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A Porous Array of Clock Qubits Joseph M. Zadrozny, Audrey T. Gallagher, T. David Harris, and Danna E. Freedman J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 28 Apr 2017 Downloaded from http://pubs.acs.org on April 28, 2017

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Journal of the American Chemical Society

A Porous Array of Clock Qubits Joseph M. Zadrozny, Audrey T. Gallagher, T. David Harris, and Danna E. Freedman†,* †

Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA. Supporting Information Placeholder metal-organic frameworks (MOFs).10 MOFs are porous materials ABSTRACT: The command of atomic-level spatial control over assembled via building-block approaches, enabling considerable qubits, the fundamental units of both quantum information prosynthetic control, and specifically facilitating installation of qubits cessing systems and quantum sensors, constitutes a crucial crosswithin the material backbone. These compounds possess three key field challenge. Toward this end, embedding electronic spin based advantages for quantum sensing. First, the strong tunability of the qubits within the framework of a crystalline porous material is a internal surface area could enable selectivity of small molecule promising approach to create precise arrays of qubits. Realizing analytes.11 Second, the chemically exposed qubit sites within porous hosts for qubits would also impact the emerging field of porous systems may enable substantial interactions between spins quantum sensing, whereby porosity enables analytes to infuse into and analytes, engendering high sensitivities (Fig. 1). Finally, MOFs a sensor matrix. Yet, building viable qubits into a porous material is enable synthetic control of the immediate chemical environment of an appreciable challenge due to the extreme sensitivity of qubits to the spin center, wherein properties can be programmed into the local magnetic noise. To insulate these frameworks from ambient spins of these materials through building block selection. Yet, magnetic signals, we borrowed from atomic physics the idea to translating all of these advantages into proof-of-concept QIP or exploit clock transitions at avoided level crossings. Here, sensitivity sensing MOF systems is a lofty goal, in large part due to the to magnetic noise is inherently limited by the flat slope of the sorequirement of long-lived electronic spin superpositions to permit called clock transition. More specifically, we created an array of sensing with hosted qubits. The oft-quoted required qubit lifetime, clock-like qubits within a metal-organic framework by combining or T2, required for QIP is 100 µs and above, while those for sensing coordination chemistry considerations with the fundamental conare more variable and connected to the specific magnetic resonance cept of atomic clock transitions. Electron paramagnetic resonance experiment. Note that longer lifetimes enable access to a larger (EPR) studies verify a clock-like transition for the hosted cobalt(II) library of potential magnetic resonance sensing schemes. Achieving spins in the framework such lifetimes is thus a necessary prerequite for the foregoing [(TCPP)Co0.07Zn0.93]3[Zr6O4(OH)4(H2O)6]2, the first demonstraapplications. However, such times have yet to be observed within tion in any porous material. The clock-like qubits display up to 14 any MOF, necessitating efforts to design long-lived qubits in these μs lifetimes despite abundant local nuclear spins, illuminating a new materials. path toward proof-of-concept quantum sensors and processors The key figure of merit for qubit lifetime is parameterized as the with high inherent structural precision. spin-spin relaxation time or phase memory time, T2. Realizing long T2 values is a daunting challenge, because interaction with the environment collapses the fragile superposition state of an INTRODUCTION electronic spin, a process known as decoherence. Magnetic noise is The design of viable qubits, the smallest units of either a an endemic source of decoherence for electronic spins.12 At a quantum information processing (QIP) or quantum sensing molecular level, magnetic noise arises from the rapid flipping of system, is an interdisciplinary challenge at the forefront of environmental nuclear spins and proximate paramagnetic chemistry, physics, and engineering.1 Fundamentally, a qubit is any molecules (e.g. O2). Within the field of coordination chemistry, object that can be placed into a quantum superposition of two states. Electronic spins are a particularly promising qubit class, wherein microwave pulses easily create and manipulate superpositions of pairs of spin orientations (MS levels). Owing to this control, electronic spin qubits are situated at the vanguard of the nascent field of quantum sensing,2,3 wherein the extremely sensitive quantum superpositions are harnessed to detect subtle environmental perturbations. Applications here include spatial thermometry in vitro4 and nuclear magnetic resonance spectroscopy on nanoscale volumes.5-8 The S = 1 nitrogen-vacancy (NV) centers in diamond are prominent quantum sensors, largely due to their long-lived electronic spin superpositions.9 Figure 1. Metal-organic frameworks possess tunable interiors and The realization of spatial control of qubits, currently a significant enable exact control over interqubit distances and orientations, challenge for NV centers, would herald a new class of quantum which may combine to be of use in creating new platforms for senssensing candidates. Further, this degree of control is a vital ing or otherwise harnessing the quantum properties of electronic prerequisite for every foreseen application of QIP. One approach to spins. the controlled placement of qubits is through incorporation within ACS Paragon Plus Environment

