Measurement of transverse hyperfine interaction by forbidden transitions

Chen, Mo; Hirose, Masashi; Cappellaro, Paola

doi:10.1103/physrevb.92.020101

Cited by 47 publications

(32 citation statements)

References 37 publications

(47 reference statements)

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“…In order to calibrate quantum gates required for the feedback-based protection algorithm (π/2-rotation), we first characterize the nuclear spin, by measuring the resonance frequency of the transition |1 q |1 a ↔ |1 q |0 a [ Fig.4-(b)] and the nuclear Rabi oscillations [ Fig.4-(c)]. We note that despite the small gyromagnetic ratio of the nitrogen (γ n = 0.308 kHz/G) its Rabi oscillations are significantly enhanced due to the transverse hyperfine coupling with the NV spin (we achieve an enhancement factor of about 20 over the bare Rabi frequency around 500 G [21]). To further characterize the nuclear spin ancillary qubit, we measured the dephasing time, T 2n , by performing a Ramey experiment [ Fig.4-(d] and obtained T 2n ≈ 3.2 ms.…”

Section: Hamiltonian Of the Nv-14 N Systemmentioning

confidence: 84%

“…The two spins are coupled by an isotropic hyperfine interaction with A = −2.16 MHz and a transverse component B = −2.62 MHz [21] that can be neglected to first order. A magnetic field is applied along the NV crystal axis [111] to lift the degeneracy of the m s = ±1 level, yielding the electron and nuclear Zeeman frequencies ω e and ω n .…”

Section: Figmentioning

confidence: 99%

“…The RF frequency is on resonance with the transition between |0, 1 and |0, 0 . The transition rate is around Ω n = 20 − 40 kHz, which already reflects an enhancement due to electronic virtual transitions mediated by the transverse component of the hyperfine coupling [21]. Since the nuclear Rabi transition rate is always smaller than the detuning given by the hyperfine interaction (Ω n A), only selective driving of the ancillary spin is available and unconditional gates need to be engineered with composite pulses.…”

Section: Hamiltonian Of the Nv-14 N Systemmentioning

confidence: 99%

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Coherent feedback control of a single qubit in diamond

Hirose

Cappellaro

2016

Nature

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Engineering desired operations on qubits subjected to the deleterious effects of their environment is a critical task in quantum information processing, quantum simulation and sensing. The most common approach is to rely on open-loop quantum control techniques, including optimal control algorithms, based on analytical [1] or numerical [2] solutions, Lyapunov design [3] and Hamiltonian engineering [4]. An alternative strategy, inspired by the success of classical control, is feedback control [5]. Because of the complications introduced by quantum measurement [6], closed-loop control is less pervasive in the quantum settings and, with exceptions [7,8], its experimental implementations have been mainly limited to quantum optics experiments. Here we implement a feedback control algorithm with a solid-state spin qubit system associated with the Nitrogen Vacancy (NV) centre in diamond, using coherent feedback [9] to overcome limitations of measurement-based feedback, and show that it can protect the qubit against intrinsic dephasing noise for milliseconds. In coherent feedback, the quantum system is connected to an auxiliary quantum controller (ancilla) that acquires information about the system's output state (by an entangling operation) and performs an appropriate feedback action (by a conditional gate). In contrast to open-loop dynamical decoupling (DD) techniques [10], feedback control can protect the qubit even against Markovian noise and for an arbitrary period of time (limited only by the ancilla coherence time), while allowing gate operations. It is thus more closely related to Quantum Error Correction schemes [11][12][13][14], which however require larger and increasing qubit overheads. Increasing the number of fresh ancillas allows protection even beyond their coherence time. We can further evaluate the robustness of the feedback protocol, which could be applied to quantum computation and sensing, by exploring an interesting tradeoff between information gain and decoherence protection, as measurement of the ancilla-qubit correlation after the feedback algorithm voids the protection, even if the rest of the dynamics is unchanged.To demonstrate coherent feedback with spin qubits, we choose two of the most common tasks for qubits, implementing the no-operation (NOOP) and NOT gates, while cancelling the effects of noise. A simple, measurementbased feedback scheme, exploiting one ancillary qubit, was proposed in [16]. The correction protocol (Fig. 1a) works by entangling the qubit-ancilla system before the desired gate operation. By selecting an entangling operation U c appropriate for the type of bath acting on the system, information about the noise action is encoded in the ancilla state. After undoing the entangling operation, the qubit coherence can be restored by a feedback action, Hadamard gates prepare and read out a superposition state of the qubit, |φ q = 1 √ 2 (|0 + |1 ). Amid entangling gates between qubit and ancilla, the qubit is subjected to noise (and possibly unitary gates U ). We assume the ancil...

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Section: Hamiltonian Of the Nv-14 N Systemmentioning

confidence: 84%

Section: Figmentioning

confidence: 99%

Section: Hamiltonian Of the Nv-14 N Systemmentioning

confidence: 99%

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Coherent feedback control of a single qubit in diamond

Hirose

Cappellaro

2016

Nature

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“…Even if the 14 N is strongly coupled to the NV (Azz = − 2.16 MHz), it usually does not give rise to an interferometric signal because of its transverse coupling Azx = 0. However, a small perpendicular field B ⊥ = 0.62 G generates an effective transverse coupling γe B ⊥ Axx /(∆0 − γe Bz ), with Axx = − 2.62 MHz (31) and γe = 2.8 MHz/G as the NV gyromagnetic ratio. This effect becomes sizable at a longitudinal magnetic field Bz = 955.7 G that almost compensates the NV zero-field splitting ∆0 = 2.87 GHz.…”

