Search

Knott et al.1 argue in their comment on our recently published study2 that the enhancement of phase sensitivity is obtained by applying a phase shift twice, and thus not from the entanglement. We clarify that the entanglement between the two non-identical qubits is the crucial and decisive factor in the achieved enhancement, and the experimental technique used to encode the phases to qubits does not affect this conclusion. By harnessing entanglement, quantum parameter estimation can yield higher statistical precision than purely classical approaches3,4,5. In our work2, two spins of different physical realization (an NV electron spin and its proximal 13C nuclear spin) are employed, and we demonstrate that their entangled state can give higher-phase statistical precision than their independent states. Phase information of spin qubits is of crucial importance because numerous external parameters, such as magnetic field6, electronic field7, temperature8 and pressure9, can be transferred into phase information and then measured with high sensitivity. The principle of quantum metrology works for all these external parameters, as it works for our encoded phases. Since the phases of microwave (MW) and radio frequency (RF) pulses are the controllable and measurable external parameters in our experiment, the claim that our scheme cannot measure an external parameter is not correct. We first emphasize that entanglement of the two qubits is necessary to produce the enhancement of phase estimation in our experiment. Due to the energy structure of this four-level system, the used microwave pulse can only manipulate the state of electron spin, and the used radio frequency pulse can only manipulate the state of nuclear spin. This allows us to selectively encode phases to different target spins, simultaneously or in a sequential manner. As shown in Fig. 1a, one phase is encoded to the electron spin and another phase is encoded to the nuclear spin. If and only if the two qubits are entangled, their phases can be merged together and thus read out by one operation. For a comparison, as shown in Fig. 1b, we can prepare the two qubits to independent states, with the same phases. But in this case no quantum enhancement can be given; the employment of two qubits is equivalent to taking two repeat measurements on one qubit. Figure 1 The quantum circuits and pulse sequences in our experiment. Also, we would like to claim that although the sequential pulses are employed to generate the entangled state, our experiment has significant differences from the sequential phase estimation scheme. As pointed in the comment and ref. 5, in such scheme, the same phase shifts are applied to the same superposition state, and no entanglement is needed (see Fig. 1c). In our entanglement-enhanced scheme, the two phases are encoded to qubits of different physical realization, by applying two completely different pulses (one is MW pulse, another is RF pulse). For a comparison, we also present a possible realization of the sequential strategy in our system (see Fig. 1c). In fact, sequential pulse is used to generate the entangled state of the hybrid quantum system, but it is not a necessary part of the phase-encoding process. We then discuss the effect of qubit decoherence in our experiment. The thermal fluctuation of the surrounding 13C spin bath will bring random phases to spin qubits if they are under free evolution. The existence of qubit decoherence will weaken or even cancel the merits of entanglement10. However, in our protocol, the phases of spin qubits are encoded by MW or RF pulses, and the phase measurement is carried out right after the encoding. There is no free evolution between the state preparation and measurement operation. Meanwhile, the pulse duration is very short compared with the dephasing time of spin qubits. Therefore, the merits of maximum entangled state are well preserved and fully exploited in our experiment. We also discussed the decoherence behaviour of our system in the Methods section2. We also wish to point out that the assumption of ϕMW≠ϕRF (a special case is ϕMW=−ϕRF), as mentioned in Knott's comment, will break all quantum metrology strategies. If the entangled qubits have different phases, their measurement should most likely give ‘destructive interference' results. Meanwhile, the proposal Eq. (8) presented in the comment is not correct. If a single pulse with a frequency of RF+MW is applied to the system with an initial state of |0 ↑〉, no entanglement state can be generated because no transition in this system is resonant with this pulse. In conclusion, we have shown that entanglement is necessary to our enhancement of phase estimation, and our work has significant difference with the sequential phase estimation scheme. In fact, the highlights of our work mainly lie in two aspects: (1) Our system has overcome the defects of postselection in the most common optical systems, which are fatal due to the fact that the measurement trials abandoned will eliminate the quantum-entanglement advantage over classical strategy. Our work in the solid system is a good complement for the previous experiments in optical systems. (2) We demonstrate a strategy with two entangled qubits of totally different physical realizations. This may enlighten further investigations on realizing quantum algorithms using different kinds of resources. Our results can benefit NV-based quantum metrology applications such as magnetometry6, thermometry8 and radio-frequency spectrum analysis11,12.

Some color centers in diamond can serve as quantum bits which can be manipulated with microwave pulses and read out with laser, even at room temperature. However, the photon collection efficiency of bulk diamond is greatly reduced by refraction at the diamond/air interface. To address this issue, we fabricated arrays of diamond nanostructures, differing in both diameter and top end shape, with HSQ and Cr as the etching mask materials, aiming toward large scale fabrication of single-photon sources with enhanced collection efficiency made of nitrogen vacancy (NV) embedded diamond. With a mixture of O2 and CHF3 gas plasma, diamond pillars with diameters down to 45 nm were obtained. The top end shape evolution has been represented with a simple model. The tests of size dependent single-photon properties confirmed an improved single-photon collection efficiency enhancement, larger than tenfold, and a mild decrease of decoherence time with decreasing pillar diameter was observed as expected. These results provide useful information for future applications of nanostructured diamond as a single-photon source.

We present the experimental results of nitrogen-vacancy (NV) electron spin decoherence, which are linked to the coexistence of electron spin bath of nitrogen impurity (P1 center) and 13C nuclear spin bath. In previous works, only one dominant decoherence source is studied: P1 electron spin bath for type-Ib diamond; or 13C nuclear spin bath for type-IIa diamond. In general, the thermal fluctuation from both spin baths can be eliminated by the Hahn echo sequence, resulting in a long coherence time (T 2) of about 400 μs. However, in a high-purity type-IIa diamond where 13C nuclear spin bath is the dominant decoherence source, dramatic decreases of NV electron spin T 2 time caused by P1 electron spin bath are observed under certain magnetic field. We further apply the engineered Hahn echo sequence to confirm the decoherence mechanism of multiple spin baths and quantitatively estimate the contribution of P1 electron spin bath. Our results are helpful to understand the NV decoherence mechanisms, which will benefit quantum computing and quantum metrology.

Sources of single photons are of fundamental importance in many applications as to provide quantum states for quantum communication and quantum information processing. Color centers in diamond are prominent candidates to generate and manipulate quantum states of light, even at room temperature. However, the efficiency of photon collection of the color centers in bulk diamond is greatly reduced by refraction at the diamond/air interface. To address this issue, diamond structuring has been investigated by various methods. Among them, focused-ion-beam (FIB) direct patterning has been recognized as the most favorable technique. But it has been noted that diamond tends to present significant challenges in FIB milling, e.g., the susceptibility of forming charging related artifacts and topographical features. In this work, periodically-positioned-rings and overlay patterning with stagger-superimposed-rings were proposed to alleviate some problems encountered in FIB milling of diamond, for improved surface morphology and shape control. Cross-scale network and uniform nanostructure arrays have been achieved in single crystalline diamond substrates. High quality diamond solid immersion lens and nanopillars were sculptured with a nitrogen-vacancy center buried at the desired position. Compared with the film counterpart, an enhancement of about ten folds in single photon collection efficiency was achieved with greatly improved signal to noise ratio. All these results indicate that FIB milling through over-lay patterning could be an effective approach to fabricate diamond structures, potentially for quantum information studies.