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carefully constructed proofs-of-concept demonstrate T2 values in the millisecond timescale via the exclusion of nuclear spins from ligand sets and solvent.13,14 Yet, this nuclear spin-free design principle necessitates a punishing chemical constraint. Deriving design principles for quantum states that persist in environments rich in magnetic noise is thus a central fundamental challenge in designing paramagnetic molecules for quantum technologies.15-21 Indeed, creating porous coordination solids wherein electronic spin superpositions are robust even in the presence of nuclear spins is a vital step forward in designing new types of sensors and spintronic materials.22,23 Atomic clock physics inspires a tantalizing approach to longlived electronic spin quantum states that persist in magnetically

Figure 2. (a) Depiction of clock concept for electronic spin qubits. Clock EPR transitions possess frequencies (f) that are insensitive to small changes in magnetic (ΔB). This property may enable a long T 2 in magnetically noisy environments relative to a conventional EPR transition. (b) The crystal structure of the parent [(TCPP)Co]3[Zr6O4(OH)4(H2O)6]2 structure (refs 30,36). This material is porous, exhibiting a high surface area (~3200 m2/g), and hosts paramagnetic cobalt(II) metal ions. (c) Close up view of the square planar cobalt(II) ions in the structure and qualitative depiction of the d-orbital splitting. The cobalt(II) ions are lowspin, featuring one unpaired electron that is strongly coupled to the I = 7/2 59Co nucleus. This strong hyperfine interaction engenders an avoided crossing like is shown in (a).

