Observation of the high-order Mollow triplet by quantum mode control with concatenated continuous driving

Abstract

The Mollow triplet is a fundamental signature of quantum optics and has been observed in numerous quantum systems. Although it arises in the "strong driving" regime of the quantized field, where the atoms undergo coherent oscillations, it can be typically analyzed within the rotating wave approximation. Here we report the first observation of high-order effects in the Mollow triplet structure due to strong driving. In experiments, we explore the regime beyond the rotating wave approximation using concatenated continuous driving that has less stringent requirements on the driving field power. We are then able to reveal additional transition frequencies, shifts in energy levels, and corrections to the transition amplitudes. In particular, we find that these amplitudes are more sensitive to high-order effects than the frequency shifts and that they still require an accurate determination in order to achieve high-fidelity quantum control. The experimental results are validated by Floquet theory, which enables the precise numerical simulation of the evolution and further provides an analytical form for an effective Hamiltonian that approximately predicts the spin dynamics beyond the rotating wave approximation.

Observation of symmetry-protected selection rules in periodically driven quantum systems

“…Here i = 0, ±1 correspond to the centerbands and sidebands, respectively, with amplitudes a [19]. The correspondence between the dipole matrix element V (n) µ,ν and the Rabi amplitudes a…”

“…To reduce the 3-level NV center to an effective TLS, we break the |m s = ±1 degeneracy by applying an external magnetic field with strength 239 Gauss in our setup [18,19,33]. Then, the |m s = 0 and |m s = −1 states form a TLS which is driven by resonant microwave.…”

“…The energy transitions form the well-known Mollow triplets, with nω m (nω m ± (λ + − λ − )) the frequencies of n th centerband (sidebands). These transitions can be probed either through conventional "pump-probe" spectroscopy, such as spontaneous emission [35], or via projective Rabi measurements in the context of coherent state evolution [19,36,37].…”

“…For example, concatenated continuous driving (CCD) is a continuous dynamical decoupling technique introduced to counteract driving inhomogeneities and achieve longer coherence times [16][17][18]. More recently, it has been shown to allow reaching the strong-coupling regime even with limited driving fields, while also enabling the observation of phenomana, such as the high-order Mollow triplets beyond the rotating wave approximation [19] that are usually "invisible" in simple driving protocols. Here we will show that not only we can exploit modulated driving to reach an effective strong-coupling regime, but also to engineer driving transitions (such as double-quantum transitions) that are not directly accessible given the driving field operators.…”

“…Although the measured centerbands are indeed the interference between many degenerate bands, we can observe each band V (n) µ,µ individually by tuning the initial condition |c µ | = 1 (quantum mode control ) [19].…”