Section: Quantum Interpolationmentioning

confidence: 99%

Quantum interpolation for high-resolution sensing

Ajoy

Liu

Saha

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. Here we introduce a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the nitrogen vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy.quantum sensing | quantum control | nanoscale NMR | NV centers P recision metrology often needs to strike a compromise between signal contrast and resolution, because the hardware apparatus sets limits on the precision and sampling rate at which the data can be acquired. In some cases, classical interpolation techniques have become a standard tool to achieve a significantly higher resolution than the bare recorded data. For instance, the Hubble Space Telescope uses classical digital image processing algorithms like variable pixel linear reconstruction [Drizzle (1)] to construct a supersampled image from multiple low-resolution images captured at slightly different angles. Unfortunately, this classical interpolation method would fail for signals obtained from a quantum sensor, where the information is encoded in its quantum phase (2). Here we introduce a technique, which we call "quantum interpolation," that can recover the intermediary quantum phase, by directly acting on the quantum probe dynamics, and effectively engineer an interpolated Hamiltonian. Crucially, by introducing an optimal interpolation construction, we can exploit otherwise deleterious quantum interferences to achieve high fidelity in the resulting quantum phase signal.Quantum systems, such as trapped ions (3), superconducting qubits (4, 5), and spin defects (6, 7) have been shown to perform as excellent spectrum analyzers and lock-in detectors for both classical and quantum fields (8-10). This sensing technique relies on modulation of the quantum probe during the interferometric detection of an external field. Such a modulation is typically achieved by a periodic sequence of π-pulses that invert the sign of the coupling of the external field to the quantum probe, leading to an effective time-dependent modulation f (t) of the field (11-13). These sequences, more frequently used for dynamical decoupling (14, 15), can be described by sharp bandpass filter functions obtained from the Fourier transform of f (t). This description lies at the basis of their application for precision spectroscopy, as the fil...

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“…For example, in QIP applications, the nuclear spins can hold quantum information [12,13], serving as part of a quantum register [1]. Accurate knowledge of the hyperfine interaction is necessary, e.g., for designing precise and fast control sequences for the nuclear spins [14,15]. With a known Hamiltonian, control sequences can be tailored by optimal control techniques to dramatically improve the speed and precision of multi-qubit gates [16][17][18][19].…”

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confidence: 99%

Characterization of hyperfine interaction between an NV electron spin and a first-shellC13nuclear spin in diamond

Rao

Suter

2016

Phys. Rev. B

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The Nitrogen-Vacancy (NV) center in diamond has attractive properties for a number of quantum technologies that rely on the spin angular momentum of the electron and the nuclei adjacent to the center. The nucleus with the strongest interaction is the 13 C nuclear spin of the first shell. Using this degree of freedom effectively hinges on precise data on the hyperfine interaction between the electronic and the nuclear spin. Here, we present detailed experimental data on this interaction, together with an analysis that yields all parameters of the hyperfine tensor, as well as its orientation with respect to the atomic structure of the center.PACS numbers: 03.67. Lx, 76.70.Hb, 33.35.+r, 61.72.JNitrogen-Vacancy (NV) centers in diamond have interesting properties for applications in room-temperature metrology, spectroscopy, and Quantum Information Processing (QIP) [1][2][3][4][5][6]. Nuclear spins, coupled by hyperfine interaction to the electron spin of the NV-center, are important for many of these applications [1,3,[6][7][8][9][10][11][12][13]. For example, in QIP applications, the nuclear spins can hold quantum information [12,13], serving as part of a quantum register [1]. Accurate knowledge of the hyperfine interaction is necessary, e.g., for designing precise and fast control sequences for the nuclear spins [14,15]. With a known Hamiltonian, control sequences can be tailored by optimal control techniques to dramatically improve the speed and precision of multi-qubit gates [16][17][18][19].The 13 C nuclear spin of the first coordination shell is a good choice for a qubit due to its large hyperfine coupling to the electronic spin of the NV center, which can be used to implement fast gate operations [3,20,21] or highspeed quantum memories [22]. Full exploitation of this potential requires accurate knowledge of the hyperfine interaction, including the anisotropic (tensor) components. The interaction tensor has been calculated by , but only a limited number of experimental studies of this hyperfine interaction exist to date [27][28][29]. In this work, we present a detailed analysis of this hyperfine interaction. The experiments were carried out on single NV centers of a diamond crystal with a natural abundance of 13 C and a nitrogen concentration of < 5 ppb using a home-built confocal microscope and microwave electronics for excitation [22].The presence of a nuclear spin in the first coordination shell reduces the symmetry of the NV center from C 3V to C S , a single mirror plane. This symmetry plane passes through the NV symmetry axis and the 13 C nuclear spin as illustrated in Fig. 1(a). The NV symmetry axis defines the z-axis of the NV frame of reference, the x-axis lies in the symmetry plane of the center, and the y-axis is perpendicular to both of them. Due to the symmetry of the system, only those elements of the hyperfine tensor that are invariant with respect to the inversion of the y-coordinate can be non-zero. Hence, the hyperfine Hamiltonian in the NV frame of reference can be written as(1) Here, S α an...

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Measurement of transverse hyperfine interaction by forbidden transitions

Cited by 47 publications

References 37 publications

Coherent feedback control of a single qubit in diamond

Coherent feedback control of a single qubit in diamond

Quantum interpolation for high-resolution sensing

Characterization of hyperfine interaction between an NV electron spin and a first-shellC13nuclear spin in diamond

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