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noisy environments. One class of atomic clocks based on trapped atoms utilizes an EPR spectroscopic transition that is extraordinarily insensitive to magnetic noise as a timekeeping element (Fig. 2a).24,25 Here, the harnessed EPR transition occurs at an avoided crossing engendered by a strong hyperfine couplinginduced mixing of MS and MI levels. At this crossing, there is no change in the EPR transition frequency (f) with small changes in the applied field (B), Δf/ΔB = 0. Consequently, these transitions display long T2 parameters even in magnetically noisy environments. Indeed, proof-of-concept designs of clock qubits enabled breakthroughs in quantum state lifetimes for the lone two prior executions of this concept, solid-state defect (Bi-doped Si)26,27 and molecular ([Ho(W5O18)2]9–)28,29 qubit systems. Generating clock transitions within a porous material offers a pathway to exploit the tunability and the structural precision of MOFs for qubit design while overcoming their magnetically noisy local environment. Moreover, expanding the number of chemical systems capable of clock-like spin behavior is a crucial step in the further development clock-like qubits. Specifically, qubits with spin ground states differing from the holmium(III) system hold particular promise. Holmium(III) possesses one of the largest magnetic moments in the periodic table, resulting from a spin ground state, S, of 2 and an unquenched orbital angular momentum, L, of 6, yielding a J = 8 ground state. Other clock qubits with smaller S values may be even less sensitive to magnetic noise, and consequently display improved T2 parameters. Herein, we fuse coordination chemistry design principles with atomic physics to create and study a tunable, porous array of clocklike qubits — electronic spins that display the magnetic noise insensitivity of atomic clocks. Specifically, we investigate the first porous material – a metal-organic framework – composed of a building block that is a clock-like qubit. This work focuses on the material [(TCPP)Co0.07Zn0.93]3[Zr6O4(OH)4(H2O)6]2 (TCPP = 5,10,15,20-tetrakis(carboxyphenyl)porphyrin, 1, Fig. 2b),30,31 which possesses porphyrin sites metalated with paramagnetic cobalt(II) and diamagnetic zinc(II) ions. Selection of cobalt(II) as the potential clock qubit was driven by coordination chemistry considerations. The ligand field of the cobalt(II) ion in this material enables an unusually strong hyperfine coupling interaction between the S = 1/2 electronic spin and the 59Co I = 7/2 nuclear spin, leading to a clock-like transition (Fig. 2c). These results encapsulate, for the first time, the design and control of an electronic spin clock-like qubit within a MOF, representing further the unprecedented isolation of clock-like spin behavior in a transition metal ion. We specifically demonstrate that this paradigm enables nearly an order of magnitude enhancement of T2 at low temperature in an environment rich in nuclear spins. This work is an important step in developing electronic structure design principles for controlling the quantum properties of metal-based spins in porous materials. RESULTS AND DISCUSSION For our proof-of-concept system, we prepared and analyzed 1, which is composed of paramagnetic cobalt(II) porphyrin units — the intended clock qubits — diluted within a diamagnetic network of zinc(II) porphyrin units and [Zr6O4(OH)4(H2O)6]6+ structural nodes. Our selection of this specific system was motivated by our interest in identifying a qubit with S = 1/2, I > 0, and a large hyperfine interaction term. The confluence of these three properties would enable the creation of multiple widely spaced transitions, allowing us to directly probe the clock transition alongside ordinary EPR transitions, effectively creating an internal control. The large hyperfine coupling interaction serves an

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Figure 3. High (X-band, 9.63 GHz) and low (S-band, 3.59 GHz) frequency EPR spectra collected on a finely ground powder of 1 and simulations using the parameters given in the main text. Spectra were collected at 15 K. additional purpose, enabling the frequency of the transition to match the microwave frequency of a commerical EPR spectrometer. Cobalt(II) ions satisfy these initial requirements, exhibiting nearly complete purity of an I = 7/2 isotope and possessing a divalent oxidation state with both S = 1/2 and S = 3/2 possible spin states. Of these, identifying a species with strong hyperfine coupling presents a more significant obstacle, as the electronic spin-bearing d-orbitals all possess angular nodes, nullifying electron density at the nucleus. Remarkably, the cobalt(II) ion in 1 is square planar and in a rare low-spin configuration, hosting a single unpaired electron in a mixed 4s-3dz2 orbital (Fig. 2c).32-35 S-orbitals are unique among the atomic orbitals in that they lack angular nodes. Thus, the 4s-character of the spin-bearing orbital in 1 allows for strong Fermi-contact and an unusually strong hyperfine interaction with the 59Co nucleus. The resulting large hyperfine coupling engenders a 9.6 GHz continuous-wave EPR spectrum that spans a nearly 0.5 T magnetic field window (Fig. 3),36 enabling facile investigation of each hyperfine transition. Note that the binding of additional ligands weakens the hyperfine coupling by delocalizing electron density away from the 59Co nucleus.37,38 Indeed, even cocrystallization of molecular cobalt-porphyrin species with diamagnetic analogues enables sufficient interaction to quench hyperfine coupling and change the EPR spectrum.35 In this light, the MOF architecture is vital, where pore evacuation protects the open coordination site and the strong hyperfine coupling. Accessing the clock transitions necessitates decreasing the applied magnetic field to enable mixing for the MS and MI levels. Thus, we acquired variable frequency EPR spectra with microwave frequencies down to 0.739 GHz to gain better insight into the hyperfine-coupled ⎪MS, MI〉 levels in the strong mixing regime (Figs. 3, S1). With decreasing frequency, the observed EPR transitions move closer to each other and to lower magnetic field, ultimately collapsing to just two resonances below 2 GHz. The frequency dependence of the observed transitions was simulated with Easyspin39 and the spin Hamiltonian Ĥ = gµBBS + IAS, where g is the g-tensor, µB is the Bohr magneton, B is the magnetic field, S is the electronic spin, I is the nuclear spin of the 59Co nucleus, and A is the electronuclear hyperfine coupling tensor (Figs. 4, S1-S3). The best simulations across all frequencies occured for axial parameters: g|| = 1.783(2), g = 3.275(5), A|| = 485(11) MHz, and A = 1123(1) MHz. These determined values of A and g are within the expected trends for the cobalt(II)-porphyrin unit.33-37 Note that A has an unusually large magnitude relative to A parameters in other first-row transition metal ions, which are often close to or ⊥

