Abstract
The decoherence of quantum objects is a critical issue in quantum science and technology. It is generally believed that stronger noise causes faster decoherence. Strikingly, recent theoretical work suggests that under certain conditions, the opposite is true for spins in quantum baths. Here we report an experimental observation of an anomalous decoherence effect for the electron spin1 of a nitrogenvacancy centre in highpurity diamond at room temperature. We demonstrate that, under dynamical decoupling, the doubletransition can have longer coherence time than the singletransition even though the former couples to the nuclear spin bath as twice strongly as the latter does. The excellent agreement between the experimental and theoretical results confirms the controllability of the weakly coupled nuclear spins in the bath, which is useful in quantum information processing and quantum metrology.
Introduction
The coupling between a quantum object and its environment causes decoherence, which is a key issue in quantum science and technology^{1,2,3}. Such coupling is usually understood in terms of classical noise, such as in the spectral diffusion theories that are widely used in, for example, magnetic resonance spectroscopy^{4,5} and optical spectroscopy^{6,7}. In modern nanotechnology and quantum science, the relevant environment of a quantum object can be of nanometre or even subnanometre size^{8,9,10,11,12,13,14,15,16,17,18,19,20,21,22}. Therefore, the environment itself is quantum in nature. In recent years, quantum theories have been developed to treat the decoherence problem in a mesoscopic quantum bath^{23,24,25,26,27,28}. These quantum theories have been successful in studying decoherence in various systems and predicted some surprising quantum effects^{27}. A number of experiments have indicated the quantum nature of nuclear spin baths^{8,10,11,12,16,17}. However, up to now, there has been no experiment explicitly addressing the fundamental difference between classical and quantum baths.
A recent theoretical study^{29} predicted an anomalous decoherence effect (ADE) of a quantum bath on a spin higher than 1/2. Considering a spin1 under a unidirectional magnetic noise b_{z} with Hamiltonian b_{z}S_{z}, the spin, initially in a superposition of the S_{z} eigenstates ψ(0)〉=a_{−}−〉+a_{0}0〉+a_{+}+〉, will evolve to ψ(t)〉=a_{−}e^{iϕ(t)}−〉+a_{0}0〉+a_{+}e^{iϕ(t)}+〉 with an accumulated random phase . The coherence of the singletransitions 0〉↔±〉 is determined by the average of the random phase factor as L_{0,±}=〈e^{±iϕ(t)}〉, whereas the doubletransition has coherence L_{−,+}=〈e^{2iϕ(t)}〉. For Gaussian noise, as commonly encountered, L_{0,±}=e^{−〈ϕ(t)ϕ(t)〉/2} and L_{−,+}=e^{−2〈ϕ(t)ϕ(t)〉}=L_{0,+}^{4}. Decoherence of the doubletransition behaves essentially the same as that of the singletransitions, but is faster as the doubletransition suffers from noise that is twice as strong as that suffered by the singletransitions. Surprisingly, in a mesoscopic quantum bath made of nuclear spins, where the noise b_{z} is the bath operator, the prediction is that the coherence time of the doubletransition under dynamical decoupling, where the bath evolution is controlled through the flips of the central spin, can be increased above that of the single spin^{29}.
The nitrogenvacancy (NV) centre in highpurity diamond, which has an electron spin1 coupled to a nanometresized nuclear spin bath, is an ideal system to study the ADE. The NV centre electron spin (referred to as the centre spin hereafter; Figure 1a displays the structure) has long coherence time (∼ms) even at room temperature^{21}, and is promising for applications in quantum information processing^{17,18,19,20,21,22,30,31,32,33,34,35} and nanometrology^{36,37,38,39,40,41}. Besides the applications, the NV centre electron spin system is also a good model system for fundamental research on decoherence^{28,29} and dynamical decoupling control^{42,43,44}. The decoherence of NV centre electron spins in typeIIa samples is caused by coupling to the quantum spin bath formed from the ^{13}C nuclear spins that lie within several nanometres from the centre^{28,29}.
