Harnessing the dynamics of a microscopic system lies at the core of quantum information processing. For quantum systems with a small number of spins, optimal control has been shown to be an efficient method to realize high-fidelity quantum control. As the number of the spins increases, it becomes challenging to steer the dynamics of the quantum system due to the exponentially increasing dimension of Hilbert space. Herein, we propose a method to realize optimal control of a spin bath consisting of hundreds of spins. A central spin is used to monitor the dynamics of the spin bath under a control Hamiltonian. The information obtained from the central spin is fed back to the control Hamilton to realize optimal control over the spin bath. We take a nitrogen vacancy (NV) center in diamond as an example, and our numerical simulation shows that the dephasing time of the NV center can be improved by more than 2 orders of magnitude. Furthermore, our method is compatible with dc magnetometry, whose sensitivity can be improved by an order of magnitude compared to conventional Ramsey interference. Our method is also feasible for various other spin-based systems, such as quantum dots, phosphorus-doped silicon, and defects in silicon carbide.
The nitrogen-vacancy (NV) center in diamond is extensively studied for a next-generation high-sensitivity magnetometer. The DC magnetic sensitivity can be improved by extending the inhomogeneous spin dephasing time through suppressing the effects of inhomogeneous fluctuations or by increasing the number of effective NV centers through expanding the sensor volume. It has been demonstrated that strain-induced dephasing can be suppressed by double quantum (DQ) technique with two-tone microwaves (MW), and spin bath-induced dephasing can be suppressed by spin bath drive (SBD) technique with multi-tone radio-frequency (RF) to drive the P1 centers. To combine these T2* -extension techniques with a bulk diamond, it is necessary to apply MW and RF uniformly to the sample. A coplanar waveguide (CPW) circuit has been reported to be useful for uniform microwave irradiation to a bulk sample. In this study, we reports the newly designed and fabricated a cross-aligned two-layer CPW circuit.
Low-field dephasing time of an optically polarized NV
− spin bath beyond the P1 limit in diamond: a cluster-correlation-expansion and exact spin-bath study
Dense ensembles of nitrogen-vacancy (NV
−) centres in nitrogen-rich diamond dephase on the electron spins of the substitutional nitrogen (P1) centres. If the paramagnetic nitrogen is instead converted into NV
− centres, the laser that initializes the sensor also pumps the bath into
ms = 0, a state with no moment along its own axis. Using cluster-correlation-expansion (CCE) calculations, combined with an exact solver for probe-bath exchange and with no adjustable parameter, this paper asks whether such an optically polarized NV
− bath dephases a sensor more slowly than a P1 bath of the same density. The answer is set by the field. In a field along [111], three quarters of the bath centres lie off the field axis, and the moment of their
ms = 0 state along the field grows from 0.04 at 25 G to 0.46 at 300 G and 0.81 at 800 G. At 25 G the polarized bath is therefore nearly silent: at
1017 cm
−3 the dephasing time
T2∗ of a separately addressed
15NV
− probe is 112 us, six times the 18.1 us of a P1 bath, and still 2.4 times at 90 % polarization; an ensemble measurement gains a factor of two. At 300 G the advantage over P1 shrinks to 1.4, and at 800 G the polarized bath dephases faster than P1. The field dependence of every bath, P1 included, follows the mean moment of its centres along the field. For the Hahn echo, exchange with on-axis bath centres and bath relaxation (
T1 = 6 ms) limit the gain to 1.2 times the P1 value at 25 G. Optical polarization of an NV
− bath at low field therefore offers dephasing times beyond the P1 limit of nitrogen-rich diamond.