Phase-controlled coherent dynamics of a single spin under closed-contour interaction

Abstract

In three-level quantum systems, interference between two simultaneously driven excitation pathways can give rise to effects such as coherent population trapping 1,2 and electromagnetically induced transparency 3 . The possibility to exploit these effects has made three-level systems a cornerstone of quantum optics. Coherent driving of the third available transition forms a closed-contour interaction (CCI), which yields fundamentally new phenomena, including phase-controlled coherent population trapping 4,5 and phase-controlled coherent population dynamics 6 . Despite attractive prospects, prevalent dephasing in experimental systems suitable for CCI driving has made its observation elusive [7][8][9][10] . Here, we exploit recently developed methods for coherent manipulation of nitrogen-vacancy electronic spins to implement and study highly coherent CCI driving of a single spin. Our experiments reveal phase-controlled quantum interference, reminiscent of electron dynamics on a closed loop threaded by a magnetic flux, which we synthesize from the driving-field phase 11

Initialization of Single Spin Dressed States using Shortcuts to Adiabaticity

“…We take the coherence time of the 2MW dressed states to be 5.91 µs. The published value is 18.9 µs for a drive strength of 1.6 MHz; for a drive strength of 500 kHz, as we use in our measurements in Barfuss et al, this corresponds to T coh = 5.91 µs, assuming T coh scales linearly with driving strength Ω [17,19,27]. We then find S 2MW = 6.43 nT/ √ Hz, which is indicated in Fig.…”

“…To find the sensitivity of superpositions of the CCI and 2MW dressed states, we find J(B min ; T coh ) as described above. The coherence times of the dressed states have been measured in Barfuss et al as a function of Φ [17]. Using experimentally obtained values of T k, coh , we find the sensitivities S k, CCI (Φ), {k, } ∈ {−1, 0, +1}, k = and plot them in Fig.…”

“…Here, we overcome these limitations with a twofold approach, where we employ recently developed protocols for 'shortcuts to adiabaticity' (STA) [21][22][23][24][25] and apply them to the initialisation of three-level dressed states that exhibit efficient coherence protection, beyond what is offered by driven two-level systems [17]. Specifically, we focus on dressed states emerging from 'closed-contour driving' (CCD) of a quantum three-level system [17] [ Fig. 1(a)].…”

“…+ Ω e iΦ | − 1 +1| + H. c. , (1) with being the reduced Planck constant. The Hamil-tonianĤ 0 (t) depends on the global driving phase Φ (Φ = ϕ + ϕ 1 − ϕ 2 , where ϕ, ϕ 1 , and ϕ 2 are the phases of the driving fields with Rabi frequecies Ω, Ω 1 , and Ω 2 , respectively) [17], which we tune to Φ = π/2. We choose this value of Φ, as it allows for a straight-forward derivation of an analytical, purely real STA correction for our system.…”

“…This transfer fidelity is experimentally limited by uncertainties in setting the global phase Φ, leakage of the MW signals, non-equal driving field amplitudes, and unwanted detunings of the driving fields. Although we calculate our ramps assuming equal driving amplitudes and zero detunings, violations of these assumptions are experimentally unavoidable, and the errors will generally fluctuate in time [17]. These factors are also responsible for the remaining, small oscillations in p 0 visible after state transfer in Fig.…”