Here we report the experimental observation of the ADE using an NV centre system at room temperature. The observed centre spin decoherence is in excellent agreement with the microscopic theory. The combined experimental and theoretical results demonstrate the capability of manipulating the evolution of the surrounding ^{13}C nuclear spins by controlling the centre spin. This manipulation paves the way for exploiting spin baths for quantum information processing^{45} and nanometrology^{39,41}.
Results
System and model
We demonstrate the ADE using paramagnetic resonance measurements and microscopic calculations. The experiments are based on optically detected magnetic resonance^{46} of single NV centres in typeIIa diamond at room temperature. After being polarized into the state 0〉 by a 532nm laser pulse, the centre spin state is manipulated by the resonant microwave pulses and the spin coherence is read out through the measurement of fluorescence intensity (Fig. 1b). The calculation is based on a quantum manybody theory^{26}, which takes into account the hyperfine coupling between the centre spin and the ^{13}C bath spins and the dipolar interaction between ^{13}C bath spins (see Methods).
Under zero field, the centre spin has three eigenstates quantized along the z direction (the NV axis, [111] direction), namely, ±〉 and 0〉. In the experiment, a weak magnetic field (<20 gauss) is applied along the NV axis to lift the degeneracy between +〉 and −〉. Each energy level of the spin states ±〉 is split into three sublevels owing to the hyperfine coupling with the ^{14}N nuclear spin in the NV centre (Fig. 1c). The coherence L_{0,+}(t) of the singletransition 0〉↔+〉 and the coherence L_{+,−}(t) of the doubletransition +〉↔−〉 (Fig. 1c) are measured for a single NV centre.
The system has a Hamiltonian H=H_{NV}+H_{B}+H_{hf}. The centre spin Hamiltonian is H_{NV}=ΔS_{z}^{2}−γ_{e}BS_{z}, where Δ denotes the zerofield splitting and γ_{e}=1.76×10^{11} s^{−1}T^{−1} is the electron gyromagnetic ratio. The bath Hamiltonian contains the nuclear spin Zeeman splitting (ω) and the dipolar interaction between nuclear spins (with coefficients ). The centre spin couples to the nuclear spins through , where A_{j} is the hyperfine coupling to the j^{th} nuclear spin I_{j}. Here the transverse components of the hyperfine coupling have been dropped because they are too weak to cause the centre spin flip (with A_{j}<Δ). Owing to its dipolar form, the hyperfine coupling strength depends inversecubically on the distance of the nuclear spin from the centre. The relevant bath spins are those located within a few nanometres from the centre (Fig. 1d). Outside this range, the nuclear spins have too weak a hyperfine coupling to contribute to the centre spin decoherence^{29}. Thus, within the decoherence timescale (
Freeinduction decay of the centre spin coherence
Viewed from the centre spin, the hyperfine coupling provides a quantum noise field . Since in general does not commute with the total Hamiltonian H, a certain noisefield eigenstate will evolve to a superposition of different eigenstates of , which leads to quantum fluctuations of the centre spin splitting. The Hamiltonian can also be expressed as
where ω_{α}=Δ−αγ_{e}B is the eigenenergy of α〉, and governs the bath dynamics conditioned on the centre spin state. Viewed from the bath, the hyperfine coupling is a back action, conditioned on the centre spin state. Thus, the centre spin decoherence is caused by conditional bath evolution, which records the whichway information of the centre spin^{25,29}.
Besides the quantum fluctuations, there are also classical thermal fluctuations due to the random orientations of nuclear spins at room temperature. Indeed, the thermal fluctuations (also called inhomogeneous broadening) are much stronger than the quantum fluctuations and cause the freeinduction decay of centre spin coherence within several microseconds. However, the inhomogeneous broadening effect can be removed by spin echo^{47}. The coexistence of classical and quantum fluctuations and their different effects under spin echo control enable the insitu comparison between the classical and quantum noises.
