Geometric spin echo under zero field

Abstract

Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors.

Polarization- and frequency-tunable microwave circuit for selective excitation of nitrogen-vacancy spins in diamond

“…Moreover, B ac from these sources is linearly polarized, while the NV spin has clear transition selection rules; The m S = 0 ↔ 1 (−1) transition is driven by σ + (σ − ) circularly polarized fields. To fully exploit the S = 1 nature of the NV spin for quantum information and metrology applications, [11][12][13][14] it is highly desired to have a reliable means to generate arbitrarily polarized microwave fields.…”

Dynamical Decoupling of a Geometric Qubit

“…The previously demonstrated robustness against electric field noise and temperature drift [32], and enhancement of magnetic field sensitivity [33] in double quantum qubit utilizing ms=±1 states in a three-level system can also be adapted to our qubit. Moreover, it has been demonstrated that the degeneracy of our qubit is required for interfacing with photon polarization [23,24], and that the coherence time in a low magnetic field regime is maximized under a zero magnetic field [9,31].…”

“…As alternatives, a composite pulse technique for achieving high-fidelity gates [3,4] and a specially designed gate sequence [2,5,6] have been developed to be independent of the initial state.A qubit is typically defined as being in a two-level system with an energy gap, which allows direct transition within the bases to implement dynamic quantum gates. Another type of qubit can also be defined in a two-level system without an energy gap; this type requires an indirect transition via a third ancillary level, and thus constitutes a V-shaped three-level system to implement geometric quantum gates [9][10][11][12]. Geometric quantum gates can be either adiabatic [13][14][15] or non-adiabatic [9][10][11][12][16][17][18][19].…”

“…Another type of qubit can also be defined in a two-level system without an energy gap; this type requires an indirect transition via a third ancillary level, and thus constitutes a V-shaped three-level system to implement geometric quantum gates [9][10][11][12]. Geometric quantum gates can be either adiabatic [13][14][15] or non-adiabatic [9][10][11][12][16][17][18][19]. In contrast to the adiabatic geometric gate, the non-adiabatic geometric gate enables faster gate operation to reduce the influence of the environmental noise, thereby resulting in high fidelity.Moreover, the degenerate two-level system is independent of the global phase of the driving field, as seen in the polarization or time-bin encoding of a photon, enabling post selection of successful operations to exclude a population loss from the qubit space spanned by the degenerate two-level system.The negatively charged nitrogen-vacancy (NV) center in diamond (Fig.…”

“…In contrast to conventional SU (2) gates, which utilize the global phase of the driving field to achieve arbitrary rotation, SU(3) gates utilize the polarization of the driving field for the demonstration of spin-photon entanglement generation [22,23] and quantum state transfer [24]. Polarization-based geometric spin rotation [10][11][12] has also been demonstrated under a zero magnetic field, where the electron spin coherence time is maximized owing to the time reversibility of the system including environmental spins [9]. However, it is likely that the population leaks from the qubit space to the ancillary space during the geometric gate operations as an additional error [26,27], limiting the previous experiments to several gate operations.…”