⊥

⊥

Figure 4. (a) Energies of ⎜MS, MI〉 levels as a function of magnetic field (B) for 1 with the cobalt-porphyrin unit oriented perpendicular to the applied field (inset). Vertical lines depict the strong EPR transitions observed at high frequency for this orientation. Energies are calculated using the spin-Hamiltonian parameters in the main text. (b) Frequencies (f) of the EPR transitions in (a) depicted as a function of magnetic field (B). Experimentally observed transitions from EPR spectra are indicated with colored data points ( , ~9.6 GHz frequencies; , less than 4 GHz frequencies). The slopes here are direct measures of Δf/ΔB. The explored transition in this study, which occurs at 0.3 kG and 3.66 GHz, where Δf/ΔB ≈ 0, is indicated ( ). below 400 MHz. This magnitude is specifically driven by the lack of a node at the nucleus for the 4s orbital relative to the 3dz2 orbital. The hyperfine interaction here is crucially reliant on the strongfield, local D4h symmetry coordination environment, which enables the 4s-3dz2 mixing. Importantly, simulations of the field and orientation dependence of the MS level energies revealed the location of a clock transition near 0.3 kG with an energy of 3.6-3.7 GHz (Figs. 4b, S2, S3), wherein Δf/ΔB = 0. As an initial step to directly assess potential clock behavior in 1, we applied pulsed EPR spectroscopy.40 We acquired an echodetected EPR spectrum at 15 K with 3.66 GHz microwaves, the energy range of an expected clock transition (Fig. 5a). This spectrum is significantly different than the high frequency spectra, lacking the readily interpreted eight-line multiplets. On the basis of transition assignments of the CW spectra, observed EPR transitions result from orientations of the cobalt(II)-porphyrin unit parallel and perpendicular to the applied magnetic field, but also from potential forbidden transitions, where ΔMS = ±1 and ΔMI ≠ 0 (see SI).41 In this report, we focus on the four resonances at 300, 782, 1184, and 1590 G, where the applied magnetic field is in the plane of the cobalt(II)-porphyrin unit, which reflect the extremely large A coupling value. Inspection of these specific transitions identifies that the 300 G resonance is clock-like, i.e. it experiences nearly no change in microwave frequency with change in magnetic field (Δf/ΔB = 0.3 MHz/G). For the other three resonances, Δf/ΔB ⊥