Figure 2 shows the freeinduction decay of the centre spin coherence. Both single and doubletransition decoherence have Gaussian decay envelopes exp(−t^{2}/T_{2}^{*2}), with the dephasing time of the doubletransition (T_{2}^{*}=1.16±0.11 μs) about half that of the singletransition (T_{2}^{*}=2.33±0.39 μs). This verifies the scaling relation
as predicted in ref. 29 for thermal fluctuations. The experimental data are in good agreement with the numerical results obtained by considering the inhomogeneous broadening of a ^{13}C nuclear spin bath.
Hahn echo of the centre spin coherence
The quantum fluctuations become relevant when the inhomogeneous effect is removed by spin echo^{47}. Figure 3 shows the Hahn echo signals under an external magnetic field B=13.5 gauss. The singletransition coherence presents periodic revivals. In contrast, the doubletransition coherence decays to zero within several microseconds and does not recover. Such qualitative differences result directly from manipulation of the quantum bath on the centre spin flip.
Under a weak magnetic field, the centre spin decoherence is mainly induced by the single ^{13}C nuclear spin dynamics^{28,39,48}. The dipolar interaction between nuclear spins can be neglected for the moment. Thus, the bath Hamiltonian H_{B} only contains the nuclear Zeeman energy (with γ_{C}B/2π∼14.4 kHz, γ_{C}=6.73×10^{7} s^{−1}T^{−1} being the gyromagnetic ratio of ^{13}C nuclei). The hyperfine field α A_{j} (with A_{j}/2π∼5 kHz for a nuclear spin I_{j} located 1.5 nm from the centre) is comparable to the Zeeman frequency. Each nuclear spin precesses about different local fields h_{j}^{(α)}=−γ_{C}B+α A j, conditioned on the centre spin state α〉. The centre spin decoherence is expressed as^{28,39,48}.
where I_{j}^{(α)}(t)〉 is the precession of the jth nuclear spin about the local field h_{j}^{(α)} starting from a randomly set initial state I_{j}〉. The conditional evolution of bath spins records the whichway information of the centre spin and causes the decoherence. Under a flip operation of the centre spin α〉↔α′〉, the nuclear spin precession is manipulated as , that is, the nuclear spin changes its precession direction and frequency. Thus, the nuclear spin bath is manipulated through control of the centre spin. The coherence at the echo time is calculated as^{28}.
When the centre spin is in the state 0〉, all the nuclear spins precess about the same local field B. This fact leads to the singletransition coherence recovery when the echo time is such that the nuclear spins complete full cycles of precession in a period of free evolution under the magnetic field (that is, γ_{C}Bτ=2nπ for integer n). This effect is shown in Figure 3a, which is consistent with previous observations^{17}. The height of the recovery peaks decays owing to the nuclear–nuclear spin interaction in the bath^{28,39,48} (Supplementary Fig. S2). For the doubletransition coherence, however, the hyperfine couplings are nonzero and, therefore, the nuclear spins have different local fields for both of the centre spin states ±〉. Consequently, the doubletransition coherence has no full recovery under the echo control in the weak field. Figure 3a,b show excellent agreement between the theory and the experimental observation.
A close up of the initial coherence collapse (for γ_{C}Bτ<2π) shows that the singletransition coherence still decays slower than the doubletransition coherence (Fig. 3c). Actually, in the initial spinecho decay under a weak magnetic field, the short time condition h_{j}^{(αα)}τ<1 is satisfied for most nuclear spins coupled to the centre spin. The short time expansion of equation (4) gives
and
which satisfy the scaling relation for classical Gaussian noise in equation (2) (Supplementary Fig. S3). Thus, in the relatively short time range, the ADE is not yet fully developed.
