at 7T (~10-5). FIG. 6D demonstrates that spin injection rate scales approximately linearly with optical power, arising from the increased rate of source e- polarization Ke at the NV center sites. Indeed, the sustained high-power optical delivery possible via FIG. 2, yields an approximately 167-fold increase in polarization injection with
respect to using a single weak laser. The experiments measure a linearized bulk injection rate of ≈0.06%/s averaged over the sample.
[0046] A number of promising variations may exist for the system and method discussed here. First, the experiments here illustrate the strengths of non-thermally polarized electrons for DNP. e-polarization can be replenished at a rate Ke> Tff and does not require cry ogenic high-field conditions (unlike Boltzmann-based DNP). This allows access to low-field regimes where MW power can be plentiful. Simultaneously applied high optical and MW power can yield bulk spin injection rates ultimately limited by only spin diffusion. Similar arguments can be extended to other non-thermally generated DNP approaches, including with parahydrogen as in J.-B. Hovener, N. Schwaderlapp, T. Lickert, S. B. Duckett, R. E. Mewis, L. A. Highton, S. M. Kenny, G. G. Green, D. Leibfritz, J. G. Korvink, et al., A hyperpolarized equilibrium for magnetic resonance, Nature communications 4, 1 (2013), R. W. Adams, J. A. Aguilar, K. D. Atkinson, M. J. Cowley, P. I. Elliott, S. B. Duckett, G. G. Green, I. G. Khazal, J. Lopez-Serrano, and D. C. Williamson, Reversible interactions with para-hydrogen enhance nmr sensitivity) by polarization transfer, Science 323, 1708 (2009), and A. N. Pravdivtsev, A. V. Yurkovskaya, H.-M. Vieth, K. L. Ivanov, and R.
Kaptein, Level anti-crossings are a key factor for understanding para-hydrogen-induced hyperpolarization in sabre experiments, ChemPhysChem 14, 3327 (2013). . The elucidation of spin injection speed limits is relevant for quantum information transfer and memories. [0047] Second, the strategy for high-power optical illumination and thermal management developed here is extensible to other systems, including organic triplet molecular systems, and UV generated non-persistent radicals. These applications could be applied to e-spin MASERs, and quantum sensors with e-spin ensembles, where reaching higher optical powers is the primary factor limiting magnetometer sensitivity. Finally, the rapidly injected spin
polarization here projects onto applications that exploit hyperpolarized 13C spins as quantum sensors, leveraging their long lifetimes in the laboratory and rotating frames. This includes magnetometers, gyroscopes, sensors for dark-matter searches, and as RF imaging agents. [0048] The embodiments here have demonstrated the ability to rapidly inject spin polarization into a lattice of nuclear spins via optical polarized electrons under simultaneously applied high-power optical and MW irradiation. In the process, the embodiments elucidated speed-limits that bottleneck bulk polarization transfer in various regimes, and showed an approximately 167-fold gain in spin-injection rate via high power excitation. These techniques inform on interesting new opportunities afforded by non- thermally polarized electrons for DNP and quantum sensing.
[0049] All features disclosed in the specification, including the claims, abstract, and drawings, and all the steps in any method or process disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. Each feature disclosed in the specification, including the claims, abstract, and draw ings, can be replaced by alternative features serving the same, equivalent, or similar purpose, unless expressly stated otherwise.
[0050] It will be appreciated that variants of the above-disclosed and other features and functions, or alternatives thereof, may be combined into many other different systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art that are also intended to be encompassed by the embodiments.
Claims
1. An apparatus for spin polarization into a collection of nuclear spins, comprising: a housing; an array of lasers arranged around a periphery of the housing; a holder configured to hold a sample of material at the center of the housing in a position that can be illuminated by the lasers; and an energy source to power the lasers to optically hyperpolarize electrons in the sample to transfer polarization from the electrons to nuclear spins in the sample.
2. The apparatus as claimed in claim 1, wherein the housing comprises a dome.
3. The apparatus as claimed in claim 2, wherein the housing includes openings into which the lasers can be inserted.
4. The apparatus as claimed in claim 1, wherein the array of lasers comprises an array of laser diodes.
5. The apparatus as claimed in claim 1, wherein the array of lasers are arranged in a staggered fashion around a central bore.
6. The apparatus as claimed in claim 1 , further comprising a heat exchange mechanism arranged to extract heat from the sample to a surrounding fluid.
7. The apparatus as claimed in claim 6, wherein the heat exchange mechanism comprises: water in the holder surrounding the sample; a cooling column having channels adjacent the holder to direct gas to cool the water; an opening at a top of the holder to allow heat to escape.
8. A method of boosting spin injection rates into an ensemble of nuclear spins, comprising:
inserting a sample into a space having a microwave coil surrounded by multiple lasers; energizing the microwave coil to apply microwave energy to the sample; and continuously applying laser illumination from multiple lasers to the sample to effect transfer of polarization to effect transfer of polarization to nuclear spins.
9. The method as claimed in claim 8, wherein the space is formed from a dome structure having bores for multiple lasers.
10. The method as claimed in claim 8, wherein continuously applying laser illumination comprises continuously applying laser illumination using multiple lasers arranged in a staggered fashion centered on the space.
11. The method as claimed in claim 8, wherein continuously applying laser illumination comprises continuously applying laser illumination using multiple lasers connected to optical fibers that transmit the light into the space.
12. The method as claimed in claim 8, wherein continuously applying laser illumination comprises continuously applying laser illumination using multiple laser diodes.
13. The method as claimed in claim 8, further comprising cooling the sample through heat exchange during the continuous laser illumination.
14. The method as claimed in claim 13, wherein cooling the sample through heat exchange comprises holding the sample in water in a holder.
15. The method as claimed in claim 13, wherein cooling the sample comprises passing a gas through channels adjacent the space to cool the sample.
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