Figure 5. (a) Echo-detected EPR spectrum collected at 15 K and 3.66 GHz (pulse sequence depicted, π/2 = 32 ns, τ = 340 ns). The indicated transition at 0.3 kG corresponds to the clock-like transition indicated in Fig. 4b. (b) Full Hahn-echo decay profile as a function of magnetic field at 15 K reveals the enhancement of T2 for the clock-like transition (green arrow) over all of the other observed EPR transitions (see also Fig S6). Intensity (z-axis) is normalized to 1 and depicted on a log10 scale. increases with increasing magnetic field, from 23.7 to 33.4 to 43.0 MHz/G for the 782, 1184, and 1590 G resonances, respectively. Thus, this range of resonances offers the potential to directly probe the influence of Δf/ΔB on T2 in 1 (Figs. 4, S4, S5). Using ⎪MS, MI〉 labels corresponding to the high magnetic field regime, the clocklike transition here is formally ⎪–(1/2), –(1/2)〉 → ⎪+(1/2), –(1/2)〉, though we acknowledge this label is less pertinent in the heavilymixed region of the avoided crossing. Upon identification of the 300 G clock transition in 1, we sought quantification of the impact of Δf/ΔB on T2 here. The stark impact of the clock-like nature on T2 for the cobalt(II) ion is revealed by performing a full variable-field evaluation of the Hahn echo decay profile (Figs. 5b, S6) at 15 K. In the contour plot of Fig. 5, the x-axis is the magnetic field of the experiment, the y-axis is the time dimension of the Hahn echo experiment, and the indicated z-axis intensity is the echo intensity. Here, the persistence of detectable echo intensity in the time domain is a reflection of the magnitude of T2 at a particular resonance. The dramatic result of a small |Δf/ΔB| is revealed on this plot, as the two-pulse Hahn echo produced at 300 G persists significantly longer than any other transition observed in the spectrum. Specific investigation of the resonances from the perpendicular orientation quantifies this impact. At 15 K, T2 = 1.96 µs at 300 G, decreasing to 774, 606, then 296 ns with increasing Δf/ΔB at the 782, 1184, and 1590 kG resonances (Figs. S6,S7). This correlation suggests that the clocklike nature of the transition is responsible for a seven-fold enhancement of T2 over the 1590 G transition, which best approximates a conventional EPR resonance (near-linear dependence of f on B) for this alignment. We examined the temperature dependence of T2 to experimentally evaluate the highest achievable T2 with the sample and the impact of thermally-activated processes on T2 for the 300 G

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Figure 6. (a) Two-pulse Hahn-echo decay curve of 1 at 0.3 kG and 5 K (same sequence parameters as in Fig. 5). The red line is an exponential decay yielding a T 2 of 13.74(9) µs. The slight oscillation is from election-spin-echo envelope modulation (ESEEM). (b) Inversion recovery curve at 5 K for 1 at 0.3 kG and pulse sequence (inset). (c) Temperature dependence of T1 and T 2 of the clock transition. Errors for the parameters are within the data symbols. transition (Figs. 6, S8). Here, the Hahn-echo experiment was repeated as a function of temperature, revealing that T2 climbs with decreasing temperature, from 1.81(1) µs at 15 K to 13.74(9) µs T2 at 5 K (Fig. 6a). The magnitude of T2 at 5 K represents a modest improvement over the 8.4 µs obtained on the only other moleculebased atomic clock, [Ho(W5O18)2]9–. The longer T2 is observed despite a significantly more spinconcentrated environment in 1 versus [Ho(W5O18)2]9–. Calculation of the paramagnetic metals per volume reveals concentrations of 1.5 × 10–5 and 1.0 × 10–7 paramagnetic metal/Å3 for 1 and Na9[Ho(W5O18)2]•nH2O (n ≈ 35), respectively. These numbers account for the respective 57456(6) and 10362.6(3) Å3 unit cell volumes for 1 and Na9[Ho(W5O18)2]•nH2O (n ≈ 35) and the relative 1:10 and 1:1000 dilutions.28,36,42 Calculating these concentrations with spins rather than metal better accounts for the relatively larger moment of the holmium(III) ion. Here, using S = 1 /2 for cobalt(II) and J = 8 for holmium(III) results in 8 × 10–6 and 8 × 10–7 spins/ Å3, respectively. In both cases, the concentration of 1 is at least an order of magnitude greater than Na9[Ho(W5O18)2]•nH2O (n ≈ 35). In summary, the discrepancy in dilution levels here suggests that 1 may be able to reach even longer T2 values at higher dilutions. Alternately, using a porous material with larger pore sizes would further dilute the spin density, thus perhaps enabling the realization of a pure cobalt porous material. We are currently pursuing these exciting prospects. Finally, we note that the temperature dependence of T2 corroborates the implication of the T2 vs. |Δf/ΔB| correlation, i.e. magnetic noiseinsensitivity of the 300 G resonance. If magnetic noise from nearby nuclear spins was the major limitation of T2 for this transition, a temperature-independent parameter would result.43