Dynamical decoupling control of the centre spin coherence
To further explore the quantum nature of the nuclear spin bath, we employ the multipulse dynamical decoupling control, to elongate the centre spin coherence time and to make the control effects on the quantum bath more pronounced. Figure 4 compares the single and doubletransition coherence under the periodic dynamical decoupling (PDD) control by equally spaced sequences of up to five pulses (applied at τ, 3τ, 5τ ..., called Carr–Purcell sequences for two or more pulses)^{42,43,44}. To focus on the initialstage decoherence, we use a weak field (B=5 gauss) so that the subsequent revival of the centre spin coherence is suppressed since the revival period (about 0.37 ms in Hahn echo and 1.85 ms in PDD5) is long as compared with the overall decoherence time^{48}. In the Hahn echo (PDD1), where the short time condition approximately holds, the singletransition coherence and the doubletransition coherence approximately satisfy the scaling relation in equation (2). With increasing the number of control pulses, the doubletransition coherence time increases more than that of the singletransition. Surprisingly, under the fivepulse control, the doubletransition has significantly longer coherence time than the singletransition. Such counterintuitive phenomena unambiguously demonstrate the quantum nature of the nuclear spin bath.
The different dependence on dynamical decoupling of the single and doubletransition decoherence, though counterintuitive, can be understood with a geometrical picture of nuclear spin precession conditioned on the centre spin state (Fig. 5). By repeated flip control α〉↔α′〉 of the centre spin, a nuclear spin I_{j} precesses alternatively about the local fields h_{j}^{(α)} and h_{j}^{(α′)}. The decoherence is caused mainly by the ^{13}C spins that are located close to the centre spin, which have hyperfine fields much stronger than the weak external field (A_{j}>γ_{C}B). The local fields h_{j}^{(±)}=−γ_{C}B±A_{j}, corresponding to the centre spin states ±〉, are approximately antiparallel and the bifurcated nuclear spin precession pathways have small distance δ_{+,−} at echo time (Fig. 5a displays a schematic of the evolution paths on the Bloch sphere, and Supplementary Movie 1 displays the animation). Thus, under dynamical decoupling control of the doubletransition, the centre spin decoherence due to the closely located nuclear spins is largely suppressed. Figure 5b shows the contributions to the doubletransition decoherence of three strongly coupled ^{13}C spins in the randomly generated spin bath (the same bath as used in calculation for Figures 2,3,4), which are largely suppressed by the dynamical decoupling control. On the contrary, this decoherence suppression mechanism does not exist in the singletransition case (Fig.5c displays a schematic diagram of the evolution paths on the Bloch sphere and Supplementary Movie 2 displays the animation). Figure 5d shows the contributions to the singletransition decoherence of the same three strongly coupled ^{13}C spins as in Figure 5b, which are much greater than in the doubletransition case. Thus, the overall coherence of the singletransition decays faster than that of the doubletransition. This explains the ADE.
Figure 4 shows excellent agreement between the measured centre spin decoherence under PDD and the calculation. Some features of slow oscillations or shoulders in the calculated decoherence do not perfectly match those in the measured data, especially for the higher order dynamical decoupling. This difference in the detail is understandable as such features are sensitive to the specific random positions of a few closely located ^{13}C spins, which are not determined. Nevertheless, the experiments unambiguously confirm the prediction that the doubletransition coherence time grows to be longer than that of the singletransitions.
Discussion
Our observation of the ADE using NV centre coherence establishes the quantum nature of nuclear spin baths at room temperature. Previous studies of coherence control of NV centre spins in electronspin baths^{32,33,34,42} show that the decoherence is well described by classical noise theory. The fundamental difference between nuclear spin baths and electron spin baths lies in the intrabath interaction strength relative to the bathcentre spin coupling^{49}. For nuclear spin baths, the dipolar interaction between nuclear spins at average distance (∼10 Hz) is much weaker than the typical hyperfine coupling (>kHz)^{28,29}. With such weak intrabath interaction, the diffusion of coherence among nuclear spins is much slower than the decoherence (of a timescale ∼ms). Thus, the centre spin and the bath can be regarded as a relatively closed quantum system. For electron spin baths, however, the coupling between bath spins at average distance is much stronger than the typical bathcentre coupling. As a result, the coherence will rapidly diffuse from closely located bath spins to those at distance during the centre spin decoherence. Therefore, an electron spin bath behaves like a macroscopic open system and the classical noise theory is valid. For NV centre spin decoherence in electron spin baths, we expect the ADE be absent and the scaling relation in equation (2) be observed instead.
