Continuous dynamical decoupling utilizing time‐dependent detuning

Abstract

The coherence times achieved with continuous dynamical decoupling techniques are often limited by fluctuations in the driving amplitude. In this work, we use time-dependent phase-modulated continuous driving to increase the robustness against such fluctuations in a dense ensemble of nitrogen-vacancy centers in diamond. Considering realistic experimental errors in the system, we identify the optimal modulation strength, and demonstrate an improvement of an order of magnitude in the spin-preservation of arbitrary states over conventional single continuous driving. The phase-modulated driving exhibits comparable results to previously examined amplitude-modulated techniques, and is expected to outperform them in experimental systems having higher phase accuracy. The proposed technique could open new avenues for quantum information processing and many body physics, in systems dominated by high-frequency spin-bath noise, for which pulsed dynamical decoupling is less effective. PACS numbers: 76.30.Mi One of the main challenges in quantum information processing, quantum computing and quantum sensing is the preservation of arbitrary spin states. For example, the sensitivity of nitrogen-vacancy (NV) ensemble-based AC magneteometry scales as a square-root of the coherence time [1-8]. Moreover, long ensemble spin coherence times could open new avenues for studying many body dynamics of interacting spins [9-11]. The commonly used technique for improving coherence times and preserving arbitrary states is dynamical decoupling (DD) sequences [12-18]. Although pulsed DD is very efficient for a variety of physical systems, continuous driving-based decoupling (i.e. spin-lock) has an advantage when the power spectrum of the noise bath contains a significant contribution from high-frequency terms, such that relevant correlation times are shorter than the duty cycle achievable by pulsed techniques [15, 16]. However, in these continuous schemes, amplitude fluctuations of the driving source itself limit the achieved coherence times, raising the need for a fault tolerant driving [16, 18-23]. One common approach for overcoming fluctuations in the driving amplitude is to flip the phase of the continuous driving every time increment τ (i.e., to apply a "rotary echo", [24]). However, in the basis of the dressed states, these techniques are equivalent to pulsed DD, having the same disadvantages, such as additional imperfections due to the application of non-ideal pulses, and the disability of mitigating amplitude fluctuations that are faster than the flipping rate 1/τ. Another approach for overcoming these fluctuations is to apply an additional continuous driving in the perpendicular axis [Fig. 1(a)]. In order to avoid the use of an extra microwave (MW) source, the same effective Hamiltonian can be generated by a time-dependent modulation of the amplitude or phase of the original driving. Recently, such time-dependent amplitude modulation was experimentally demonstrated in a system of single isolated NV centers, achieving an order of magnitu...

Robust optical clock transitions in trapped ions using dynamical decoupling

“…In our analysis we assumed that all driving fields suffer from driving fluctuations. Generating the second driving fields (Ω 2 and Ω 4 ) by a phase modulation, as proposed in [41], should result in stable driving fields with negligible amplitude fluctuations. In this case we expect a further improvement in the performance of the scheme.…”

“…Achieving insensitivity of atomic energy levels to external field fluctuations has been theoretically investigated using pulsed or continuous dynamical decoupling (CDD) [38][39][40][41][42][43][44][45][46][47][48]. Such schemes have been experimentally implemented in various systems ranging from NV centers and solid state spin systems [49][50][51][52][53][54][55][56][57] to neutral atoms [58] and trapped ions [59][60][61][62][63][64].…”

Mixed dynamical decoupling

“…3a). The remaining decay is due to the noise of the driving field itself, as shown in previous publications [19]. We note that we define the T 2 of the fidelity as the time it takes to drop to from 1 to ≈ 0.79, which corresponds to a 1/e drop in the difference from the quantum limit of 0.67.…”

“…Major drawbacks of this approach are the complexity due to operation with multiple fields and the lower energy gap in the highest order dressed basis, which leads to slower operation. Apart from dressing field concatenation, an alternative approach was proposed recently, where a time dependent phase was added to a continuous driving field, yielding a time-dependent detuning [19]. The latter acts like the second driving field of the concatenated CDD and its noise can be negligible in some experiments at the expense of complexity of implementation, e.g., of the time-dependent detuning.…”

High-precision gravimeter based on a nano-mechanical resonator hybrid with an electron spin

“…For the trapped nanoparticle scheme, the coherence time of NV center can be prolonged to the limit of T 1 by decoherence decoupling techniques. In our proposal, no transition between | ± 1 is needed during the propagation, therefore it is convenient to use a continuous dynamical decoupling which prolong the quantum memory to T 2 ∼ 2 ms. For example, we can use the timedependent detuning method described in [46]. Considering only the states | ± 1 during the propagation, the two-level system with an ambient magnetic field noise δB(t) is described by…”