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When T2 is temperature dependent, thermal processes leading to spin-lattice relaxation (T1) govern the magnitude of T2. To better evaluate the importance of T1 on T2, we explored the temperature dependence of T1 via inversion recovery experiments. In these experiments, a pulse of microwaves inverts the spins of 1 at the clock-like transition and then recovery back to alignment with the magnetic field is monitored by Hahn-echo detection (Figs. 6b, S9). At 5 K, these measurements yield a T1 of 34.49(6) µs, and this value hastens with increasing temperature to approach T2 around 15 K (Fig. 6c). This observed convergence suggests a rapidly growing importance of a thermally driven relaxation process for T2 with increasing temperature, which appears nearly complete above 15 K. The earlier |Δf/ΔB| comparison suggests that resistance to magnetic noise retains an important role for T2 at this temperature, despite dominant spin-lattice relaxation effects. Future studies will focus on deriving insight into these possible mechanisms, particularly at the lowest temperatures, where processes other than T1 are more prominent. Nevertheless, important evidence exists for a long T2 here enabled at high concentration of spin centers by the clock-like nature of the electronic spin.

OUTLOOK The foregoing report highlights an important initial step toward realizing long T2 values in a spin-concentrated porous material. Importantly, the results embody an advance for chemically controlling the quantum properties of spins, harnessing coordination chemistry design principles to isolate and study the first clock-like transitions in a 3d transition metal ion. These results are a proof-of-concept for a potential new class of quantum sensor embedded within a porous material. These initial results will catalyze divergent areas of research within our laboratory to realize the promise of porous sensors. Our initial studies will focus on sensing gas molecules within these frameworks, and indeed, these studies are currently progressing. Progressing further, one fascinating challenge is enabling optical detection, which would enable analogous functionality to diamond and much higher sensitivity. Thus, integrating the present work with phosphorescence in MOFs44,45 is a prime step toward sensing capability. In a separate aim, the clock-like nature of the transition may counteract applicability for proposed magnetic field sensing methods. Thus, there may be an optimum clock-like nature for sensing, wherein T2 is lengthened yet interaction with nearby nuclear spins is still possible. Relatedly, finding clock resonances wherein the avoided crossing is exceptionally shallow and wide is a promising strategy to qubits with the highest degree of insensitivity to magnetic noise. This latter strategy, coupled with judicious tuning of interqubit distances, may enable progression from random distributions of qubits to completely ordered arrays, wherein each qubit node possesses a long T2. We look forward to pursuing the answers to these questions over the next decade of research.

ASSOCIATED CONTENT Supporting Information. Full experimental and spectroscopic details, and additional spectroscopic data. This material is available free of charge via the Internet at http://pubs.acs.org/.

Corresponding Author *[email protected]

ACKNOWLEDGMENT

We are grateful to Drs. W. E. Antholine and M. J. Nilges for experimental assistance and enlightening discussions. This work is supported by Northwestern University, the State of Illinois, the Institute for Sustainability and Energy at Northwestern, the National Science Foundation for CAREER Award No. CHE-1455017 (J.M.Z. and D.E.F.), and the U. S. Army Research Office (W911NF-14-1-0168, A.T.G. and T.D.H.). D.E.F. and T.D.H. thank the Alfred P. Sloan Foundation. A.T.G. is supported by the National Science Foundation through the Graduate Research Fellowship Program. A portion of this work was performed at the National Biomedical EPR Center at the Medical College of Wisconsin (supported by NIH grant EB001980).

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A Porous Array of Clock Qubits - American Chemical Society

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