The quantum nature of nuclear spin baths can also be understood by the backaction of the centre spin to the bath. For the transition α〉↔α′〉, the Hamiltonian in equation (1) can be expressed in a pseudospin form as , where σ_{z}=α〉〈α−α′〉〈α′ is the pseudospin operator, b_{αα′}=H^{(α)}−H^{(α′)} is the effective noise field to the pseudospin and is the effective bath Hamiltonian. For the singletransitions 0〉↔±〉, the effective noise field is , and the doubletransition +〉↔−〉 has a twice stronger noise as . For the doubletransition, the effective bath Hamiltonian is H_{+−}=H_{B}, but for the singletransition the effective bath Hamiltonian is with the extra term owing to the hyperfine coupling, which is the backaction of the centre spin to the bath. For the nuclear spin bath, the hyperfine coupling is typically stronger than the intrabath interactions and the backaction strongly modifies the effective bath Hamiltonian. In particular, for this work, the hyperfine coupling provides a much stronger local field than the applied magnetic field for nuclear spins close to the centre spin. In the singletransition case, because of the backaction, the nuclear spins have enhanced precession frequencies in comparison to the doubletransition case. Thus, viewed from the centre spin, the effective bath for the doubletransition produces noise with lower frequencies than in the singletransition case and, therefore, the centre spin coherence is better protected by the dynamical decoupling control. This explains the ADE observed in nuclear spin baths. In contrast, for electron spin baths, the coupling strength within the bath Hamiltonian H_{B} is much larger than the backaction term (refs 32, 33, 34, 42, 49). For different centre spin transitions the modification of the bath dynamics due to the backaction is negligible. In this sense, the electron spin bath behaves as a classical bath and the ADE should not occur.
Finally, we point out that, in this work, the ADE is demonstrated in the weak magnetic field regime (<20 gauss) in which the quantum fluctuations is caused mainly by single nuclear spin dynamics. The ADE was predicted in ref. 29 in the strong field regime, where the fluctuations are caused mainly by nuclear spin pair dynamics. These works indicate that the ADE is robust against the details of the decoherence mechanisms but is a universal phenomena due to the quantum nature of mesoscopic baths.
Methods
Experimental setup
All the experiments are carried out at room temperature. The typeIIa diamond single crystal sample has nitrogen density less than 5 ppb and the natural abundance of the ^{13}C isotope. Individual NV centres are optically addressed by a confocal microscope mounted on a piezoelectric scanner, and are identified by the measurement of the antibunching effect through the secondorder correlation function (Supplementary Fig. S4). To avoid the influence of the surface, an NV centre located 10 μm below the surface is used in the experiments. The weak magnetic field is generated by three pairs of Helmholtz coils with an accuracy of 1 degree for the direction and 0.01 gauss for the magnitude. All the pulse signals used in the experiments are synchronized by a pulse generator with time resolution of about 4 ns.
Centre spin initialization and readout
The centre spin state is initialized and read out by a 532 nm continuouswave laser, which is gated using an acoustooptical modulator. A 10 μs optical pulse with an extra 5 μs waiting time pumps the system into the state 0〉. To read out the spin state, a 420 ns counting pulse is applied with a 620 ns waiting time after turning on the laser.
Centre spin manipulation
The centre spin is manipulated by resonant microwave pulses. A linear amplifier boosts microwave pulse power to the desired amplitude and a 20 μm diameter copper wire couples the microwave field into the diamond.
The doubletransition coherence is generated and controlled by composite pulses (Fig. 6). The π/2rotation of +〉↔−〉 is realized by a π/2rotation of 0〉↔+〉 followed by a πrotation of 0〉↔−〉, and the πrotation of +〉↔−〉 is realized by two πrotation of 0〉↔−〉 sandwiched by a πrotation of 0〉↔+〉. For a fair comparison, the duration of a control in the singletransition coherence measurement is kept approximately the same as the total duration of the corresponding composite control in the doubletransition coherence measurement. This is realized either by replacing π/2 and π rotations with 3π/2 and 3π rotations (amplitude kept the same but duration varied, Fig. 6a,b), as in the experiments in Figures 2 and 3 where B=13.5 gauss, or by using pulses of smaller amplitudes in the singletransition coherence measurement (Fig. 6c), as in the experiments in Figure 4 where B=5 gauss.
With different pulse amplitudes under different magnetic field, the microwave pulse errors caused by coupling to the ^{14}N nuclear spin are greatly suppressed. Because of the hyperfine coupling to the ^{14}N nuclear spin, the microwave control is described by the Hamiltonian in the rotatingframe reference as H=A_{0}S_{z}I_{Z}+√2B_{1}S_{x}, where A_{0}=2.18 MHz, is the hyperfine coupling strength and B_{1} is the Rabi frequency of the driven field. Errors would result if the π pulses do not fully flip all the three hyperfinesplit lines.
Under a magnetic field B=13.5 gauss, a typical π pulse has a duration of 50 ns (corresponding to the Rabi frequency of about 10 MHz). Thus, the two centre spin singletransitions 0〉↔±〉 are well resolved whereas the three transition lines for different states of the ^{14}N nuclear spin1 are all spectrally covered (Fig. 6d). Under a magnetic field B=5 gauss it is difficult to spectrally resolve the two singletransitions without selection of different ^{14}N states. Therefore we use soft pulses (1.1 μs and 0.39 μs for the πrotation in the single and doubletransition coherence measurements, respectively, corresponding to the Rabi frequencies of 0.45 MHz and 1.3 MHz) to selectively excite the singletransitions corresponding to only one of the ^{14}N states (namely the 0〉_{14N} state, Figure 6d) and to maximally suppress the transitions when the ^{14}N nuclear spin is in the other two states (±1〉_{14N}). The selective and nonselective excitations are confirmed by the measurements of Rabi oscillations (Fig. 6e). The contrast measured by the selective pulse is one third of that measured by the nonselective pulse.
Data processing and error analysis
The measured contrast is given by the relative change in fluorescence intensity as C=(I_{M}−I_{∞})/I_{0}, where I_{M} is the signal, I_{∞} is the fluorescence where the spin coherence has totally decayed and I_{0} is the fluorescence when the centre spin is in the state 0〉, all of which are measured independently in every experimental run. The contrast is normalized to the averaged value at the initial decoherence stage (for small time, where the coherence presents the plateau feature). The results, however, do not depend on the normalization (Supplementary Fig. S5).
The statistical errors come mainly from the photoncounting shot noises and laserfocusing spot drifting. To suppress errors from the laserfocus drifting, the laser is refocused every 20 min during the measurement. To reduce the effect of the shot noises, each measurement has been repeated about 10^{6} times. The background photon counting I_{0} is measured by more than 10^{7} times so that its statistical fluctuation can be neglected. Besides the statistical fluctuations, there are two major causes of systematic errors: first, the MW pulse frequencies are determined with an error about ±20 kHz, less than 4% of the Rabi frequencies; and second, the durations of the pulses are determined up to an error of ±2 ns, which induces an error in the Rabi frequencies of about 4% in the case of short control pulse used in the experiments in Figures 2 and 3 (where the π pulses have durations of about 50 ns), but has negligible effect in the case of soft control pulse used in the experiments in Figure 4. The above factors contribute to the error bars estimated and shown in Figures 2,3,4.
Theoretical model and numerical simulation methods
In the numerical calculation, the nuclear spin bath is generated by randomly placing ^{13}C atoms on the diamond lattice around the NV centre with a natural abundance 1.1%. Inclusion of about 100 ^{13}C nuclear spins within 2 nm from the NV centre is sufficient for a converged result of the centre spin decoherence in the timescale considered in this paper. The inhomogeneous broadening and decoherence times depend on the random positions of the ^{13}C atoms in the lattice^{28,48}. In the simulation, the configuration of ^{13}C atom positions is randomly chosen to produce a singletransition dephasing time T_{2}^{*} and a singletransition decoherence time in Hahn echo (T_{2}) close to the experimental results (under 13.5 gauss field). Otherwise, there is no fitting parameter. Different random configurations of the ^{13}C atom positions do not affect the essential results but result in differences in the detailed features (Supplementary Fig. S6). The generated bath does not contain a ^{13}C in the first few coordinate shells of the NV centre (which has hyperfine coupling >1 MHz), to be consistent with the NV centre under the experimental observation. The hyperfine interaction is assumed to have a dipolar form with the electron spin located at the vacancy site. The spin coherence is calculated by applying the cluster correlation expansion method^{26}, which takes into account, order by order, the manybody correlations induced by the dipolar interactions between nuclear spins, and can identify the contribution of each nuclear spin cluster to the total decoherence. The converged results are obtained by including clusters containing up to 3 nuclear spins. The microwave pulses are modelled by instantaneous pulses, which is a good approximation considering the fact that the pulse durations are all much shorter than the decoherence times in the experiments.
Additional information
How to cite this article: Huang, P. et al. Observation of an anomalous decoherence effect in a quantum bath at room temperature. Nat. Commun. 2:570 doi: 10.1038/ncomms1579 (2011).
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Acknowledgements
This work was supported by National Natural Science Foundation of China under Grant No. 11028510 and 10834005; the Chinese Academy of Sciences and the National Fundamental Research Program of China under Grant No. 2007CB925200; Hong Kong Research Grant Council/General Research Fund CUHK402410; The Chinese University of Hong Kong Focused Investments Scheme; and Hong Kong Research Grant Council HKU10/CRF/08.
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J.D. designed and supervised the experiments. X.K., F.S., P.W., X.R. and J.D. prepared the experimental setup. P.H. and X.K. performed the experiments. R.B.L. conceived the effect. R.B.L. and N.Z. formulated the theory. N.Z. carried out the calculation. R.B.L., N.Z. and P.H. wrote the paper. All authors analysed the data, discussed the results and commented on the manuscript.
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Supplementary Figures S1S6, Supplementary Notes 13 and Supplementary Reference (PDF 700 kb)
Movie 1
Movie 1: Bifurcated nuclear spin precession under the 2pulse PDD control of the doubletransition. When the centre spin doubletransition is excited, the single 13C nuclear spin will precess about the local fields h(+)j and h()j conditioned on the centre spin states +> and > respectively. When the centre spin state is flipped at t=t and 3t, the precession axes are exchanged. The distance d+, between the two bifurcated pathways on the Bloch sphere determines the centre spin decoherence due to the single 13C nuclear spin. In the doubletransition case, the local fields h(+)j and h()j are approximately antiparallel to each other, so the distance d+, and hence the decoherence are small at the echo time. Thus, the centre spin decoherence due to the single 13C nuclear spin is suppressed. (MOV 1311 kb)
Movie 2
Movie 2: Bifurcated nuclear spin precession under the 2pulse PDD control of the singletransition. When the centre spin single transition is excited, the single 13C nuclear spin will precess about the local fields h(+)j and h(0)j conditioned on the centre spin states +> and 0> respectively. When the centre spin state is flipped at t=t and 3t, the precession axes are exchanged. The distance d+,0 between the two bifurcated pathways on the Bloch sphere determines the centre spin decoherence due to the single 13C nuclear spin. In the singletransition case, the local fields h(+)j and h(0)j are in general not antiparallel, so the distance d+,0 and hence the decoherence can be large at the echo time. Thus, the single 13C nuclear spin has a significant contribution to the centre spin decoherence. (MOV 1103 kb)
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Huang, P., Kong, X., Zhao, N. et al. Observation of an anomalous decoherence effect in a quantum bath at room temperature. Nat Commun 2, 570 (2011). https://doi.org/10.1038/ncomms1579
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DOI: https://doi.org/10.1038/ncomms1579
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